miscon:math.fractions.invert-dividend · draft · trust low · v0.1.1 · kind procedural-bug

Inverting the first fraction when dividing

To divide fractions you flip the first fraction and then multiply.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.invert-dividend
UUID
33e03294-fca9-4bef-92bc-386f55ec81de
Domain
math.fractions
Level band
middle, secondary, adult
Locale
en
About
CCSS 6.NS.A.1 http://corestandards.org/Math/Content/6/NS/A/1/

Evidence patterns

Pattern 0: divide two proper fractions

inverts the dividend instead of the divisor and multiplies

Item1/2 / 3/4 = ?
Expected2/3
Response6/4 (= 3/2)

Discriminators

vs a 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.

vs 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
CCSS 6.NS.A.1: interpret and compute quotients of fractions http://corestandards.org/Math/Content/6/NS/A/1/
resolved_by
CCSS 6.NS.A.1: interpret and compute quotients of fractions http://corestandards.org/Math/Content/6/NS/A/1/
confusable_with
math.fractions.invert-both
math.fractions.divide-makes-smaller

Alignments

Provenance

Origin: llm-drafted

  1. Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon.
  2. 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
    Invert-and-multiply errors among preservice teachers.
  3. Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918. doi:10.1037/edu0000025
  4. 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
    Models fraction arithmetic bugs as mis-selected procedures.

Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review.

Review status

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Formats

Cite

miscon:math.fractions.invert-dividend
https://open-misconceptions.github.io/miscon-data/m/math.fractions.invert-dividend