miscon:math.decimals.longer-is-larger · draft · trust low · v0.1.1 · kind overgeneralization

Longer decimal is larger

A decimal with more digits after the point is a larger number, because the digits after the point make a bigger whole number.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.decimals.longer-is-larger
UUID
b9976592-9045-4327-8b17-485c7114d359
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 shorter is larger

chooses the decimal with more digits after the point

ItemWhich is larger, 0.5 or 0.25?
Expected0.5
Response0.25

Pattern 1: order decimals of different lengths

orders by the digits after the point read as whole numbers

ItemOrder from smallest to largest: 0.3, 0.125, 0.45
Expected0.125, 0.3, 0.45
Response0.3, 0.45, 0.125

Discriminators

vs a slip. A slip is one wrong comparison. The belief is diagnosed by a consistent pattern on length-incongruent items and a justification such as 'twenty-five is more than five'.

vs math.decimals.shorter-is-larger. Mirror belief. Include items where the longer decimal is larger (0.75 vs 0.8): longer-is-larger gets those right and shorter-is-larger gets them wrong.

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.shorter-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
    Whole-number 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.
    Longer-is-larger classification and its sub-types.
  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.longer-is-larger
https://open-misconceptions.github.io/miscon-data/m/math.decimals.longer-is-larger