miscon:math.fractions.two-whole-numbers · draft · trust low · v0.1.1 · kind overgeneralization

A fraction is two separate whole numbers

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.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.two-whole-numbers
UUID
dd52364b-0b0d-4ab8-a0f5-51bcb845f7fc
Domain
math.fractions
Level band
primary, middle
Locale
en
About
CCSS 3.NF.A.2 http://corestandards.org/Math/Content/3/NF/A/2/
CCSS 6.NS.C.6 http://corestandards.org/Math/Content/6/NS/C/6/

Evidence patterns

Pattern 0: place a fraction on a number line marked 0 to 10

places the fraction at the numerator, the denominator, or their sum

ItemMark 3/4 on a number line from 0 to 10
Expectedbetween 0 and 1, three quarters of the way
Responseat 3 (or at 4, or at 7)

Pattern 1: say which whole numbers a fraction lies between

answers with the numerator and denominator themselves

ItemBetween which two whole numbers is 5/8?
Expected0 and 1
Response5 and 8

Discriminators

vs a 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
CCSS 3.NF.A.2: understand a fraction as a number on the number line http://corestandards.org/Math/Content/3/NF/A/2/
CCSS 6.NS.C.6: understand a rational number as a point on the number line http://corestandards.org/Math/Content/6/NS/C/6/
resolved_by
CCSS 3.NF.A.2: understand a fraction as a number on the number line http://corestandards.org/Math/Content/3/NF/A/2/
confusable_with
math.fractions.number-line-whole-is-line

Alignments

Provenance

Origin: llm-drafted

  1. 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
    Whole number bias: the components of a fraction are treated as independent natural numbers.
  2. 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
  3. 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
    Fraction magnitude understanding as the core of fraction knowledge; its absence underlies this belief.
  4. 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

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

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Cite

miscon:math.fractions.two-whole-numbers
https://open-misconceptions.github.io/miscon-data/m/math.fractions.two-whole-numbers