miscon:math.decimals.shorter-is-larger · draft · trust low · v0.1.1 · kind misapplied-analogy

Shorter decimal is larger

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.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.decimals.shorter-is-larger
UUID
e3685617-2ee2-41c1-875f-5e0d835be18f
Domain
math.decimals
Level band
primary, middle
Locale
en
About
CCSS 4.NF.C.7 http://corestandards.org/Math/Content/4/NF/C/7/
CCSS 5.NBT.A.3 http://corestandards.org/Math/Content/5/NBT/A/3/

Evidence patterns

Pattern 0: compare two decimals where the longer decimal is larger

chooses the decimal with fewer digits after the point

ItemWhich is larger, 0.85 or 0.8?
Expected0.85
Response0.8

Length-incongruent item; a longer-is-larger believer answers this correctly.

Pattern 1: compare two decimals where the longer is larger and the shorter has a smaller leading digit

picks the shorter decimal despite a smaller leading digit

ItemWhich is larger, 0.4 or 0.45?
Expected0.45
Response0.4

Discriminators

vs a 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
CCSS 4.NF.C.7: compare two decimals to hundredths by reasoning about their size http://corestandards.org/Math/Content/4/NF/C/7/
resolved_by
CCSS 4.NF.C.7: compare two decimals to hundredths by reasoning about their size http://corestandards.org/Math/Content/4/NF/C/7/
CCSS 5.NBT.A.3: read, write and compare decimals to thousandths http://corestandards.org/Math/Content/5/NBT/A/3/
confusable_with
math.decimals.longer-is-larger

Alignments

Provenance

Origin: llm-drafted

  1. 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
    Fraction rule for decimal comparison.
  2. Stacey, K., & Steinle, V. (1998). Refining the classification of students' interpretations of decimal notation. Hiroshima Journal of Mathematics Education, 6, 49-69.
    Shorter-is-larger classification.
  3. 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

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.decimals.shorter-is-larger
https://open-misconceptions.github.io/miscon-data/m/math.decimals.shorter-is-larger