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¶
Claim · All claims
Evidence · 2 studies · 2 causalr2·q3
Currency · newest study 2017 · not yet checked against its sources · not reviewed by a person
Subclaims¶
Reading the evidence codes
q is the design tier, i the impact, n the sample, and the kind with its r
the rigour judged within that kind: what each code means.
This claim: no standardized effect is recorded in observations/ for it yet, so no benchmark reading is possible.
q3 i? Confidence ratings were lower for division than multiplication and lower for multiplication than addition and subtraction, with no difference between problems with decimals above versus below one among students whose judgments always followed whole number arithmetic. → Lortie-Forgues 2017
q3 i? Among the 49% of students whose judgments always matched whole number direction of effect, confidence did not differ between problems with numbers above and below one. → Lortie-Forgues 2017 (2)
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 · i? · causal · r2
Study 1 repeated-measures ANOVA of 5-point confidence ratings yielded a main effect of operation (F(3, 159) = 20.31, p < 0.001, ηp2 = 0.28); "Confidence in direction of effect judgments was lower for division" than multiplication and lower for multiplication than addition or subtraction.
"Confidence in direction of effect judgments was lower for division (M = 3.97, SD = 1.01) than for multiplication (M = 4.37, SD = 0.72; t(54) = 4.24, p < 0.001), and lower for multiplication than for addition"
Lortie-Forgues 2017 (2)¶
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 · i? · causal · r2
Subgroup analysis of the 49% of Study 1 participants whose judgments always followed whole number direction of effect showed "Confidence ratings did not differ between problems with numbers above and below one", consistent with the operation knowledge hypothesis rather than strong conviction.
"Confidence ratings did not differ between problems with numbers above and below one (for problems above one, M = 4.44, SD = 0.58; for problems below one, M = 4.46, SD = 0.58; t(26) = 0.42, p = 0.7)."
Discussion¶
Related Claims¶
- Direction Of Effect Confidence Three Hypotheses
- 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 — related
- Working memory demand increases with the complexity of arithmetic and math problems, including operand size and number of solution steps — related
- 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
Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
confidence-lower-multiplication-division-than-addition-subtraction |
title |
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 |
description |
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 |
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 |
2 — lortie-forgues-2017, lortie-forgues-2017-2 |
Frontmatter is the page's machine-readable record — see the Schema & Guide.