miscon:math.fractions.division-is-sharing-only · draft · trust low · v0.1.1 · kind undergeneralization

Division of fractions only means sharing

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.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.division-is-sharing-only
UUID
50e4d120-cd01-49b2-95e6-5ec8df0762d1
Domain
math.fractions
Level band
primary, middle, adult
Locale
en
About
CCSS 6.NS.A.1 http://corestandards.org/Math/Content/6/NS/A/1/
CCSS 5.NF.B.7 http://corestandards.org/Math/Content/5/NF/B/7/

Evidence patterns

Pattern 0: choose the operation for a measurement-division word problem

rejects division and multiplies or divides by the wrong number, because 'you can't share among half a person'

ItemHow many 1/2-cup servings are in 3 cups?
Expected3 / 1/2 = 6
Response3 / 2 = 1.5 (or 3 x 2 = 6 'because it can't be division')

Pattern 1: write a word problem for a given fraction division

writes a sharing story that does not match the expression, or says it is impossible

ItemWrite a story problem for 3/4 / 1/4
ExpectedHow many quarter-cups are in three quarters of a cup?
ResponseThree quarters shared between a quarter of a person (or: 'you can't')

Discriminators

vs a 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
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/
CCSS 5.NF.B.7: divide unit fractions by whole numbers and whole numbers by unit fractions http://corestandards.org/Math/Content/5/NF/B/7/
confusable_with
math.fractions.divide-makes-smaller

Alignments

Provenance

Origin: llm-drafted

  1. 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
    Partitive (sharing) model as the primitive model of division.
  2. 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
  3. 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.
    Measurement, partitive and other interpretations of fraction division.

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.division-is-sharing-only
https://open-misconceptions.github.io/miscon-data/m/math.fractions.division-is-sharing-only