Emphasize fluent retrieval of verbal arithmetic facts and partially different memory processes when instructing multiplication, in contrast to addition and subtraction¶

Strategy · All strategies
Evidence · 9 claims (9 for) · 2 studies (2 associational), q3 · 1 of 2 report an effect size · 9 claims rest on one study

Description¶

Based on the study's finding that arithmetic operations vary in their reliance on retrieval processes after formal skill acquisition, the article proposes that multiplication instruction should attend to fluent fact retrieval from verbal memory prompted by visuo-orthographic stimuli, more so than addition and subtraction instruction. The educational impact statement says: "It is proposed that multiplication, in relation to addition and subtraction, relies to a greater extent on fluent retrieval of verbal information prompted by visuo-ortographical stimuli as well as on partially different memory processes, which were more similar to those involved in reading fluency." The article also notes multiplication is bridged to addition through repeated addition and, in contrast with other operations, to a greater extent rote learning.

Design Implications¶

Context¶

Requirements¶

• Formal skill acquisition phase with direct instruction and intensive practice should precede the emphasis on retrieval processes

Constraints¶

• The article notes that the extent to which operations are taught using procedural or retrieval approaches varies across cultures and curricula, which may shape these retrieval contributions

Target Learners¶

• primary school children learning multiplication after addition and subtraction

Target Learning Goals¶

• multiplication fact fluency and automatized fact retrieval

Affordances¶

• Hierarchical Arithmetic Development Framework

Claims¶

• Multiplication employs fact retrieval processes to a larger extent than addition and subtraction, though the regressive difference is slight [+W]
• Adults use a mix of retrieval and procedural strategies in single-digit arithmetic, with retrieval more frequent in multiplication and procedures more frequent in subtraction [+W]
• Adults with developmental dyslexia use arithmetic fact retrieval less frequently than matched controls during single-digit multiplication and subtraction [+W]
• Adults with dyslexia are slower than controls on single-digit arithmetic, with a larger multiplication-minus-subtraction reaction-time difference, even after controlling digit identification speed [+W]
• Addition fluency strongly predicts third-grade multiplication fluency, and a significant working memory association emerges after controlling for addition fluency [+W]
• Subtraction fluency predicts third-grade multiplication fluency on par with addition fluency, with a similar emergent working memory association [+W]
• Numerical abilities and serial retrieval fluency predict third-grade multiplication fluency, while working memory shows no significant association in the baseline model [+W]
• In the reading fluency contrast model, numerical abilities and serial retrieval fluency predict multiplication fluency but working memory does not, indicating partial domain-specificity [+W]
• Addition fluency captures more shared variance with serial retrieval fluency than subtraction fluency does [+W]

Related Strategies¶

Examples¶

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Key Sources¶

• Rautiainen, J., Aro, T., Aro, M., Tolvanen, A., & Koponen, T. (2026). Hierarchical Nature of Arithmetic Skills: Similarities and Differences Between Arithmetic Operations. Journal of Educational Psychology, Early online. https://doi.org/10.1037/edu0001066