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¶

Claim · All claims
Evidence · 2 studies · 1 causal r2, 1 associational r1 · q3
Currency · newest study 2017 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? Operation-and-operand explanations, though stated on only 26% of multiplication and 16% of division trials with operands below one, accompanied 65% of correct multiplication and 54% of correct division judgments. → Lortie-Forgues 2017 q3 i? Unconditional operation explanations (e.g., multiplication makes bigger) were associated with less than 10% correct judgments on multiplication and division problems with operands 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? · associational · r1

Study 2 judgment-plus-explanation task; two raters classified explanations (91% agreement, Cohen's kappa = 0.85). "Despite this type of explanation being stated on only 26% of multiplication and 16% of division trials", operation-and-operand explanations accompanied most correct judgments.

"Despite this type of explanation being stated on only 26% of multiplication and 16% of division trials with operands below one, it was advanced on 65% of trials with correct multiplication judgments and 54% of trials with correct division judgments."

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

In the same Study 2 explanation analysis, "unconditional operation explanations were associated with very low accuracy" on multiplication and division problems with operands below one, reflecting the assumption that operand size is irrelevant to direction of effect.

"In contrast, unconditional operation explanations were associated with very low accuracy on both multiplication and division problems with operands below one, less than 10% correct."

Discussion¶

Learner Variables¶

• Operations and Place Value — predictor: learners who differ on it differ in outcomes

Related Claims¶

• Below Chance Direction Of Effect Decimals Below One
• 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' explanations rarely use repeated addition for whole-number-by-decimal multiplication; many instead invoke a part-whole logic — related
• Direction of effect judgments for multiplication of decimals below one are more accurate when one operand is a whole number than when both operands are decimals — 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