Middle school students judge the direction of effect of multiplication and division of decimals below one below chance, while remaining highly accurate on all other operation-operand combinations¶
Claim · All claims
Evidence · 1 study · associationalr1·q3·i3large
Currency · newest study 2017 · not yet checked against its sources · not reviewed by a person
Subclaims¶
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This claim: no standardized effect is recorded in observations/ for it yet, so no benchmark reading is possible.
q3 i3 Accuracy on direction of effect judgments for multiplication and division of decimals below one fell below the 50% chance level, whereas judgments for addition, subtraction, and operations on decimals above one were highly accurate. → Lortie-Forgues 2017
Evidence¶
Lortie-Forgues 2017¶
Lortie-Forgues, Hugues and Siegler, Robert S (2017) Conceptual knowledge of decimal arithmetic. Journal of Educational Psychology. pp. 374-391. ISSN: 0022-0620. https://doi.org/10.1037/edu0000148
q3 · i3 · associational · r1
Study 1, a repeated-measures ANOVA of direction of effect judgments by 55 middle school students on 16 inequalities, showed the decimal size X operation interaction (F(3, 159) = 38.24, p < 0.001, ηp2 = 0.42); accuracy was "below the chance level of 50% with decimals below one" for multiplication and division.
"Accuracy was below the chance level of 50% with decimals below one for both multiplication (t(54) = 6.05, p < 0.001) and division (t(54) = 6.49, p < 0.001)."
Discussion¶
Related Claims¶
- Wd Multiplication More Accurate Than Dd Decimals Below One
- Direction Of Effect Errors Not Attributable Computation
- Explanations citing both the arithmetic operation and the operands' magnitudes are strongly associated with accurate direction of effect judgments, while unconditional operation rules are associated with very low accuracy — related
- Decimal magnitude comparison accuracy is unrelated to direction of effect judgment accuracy, indicating the errors do not stem from poor access to decimal magnitudes — related
- Students are less confident in direction of effect judgments for multiplication and division than for addition and subtraction, but equally confident regardless of operand size — related
- Students' explanations rarely use repeated addition for whole-number-by-decimal multiplication; many instead invoke a part-whole logic — related
Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
below-chance-direction-of-effect-decimals-below-one |
title |
Middle school students judge the direction of effect of multiplication and division of decimals below one below chance, while remaining highly accurate on all other operation-operand combinations |
description |
Middle school students judge the direction of effect of multiplication and division of decimals below one below chance, while remaining highly accurate on all other operation-operand combinations |
status |
review |
evidence_strength |
moderate |
newest_evidence |
2017 |
generated |
by process:wiki-ingest on 2026-10-23 |
trust |
unverified — no one has confirmed this page's content |
sources |
1 — lortie-forgues-2017 |
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