Use whole-number-by-decimal problems as a transition context for building decimal multiplication understanding¶

Strategy · All strategies
Evidence · 4 claims (4 for) · 2 studies (2 causal), q3 · 1 of 2 report an effect size · 3 claims rest on one study

Description¶

The article suggests that problems involving a whole number and a decimal below one "provide a possible transition context through which instruction could build on students’ understanding of whole number arithmetic and extend it to decimals". Because judgments were more accurate on WD than DD multiplication problems below one, instruction can start from WD problems before moving to two-decimal problems. The article also notes that explanations citing both the operation and the operands' magnitudes were strongly associated with accurate judgments, suggesting instruction should target that integrated reasoning.

Design Implications¶

Context¶

Requirements¶

• Students already have reliable whole number arithmetic direction of effect knowledge

Constraints¶

• The WD advantage held only for multiplication, not division; accuracy on WD multiplication below one was still only 47% and not above chance

Target Learners¶

• middle school students learning decimal arithmetic

Target Learning Goals¶

• accurate direction of effect judgments for decimal multiplication and division

Claims¶

• 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 [+W]
• Students' explanations rarely use repeated addition for whole-number-by-decimal multiplication; many instead invoke a part-whole logic [+W]
• 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 [+M]
• 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 [+W]

Related Strategies¶

Examples¶

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Key Sources¶

• 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