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{"id": "math.decimals.longer-is-larger", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.decimals.longer-is-larger", "uuid": "b9976592-9045-4327-8b17-485c7114d359", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Longer decimal is larger", "statement": "A decimal with more digits after the point is a larger number, because the digits after the point make a bigger whole number.", "kind": "overgeneralization", "domain": "math.decimals", "about": [{"scheme": "CCSS", "code": "4.NF.C.7", "uri": "http://corestandards.org/Math/Content/4/NF/C/7/"}, {"scheme": "CCSS", "code": "5.NBT.A.3", "uri": "http://corestandards.org/Math/Content/5/NBT/A/3/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "compare two decimals where the shorter is larger", "signature": "chooses the decimal with more digits after the point", "example": {"item": "Which is larger, 0.5 or 0.25?", "expected": "0.5", "response": "0.25"}}, {"item_shape": "order decimals of different lengths", "signature": "orders by the digits after the point read as whole numbers", "example": {"item": "Order from smallest to largest: 0.3, 0.125, 0.45", "expected": "0.125, 0.3, 0.45", "response": "0.3, 0.45, 0.125"}}], "discriminators": {"vs_slip": "A slip is one wrong comparison. The belief is diagnosed by a consistent pattern on length-incongruent items and a justification such as 'twenty-five is more than five'.", "vs": {"math.decimals.shorter-is-larger": "Mirror belief. Include items where the longer decimal is larger (0.75 vs 0.8): longer-is-larger gets those right and shorter-is-larger gets them wrong."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/C/7/", "label": "CCSS 4.NF.C.7: compare two decimals to hundredths by reasoning about their size"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/C/7/", "label": "CCSS 4.NF.C.7: compare two decimals to hundredths by reasoning about their size"}, {"external": "http://corestandards.org/Math/Content/5/NBT/A/3/", "label": "CCSS 5.NBT.A.3: read, write and compare decimals to thousandths"}], "confusable_with": ["math.decimals.shorter-is-larger"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.C.7", "uri": "http://corestandards.org/Math/Content/4/NF/C/7/", "relation": "about"}, {"scheme": "CCSS", "code": "5.NBT.A.3", "uri": "http://corestandards.org/Math/Content/5/NBT/A/3/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8-27.", "doi": "10.5951/jresematheduc.20.1.0008", "note": "Whole-number rule for decimal comparison."}, {"type": "paper", "citation": "Stacey, K., & Steinle, V. (1998). Refining the classification of students' interpretations of decimal notation. Hiroshima Journal of Mathematics Education, 6, 49-69.", "note": "Longer-is-larger classification and its sub-types."}, {"type": "paper", "citation": "Durkin, K., & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37, 21-29.", "doi": "10.1016/j.learninstruc.2014.08.003"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.decimals.shorter-is-larger", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.decimals.shorter-is-larger", "uuid": "e3685617-2ee2-41c1-875f-5e0d835be18f", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Shorter decimal is larger", "statement": "A decimal with fewer digits after the point is a larger number, because more digits mean smaller pieces, like a fraction with a bigger denominator.", "kind": "misapplied-analogy", "domain": "math.decimals", "about": [{"scheme": "CCSS", "code": "4.NF.C.7", "uri": "http://corestandards.org/Math/Content/4/NF/C/7/"}, {"scheme": "CCSS", "code": "5.NBT.A.3", "uri": "http://corestandards.org/Math/Content/5/NBT/A/3/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "compare two decimals where the longer decimal is larger", "signature": "chooses the decimal with fewer digits after the point", "example": {"item": "Which is larger, 0.85 or 0.8?", "expected": "0.85", "response": "0.8"}, "notes": "Length-incongruent item; a longer-is-larger believer answers this correctly."}, {"item_shape": "compare two decimals where the longer is larger and the shorter has a smaller leading digit", "signature": "picks the shorter decimal despite a smaller leading digit", "example": {"item": "Which is larger, 0.4 or 0.45?", "expected": "0.45", "response": "0.4"}}], "discriminators": {"vs_slip": "Consistent preference for the shorter decimal on length-incongruent items, with a fraction-based justification ('hundredths are smaller than tenths').", "vs": {"math.decimals.longer-is-larger": "Mirror belief; use items of both congruence types to separate them."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/C/7/", "label": "CCSS 4.NF.C.7: compare two decimals to hundredths by reasoning about their size"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/C/7/", "label": "CCSS 4.NF.C.7: compare two decimals to hundredths by reasoning about their size"}, {"external": "http://corestandards.org/Math/Content/5/NBT/A/3/", "label": "CCSS 5.NBT.A.3: read, write and compare decimals to thousandths"}], "confusable_with": ["math.decimals.longer-is-larger"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.C.7", "uri": "http://corestandards.org/Math/Content/4/NF/C/7/", "relation": "about"}, {"scheme": "CCSS", "code": "5.NBT.A.3", "uri": "http://corestandards.org/Math/Content/5/NBT/A/3/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8-27.", "doi": "10.5951/jresematheduc.20.1.0008", "note": "Fraction rule for decimal comparison."}, {"type": "paper", "citation": "Stacey, K., & Steinle, V. (1998). Refining the classification of students' interpretations of decimal notation. Hiroshima Journal of Mathematics Education, 6, 49-69.", "note": "Shorter-is-larger classification."}, {"type": "paper", "citation": "Durkin, K., & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37, 21-29.", "doi": "10.1016/j.learninstruc.2014.08.003"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.add-across", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.add-across", "uuid": "20f1dd60-ea8a-4e14-ab41-12addc94b751", "version": "1.1.0", "status": "reviewed", "trust": "high", "title": "Adding fractions across numerators and denominators", "statement": "Fractions are added by adding the numerators together and adding the denominators together.", "notes": "Likely origins: whole-number bias (numerator and denominator treated as independent whole numbers) and overgeneralisation from the multiplication rule.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "5.NF.A.1", "uri": "http://corestandards.org/Math/Content/5/NF/A/1/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "add two fractions with unlike denominators", "signature": "response numerator = a + c and response denominator = b + d for a/b + c/d, with no attempt at a common denominator", "example": {"item": "1/2 + 1/3", "expected": "5/6", "response": "2/5"}, "notes": "Strongest single indicator: the response is smaller than at least one addend, which the learner rarely notices."}, {"item_shape": "add two fractions with like denominators", "signature": "response numerator = a + c and response denominator = b + b for a/b + c/b; denominators are added even though they match", "example": {"item": "1/4 + 2/4", "expected": "3/4", "response": "3/8"}, "notes": "Discriminates from math.fractions.add-numerators-keep-denominator, which answers like-denominator items correctly."}], "discriminators": {"vs_slip": "A slip appears on one item and not on the next of the same shape, and the learner self-corrects when asked to check with a diagram or with 1/2 + 1/2. A holder of this belief applies the rule consistently across unlike- and like-denominator items and defends 1/2 + 1/2 = 2/4 as correct.", "vs": {"math.fractions.add-numerators-keep-denominator": "Give a like-denominator item. Add-across produces a doubled denominator (1/4 + 2/4 = 3/8); add-numerators-keep-denominator produces the correct 3/4 and only fails on unlike denominators."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/5/NF/A/1/", "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/5/NF/A/1/", "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"}, {"external": "http://corestandards.org/Math/Content/3/NF/A/1/", "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"}], "confusable_with": ["math.fractions.add-numerators-keep-denominator"]}, "alignments": [{"scheme": "CCSS", "code": "5.NF.A.1", "uri": "http://corestandards.org/Math/Content/5/NF/A/1/", "relation": "about", "note": "Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions. CASE Network GUID for this item to be added when the CASE Network export of CCSS Math is confirmed."}], "provenance": {"sources": [{"type": "paper", "citation": "Brown, J. S., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4(4), 379-426.", "doi": "10.1207/s15516709cog0404_3", "note": "Frames systematic errors as stable procedural bugs, distinct from slips; the add-across rule is the canonical fraction example in the repair-theory tradition."}, {"type": "paper", "citation": "Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.", "doi": "10.1207/s15326985ep4001_3", "note": "Whole number bias: treating numerator and denominator as separate whole numbers."}, {"type": "paper", "citation": "Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296.", "doi": "10.1016/j.cogpsych.2011.03.001", "note": "Reports independent whole-number operations on numerators and denominators as the most common fraction-arithmetic error."}, {"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon.", "note": "Practitioner catalogue of computational error patterns including this one."}], "origin": "literature", "notes": "Statement and examples written for Open Misconceptions. No text reused from any proprietary item bank."}, "reviews": [{"kind": "human", "by": "Vikram Maram (github:vikram-learnco)", "date": "2026-09-05", "scope": ["statement", "evidence", "discriminators", "sources"], "verdict": "accept", "notes": "Reviewed in session against the design worked example; statement trimmed to the belief; cause moved to notes."}, {"kind": "model", "by": "claude-fable-5-1", "date": "2026-09-05", "scope": ["statement", "evidence", "discriminators", "sources"], "verdict": "accept"}, {"kind": "attested", "by": 0, "date": "2026-09-05", "scope": ["statement"], "verdict": "accept", "notes": "Brown & VanLehn (1980): add-across as the canonical fraction bug in repair theory."}, {"kind": "attested", "by": 2, "date": "2026-09-05", "scope": ["statement"], "verdict": "accept", "notes": "Siegler, Thompson & Schneider (2011): independent whole-number operations on numerators and denominators as the most common fraction-arithmetic error."}], "history": {"changelog": [{"version": "1.0.0", "date": "2026-09-05", "change": "Initial record."}, {"version": "1.1.0", "date": "2026-09-05", "change": "Statement trimmed to the belief; likely origins moved to notes; about scheme relabelled CCSS; review replaced by reviews[] (human, model, two attested); trust computed. Review closed with Vikram Maram, 2026-09-05."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.add-numerators-keep-denominator", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.add-numerators-keep-denominator", "uuid": "434a29b0-8c52-4db3-a2d6-81c86e5e5d6c", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Adding numerators and keeping one denominator", "statement": "To add fractions you add the numerators and keep the denominator, whichever denominator is written, because the denominator is just a label that does not take part in the sum.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "5.NF.A.1", "uri": "http://corestandards.org/Math/Content/5/NF/A/1/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "add two fractions with unlike denominators", "signature": "response numerator = a + c; response denominator is one of the given denominators (usually the first or the larger), with no conversion of the addends", "example": {"item": "1/2 + 1/3", "expected": "5/6", "response": "2/3"}, "notes": "Like-denominator items are answered correctly, which is the discriminator against math.fractions.add-across."}], "discriminators": {"vs_slip": "Consistent across unlike-denominator items; the learner can state the rule (\"the bottom stays\") when asked.", "vs": {"math.fractions.add-across": "Give a like-denominator item. This belief answers 1/4 + 2/4 = 3/4 correctly; add-across gives 3/8."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/5/NF/A/1/", "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/5/NF/A/1/", "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"}], "confusable_with": ["math.fractions.add-across"]}, "alignments": [{"scheme": "CCSS", "code": "5.NF.A.1", "uri": "http://corestandards.org/Math/Content/5/NF/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}, {"type": "paper", "citation": "Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.", "doi": "10.1207/s15326985ep4001_3"}], "origin": "literature", "notes": "Stub created so that math.fractions.add-across's discriminator resolves. Needs a second evidence pattern and review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.add-whole-to-numerator", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.add-whole-to-numerator", "uuid": "692fc169-3842-429b-bf5a-36be6eb6e910", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Adding a whole number to the numerator", "statement": "To add a whole number and a fraction you add the whole number to the numerator.", "kind": "procedural-bug", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.B.3", "uri": "http://corestandards.org/Math/Content/4/NF/B/3/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "add a whole number and a proper fraction", "signature": "adds the whole number to the numerator and keeps the denominator", "example": {"item": "2 + 1/3 = ?", "expected": "2 1/3 (= 7/3)", "response": "3/3 (= 1)"}}], "discriminators": {"vs_slip": "The result is smaller than the whole-number addend and the learner accepts it, consistently. A slip is not repeated across items.", "vs": {"math.fractions.mixed-to-improper-add-all": "That bug adds all three numbers when converting a mixed number; this one appears when a whole number and fraction are added with a plus sign."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/B/3/", "label": "CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/B/3/", "label": "CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b"}], "confusable_with": ["math.fractions.mixed-to-improper-add-all"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.B.3", "uri": "http://corestandards.org/Math/Content/4/NF/B/3/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}, {"type": "book", "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."}, {"type": "paper", "citation": "Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625.", "doi": "10.1037/rev0000072"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.bigger-denominator-bigger-fraction", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.bigger-denominator-bigger-fraction", "uuid": "1288d189-d36c-4a7d-925d-62c88196a161", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Bigger denominator means bigger fraction", "statement": "The fraction with the bigger denominator is the bigger fraction, because the denominator is a bigger number.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "3.NF.A.3", "uri": "http://corestandards.org/Math/Content/3/NF/A/3/"}, {"scheme": "CCSS", "code": "4.NF.A.2", "uri": "http://corestandards.org/Math/Content/4/NF/A/2/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "compare two unit fractions", "signature": "picks the unit fraction with the larger denominator as larger; on 1/b vs 1/d chooses the one with the larger b", "example": {"item": "Which is larger, 1/3 or 1/8?", "expected": "1/3", "response": "1/8"}}, {"item_shape": "order a set of unit fractions", "signature": "orders unit fractions by denominator ascending as if ordering whole numbers", "example": {"item": "Order from smallest to largest: 1/2, 1/5, 1/3", "expected": "1/5, 1/3, 1/2", "response": "1/2, 1/3, 1/5"}}], "discriminators": {"vs_slip": "A slip is a single reversed choice among otherwise correct comparisons. The belief shows as a consistent preference for the larger denominator across unit-fraction items and a justification such as 'eight is more than three'.", "vs": {"math.fractions.compare-whole-number-components": "Use an item where the larger denominator goes with the smaller numerator (2/3 vs 1/8). The component-comparison belief gives no clear answer or picks by numerator; this belief still picks 1/8.", "math.fractions.compare-by-gap": "Gap thinking on 1/3 vs 1/8 says both are 'one piece away from nothing' and compares the pieces; it answers 1/3. This belief answers 1/8."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/3/NF/A/3/", "label": "CCSS 3.NF.A.3: explain equivalence of fractions and compare fractions by reasoning about their size"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/3/NF/A/1/", "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"}, {"external": "http://corestandards.org/Math/Content/3/NF/A/3/", "label": "CCSS 3.NF.A.3: explain equivalence of fractions and compare fractions by reasoning about their size"}], "specializes": ["math.fractions.compare-whole-number-components"], "confusable_with": ["math.fractions.compare-by-gap"]}, "alignments": [{"scheme": "CCSS", "code": "3.NF.A.3", "uri": "http://corestandards.org/Math/Content/3/NF/A/3/", "relation": "about"}, {"scheme": "CCSS", "code": "4.NF.A.2", "uri": "http://corestandards.org/Math/Content/4/NF/A/2/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Stafylidou, S., & Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.", "doi": "10.1016/j.learninstruc.2004.06.015", "note": "Reports the 'fraction increases as the denominator increases' interpretation as an early developmental stage."}, {"type": "paper", "citation": "Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.", "doi": "10.1207/s15326985ep4001_3"}, {"type": "paper", "citation": "Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90(1), 39-56.", "doi": "10.1007/s10649-015-9613-3"}, {"type": "paper", "citation": "DeWolf, M., & Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39-49.", "doi": "10.1016/j.learninstruc.2014.07.002"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.cancel-matching-digits", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.cancel-matching-digits", "uuid": "9b81e6e0-ad37-42aa-9494-bc6892e7140b", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Cancelling matching digits", "statement": "A fraction is simplified by crossing out a digit that appears in both the numerator and the denominator.", "kind": "notation-confusion", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.A.1", "uri": "http://corestandards.org/Math/Content/4/NF/A/1/"}], "level_band": ["middle", "secondary"], "locale": "en", "evidence_patterns": [{"item_shape": "simplify a fraction whose numerator and denominator share a digit", "signature": "deletes the shared digit from both numbers", "example": {"item": "Simplify 12/24", "expected": "1/2", "response": "1/4 (cancelling the 2s)"}, "notes": "16/64 = 1/4 and 19/95 = 1/5 happen to be true, which reinforces the rule."}], "discriminators": {"vs_slip": "Ask the learner to simplify 16/64 and then 12/24 and explain. The belief is 'the sixes cancel'; a slip has no digit-based rule.", "vs": {"math.fractions.equivalence-additive": "Additive reasoners subtract from both parts; digit cancellers delete a digit and leave the rest."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/A/1/", "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/A/1/", "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"}], "confusable_with": ["math.fractions.equivalence-additive"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.A.1", "uri": "http://corestandards.org/Math/Content/4/NF/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}, {"type": "paper", "citation": "Brown, J. S., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4(4), 379-426.", "doi": "10.1207/s15516709cog0404_3", "note": "Repair theory: bugs formed by over-literal reading of a procedure's surface form."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.compare-by-gap", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.compare-by-gap", "uuid": "c2797bf8-5aff-4019-98c3-3462a3c42f71", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Comparing fractions by the gap between numerator and denominator", "statement": "The size of a fraction is decided by how many pieces are missing from the whole; fractions with the same gap between numerator and denominator are equal.", "kind": "misapplied-analogy", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.A.2", "uri": "http://corestandards.org/Math/Content/4/NF/A/2/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "compare two fractions with the same numerator-denominator gap", "signature": "declares the fractions equal because each is the same number of pieces short of one whole", "example": {"item": "Which is larger, 5/6 or 7/8?", "expected": "7/8", "response": "They are the same"}, "notes": "The gap is an additive comparison; the learner ignores that eighths are smaller than sixths."}, {"item_shape": "compare two fractions with different gaps where the smaller gap belongs to the smaller fraction", "signature": "picks the fraction with the smaller numerator-denominator gap as larger regardless of denominators", "example": {"item": "Which is larger, 2/3 or 7/10?", "expected": "7/10", "response": "2/3"}, "notes": "Gaps are 1 and 3; the learner reasons 'two thirds is only one piece away'."}], "discriminators": {"vs_slip": "Ask the learner to explain. Gap thinkers say 'both are one away from a whole' or 'this one is closer'. A slip comes with no such rule and is not repeated on 3/4 vs 9/10.", "vs": {"math.fractions.compare-whole-number-components": "On 5/6 vs 7/8 component comparison picks 7/8; gap thinking says equal.", "math.fractions.bigger-denominator-bigger-fraction": "On 1/3 vs 1/8 gap thinking compares the size of one piece and often answers correctly; the denominator rule picks 1/8."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/A/2/", "label": "CCSS 4.NF.A.2: compare two fractions with different numerators and different denominators"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/3/NF/A/3/", "label": "CCSS 3.NF.A.3: explain equivalence of fractions and compare fractions by reasoning about their size"}, {"external": "http://corestandards.org/Math/Content/4/NF/A/2/", "label": "CCSS 4.NF.A.2: compare two fractions with different numerators and different denominators"}], "confusable_with": ["math.fractions.compare-whole-number-components", "math.fractions.bigger-denominator-bigger-fraction"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.A.2", "uri": "http://corestandards.org/Math/Content/4/NF/A/2/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Pearn, C., & Stephens, M. (2004). Why you have to probe to discover what Year 8 students really think about fractions. In I. Putt, R. Faragher & M. McLean (Eds.), Mathematics Education for the Third Millennium: Towards 2010 (Proceedings of MERGA 27, pp. 430-437). MERGA.", "note": "Names and documents 'gap thinking' in Year 8 students."}, {"type": "paper", "citation": "Clarke, D. M., & Roche, A. (2009). Students' fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127-138.", "doi": "10.1007/s10649-009-9198-9", "note": "Classifies gap thinking among fraction comparison strategies and shows it is not a robust strategy."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.compare-whole-number-components", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.compare-whole-number-components", "uuid": "210d5db3-daa8-49be-aaf9-aa453ea6b234", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Comparing fractions by their whole-number parts", "statement": "To compare two fractions you compare the numerators and the denominators as whole numbers; a fraction with bigger numbers is a bigger fraction.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.A.2", "uri": "http://corestandards.org/Math/Content/4/NF/A/2/"}], "level_band": ["primary", "middle", "secondary"], "locale": "en", "evidence_patterns": [{"item_shape": "compare two fractions where the larger fraction has the smaller numerator and denominator", "signature": "chooses the fraction whose numerator and denominator are both larger", "example": {"item": "Which is larger, 4/5 or 5/9?", "expected": "4/5", "response": "5/9"}, "notes": "Incongruent item: whole-number ordering and fraction ordering disagree, so the error is diagnostic. Pair with a congruent item (2/7 vs 3/8) which this belief answers correctly; near-perfect congruent accuracy with systematic incongruent errors is the signature."}], "discriminators": {"vs_slip": "Compare accuracy on congruent and incongruent items. A holder of this belief is near-perfect on congruent items and systematically wrong on incongruent ones; a slip does not follow that split.", "vs": {"math.fractions.bigger-denominator-bigger-fraction": "Unit-fraction items isolate the denominator rule. Component comparison also covers non-unit fractions such as 4/5 vs 5/9.", "math.fractions.compare-by-gap": "On 5/6 vs 7/8 gap thinking says they are equal; component comparison picks 7/8."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/A/2/", "label": "CCSS 4.NF.A.2: compare two fractions with different numerators and different denominators"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/3/NF/A/3/", "label": "CCSS 3.NF.A.3: explain equivalence of fractions and compare fractions by reasoning about their size"}, {"external": "http://corestandards.org/Math/Content/4/NF/A/2/", "label": "CCSS 4.NF.A.2: compare two fractions with different numerators and different denominators"}], "confusable_with": ["math.fractions.compare-by-gap"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.A.2", "uri": "http://corestandards.org/Math/Content/4/NF/A/2/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64-72.", "doi": "10.1016/j.learninstruc.2013.05.003", "note": "Congruent/incongruent comparison paradigm; the bias persists in reaction times even for experts."}, {"type": "paper", "citation": "Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90(1), 39-56.", "doi": "10.1007/s10649-015-9613-3"}, {"type": "paper", "citation": "DeWolf, M., & Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39-49.", "doi": "10.1016/j.learninstruc.2014.07.002"}, {"type": "paper", "citation": "Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.", "doi": "10.1207/s15326985ep4001_3"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.cross-multiply-to-multiply", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.cross-multiply-to-multiply", "uuid": "fef262fa-6980-416d-bd92-851b64e59458", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Cross-multiplying to multiply fractions", "statement": "To multiply two fractions you multiply diagonally: the first numerator by the second denominator over the first denominator by the second numerator.", "kind": "procedural-bug", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "5.NF.B.4", "uri": "http://corestandards.org/Math/Content/5/NF/B/4/"}], "level_band": ["middle", "secondary"], "locale": "en", "evidence_patterns": [{"item_shape": "multiply two proper fractions", "signature": "product numerator = a x d and product denominator = b x c for a/b x c/d", "example": {"item": "2/3 x 4/5 = ?", "expected": "8/15", "response": "10/12"}}], "discriminators": {"vs_slip": "Consistent across items and usually accompanied by the word 'cross-multiply'. A slip is one diagonal product.", "vs": {"math.fractions.multiply-with-common-denominator": "Common-denominator multipliers show a conversion step in their working; cross-multipliers do not."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/5/NF/B/4/", "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/5/NF/B/4/", "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"}], "confusable_with": ["math.fractions.multiply-with-common-denominator"]}, "alignments": [{"scheme": "CCSS", "code": "5.NF.B.4", "uri": "http://corestandards.org/Math/Content/5/NF/B/4/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}, {"type": "paper", "citation": "Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110.", "doi": "10.3102/0002831208320851", "note": "Cross-multiplication misapplied to multiplication and addition."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.divide-larger-by-smaller", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.divide-larger-by-smaller", "uuid": "78a649f3-688d-49a2-a85c-7be491860757", "version": "0.1.1", "status": "draft", "trust": "low", "title": "You can only divide a larger number by a smaller one", "statement": "In a division the bigger number must be divided by the smaller number, so if the divisor is bigger the two numbers should be swapped.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/"}], "level_band": ["primary", "middle", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "divide a fraction by a larger whole number", "signature": "swaps dividend and divisor so that the larger number is divided by the smaller", "example": {"item": "1/2 / 3 = ?", "expected": "1/6", "response": "6"}}, {"item_shape": "write the division for a word problem where the dividend is smaller than the divisor", "signature": "writes the numbers in the order that makes the dividend larger", "example": {"item": "3/4 of a litre is shared equally between 3 people. Write the division.", "expected": "3/4 / 3", "response": "3 / 3/4"}}], "discriminators": {"vs_slip": "A slip is one reversed pair. The belief is a stated rule ('you can't divide a small number by a big one') and is applied to whole numbers too (3 / 12 rewritten as 12 / 3).", "vs": {"math.fractions.divide-makes-smaller": "Divide-makes-smaller keeps the order and gets a smaller wrong result; this belief changes the order."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}, {"external": "http://corestandards.org/Math/Content/5/NF/B/7/", "label": "CCSS 5.NF.B.7: divide unit fractions by whole numbers and whole numbers by unit fractions"}]}, "alignments": [{"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17.", "doi": "10.5951/jresematheduc.16.1.0003"}, {"type": "paper", "citation": "Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102.", "doi": "10.5951/jresematheduc.20.1.0095", "note": "Preservice teachers reversing dividend and divisor so the divisor is smaller."}, {"type": "paper", "citation": "Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.", "doi": "10.2307/749817"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.divide-makes-smaller", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.divide-makes-smaller", "uuid": "72884d31-1a9a-418f-92ee-f073eef02008", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Division always makes smaller", "statement": "Dividing always gives a result smaller than the number you started with, so dividing by a fraction cannot make a number bigger.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "5.NF.B.7", "uri": "http://corestandards.org/Math/Content/5/NF/B/7/"}, {"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/"}], "level_band": ["primary", "middle", "secondary", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "predict whether a quotient will be larger or smaller than the dividend, without calculating", "signature": "predicts the quotient of a number divided by a proper fraction is smaller than the number", "example": {"item": "Without calculating, is 6 / 1/2 more or less than 6?", "expected": "More (it is 12)", "response": "Less"}}, {"item_shape": "evaluate a whole number divided by a unit fraction", "signature": "halves the number instead of doubling it", "example": {"item": "6 / 1/2 = ?", "expected": "12", "response": "3"}}], "discriminators": {"vs_slip": "A slip is one wrong prediction. The belief is stated as a rule ('dividing makes it smaller') and holds for decimals too; it often coexists with math.fractions.multiply-makes-bigger.", "vs": {"math.fractions.multiply-makes-bigger": "Mirror belief; test each separately.", "math.fractions.invert-dividend": "Ask the learner to predict before calculating. Procedure bugs give a wrong number but often a correct prediction of direction; this belief gets the direction wrong.", "math.fractions.division-is-sharing-only": "Sharing-only believers say 6 / 1/2 'makes no sense' or reinterpret it; this belief answers confidently with a smaller number."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/5/NF/B/7/", "label": "CCSS 5.NF.B.7: divide unit fractions by whole numbers and whole numbers by unit fractions"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/5/NF/B/7/", "label": "CCSS 5.NF.B.7: divide unit fractions by whole numbers and whole numbers by unit fractions"}, {"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}], "confusable_with": ["math.fractions.invert-dividend", "math.fractions.division-is-sharing-only"]}, "alignments": [{"scheme": "CCSS", "code": "5.NF.B.7", "uri": "http://corestandards.org/Math/Content/5/NF/B/7/", "relation": "about"}, {"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17.", "doi": "10.5951/jresematheduc.16.1.0003", "note": "Implicit partitive model of division: the quotient must be smaller than the dividend."}, {"type": "paper", "citation": "Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.", "doi": "10.2307/749817"}, {"type": "paper", "citation": "Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102.", "doi": "10.5951/jresematheduc.20.1.0095"}, {"type": "paper", "citation": "Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918.", "doi": "10.1037/edu0000025"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.division-is-sharing-only", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.division-is-sharing-only", "uuid": "50e4d120-cd01-49b2-95e6-5ec8df0762d1", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Division of fractions only means sharing", "statement": "Dividing means sharing a quantity equally among a number of people, so a division by a fraction has no meaning and must be a mistake or a different operation.", "kind": "undergeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/"}, {"scheme": "CCSS", "code": "5.NF.B.7", "uri": "http://corestandards.org/Math/Content/5/NF/B/7/"}], "level_band": ["primary", "middle", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "choose the operation for a measurement-division word problem", "signature": "rejects division and multiplies or divides by the wrong number, because 'you can't share among half a person'", "example": {"item": "How many 1/2-cup servings are in 3 cups?", "expected": "3 / 1/2 = 6", "response": "3 / 2 = 1.5 (or 3 x 2 = 6 'because it can't be division')"}}, {"item_shape": "write a word problem for a given fraction division", "signature": "writes a sharing story that does not match the expression, or says it is impossible", "example": {"item": "Write a story problem for 3/4 / 1/4", "expected": "How many quarter-cups are in three quarters of a cup?", "response": "Three quarters shared between a quarter of a person (or: 'you can't')"}}], "discriminators": {"vs_slip": "A slip is one wrong operation choice. The belief is revealed when the learner is asked to model or explain division and only ever produces sharing stories.", "vs": {"math.fractions.divide-makes-smaller": "Divide-makes-smaller computes an answer with the wrong direction; this belief refuses or reinterprets the operation."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}, {"external": "http://corestandards.org/Math/Content/5/NF/B/7/", "label": "CCSS 5.NF.B.7: divide unit fractions by whole numbers and whole numbers by unit fractions"}], "confusable_with": ["math.fractions.divide-makes-smaller"]}, "alignments": [{"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17.", "doi": "10.5951/jresematheduc.16.1.0003", "note": "Partitive (sharing) model as the primitive model of division."}, {"type": "paper", "citation": "Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.", "doi": "10.2307/749817"}, {"type": "book", "citation": "Sinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller & G. Bright (Eds.), Making Sense of Fractions, Ratios, and Proportions: 2002 Yearbook (pp. 153-161). NCTM.", "note": "Measurement, partitive and other interpretations of fraction division."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.equivalence-additive", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.equivalence-additive", "uuid": "5aadfc6d-33f3-4336-908b-02c278e40508", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Equivalent fractions by adding the same number", "statement": "You get an equivalent fraction by adding the same number to the numerator and the denominator, or by subtracting the same number from both.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.A.1", "uri": "http://corestandards.org/Math/Content/4/NF/A/1/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "complete an equivalent fraction with a given denominator", "signature": "adds the difference in denominators to the numerator", "example": {"item": "2/3 = ?/6", "expected": "4/6", "response": "5/6"}}, {"item_shape": "simplify a fraction", "signature": "subtracts the same number from numerator and denominator", "example": {"item": "Simplify 6/8", "expected": "3/4", "response": "5/7 (or 4/6)"}}], "discriminators": {"vs_slip": "Consistent across items; the learner defends it as 'you have to do the same to both'. A slip is a single wrong numerator with multiplicative reasoning elsewhere.", "vs": {"math.fractions.cancel-matching-digits": "Digit cancellers only act when a digit repeats (16/64); additive reasoners act on any fraction."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/A/1/", "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/A/1/", "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"}], "confusable_with": ["math.fractions.cancel-matching-digits"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.A.1", "uri": "http://corestandards.org/Math/Content/4/NF/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)", "note": "CSMS: additive strategies on equivalence items."}, {"type": "book", "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."}, {"type": "paper", "citation": "Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323-341.", "doi": "10.5951/jresematheduc.15.5.0323"}, {"type": "book", "citation": "Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge.", "note": "Additive versus multiplicative reasoning."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.fraction-decimal-digit-copy", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.fraction-decimal-digit-copy", "uuid": "fb3c3db0-26d5-4aba-a7ea-c9ce84089d88", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Writing a fraction as a decimal by copying its digits", "statement": "A fraction is written as a decimal by putting its numerator, or its denominator, after the decimal point.", "kind": "notation-confusion", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.C.6", "uri": "http://corestandards.org/Math/Content/4/NF/C/6/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "convert a unit fraction to a decimal", "signature": "writes 0.<denominator>", "example": {"item": "Write 1/4 as a decimal", "expected": "0.25", "response": "0.4"}}, {"item_shape": "convert a decimal to a fraction", "signature": "writes the digits after the point as the numerator over the denominator that matches their count in the 'other direction', or over 1", "example": {"item": "Write 0.2 as a fraction", "expected": "2/10 (= 1/5)", "response": "1/2"}}], "discriminators": {"vs_slip": "Consistent across fractions, and the learner cannot say whether 0.4 and 1/4 are the same size. A slip is one wrong conversion with correct ones nearby."}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/C/6/", "label": "CCSS 4.NF.C.6: use decimal notation for fractions with denominators 10 or 100"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/C/6/", "label": "CCSS 4.NF.C.6: use decimal notation for fractions with denominators 10 or 100"}]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.C.6", "uri": "http://corestandards.org/Math/Content/4/NF/C/6/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."}, {"type": "paper", "citation": "Markovits, Z., & Sowder, J. T. (1991). Students' understanding of the relationship between fractions and decimals. Focus on Learning Problems in Mathematics, 13(1), 3-11."}, {"type": "book", "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.improper-impossible", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.improper-impossible", "uuid": "5211ad46-cba5-4c3d-92ff-9fa79d9ed753", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A fraction cannot be more than one whole", "statement": "A fraction is always part of one whole, so the numerator can never be bigger than the denominator and a fraction can never be greater than 1.", "kind": "undergeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.B.3", "uri": "http://corestandards.org/Math/Content/4/NF/B/3/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "add two proper fractions whose sum exceeds one", "signature": "adjusts the result so it stays below or equal to one", "example": {"item": "3/4 + 3/4 = ?", "expected": "6/4 (= 1 1/2)", "response": "6/8 (or 1)"}}, {"item_shape": "place an improper fraction on a number line", "signature": "places it below 1 or says it cannot be placed", "example": {"item": "Mark 5/4 on a number line from 0 to 2", "expected": "one quarter past 1", "response": "just below 1 (or 'not a real fraction')"}}], "discriminators": {"vs_slip": "Ask directly whether 7/4 is a number. A slip is an arithmetic error; the belief is the stated rule 'the top can't be bigger than the bottom'.", "vs": {"math.fractions.mixed-to-improper-add-all": "That bug accepts improper fractions but converts to them wrongly; this belief rejects them."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/B/3/", "label": "CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/B/3/", "label": "CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b"}, {"external": "http://corestandards.org/Math/Content/3/NF/A/2/", "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"}], "confusable_with": ["math.fractions.mixed-to-improper-add-all"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.B.3", "uri": "http://corestandards.org/Math/Content/4/NF/B/3/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Stafylidou, S., & Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.", "doi": "10.1016/j.learninstruc.2004.06.015", "note": "A developmental stage in which fractions are understood as always smaller than the unit."}, {"type": "book", "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."}, {"type": "book", "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.invert-both", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.invert-both", "uuid": "aa675277-3fb6-44fe-aad9-20dacc62d775", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Inverting both fractions when dividing", "statement": "To divide fractions you flip both fractions and then multiply.", "kind": "procedural-bug", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/"}], "level_band": ["middle", "secondary", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "divide two proper fractions", "signature": "inverts both dividend and divisor and multiplies", "example": {"item": "1/2 / 3/4 = ?", "expected": "2/3", "response": "8/3"}}], "discriminators": {"vs_slip": "Consistent across items. A slip produces one inverted-both answer; the bug produces it every time and the learner can recite 'flip them and multiply'.", "vs": {"math.fractions.invert-dividend": "Invert-dividend gives 6/4 on 1/2 / 3/4; invert-both gives 8/3."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}], "confusable_with": ["math.fractions.invert-dividend"]}, "alignments": [{"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}, {"type": "paper", "citation": "Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110.", "doi": "10.3102/0002831208320851"}, {"type": "paper", "citation": "Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625.", "doi": "10.1037/rev0000072"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.invert-dividend", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.invert-dividend", "uuid": "33e03294-fca9-4bef-92bc-386f55ec81de", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Inverting the first fraction when dividing", "statement": "To divide fractions you flip the first fraction and then multiply.", "kind": "procedural-bug", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/"}], "level_band": ["middle", "secondary", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "divide two proper fractions", "signature": "inverts the dividend instead of the divisor and multiplies", "example": {"item": "1/2 / 3/4 = ?", "expected": "2/3", "response": "6/4 (= 3/2)"}}], "discriminators": {"vs_slip": "Apply to several items. The bug inverts the first fraction every time; a slip flips the wrong one once and self-corrects when asked which fraction is the divisor.", "vs": {"math.fractions.invert-both": "Invert-both gives 2/1 x 4/3 = 8/3 on the same item; invert-dividend gives 2/1 x 3/4 = 6/4.", "math.fractions.divide-makes-smaller": "Ask the learner to predict the size of the answer first; the procedure bug gets the direction right and the number wrong."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/6/NS/A/1/", "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"}], "confusable_with": ["math.fractions.invert-both", "math.fractions.divide-makes-smaller"]}, "alignments": [{"scheme": "CCSS", "code": "6.NS.A.1", "uri": "http://corestandards.org/Math/Content/6/NS/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}, {"type": "paper", "citation": "Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110.", "doi": "10.3102/0002831208320851", "note": "Invert-and-multiply errors among preservice teachers."}, {"type": "paper", "citation": "Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918.", "doi": "10.1037/edu0000025"}, {"type": "paper", "citation": "Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625.", "doi": "10.1037/rev0000072", "note": "Models fraction arithmetic bugs as mis-selected procedures."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.mixed-to-improper-add-all", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.mixed-to-improper-add-all", "uuid": "be94771a-f7b8-4af6-acb3-a3fe723a0d20", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Converting a mixed number by adding all its numbers", "statement": "To write a mixed number as an improper fraction you add the whole number to the numerator and keep the denominator.", "kind": "procedural-bug", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.B.3", "uri": "http://corestandards.org/Math/Content/4/NF/B/3/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "convert a mixed number to an improper fraction", "signature": "numerator = whole + numerator; denominator unchanged", "example": {"item": "Write 2 1/3 as an improper fraction", "expected": "7/3", "response": "3/3"}}], "discriminators": {"vs_slip": "Consistent across items. A slip is a wrong product within the multiply-then-add method.", "vs": {"math.fractions.add-whole-to-numerator": "Same surface result on 2 + 1/3, but this bug is triggered by mixed-number notation, not by a plus sign.", "math.fractions.improper-impossible": "Improper-impossible believers refuse to write 7/3 at all."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/B/3/", "label": "CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/B/3/", "label": "CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b"}], "confusable_with": ["math.fractions.add-whole-to-numerator", "math.fractions.improper-impossible"]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.B.3", "uri": "http://corestandards.org/Math/Content/4/NF/B/3/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}, {"type": "book", "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.multiply-makes-bigger", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-makes-bigger", "uuid": "04246969-9c77-41b0-a67b-b48be9b2f5a3", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Multiplication always makes bigger", "statement": "Multiplying always gives a result larger than the number you started with, so multiplying by a fraction cannot make a number smaller.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "5.NF.B.5", "uri": "http://corestandards.org/Math/Content/5/NF/B/5/"}], "level_band": ["primary", "middle", "secondary", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "predict whether a product will be larger or smaller than a factor, without calculating", "signature": "predicts the product of a number and a proper fraction is larger than the number", "example": {"item": "Without calculating, is 8 x 3/4 more or less than 8?", "expected": "Less", "response": "More"}}, {"item_shape": "choose the operation for a word problem with a fractional multiplier", "signature": "rejects multiplication because the answer must be smaller, and divides instead", "example": {"item": "A recipe uses 2/3 of a 6-cup bag of flour. How much flour is used? Which operation?", "expected": "6 x 2/3 = 4", "response": "6 / 2/3 (or 6 / 2 = 3)"}}], "discriminators": {"vs_slip": "A slip is one wrong prediction. The belief is stated as a rule and generalises to decimals (0.5 x 8 'must be more than 8'); it often coexists with math.fractions.divide-makes-smaller.", "vs": {"math.fractions.divide-makes-smaller": "Mirror belief; test each separately with prediction items for multiplication and division by a proper fraction."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/5/NF/B/5/", "label": "CCSS 5.NF.B.5: interpret multiplication as scaling"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/5/NF/B/5/", "label": "CCSS 5.NF.B.5: interpret multiplication as scaling"}, {"external": "http://corestandards.org/Math/Content/5/NF/B/4/", "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"}]}, "alignments": [{"scheme": "CCSS", "code": "5.NF.B.5", "uri": "http://corestandards.org/Math/Content/5/NF/B/5/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17.", "doi": "10.5951/jresematheduc.16.1.0003", "note": "Implicit repeated-addition model of multiplication: the product must exceed the multiplicand."}, {"type": "paper", "citation": "Bell, A., Swan, M., & Taylor, G. (1981). Choice of operation in verbal problems with decimal numbers. Educational Studies in Mathematics, 12(4), 399-420.", "doi": "10.1007/BF00308139"}, {"type": "paper", "citation": "Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102.", "doi": "10.5951/jresematheduc.20.1.0095"}, {"type": "paper", "citation": "Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918.", "doi": "10.1037/edu0000025", "note": "Direction-of-effect items show adults and children expecting multiplication to increase."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.multiply-mixed-parts-separately", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-mixed-parts-separately", "uuid": "89ca96fb-84d7-4b24-a0f0-c24cf282e25c", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Multiplying mixed numbers part by part", "statement": "To multiply mixed numbers you multiply the whole numbers together and the fractions together and put the two results back together.", "kind": "procedural-bug", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "5.NF.B.4", "uri": "http://corestandards.org/Math/Content/5/NF/B/4/"}], "level_band": ["middle"], "locale": "en", "evidence_patterns": [{"item_shape": "multiply two mixed numbers", "signature": "product = (whole x whole) and (fraction x fraction) written as a mixed number; the cross terms are dropped", "example": {"item": "2 1/2 x 3 1/3 = ?", "expected": "8 1/3", "response": "6 1/6"}}], "discriminators": {"vs_slip": "The answer is too small by exactly the two cross products and the pattern holds across items. A slip is an arithmetic error within the full method.", "vs": {"math.fractions.multiply-with-common-denominator": "That bug appears on proper-fraction items; this one only appears with mixed numbers."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/5/NF/B/4/", "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/5/NF/B/4/", "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"}], "confusable_with": ["math.fractions.multiply-with-common-denominator"]}, "alignments": [{"scheme": "CCSS", "code": "5.NF.B.4", "uri": "http://corestandards.org/Math/Content/5/NF/B/4/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}, {"type": "paper", "citation": "Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110.", "doi": "10.3102/0002831208320851"}, {"type": "book", "citation": "Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.multiply-with-common-denominator", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-with-common-denominator", "uuid": "116cbd32-81bd-4fbb-b5b2-31a47ff576b4", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Multiplying needs a common denominator", "statement": "Before multiplying fractions you must write them with a common denominator, then multiply the numerators and keep the denominator.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "5.NF.B.4", "uri": "http://corestandards.org/Math/Content/5/NF/B/4/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "multiply two fractions with unlike denominators", "signature": "converts to a common denominator, multiplies numerators and keeps the common denominator", "example": {"item": "1/2 x 1/3 = ?", "expected": "1/6", "response": "3/6 x 2/6 = 6/6 = 1"}}, {"item_shape": "multiply two fractions with like denominators", "signature": "multiplies numerators and keeps the shared denominator", "example": {"item": "2/5 x 3/5 = ?", "expected": "6/25", "response": "6/5"}}], "discriminators": {"vs_slip": "The extra common-denominator step is visible in the working and repeated across items. A slip does not add that step.", "vs": {"math.fractions.cross-multiply-to-multiply": "Cross-multipliers do not convert denominators; they give 1/2 x 1/3 = (1x3)/(2x1) = 3/2.", "math.fractions.add-across": "Add-across is the mirror error (addition treated like multiplication). A learner with both answers 1/2 + 1/3 = 2/5 and 1/2 x 1/3 = 6/6."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/5/NF/B/4/", "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/5/NF/B/4/", "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"}], "confusable_with": ["math.fractions.cross-multiply-to-multiply", "math.fractions.multiply-mixed-parts-separately"]}, "alignments": [{"scheme": "CCSS", "code": "5.NF.B.4", "uri": "http://corestandards.org/Math/Content/5/NF/B/4/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110.", "doi": "10.3102/0002831208320851", "note": "Overgeneralisation of the addition procedure to multiplication."}, {"type": "paper", "citation": "Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918.", "doi": "10.1037/edu0000025"}, {"type": "paper", "citation": "Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625.", "doi": "10.1037/rev0000072"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.no-number-between", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.no-number-between", "uuid": "a18f0879-fc85-4c07-8da5-d1e68e72c460", "version": "0.1.1", "status": "draft", "trust": "low", "title": "No number between neighbouring fractions", "statement": "Fractions come one after another like whole numbers, so between two fractions that are 'next to each other' there is no other number.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "6.NS.C.6", "uri": "http://corestandards.org/Math/Content/6/NS/C/6/"}], "level_band": ["middle", "secondary"], "locale": "en", "evidence_patterns": [{"item_shape": "ask how many numbers lie between two fractions", "signature": "answers none, or a small finite count found by listing", "example": {"item": "How many numbers are there between 1/5 and 2/5?", "expected": "Infinitely many", "response": "None"}}, {"item_shape": "ask for a fraction between two given fractions with consecutive numerators", "signature": "says there is none, or gives one only by changing to a bigger denominator and then says that is the only one", "example": {"item": "Name a fraction between 3/7 and 4/7", "expected": "any of 7/14 ... e.g. 1/2", "response": "There isn't one"}}], "discriminators": {"vs_slip": "A slip is failing to find one on a single item. The belief is a stated rule ('there's nothing between them') that survives being shown an example, or is repaired to 'there are a few, but not infinitely many'."}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/6/NS/C/6/", "label": "CCSS 6.NS.C.6: understand a rational number as a point on the number line"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/6/NS/C/6/", "label": "CCSS 6.NS.C.6: understand a rational number as a point on the number line"}, {"external": "http://corestandards.org/Math/Content/4/NF/A/1/", "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"}], "specializes": ["math.fractions.two-whole-numbers"]}, "alignments": [{"scheme": "CCSS", "code": "6.NS.C.6", "uri": "http://corestandards.org/Math/Content/6/NS/C/6/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction, 14(5), 453-467.", "doi": "10.1016/j.learninstruc.2004.06.013", "note": "Discreteness of the rational number set as a synthetic model carried over from natural numbers."}, {"type": "paper", "citation": "Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students' understanding of rational numbers and their notation. Cognition and Instruction, 28(2), 181-209.", "doi": "10.1080/07370001003676603"}, {"type": "paper", "citation": "Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90(1), 39-56.", "doi": "10.1007/s10649-015-9613-3"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.number-line-whole-is-line", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.number-line-whole-is-line", "uuid": "fb647fd2-a6ef-40a4-a0ac-abd0d497e750", "version": "0.1.1", "status": "draft", "trust": "low", "title": "The whole line is the whole", "statement": "On a number line the fraction refers to the whole line drawn, so 1/2 is at the middle of the line wherever the line ends.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "3.NF.A.2", "uri": "http://corestandards.org/Math/Content/3/NF/A/2/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "place a fraction on a number line longer than one unit", "signature": "places the fraction at that fraction of the whole drawn segment rather than of the unit interval", "example": {"item": "Mark 1/2 on a number line from 0 to 3", "expected": "halfway between 0 and 1", "response": "at 1 1/2, the middle of the line"}, "notes": "On a 0-to-2 line the two placements for 1/2 differ (1/2 vs 1); on 0-to-1 they coincide, so 0-to-1 lines cannot detect this belief."}, {"item_shape": "read the fraction shown by a point on a number line longer than one unit", "signature": "reports the point's position as a fraction of the drawn line", "example": {"item": "A point is at 1 1/2 on a line from 0 to 3. What number is it?", "expected": "1 1/2", "response": "1/2"}}], "discriminators": {"vs_slip": "Correct on 0-to-1 lines and wrong on longer lines, consistently. A slip has no such dependence on line length.", "vs": {"math.fractions.two-whole-numbers": "Learners who see a fraction as two whole numbers fail 0-to-1 lines too, placing 3/4 at 3 or 4."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/3/NF/A/2/", "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/3/NF/A/2/", "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"}, {"external": "http://corestandards.org/Math/Content/3/NF/A/1/", "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"}], "confusable_with": ["math.fractions.two-whole-numbers"]}, "alignments": [{"scheme": "CCSS", "code": "3.NF.A.2", "uri": "http://corestandards.org/Math/Content/3/NF/A/2/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Bright, G. W., Behr, M. J., Post, T. R., & Wachsmuth, I. (1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19(3), 215-232.", "doi": "10.5951/jresematheduc.19.3.0215", "note": "Number-line tasks: students using the whole line rather than the unit interval."}, {"type": "book", "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.of-quantity-swap-roles", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.of-quantity-swap-roles", "uuid": "721c3f30-4b4e-4ffb-ac77-3433d1a18164", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Swapping numerator and denominator when finding a fraction of a quantity", "statement": "To find a/b of a quantity you divide the quantity by a and multiply by b.", "kind": "procedural-bug", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "4.NF.B.4", "uri": "http://corestandards.org/Math/Content/4/NF/B/4/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "find a non-unit fraction of a whole-number quantity", "signature": "divides by the numerator and multiplies by the denominator", "example": {"item": "Find 3/4 of 20", "expected": "15", "response": "26 2/3 (20 / 3 x 4)"}}, {"item_shape": "find a unit fraction of a quantity", "signature": "divides by 1 and multiplies by the denominator", "example": {"item": "Find 1/5 of 30", "expected": "6", "response": "150"}}], "discriminators": {"vs_slip": "The answer is larger than the original quantity for a proper fraction and the learner does not object. A slip is a wrong division or multiplication within the right method."}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/4/NF/B/4/", "label": "CCSS 4.NF.B.4: multiply a fraction by a whole number"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/4/NF/B/4/", "label": "CCSS 4.NF.B.4: multiply a fraction by a whole number"}, {"external": "http://corestandards.org/Math/Content/3/NF/A/1/", "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"}]}, "alignments": [{"scheme": "CCSS", "code": "4.NF.B.4", "uri": "http://corestandards.org/Math/Content/4/NF/B/4/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)", "note": "CSMS fractions: errors on 'fraction of a quantity' items."}, {"type": "book", "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.part-to-part", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.part-to-part", "uuid": "15a57c88-bbde-47b3-bd0d-6771a62e6cec", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Writing the shaded part over the unshaded part", "statement": "A fraction compares the shaded part with the unshaded part, so the number of shaded pieces goes on top and the number of unshaded pieces goes underneath.", "kind": "notation-confusion", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "3.NF.A.1", "uri": "http://corestandards.org/Math/Content/3/NF/A/1/"}], "level_band": ["early-primary", "primary"], "locale": "en", "evidence_patterns": [{"item_shape": "name the fraction shaded in a shape divided into equal parts", "signature": "writes shaded/unshaded instead of shaded/total", "example": {"item": "A bar is cut into 5 equal parts and 3 are shaded. What fraction is shaded?", "expected": "3/5", "response": "3/2"}}], "discriminators": {"vs_slip": "Consistent across items, and the learner produces 'fractions' larger than one for a majority-shaded shape without noticing. A slip is one miswritten denominator.", "vs": {"math.fractions.unequal-parts": "Unequal-parts believers write the correct denominator (the total count) on equal-parts shapes; part-to-part writers do not."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/3/NF/A/1/", "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/3/NF/A/1/", "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"}], "confusable_with": ["math.fractions.unequal-parts"]}, "alignments": [{"scheme": "CCSS", "code": "3.NF.A.1", "uri": "http://corestandards.org/Math/Content/3/NF/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)", "note": "CSMS fractions items: part-part responses on shaded-region tasks."}, {"type": "book", "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."}, {"type": "book", "citation": "Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge.", "note": "Distinguishes part-whole from ratio (part-part) interpretations."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.subtract-across", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.subtract-across", "uuid": "f9b8d0fd-1f46-47ac-8fc7-d4923e7ef2c8", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Subtracting fractions across numerators and denominators", "statement": "Fractions are subtracted by subtracting the numerators and subtracting the denominators.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "5.NF.A.1", "uri": "http://corestandards.org/Math/Content/5/NF/A/1/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "subtract two fractions with unlike denominators", "signature": "difference numerator = a - c and difference denominator = b - d for a/b - c/d", "example": {"item": "3/4 - 1/2 = ?", "expected": "1/4", "response": "2/2 (= 1)"}}, {"item_shape": "subtract two fractions with like denominators", "signature": "subtracts denominators to get zero and cannot finish, or writes the numerator difference over 0", "example": {"item": "3/5 - 1/5 = ?", "expected": "2/5", "response": "2/0 (or 'impossible')"}}], "discriminators": {"vs_slip": "Like-denominator items are diagnostic: the bug produces a zero denominator and the learner stalls. A slip does not.", "vs": {"math.fractions.add-across": "Same mechanism for the other operation. Most learners with one have the other; test both."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/5/NF/A/1/", "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/5/NF/A/1/", "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"}]}, "alignments": [{"scheme": "CCSS", "code": "5.NF.A.1", "uri": "http://corestandards.org/Math/Content/5/NF/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296.", "doi": "10.1016/j.cogpsych.2011.03.001"}, {"type": "paper", "citation": "Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625.", "doi": "10.1037/rev0000072"}, {"type": "book", "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.two-whole-numbers", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.two-whole-numbers", "uuid": "dd52364b-0b0d-4ab8-a0f5-51bcb845f7fc", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A fraction is two separate whole numbers", "statement": "A fraction is two whole numbers written one above the other, not a single number with its own size; the numerator and denominator can be read and handled separately.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "3.NF.A.2", "uri": "http://corestandards.org/Math/Content/3/NF/A/2/"}, {"scheme": "CCSS", "code": "6.NS.C.6", "uri": "http://corestandards.org/Math/Content/6/NS/C/6/"}], "level_band": ["primary", "middle"], "locale": "en", "evidence_patterns": [{"item_shape": "place a fraction on a number line marked 0 to 10", "signature": "places the fraction at the numerator, the denominator, or their sum", "example": {"item": "Mark 3/4 on a number line from 0 to 10", "expected": "between 0 and 1, three quarters of the way", "response": "at 3 (or at 4, or at 7)"}}, {"item_shape": "say which whole numbers a fraction lies between", "signature": "answers with the numerator and denominator themselves", "example": {"item": "Between which two whole numbers is 5/8?", "expected": "0 and 1", "response": "5 and 8"}}], "discriminators": {"vs_slip": "A slip is one misplaced point. The belief is stable across fractions and shows in language: the learner describes 3/4 as 'three and four' or 'three out of four' but cannot say whether it is more or less than one.", "vs": {"math.fractions.number-line-whole-is-line": "Give a 0-to-1 line. Learners who treat the whole line as the unit place 3/4 correctly on a 0-1 line but not on a 0-2 line; learners with this belief fail both and place by the numerator."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/3/NF/A/2/", "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"}, {"external": "http://corestandards.org/Math/Content/6/NS/C/6/", "label": "CCSS 6.NS.C.6: understand a rational number as a point on the number line"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/3/NF/A/2/", "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"}], "confusable_with": ["math.fractions.number-line-whole-is-line"]}, "alignments": [{"scheme": "CCSS", "code": "3.NF.A.2", "uri": "http://corestandards.org/Math/Content/3/NF/A/2/", "relation": "about"}], "provenance": {"sources": [{"type": "paper", "citation": "Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.", "doi": "10.1207/s15326985ep4001_3", "note": "Whole number bias: the components of a fraction are treated as independent natural numbers."}, {"type": "paper", "citation": "Stafylidou, S., & Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.", "doi": "10.1016/j.learninstruc.2004.06.015"}, {"type": "paper", "citation": "Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296.", "doi": "10.1016/j.cogpsych.2011.03.001", "note": "Fraction magnitude understanding as the core of fraction knowledge; its absence underlies this belief."}, {"type": "paper", "citation": "Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441.", "doi": "10.5951/jresematheduc.26.5.0422"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "math.fractions.unequal-parts", "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.unequal-parts", "uuid": "e7a0875c-e339-4404-9f39-1f73cfe9206f", "version": "0.1.2", "status": "draft", "trust": "low", "title": "Any part of a shape cut into b pieces is 1/b", "statement": "If a shape is cut into b pieces, each piece is one b-th of the shape, whether or not the pieces are the same size.", "kind": "overgeneralization", "domain": "math.fractions", "about": [{"scheme": "CCSS", "code": "3.NF.A.1", "uri": "http://corestandards.org/Math/Content/3/NF/A/1/"}], "level_band": ["early-primary", "primary"], "locale": "en", "evidence_patterns": [{"item_shape": "name the fraction shaded in a shape divided into unequal parts", "signature": "counts pieces and writes shaded/total, ignoring the sizes of the pieces", "example": {"item": "A rectangle is cut into 4 pieces of different sizes; the largest is shaded. What fraction is shaded?", "expected": "Cannot tell from the count; it is more than 1/4", "response": "1/4"}}, {"item_shape": "judge whether a shape shows a given fraction", "signature": "accepts an unequal partition as showing the fraction", "example": {"item": "Does this circle, cut into 3 pieces of different sizes with 1 shaded, show 1/3?", "expected": "No, the parts are not equal", "response": "Yes"}}], "discriminators": {"vs_slip": "Ask directly whether the pieces need to be the same size. A slip is a miscount with equal parts assumed; the belief is a stated 'it doesn't matter, there are four pieces'.", "vs": {"math.fractions.part-to-part": "Use a shape with equal parts. Part-to-part writers give 3/2 for 3 shaded of 5; this belief gives 3/5 correctly and only fails on unequal partitions."}}, "relations": {"conflicts_with": [{"external": "http://corestandards.org/Math/Content/3/NF/A/1/", "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"}], "resolved_by": [{"external": "http://corestandards.org/Math/Content/3/NF/A/1/", "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"}], "confusable_with": ["math.fractions.part-to-part"]}, "alignments": [{"scheme": "CCSS", "code": "3.NF.A.1", "uri": "http://corestandards.org/Math/Content/3/NF/A/1/", "relation": "about"}], "provenance": {"sources": [{"type": "book", "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."}, {"type": "book", "citation": "Steffe, L. P., & Olive, J. (2010). Children's Fractional Knowledge. Springer.", "doi": "10.1007/978-1-4419-0591-8", "note": "Equipartitioning as a prerequisite scheme for fractional knowledge."}, {"type": "book", "citation": "Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}, {"version": "0.1.2", "date": "2026-09-07", "change": "Re-kinded from the withdrawn `missing-prerequisite` to `overgeneralization`: the belief is the b-pieces-means-b-ths rule applied past the equal-parts condition it depends on, which is a belief the learner holds rather than an absence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.arrays.arrays-grow", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.arrays.arrays-grow", "uuid": "c14aea0d-dc29-4cdc-9e08-bde06dfa0014", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Arrays grow when you add to them", "statement": "An array gets bigger by itself when you store something past its end, so its size does not need to be decided in advance.", "kind": "overgeneralization", "domain": "programming.arrays", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.arrays.fixed-size"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict a write one past the end of an array", "signature": "predicts the array now has one more element", "example": {"item": "int[] a = new int[3];\na[3] = 7;\nSystem.out.println(a.length);", "expected": "ArrayIndexOutOfBoundsException", "response": "4"}}], "discriminators": {"vs_slip": "Consistent across items; the learner treats arrays like lists. A slip is a single off-by-one index."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.arrays.fixed-size", "label": "An array has a fixed length set when it is created"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.arrays.fixed-size", "label": "An array has a fixed length set when it is created"}]}, "alignments": [{"scheme": "progmiscon", "code": "Java/ArraysGrow", "uri": "https://progmiscon.org/misconceptions/Java/ArraysGrow", "relation": "close-match"}, {"scheme": "progmiscon", "code": "Java/ArrayListIsArray", "uri": "https://progmiscon.org/misconceptions/Java/ArrayListIsArray", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Kaczmarczyk, L. C., Petrick, E. R., East, J. P., & Herman, G. L. (2010). Identifying student misconceptions of programming. In Proceedings of the 41st ACM Technical Symposium on Computer Science Education (SIGCSE '10), 107-111.", "doi": "10.1145/1734263.1734299"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.arrays.length-is-a-method", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.arrays.length-is-a-method", "uuid": "38f22ed3-8b31-4032-9be3-581599629ee5", "version": "0.1.1", "status": "draft", "trust": "low", "title": "An array's length is a method call", "statement": "You get the length of an array by calling a method on it, in the same way as for a string or a list.", "kind": "notation-confusion", "domain": "programming.arrays", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.arrays.length"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "write the length of an array", "signature": "writes length() or size() on an array", "example": {"item": "Given int[] a, write an expression for its length.", "expected": "a.length", "response": "a.length() (or a.size())"}}], "discriminators": {"vs_slip": "A slip is a typo fixed on the first compile error. The belief persists across items and the learner explains that 'everything is a method'."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.arrays.length", "label": "An array's length is a property, not a method"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.arrays.length", "label": "An array's length is a property, not a method"}]}, "alignments": [{"scheme": "progmiscon", "code": "Java/ArrayHasLengthMethod", "uri": "https://progmiscon.org/misconceptions/Java/ArrayHasLengthMethod", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.booleans.must-compare-with-literal", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.booleans.must-compare-with-literal", "uuid": "1e4090f5-0d1e-4bf3-af12-7671e11aaf09", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A boolean must be compared with true to be used as a condition", "statement": "A boolean variable or expression cannot be used directly as a condition; it has to be compared with true or false first, and a comparison is the only thing that produces a condition.", "kind": "undergeneralization", "domain": "programming.boolean", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.booleans.expression"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "write a condition from a boolean variable", "signature": "writes == true (or == True) and cannot explain what if done: alone would do", "example": {"item": "done is a boolean. Write the condition for 'if done'.", "expected": "if done:", "response": "if done == True:"}, "notes": "The == True form runs correctly, so this is only diagnosable by asking, or from a follow-up item."}, {"item_shape": "return a boolean from a comparison", "signature": "wraps the comparison in if/else returning literal true and false", "example": {"item": "Return whether n is even.", "expected": "return n % 2 == 0", "response": "if n % 2 == 0:\n return True\nelse:\n return False"}}], "discriminators": {"vs_slip": "A slip is a stylistic habit the learner can drop when asked. The belief is the claim that if done: is invalid or that a comparison is not a value."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.booleans.expression", "label": "A boolean expression is itself a value"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.booleans.expression", "label": "A boolean expression is itself a value"}]}, "alignments": [{"scheme": "progmiscon", "code": "Java/ComparisonWithBooleanLiteral", "uri": "https://progmiscon.org/misconceptions/Java/ComparisonWithBooleanLiteral", "relation": "close-match"}, {"scheme": "progmiscon", "code": "Python/ComparisonWithBoolLiteral", "uri": "https://progmiscon.org/misconceptions/Python/ComparisonWithBoolLiteral", "relation": "close-match"}, {"scheme": "progmiscon", "code": "Python/MapToBooleanWithIf", "uri": "https://progmiscon.org/misconceptions/Python/MapToBooleanWithIf", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.booleans.no-short-circuit", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.booleans.no-short-circuit", "uuid": "835a754e-f33f-4ab3-88a1-2cc87dc58918", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Both operands of and/or are always evaluated", "statement": "A logical and or or always evaluates both of its operands, whatever the first one turns out to be.", "kind": "undergeneralization", "domain": "programming.boolean", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.booleans.short-circuit"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict whether a guarded expression raises an error", "signature": "predicts an error from the second operand even though the first operand decides the result", "example": {"item": "items = []\nif len(items) > 0 and items[0] == 'x':\n print('yes')\nelse:\n print('no')", "expected": "no", "response": "IndexError"}}, {"item_shape": "predict a side effect in the second operand", "signature": "predicts the side effect happens when the first operand already decides the result", "example": {"item": "def f():\n print('called')\n return True\nresult = False and f()", "expected": "(nothing printed)", "response": "called"}}], "discriminators": {"vs_slip": "Consistent across items; the learner can state 'it checks both'. A slip is a single wrong prediction."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.booleans.short-circuit", "label": "Logical and/or stop evaluating once the result is known"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.booleans.short-circuit", "label": "Logical and/or stop evaluating once the result is known"}]}, "alignments": [{"scheme": "progmiscon", "code": "Java/NoShortCircuit", "uri": "https://progmiscon.org/misconceptions/Java/NoShortCircuit", "relation": "close-match"}, {"scheme": "progmiscon", "code": "Python/NoShortCircuit", "uri": "https://progmiscon.org/misconceptions/Python/NoShortCircuit", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Qian, Y., & Lehman, J. (2017). Students' misconceptions and other difficulties in introductory programming: A literature review. ACM Transactions on Computing Education, 18(1), Article 1.", "doi": "10.1145/3077618"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.control.conditional-is-sequence", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.control.conditional-is-sequence", "uuid": "7e5b6c85-5df3-4013-8746-0f18576e8b5a", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Both branches of an if-else run in turn", "statement": "In an if-else statement the if branch runs when the condition is true and then the else branch runs afterwards as well, because it comes next in the code.", "kind": "overgeneralization", "domain": "programming.control", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.control.conditional"}], "level_band": ["primary", "middle", "secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace an if-else where the condition is true", "signature": "reports the effects of both branches", "example": {"item": "x = 5\nif x > 0:\n print('positive')\nelse:\n print('not positive')", "expected": "positive", "response": "positive\nnot positive"}}], "discriminators": {"vs_slip": "Consistent across items and the learner explains 'it does this one and then that one'. A slip is a single wrong branch.", "vs": {"programming.control.if-is-loop": "If-loopers repeat one branch; sequence believers run both once."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.conditional", "label": "An if statement evaluates its condition once and runs at most one branch"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.conditional", "label": "An if statement evaluates its condition once and runs at most one branch"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.sequential-execution", "label": "Statements run one at a time in order"}], "confusable_with": ["programming.control.if-is-loop"]}, "alignments": [{"scheme": "progmiscon", "code": "Java/ConditionalIsSequence", "uri": "https://progmiscon.org/misconceptions/Java/ConditionalIsSequence", "relation": "close-match"}, {"scheme": "progmiscon", "code": "Scratch/ConditionalIsSequence", "uri": "https://progmiscon.org/misconceptions/Scratch/ConditionalIsSequence", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Swidan, A., Hermans, F., & Smit, M. (2018). Programming misconceptions for school students. In Proceedings of the 2018 ACM Conference on International Computing Education Research (ICER '18), 151-159.", "doi": "10.1145/3230977.3230995", "note": "Scratch learners treating if-then-else as sequential blocks."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.control.if-is-loop", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.control.if-is-loop", "uuid": "aa78ad26-c8b4-4d72-8e2f-84a48c0efed1", "version": "0.1.1", "status": "draft", "trust": "low", "title": "An if statement repeats while its condition holds", "statement": "The body of an if statement keeps running for as long as the condition is true, like a while loop.", "kind": "misapplied-analogy", "domain": "programming.control", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.control.conditional"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace an if statement whose body keeps its condition true", "signature": "predicts repeated execution of the body", "example": {"item": "x = 0\nif x < 3:\n x = x + 1\nprint(x)", "expected": "1", "response": "3"}}], "discriminators": {"vs_slip": "Consistent across items; the learner describes the if as 'checking until'. A slip is a single wrong count.", "vs": {"programming.control.while-checked-continuously": "That belief is about while loops exiting mid-body; this one is about if statements looping.", "programming.control.conditional-is-sequence": "Sequence believers run both branches once; if-loopers run one branch many times."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.conditional", "label": "An if statement evaluates its condition once and runs at most one branch"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.conditional", "label": "An if statement evaluates its condition once and runs at most one branch"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.loop", "label": "A loop checks its condition only at defined points and repeats its whole body"}], "confusable_with": ["programming.control.conditional-is-sequence", "programming.control.while-checked-continuously"]}, "alignments": [{"scheme": "progmiscon", "code": "Java/IfIsLoop", "uri": "https://progmiscon.org/misconceptions/Java/IfIsLoop", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}, {"type": "paper", "citation": "Sirkiä, T., & Sorva, J. (2012). Exploring programming misconceptions: An analysis of student mistakes in visual program simulation exercises. In Proceedings of the 12th Koli Calling International Conference on Computing Education Research, 19-28.", "doi": "10.1145/2401796.2401799"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.control.loop-body-variables-reset", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.control.loop-body-variables-reset", "uuid": "300e50db-d430-4eaa-928f-d34e302f6c48", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Variables reset at the start of every loop iteration", "statement": "Every time a loop body starts again, the variables changed inside it go back to what they were before the loop.", "kind": "overgeneralization", "domain": "programming.control", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.control.loop"}, {"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.variable"}], "level_band": ["primary", "middle", "secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace an accumulator updated inside a loop", "signature": "reports the value from a single iteration rather than the accumulated value", "example": {"item": "total = 0\nfor n in [1, 2, 3]:\n total = total + n\nprint(total)", "expected": "6", "response": "3"}}], "discriminators": {"vs_slip": "Consistent across accumulator items; the learner explains that the loop 'starts over'. A slip is an arithmetic error in the running total.", "vs": {"programming.variables.variable-keeps-history": "History-keepers report too many values; resetters report only the last iteration's contribution."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.variable", "label": "A variable holds exactly one value at a time"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.loop", "label": "A loop checks its condition only at defined points and repeats its whole body"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.variable", "label": "A variable holds exactly one value at a time"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.loop", "label": "A loop checks its condition only at defined points and repeats its whole body"}], "confusable_with": ["programming.variables.variable-keeps-history"]}, "alignments": [{"scheme": "progmiscon", "code": "Scratch/ResetStateEachLoopIteration", "uri": "https://progmiscon.org/misconceptions/Scratch/ResetStateEachLoopIteration", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Swidan, A., Hermans, F., & Smit, M. (2018). Programming misconceptions for school students. In Proceedings of the 2018 ACM Conference on International Computing Education Research (ICER '18), 151-159.", "doi": "10.1145/3230977.3230995"}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.control.while-checked-continuously", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.control.while-checked-continuously", "uuid": "8ed015e5-884f-4e76-91d6-2d5f339b2392", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A while loop stops the instant its condition becomes false", "statement": "The condition of a while loop is watched continuously, so the loop exits in the middle of the body the moment the condition turns false.", "kind": "misapplied-analogy", "domain": "programming.control", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.control.loop"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace a while loop whose condition becomes false partway through the body", "signature": "stops the trace before the rest of the body runs on the final iteration", "example": {"item": "i = 0\nwhile i < 2:\n i = i + 1\n print(i)", "expected": "1\n2", "response": "1"}}], "discriminators": {"vs_slip": "Consistent across items, especially when the update comes before other statements in the body. A slip is a single dropped line.", "vs": {"programming.control.if-is-loop": "Different statement; test each with its own item."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.loop", "label": "A loop checks its condition only at defined points and repeats its whole body"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.control.loop", "label": "A loop checks its condition only at defined points and repeats its whole body"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.sequential-execution", "label": "Statements run one at a time in order"}], "specializes": ["programming.execution.all-statements-active"], "confusable_with": ["programming.control.if-is-loop"]}, "provenance": {"sources": [{"type": "paper", "citation": "Pea, R. D. (1986). Language-independent conceptual \"bugs\" in novice programming. Journal of Educational Computing Research, 2(1), 25-36.", "doi": "10.2190/689T-1R2A-X4W4-29J2", "note": "Parallelism bug: several lines believed to be active at once."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}, {"type": "paper", "citation": "Swidan, A., Hermans, F., & Smit, M. (2018). Programming misconceptions for school students. In Proceedings of the 2018 ACM Conference on International Computing Education Research (ICER '18), 151-159.", "doi": "10.1145/3230977.3230995"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.execution.all-statements-active", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.execution.all-statements-active", "uuid": "a3989f3c-0cf8-4317-874b-f9b8fd9c12e2", "version": "0.1.1", "status": "draft", "trust": "low", "title": "All the statements in a program are active at once", "statement": "Every line of a program is active at the same time, so a later line can affect what an earlier line did, and a condition anywhere is watched continuously.", "kind": "misapplied-analogy", "domain": "programming.execution", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.sequential-execution"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace a program where a later assignment would matter if it applied retroactively", "signature": "applies the later value to the earlier output", "example": {"item": "x = 1\nprint(x)\nx = 2", "expected": "1", "response": "2"}}], "discriminators": {"vs_slip": "Consistent across items; the learner talks about the program 'as a whole' rather than step by step. A slip is a single wrong step.", "vs": {"programming.control.while-checked-continuously": "The while case is a special case of this belief; a learner may show it only for loop conditions."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.sequential-execution", "label": "Statements run one at a time in order"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.sequential-execution", "label": "Statements run one at a time in order"}]}, "provenance": {"sources": [{"type": "paper", "citation": "Pea, R. D. (1986). Language-independent conceptual \"bugs\" in novice programming. Journal of Educational Computing Research, 2(1), 25-36.", "doi": "10.2190/689T-1R2A-X4W4-29J2", "note": "Parallelism bug."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.execution.computer-infers-intent", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.execution.computer-infers-intent", "uuid": "0b67ef75-97f2-4e35-8de8-058b5a78261b", "version": "0.1.1", "status": "draft", "trust": "low", "title": "The computer fills in what you meant", "statement": "The computer understands the purpose of the program and fills in steps that were left out, so a program does what you meant as long as the intention is clear.", "kind": "misapplied-analogy", "domain": "programming.execution", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.literal-interpretation"}], "level_band": ["primary", "middle", "secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict the output of a program with a missing step", "signature": "predicts the intended output rather than the literal one", "example": {"item": "numbers = [3, 1, 2]\nprint(numbers) # print sorted", "expected": "[3, 1, 2]", "response": "[1, 2, 3]"}}], "discriminators": {"vs_slip": "Consistent across items and the learner appeals to what the program is 'for'. A slip is a single misread.", "vs": {"programming.variables.names-meaningful-to-machine": "The variable-name case is a special case; test with an item where the intention is stated only in a comment."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.literal-interpretation", "label": "The machine does exactly what the code says"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.literal-interpretation", "label": "The machine does exactly what the code says"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.sequential-execution", "label": "Statements run one at a time in order"}]}, "provenance": {"sources": [{"type": "paper", "citation": "Pea, R. D. (1986). Language-independent conceptual \"bugs\" in novice programming. Journal of Educational Computing Research, 2(1), 25-36.", "doi": "10.2190/689T-1R2A-X4W4-29J2", "note": "Intentionality and egocentrism bugs."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}, {"type": "paper", "citation": "Qian, Y., & Lehman, J. (2017). Students' misconceptions and other difficulties in introductory programming: A literature review. ACM Transactions on Computing Education, 18(1), Article 1.", "doi": "10.1145/3077618"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.functions.argument-name-must-match-parameter", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.functions.argument-name-must-match-parameter", "uuid": "e7df53b7-374a-4b33-86e9-3c2883c5374f", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Arguments are matched to parameters by name", "statement": "The variable passed to a function has to have the same name as the parameter, or the function will not receive it.", "kind": "misapplied-analogy", "domain": "programming.functions", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.parameter-passing"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict the output of a call whose argument name differs from the parameter name", "signature": "predicts an error or that the parameter is unset", "example": {"item": "def show(n):\n print(n)\nvalue = 5\nshow(value)", "expected": "5", "response": "Error: n is not defined (or 'nothing')"}}, {"item_shape": "write a call to a given function", "signature": "renames the local variable to match the parameter before calling", "example": {"item": "Given def area(width, height), compute the area of a rectangle whose sides are stored in w and h.", "expected": "area(w, h)", "response": "width = w\nheight = h\narea(width, height)"}}], "discriminators": {"vs_slip": "Consistent renaming or predicted errors across items. A slip is a single wrong name.", "vs": {"programming.functions.parameters-alias-arguments": "Aliasers accept different names but expect changes to the parameter to flow back; name-matchers do not accept different names at all."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.parameter-passing", "label": "Arguments are matched to parameters by position and copied in"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.parameter-passing", "label": "Arguments are matched to parameters by position and copied in"}], "confusable_with": ["programming.functions.parameters-alias-arguments"]}, "provenance": {"sources": [{"type": "paper", "citation": "Fleury, A. E. (1991). Parameter passing: The rules the students construct. In Proceedings of the 22nd SIGCSE Technical Symposium on Computer Science Education (SIGCSE '91), 283-286.", "doi": "10.1145/107004.107066", "note": "Student-constructed rules for parameter passing."}, {"type": "paper", "citation": "Madison, S., & Gifford, J. (2002). Modular programming: Novice misconceptions. Journal of Research on Technology in Education, 34(3), 217-229.", "doi": "10.1080/15391523.2002.10782346"}, {"type": "paper", "citation": "Qian, Y., & Lehman, J. (2017). Students' misconceptions and other difficulties in introductory programming: A literature review. ACM Transactions on Computing Education, 18(1), Article 1.", "doi": "10.1145/3077618"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.functions.base-case-not-needed", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.functions.base-case-not-needed", "uuid": "09dac977-0121-45e8-8a5c-0aa059faf59c", "version": "0.1.2", "status": "draft", "trust": "low", "title": "A recursive function stops by itself", "statement": "A recursive function stops calling itself when there is nothing left to do, so it does not need an explicit base case.", "kind": "misapplied-analogy", "domain": "programming.functions", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.base-case"}], "level_band": ["middle", "secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict the behaviour of a recursive function with no base case", "signature": "predicts termination with a sensible answer", "example": {"item": "def count_down(n):\n print(n)\n count_down(n - 1)\ncount_down(3)", "expected": "3 2 1 0 -1 ... until the recursion limit is hit", "response": "3 2 1"}}, {"item_shape": "write a recursive function", "signature": "omits the base case", "example": {"item": "Write factorial(n) recursively.", "expected": "if n == 0: return 1\nreturn n * factorial(n - 1)", "response": "return n * factorial(n - 1)"}}], "discriminators": {"vs_slip": "A slip is one forgotten base case the learner adds when asked how it stops. The belief is the answer 'it stops when n runs out'.", "vs": {"programming.functions.recursion-as-loop": "Loop-model holders often include a base case but expect only one copy of the variables; base-case omitters expect the function to stop on its own."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.base-case", "label": "A recursive function stops only when a base case returns"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.base-case", "label": "A recursive function stops only when a base case returns"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.recursion", "label": "Each recursive call has its own activation with its own variables"}], "confusable_with": ["programming.functions.recursion-as-loop"]}, "alignments": [{"scheme": "progmiscon", "code": "Scratch/BaseCaseNotNeeded", "uri": "https://progmiscon.org/misconceptions/Scratch/BaseCaseNotNeeded", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Kahney, H. (1983). What do novice programmers know about recursion? In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI '83), 235-239.", "doi": "10.1145/800045.801618"}, {"type": "paper", "citation": "Götschi, T., Sanders, I., & Galpin, V. (2003). Mental models of recursion. In Proceedings of the 34th SIGCSE Technical Symposium on Computer Science Education (SIGCSE '03), 346-350.", "doi": "10.1145/611892.612004"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}, {"version": "0.1.2", "date": "2026-09-07", "change": "Re-kinded from the withdrawn `missing-prerequisite` to `misapplied-analogy`: the belief carries everyday stopping-when-done reasoning, and loop intuition, into recursion, which is a belief the learner holds rather than an absence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.functions.multiple-return-values", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.functions.multiple-return-values", "uuid": "ba72c8c8-9a30-4f6a-9c9f-50370cde1a2f", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A function can return several separate values", "statement": "return a, b sends back two separate values, so the caller receives two things rather than one tuple.", "kind": "undergeneralization", "domain": "programming.functions", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.single-return-value"}], "level_band": ["undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict the type of a call that returns a comma-separated list", "signature": "predicts two values, or that the second is lost, rather than one tuple", "example": {"item": "def f():\n return 1, 2\nx = f()\nprint(type(x))", "expected": "<class 'tuple'>", "response": "int (or 'error, two values into one variable')"}}], "discriminators": {"vs_slip": "Consistent across items and revealed by asking what x holds after x = f(). A slip is a single wrong type."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.single-return-value", "label": "A function returns one value; several values travel as one tuple"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.single-return-value", "label": "A function returns one value; several values travel as one tuple"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.return", "label": "return hands a value back to the caller and ends the call"}]}, "alignments": [{"scheme": "progmiscon", "code": "Python/MultipleValuesReturn", "uri": "https://progmiscon.org/misconceptions/Python/MultipleValuesReturn", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.functions.parameters-alias-arguments", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.functions.parameters-alias-arguments", "uuid": "7e500e88-daa7-49cb-a8f4-d0e0d6a62db0", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Changing a parameter changes the caller's variable", "statement": "A parameter is the same variable as the argument that was passed in, so assigning to the parameter inside the function changes the caller's variable, even for numbers and strings.", "kind": "overgeneralization", "domain": "programming.functions", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.parameter-passing"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace a function that reassigns a primitive parameter", "signature": "reports the caller's variable as changed", "example": {"item": "def bump(n):\n n = n + 1\nx = 1\nbump(x)\nprint(x)", "expected": "1", "response": "2"}}], "discriminators": {"vs_slip": "Consistent across items with primitive arguments. A slip is a single wrong trace.", "vs": {"programming.functions.argument-name-must-match-parameter": "Name-matchers predict errors when names differ; aliasers accept different names.", "programming.objects.assignment-copies-object": "The mirror: aliasers expect sharing where there is none; object-copiers expect independence where there is sharing. Test with a primitive item and a mutable-object item."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.parameter-passing", "label": "Arguments are matched to parameters by position and copied in"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.parameter-passing", "label": "Arguments are matched to parameters by position and copied in"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment", "label": "Assignment copies a value into a variable at one moment"}], "confusable_with": ["programming.functions.argument-name-must-match-parameter"]}, "provenance": {"sources": [{"type": "paper", "citation": "Fleury, A. E. (1991). Parameter passing: The rules the students construct. In Proceedings of the 22nd SIGCSE Technical Symposium on Computer Science Education (SIGCSE '91), 283-286.", "doi": "10.1145/107004.107066"}, {"type": "paper", "citation": "Madison, S., & Gifford, J. (2002). Modular programming: Novice misconceptions. Journal of Research on Technology in Education, 34(3), 217-229.", "doi": "10.1080/15391523.2002.10782346"}, {"type": "paper", "citation": "Ma, L., Ferguson, J., Roper, M., & Wood, M. (2007). Investigating the viability of mental models held by novice programmers. In Proceedings of the 38th SIGCSE Technical Symposium on Computer Science Education (SIGCSE '07), 499-503.", "doi": "10.1145/1227310.1227481"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.functions.print-is-return", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.functions.print-is-return", "uuid": "c75e0b4a-c9c4-41af-af83-a095635ace63", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Printing a value is the same as returning it", "statement": "A function gives its result back by printing it, so a function that prints its answer can be used in an expression, and return is just another way to display.", "kind": "misapplied-analogy", "domain": "programming.functions", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.return"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "use the result of a function that prints instead of returning", "signature": "expects the printed value to be available to the caller", "example": {"item": "def double(n):\n print(n * 2)\nx = double(4)\nprint(x + 1)", "expected": "8 then TypeError (x is None)", "response": "9"}}, {"item_shape": "write a function that should return a value", "signature": "prints the value and omits return", "example": {"item": "Write square(n) so that square(3) + 1 is 10.", "expected": "def square(n):\n return n * n", "response": "def square(n):\n print(n * n)"}}], "discriminators": {"vs_slip": "A slip is one missing return the learner spots on rereading. The belief is a stated equivalence ('print gives it back') and persists after seeing None."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.return", "label": "return hands a value back to the caller and ends the call"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.return", "label": "return hands a value back to the caller and ends the call"}]}, "provenance": {"sources": [{"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534", "note": "Catalogue entry on confusing output with return values."}, {"type": "paper", "citation": "Kaczmarczyk, L. C., Petrick, E. R., East, J. P., & Herman, G. L. (2010). Identifying student misconceptions of programming. In Proceedings of the 41st ACM Technical Symposium on Computer Science Education (SIGCSE '10), 107-111.", "doi": "10.1145/1734263.1734299"}, {"type": "paper", "citation": "Qian, Y., & Lehman, J. (2017). Students' misconceptions and other difficulties in introductory programming: A literature review. ACM Transactions on Computing Education, 18(1), Article 1.", "doi": "10.1145/3077618"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.functions.recursion-as-loop", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.functions.recursion-as-loop", "uuid": "fee3c932-6d7c-4816-aab9-c1dfe916ef15", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A recursive call jumps back to the start", "statement": "A recursive call is a jump back to the beginning of the function, using the same variables, so there is only ever one copy of the function running.", "kind": "misapplied-analogy", "domain": "programming.functions", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.recursion"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace a recursive function that does work after the recursive call", "signature": "omits or misorders the work done after each call returns", "example": {"item": "def show(n):\n if n == 0:\n return\n show(n - 1)\n print(n)\nshow(3)", "expected": "1\n2\n3", "response": "3 2 1 (or nothing, or 1 only)"}}], "discriminators": {"vs_slip": "Consistent across items with post-call work; the learner draws a single frame. A slip is a single ordering error.", "vs": {"programming.functions.base-case-not-needed": "Base-case omitters are diagnosed by termination questions; loop-model holders by post-call ordering."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.recursion", "label": "Each recursive call has its own activation with its own variables"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.functions.recursion", "label": "Each recursive call has its own activation with its own variables"}], "confusable_with": ["programming.functions.base-case-not-needed"]}, "provenance": {"sources": [{"type": "paper", "citation": "Kahney, H. (1983). What do novice programmers know about recursion? In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI '83), 235-239.", "doi": "10.1145/800045.801618", "note": "The 'looping' model of recursion."}, {"type": "paper", "citation": "Götschi, T., Sanders, I., & Galpin, V. (2003). Mental models of recursion. In Proceedings of the 34th SIGCSE Technical Symposium on Computer Science Education (SIGCSE '03), 346-350.", "doi": "10.1145/611892.612004", "note": "Mental models of recursion including looping and active/passive-flow models."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.objects.assignment-copies-object", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.objects.assignment-copies-object", "uuid": "bf369c82-773c-4072-950c-55b6d9464684", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Assigning an object makes a copy", "statement": "Assigning one object variable to another makes a second, independent copy of the object, so changing one does not affect the other.", "kind": "overgeneralization", "domain": "programming.objects", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.reference"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace a mutation through an aliased object", "signature": "reports the other variable's object as unchanged", "example": {"item": "a = [1, 2]\nb = a\nb.append(3)\nprint(a)", "expected": "[1, 2, 3]", "response": "[1, 2]"}}], "discriminators": {"vs_slip": "Consistent across items with mutable objects, and the learner is surprised by the result. A slip is a single wrong trace.", "vs": {"programming.objects.variables-hold-objects": "Same observable error; variables-hold-objects is the underlying model (the variable is the object). Ask the learner to draw a and b: two boxes with contents versus two arrows to one object.", "programming.variables.assignment-links-variables": "The primitive mirror image. Test with an int item and a list item."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.reference", "label": "An object variable holds a reference; assignment copies the reference"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.reference", "label": "An object variable holds a reference; assignment copies the reference"}], "confusable_with": ["programming.objects.variables-hold-objects"]}, "alignments": [{"scheme": "progmiscon", "code": "Java/AssignmentCopiesObject", "uri": "https://progmiscon.org/misconceptions/Java/AssignmentCopiesObject", "relation": "close-match"}, {"scheme": "progmiscon", "code": "Python/AssignmentCopiesObject", "uri": "https://progmiscon.org/misconceptions/Python/AssignmentCopiesObject", "relation": "close-match"}, {"scheme": "progmiscon", "code": "JavaScript/AssignmentCopiesObject", "uri": "https://progmiscon.org/misconceptions/JavaScript/AssignmentCopiesObject", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Ma, L., Ferguson, J., Roper, M., & Wood, M. (2007). Investigating the viability of mental models held by novice programmers. In Proceedings of the 38th SIGCSE Technical Symposium on Computer Science Education (SIGCSE '07), 499-503.", "doi": "10.1145/1227310.1227481", "note": "Non-viable models of reference assignment."}, {"type": "paper", "citation": "Holland, S., Griffiths, R., & Woodman, M. (1997). Avoiding object misconceptions. In Proceedings of the 28th SIGCSE Technical Symposium on Computer Science Education (SIGCSE '97), 131-134.", "doi": "10.1145/268084.268132"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.objects.constant-reference-is-immutable", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.objects.constant-reference-is-immutable", "uuid": "371c613b-da3c-49d9-917e-3758758a1a81", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A constant reference means an unchangeable object", "statement": "Declaring an object variable final or const makes the object it refers to unchangeable, so its fields or elements cannot be modified.", "kind": "overgeneralization", "domain": "programming.objects", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.immutability"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict a mutation through a final/const reference", "signature": "predicts an error", "example": {"item": "const items = [1, 2];\nitems.push(3);\nconsole.log(items);", "expected": "[1, 2, 3]", "response": "TypeError (or 'not allowed')"}}], "discriminators": {"vs_slip": "Consistent across items and the learner says const 'freezes' the value. A slip is a single wrong prediction."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.immutability", "label": "A constant reference does not make the referenced object immutable"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.immutability", "label": "A constant reference does not make the referenced object immutable"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.reference", "label": "An object variable holds a reference; assignment copies the reference"}]}, "alignments": [{"scheme": "progmiscon", "code": "Java/FinalReferenceImpliesImmutability", "uri": "https://progmiscon.org/misconceptions/Java/FinalReferenceImpliesImmutability", "relation": "close-match"}, {"scheme": "progmiscon", "code": "JavaScript/ConstReferenceImpliesImmutability", "uri": "https://progmiscon.org/misconceptions/JavaScript/ConstReferenceImpliesImmutability", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.objects.constructor-returns-object", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.objects.constructor-returns-object", "uuid": "82998d6e-dc24-425a-984e-e60d6a3b1de6", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A constructor must return the object", "statement": "A constructor creates the object and has to return it at the end, so a constructor without a return statement produces nothing.", "kind": "overgeneralization", "domain": "programming.objects", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.constructor"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "write a constructor", "signature": "adds return this (or return self) at the end, or a return type to the constructor header", "example": {"item": "Write a constructor for Point that stores x and y.", "expected": "Point(int x, int y) { this.x = x; this.y = y; }", "response": "Point Point(int x, int y) { this.x = x; this.y = y; return this; }"}}], "discriminators": {"vs_slip": "A slip is a stray return removed when noticed. The belief is stated ('otherwise you don't get the object back') and the learner also expects new Point(1, 2) to be 'empty' without it."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.constructor", "label": "A constructor initialises an object the runtime has already created"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.constructor", "label": "A constructor initialises an object the runtime has already created"}]}, "alignments": [{"scheme": "progmiscon", "code": "Java/ConstructorReturnsObject", "uri": "https://progmiscon.org/misconceptions/Java/ConstructorReturnsObject", "relation": "close-match"}, {"scheme": "progmiscon", "code": "Python/InitReturnsObject", "uri": "https://progmiscon.org/misconceptions/Python/InitReturnsObject", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Ragonis, N., & Ben-Ari, M. (2005). A long-term investigation of the comprehension of OOP concepts by novices. Computer Science Education, 15(3), 203-221.", "doi": "10.1080/08993400500224310", "note": "Novice comprehension of constructors and object creation."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.objects.equality-compares-contents", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.objects.equality-compares-contents", "uuid": "23722159-9645-4246-a122-1d6ea3fd6ddf", "version": "0.1.1", "status": "draft", "trust": "low", "title": "== compares the contents of objects", "statement": "Comparing two object variables with == compares what is inside the objects, so two objects with the same field values are equal.", "kind": "overgeneralization", "domain": "programming.objects", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.identity-vs-equality"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict == on two distinct objects with equal contents", "signature": "predicts true", "example": {"item": "String a = new String(\"hi\");\nString b = new String(\"hi\");\nSystem.out.println(a == b);", "expected": "false", "response": "true"}}], "discriminators": {"vs_slip": "Consistent across items and the learner sees no difference between == and equals. A slip is choosing the wrong operator once while knowing the difference.", "vs": {"programming.objects.variables-hold-objects": "Learners with no reference concept also predict true, but for a different reason (they see no identity to compare). Ask what == compares."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.identity-vs-equality", "label": "== on references compares identity, not contents"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.identity-vs-equality", "label": "== on references compares identity, not contents"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.reference", "label": "An object variable holds a reference; assignment copies the reference"}], "confusable_with": ["programming.objects.variables-hold-objects"]}, "alignments": [{"scheme": "progmiscon", "code": "Java/EqualityOperatorComparesObjectsValues", "uri": "https://progmiscon.org/misconceptions/Java/EqualityOperatorComparesObjectsValues", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Holland, S., Griffiths, R., & Woodman, M. (1997). Avoiding object misconceptions. In Proceedings of the 28th SIGCSE Technical Symposium on Computer Science Education (SIGCSE '97), 131-134.", "doi": "10.1145/268084.268132"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.objects.variables-hold-objects", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.objects.variables-hold-objects", "uuid": "d4a1fd15-44b9-4752-b086-b9a07a1e7ae7", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A variable contains the whole object", "statement": "An object variable contains the object itself, not a reference to it, so every variable is its own object and passing it around passes the object.", "kind": "misapplied-analogy", "domain": "programming.objects", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.reference"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "draw or describe memory after two variables refer to one object", "signature": "draws two separate objects, one inside each variable", "example": {"item": "p = Point(1, 2)\nq = p\nDraw p and q.", "expected": "Two variables, both pointing to one Point object", "response": "Two boxes, each containing a Point(1, 2)"}}, {"item_shape": "predict identity comparison of two variables assigned from one another", "signature": "predicts they are different objects", "example": {"item": "p = Point(1, 2)\nq = p\nprint(p is q)", "expected": "True", "response": "False"}}], "discriminators": {"vs_slip": "Diagnosed by the drawing or by identity questions; the model is consistent. A slip is a single wrong prediction with a correct drawing.", "vs": {"programming.objects.assignment-copies-object": "Assignment-copies is the behavioural prediction; this record is the memory model behind it. Use the drawing task to separate learners who know about references but think assignment copies from those with no reference concept."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.reference", "label": "An object variable holds a reference; assignment copies the reference"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.objects.reference", "label": "An object variable holds a reference; assignment copies the reference"}], "confusable_with": ["programming.objects.assignment-copies-object", "programming.objects.equality-compares-contents"]}, "alignments": [{"scheme": "progmiscon", "code": "Python/VariablesHoldObjects", "uri": "https://progmiscon.org/misconceptions/Python/VariablesHoldObjects", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Sorva, J. (2013). Notional machines and introductory programming education. ACM Transactions on Computing Education, 13(2), Article 8.", "doi": "10.1145/2483710.2483713", "note": "Notional machine: references versus values."}, {"type": "paper", "citation": "Ma, L., Ferguson, J., Roper, M., & Wood, M. (2007). Investigating the viability of mental models held by novice programmers. In Proceedings of the 38th SIGCSE Technical Symposium on Computer Science Education (SIGCSE '07), 499-503.", "doi": "10.1145/1227310.1227481"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.strings.plus-adds-before-concatenating", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.strings.plus-adds-before-concatenating", "uuid": "71cc8015-8e64-4cbf-aec0-1227ef5023f9", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Plus adds numbers before it concatenates", "statement": "In an expression that mixes strings and numbers with +, the numbers are added together first and the string is attached afterwards.", "kind": "overgeneralization", "domain": "programming.strings", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.strings.concatenation-order"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict a left-to-right mixed concatenation", "signature": "adds the numeric operands regardless of their position", "example": {"item": "System.out.println(\"x\" + 1 + 2);", "expected": "x12", "response": "x3"}}], "discriminators": {"vs_slip": "Consistent across items; the learner explains that 'plus means add'. A slip is one wrong prediction."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.strings.concatenation-order", "label": "Operators of equal precedence apply left to right"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.strings.concatenation-order", "label": "Operators of equal precedence apply left to right"}]}, "alignments": [{"scheme": "progmiscon", "code": "Java/ArithmeticPlusPrecedes", "uri": "https://progmiscon.org/misconceptions/Java/ArithmeticPlusPrecedes", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.types.integer-division-gives-fraction", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.types.integer-division-gives-fraction", "uuid": "f884573f-e177-4865-9cbb-e334397e406a", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Dividing two integers gives a fraction", "statement": "Dividing one whole number by another gives the exact mathematical result with a fractional part, whatever the types involved.", "kind": "overgeneralization", "domain": "programming.types", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.types.integer-division"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict the result of integer division in a language that truncates", "signature": "predicts the exact quotient", "example": {"item": "int x = 7 / 2;\nSystem.out.println(x);", "expected": "3", "response": "3.5"}}, {"item_shape": "compute an average of integers", "signature": "divides an int sum by an int count and expects a decimal average", "example": {"item": "int total = 7, n = 2;\ndouble avg = total / n;", "expected": "3.0 (integer division happens first)", "response": "3.5"}}], "discriminators": {"vs_slip": "Consistent across items; the learner is surprised by 3 and cannot explain it. A slip is forgetting a cast once while knowing the rule."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.types.integer-division", "label": "Dividing two integers gives an integer result"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.types.integer-division", "label": "Dividing two integers gives an integer result"}]}, "provenance": {"sources": [{"type": "paper", "citation": "Qian, Y., & Lehman, J. (2017). Students' misconceptions and other difficulties in introductory programming: A literature review. ACM Transactions on Computing Education, 18(1), Article 1.", "doi": "10.1145/3077618", "note": "Integer division and type-related misconceptions in the review."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.variables.assignment-is-equation", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.variables.assignment-is-equation", "uuid": "1d678f7e-ebf2-49bf-979f-eb433148cc0e", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Assignment states an equation", "statement": "The equals sign in an assignment states that the two sides are equal, as in algebra, so x = x + 1 is a contradiction and a = b and b = a mean the same thing.", "kind": "misapplied-analogy", "domain": "programming.variables", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment"}], "level_band": ["secondary", "undergraduate", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "trace an assignment whose right-hand side uses the variable being assigned", "signature": "declares the statement impossible or leaves the variable unchanged", "example": {"item": "x = 5\nx = x + 1\nWhat is x?", "expected": "6", "response": "'Impossible, x can't equal x + 1' (or 5)"}}, {"item_shape": "trace an assignment with the variables in the 'wrong' order", "signature": "treats a = b as also setting b from a, or asks which one changes", "example": {"item": "a = 1\nb = 2\na = b\nWhat are a and b?", "expected": "a is 2, b is 2", "response": "a is 1, b is 1 (or 'they are now the same variable')"}}], "discriminators": {"vs_slip": "Consistent across items; the learner uses the words 'equals' or 'is the same as' and objects to x = x + 1. A slip is a wrong final value with an otherwise correct trace.", "vs": {"programming.variables.assignment-links-variables": "Linkers accept a = b as directional but expect later changes to b to show up in a; equation believers object at the moment of assignment.", "programming.variables.assignment-moves-value": "Movers empty the source variable; equation believers keep both sides equal."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment", "label": "Assignment copies a value into a variable at one moment"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment", "label": "Assignment copies a value into a variable at one moment"}], "confusable_with": ["programming.variables.assignment-links-variables", "programming.variables.assignment-moves-value"]}, "alignments": [{"scheme": "progmiscon", "code": "Java/AssignCompares", "uri": "https://progmiscon.org/misconceptions/Java/AssignCompares", "relation": "close-match", "note": "progmiscon's entry covers reading = as a comparison; this record covers the underlying algebraic reading."}], "provenance": {"sources": [{"type": "paper", "citation": "du Boulay, B. (1986). Some difficulties of learning to program. Journal of Educational Computing Research, 2(1), 57-73.", "doi": "10.2190/3LFX-9RRF-67T8-UVK9", "note": "Notional machine difficulties; the equals sign carrying its mathematical meaning."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}, {"type": "paper", "citation": "Qian, Y., & Lehman, J. (2017). Students' misconceptions and other difficulties in introductory programming: A literature review. ACM Transactions on Computing Education, 18(1), Article 1.", "doi": "10.1145/3077618"}, {"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.variables.assignment-links-variables", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.variables.assignment-links-variables", "uuid": "3c50552e-a1f7-4d39-b0e5-1e1673032c7b", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Assignment links two variables", "statement": "After a = b the two variables are connected, so whenever b changes later, a changes too.", "kind": "misapplied-analogy", "domain": "programming.variables", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment"}], "level_band": ["secondary", "undergraduate", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "trace a change to the source variable after an assignment between primitives", "signature": "reports the destination variable as having the source's new value", "example": {"item": "a = 1\nb = a\na = 7\nWhat is b?", "expected": "1", "response": "7"}}], "discriminators": {"vs_slip": "A slip gives the wrong value once. The belief is stated ('b is a now') and holds on every item where the source is later reassigned.", "vs": {"programming.variables.assignment-is-equation": "Equation believers object to x = x + 1; linkers do not.", "programming.objects.assignment-copies-object": "The object case is the mirror image: there the learner expects independence and gets aliasing. Test with a primitive and an object item."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment", "label": "Assignment copies a value into a variable at one moment"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment", "label": "Assignment copies a value into a variable at one moment"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.variable", "label": "A variable holds exactly one value at a time"}], "confusable_with": ["programming.variables.assignment-is-equation", "programming.variables.assignment-moves-value"]}, "provenance": {"sources": [{"type": "paper", "citation": "Ma, L., Ferguson, J., Roper, M., & Wood, M. (2007). Investigating the viability of mental models held by novice programmers. In Proceedings of the 38th SIGCSE Technical Symposium on Computer Science Education (SIGCSE '07), 499-503.", "doi": "10.1145/1227310.1227481", "note": "Non-viable mental models of value assignment among novices."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}, {"type": "paper", "citation": "Sirkiä, T., & Sorva, J. (2012). Exploring programming misconceptions: An analysis of student mistakes in visual program simulation exercises. In Proceedings of the 12th Koli Calling International Conference on Computing Education Research, 19-28.", "doi": "10.1145/2401796.2401799"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.variables.assignment-moves-value", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.variables.assignment-moves-value", "uuid": "55c0374e-b4f9-4b70-aef3-8d020d2c99c1", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Assignment moves the value out of the source", "statement": "Assigning a = b moves the value from b into a, so b is empty or zero afterwards.", "kind": "misapplied-analogy", "domain": "programming.variables", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment"}], "level_band": ["secondary", "undergraduate", "adult"], "locale": "en", "evidence_patterns": [{"item_shape": "trace the source variable after an assignment", "signature": "reports the source as empty, zero or undefined", "example": {"item": "b = 4\na = b\nWhat is b?", "expected": "4", "response": "0 (or 'nothing')"}}], "discriminators": {"vs_slip": "Consistent across items; the learner explains that the value 'went into' the other variable. A slip does not empty the source.", "vs": {"programming.variables.assignment-links-variables": "Linkers keep both variables and couple them; movers empty the source."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment", "label": "Assignment copies a value into a variable at one moment"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment", "label": "Assignment copies a value into a variable at one moment"}], "confusable_with": ["programming.variables.assignment-links-variables", "programming.variables.assignment-is-equation"]}, "provenance": {"sources": [{"type": "paper", "citation": "Bayman, P., & Mayer, R. E. (1983). A diagnosis of beginning programmers' misconceptions of BASIC programming statements. Communications of the ACM, 26(9), 677-679.", "doi": "10.1145/358172.358408", "note": "LET statements understood as moving a value."}, {"type": "paper", "citation": "du Boulay, B. (1986). Some difficulties of learning to program. Journal of Educational Computing Research, 2(1), 57-73.", "doi": "10.2190/3LFX-9RRF-67T8-UVK9"}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.variables.names-meaningful-to-machine", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.variables.names-meaningful-to-machine", "uuid": "b34639bb-e7b4-400a-bd2a-ced15052078b", "version": "0.1.1", "status": "draft", "trust": "low", "title": "The computer understands variable names", "statement": "The name of a variable tells the computer what it is for, so a variable called total will add things up and one called largest will hold the biggest value.", "kind": "misapplied-analogy", "domain": "programming.variables", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.naming"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict the value of a descriptively named variable that is never updated", "signature": "predicts the value the name suggests rather than the value assigned", "example": {"item": "largest = 0\nfor n in [4, 9, 2]:\n pass\nprint(largest)", "expected": "0", "response": "9"}}], "discriminators": {"vs_slip": "The prediction follows the name on every item, and renaming the variable to x changes the learner's answer. A slip does not depend on the name."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.naming", "label": "Identifiers are labels with no meaning to the machine"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.naming", "label": "Identifiers are labels with no meaning to the machine"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.execution.literal-interpretation", "label": "The machine does exactly what the code says"}], "specializes": ["programming.execution.computer-infers-intent"]}, "provenance": {"sources": [{"type": "paper", "citation": "Pea, R. D. (1986). Language-independent conceptual \"bugs\" in novice programming. Journal of Educational Computing Research, 2(1), 25-36.", "doi": "10.2190/689T-1R2A-X4W4-29J2", "note": "Egocentrism bug: attributing interpretive intelligence to the machine."}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}, {"type": "paper", "citation": "Kaczmarczyk, L. C., Petrick, E. R., East, J. P., & Herman, G. L. (2010). Identifying student misconceptions of programming. In Proceedings of the 41st ACM Technical Symposium on Computer Science Education (SIGCSE '10), 107-111.", "doi": "10.1145/1734263.1734299"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.variables.uninitialized-is-zero", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.variables.uninitialized-is-zero", "uuid": "436c64f5-62ac-40c8-86f7-60b05c57c1de", "version": "0.1.1", "status": "draft", "trust": "low", "title": "Uninitialised variables start at zero", "statement": "A variable that has been declared but never assigned holds zero, or an empty value, so it can be safely read or added to.", "kind": "overgeneralization", "domain": "programming.variables", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.initialization"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "predict the outcome of reading a declared but unassigned local variable", "signature": "predicts 0 or empty output rather than a compile error or garbage value", "example": {"item": "int count;\ncount = count + 1;\nSystem.out.println(count);", "expected": "Compile error: count might not have been initialized", "response": "1"}}], "discriminators": {"vs_slip": "A slip is forgetting one initialisation while knowing it is needed. The belief is stated ('it starts at zero') and the learner omits initialisation habitually."}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.initialization", "label": "A variable has no usable value until it is assigned"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.initialization", "label": "A variable has no usable value until it is assigned"}]}, "alignments": [{"scheme": "progmiscon", "code": "Java/LocalVariablesAutoInitialized", "uri": "https://progmiscon.org/misconceptions/Java/LocalVariablesAutoInitialized", "relation": "close-match"}], "provenance": {"sources": [{"type": "inventory", "citation": "Chiodini, L., Moreno Santos, I., Gallidabino, A., Tafliovich, A., Santos, A. L., & Hauswirth, M. (2021). A curated inventory of programming language misconceptions. In Proceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE '21), 380-386.", "doi": "10.1145/3430665.3456343", "url": "https://progmiscon.org/", "note": "Inventory consulted for the misconception name and scope only; progmiscon publishes no licence for its text, so Open Misconceptions' statements and examples are written independently."}, {"type": "paper", "citation": "Kaczmarczyk, L. C., Petrick, E. R., East, J. P., & Herman, G. L. (2010). Identifying student misconceptions of programming. In Proceedings of the 41st ACM Technical Symposium on Computer Science Education (SIGCSE '10), 107-111.", "doi": "10.1145/1734263.1734299", "note": "Memory-model misconceptions including uninitialised storage."}, {"type": "paper", "citation": "Qian, Y., & Lehman, J. (2017). Students' misconceptions and other difficulties in introductory programming: A literature review. ACM Transactions on Computing Education, 18(1), Article 1.", "doi": "10.1145/3077618"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}
{"id": "programming.variables.variable-keeps-history", "uri": "https://open-misconceptions.github.io/miscon-data/m/programming.variables.variable-keeps-history", "uuid": "1ee84937-cc32-4577-ae23-3d6e015807c3", "version": "0.1.1", "status": "draft", "trust": "low", "title": "A variable remembers every value it has held", "statement": "A variable stores every value ever assigned to it, so an earlier value can still be read out later.", "kind": "misapplied-analogy", "domain": "programming.variables", "about": [{"scheme": "Miscon", "uri": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.variable"}], "level_band": ["secondary", "undergraduate"], "locale": "en", "evidence_patterns": [{"item_shape": "trace repeated assignment to one variable and then use it", "signature": "uses an earlier value, or sums the values, instead of the most recent one", "example": {"item": "x = 3\nx = 5\nprint(x)", "expected": "5", "response": "3 5 (or 8)"}}, {"item_shape": "accumulate in a loop", "signature": "expects the variable to hold the list of values seen rather than the running total", "example": {"item": "total = 0\nfor n in [1, 2, 3]:\n total = total + n\nprint(total)", "expected": "6", "response": "1 2 3 (or 0 1 3 6)"}}], "discriminators": {"vs_slip": "Consistent across items; the learner talks about the variable 'having' several values. A slip is a single wrong trace step.", "vs": {"programming.control.loop-body-variables-reset": "Resetters lose values between iterations (total becomes 3); history-keepers retain too many."}}, "relations": {"conflicts_with": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.variable", "label": "A variable holds exactly one value at a time"}], "resolved_by": [{"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.variable", "label": "A variable holds exactly one value at a time"}, {"external": "https://open-misconceptions.github.io/miscon-data/c/programming.variables.assignment", "label": "Assignment copies a value into a variable at one moment"}], "confusable_with": ["programming.control.loop-body-variables-reset"]}, "provenance": {"sources": [{"type": "paper", "citation": "du Boulay, B. (1986). Some difficulties of learning to program. Journal of Educational Computing Research, 2(1), 57-73.", "doi": "10.2190/3LFX-9RRF-67T8-UVK9"}, {"type": "paper", "citation": "Bayman, P., & Mayer, R. E. (1983). A diagnosis of beginning programmers' misconceptions of BASIC programming statements. Communications of the ACM, 26(9), 677-679.", "doi": "10.1145/358172.358408"}, {"type": "book", "citation": "Sorva, J. (2012). Visual Program Simulation in Introductory Programming Education (Doctoral dissertation, Aalto University). Appendix A catalogues introductory programming misconceptions from the literature.", "url": "https://aaltodoc.aalto.fi/handle/123456789/3534"}], "origin": "llm-drafted", "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."}, "history": {"changelog": [{"version": "0.1.1", "date": "2026-09-05", "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."}]}, "license": "CC-BY-4.0"}