miscon:math.fractions.bigger-denominator-bigger-fraction · draft · trust low · v0.1.1 · kind overgeneralization

Bigger denominator means bigger fraction

The fraction with the bigger denominator is the bigger fraction, because the denominator is a bigger number.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.bigger-denominator-bigger-fraction
UUID
1288d189-d36c-4a7d-925d-62c88196a161
Domain
math.fractions
Level band
primary, middle
Locale
en
About
CCSS 3.NF.A.3 http://corestandards.org/Math/Content/3/NF/A/3/
CCSS 4.NF.A.2 http://corestandards.org/Math/Content/4/NF/A/2/

Evidence patterns

Pattern 0: compare two unit fractions

picks the unit fraction with the larger denominator as larger; on 1/b vs 1/d chooses the one with the larger b

ItemWhich is larger, 1/3 or 1/8?
Expected1/3
Response1/8

Pattern 1: order a set of unit fractions

orders unit fractions by denominator ascending as if ordering whole numbers

ItemOrder from smallest to largest: 1/2, 1/5, 1/3
Expected1/5, 1/3, 1/2
Response1/2, 1/3, 1/5

Discriminators

vs a 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.

vs 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
CCSS 3.NF.A.3: explain equivalence of fractions and compare fractions by reasoning about their size http://corestandards.org/Math/Content/3/NF/A/3/
resolved_by
CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts http://corestandards.org/Math/Content/3/NF/A/1/
CCSS 3.NF.A.3: explain equivalence of fractions and compare fractions by reasoning about their size http://corestandards.org/Math/Content/3/NF/A/3/
specializes
math.fractions.compare-whole-number-components
confusable_with
math.fractions.compare-by-gap

Alignments

Provenance

Origin: llm-drafted

  1. 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
    Reports the 'fraction increases as the denominator increases' interpretation as an early developmental stage.
  2. 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
  3. 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
  4. 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

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.bigger-denominator-bigger-fraction
https://open-misconceptions.github.io/miscon-data/m/math.fractions.bigger-denominator-bigger-fraction