A superordinate structuring term such as “bouquet” increases use of the factorization algorithm in isomorphic multiplication problems¶

Claim · All claims
Evidence · 1 study (2 entries) · causal r? · q2
Currency · newest study 2020 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Among 5th graders, problems without a structuring term were less often solved by factorization (44%) than identical problems mentioning a bouquet (68%), because the term evokes world semantics of grouping flowers into one set. → Hippolyte Gros 2020 q2 i? With the structuring term present, factorization 14 × (5 + 7) was the strategy mostly used by solvers. → Hippolyte Gros 2020 (2)

Evidence¶

Hippolyte Gros 2020¶

Hippolyte Gros, Jean-Pierre Thibaut, Emmanuel Sander. (2020). Semantic Congruence in Arithmetic: A New Conceptual Model for Word Problem Solving. Educational Psychologist. https://doi.org/10.1080/00461520.2019.1691004

q2 · i? · causal · r?

The article reports, citing Coquin-Viennot and Moreau (2003), a study of 3rd and 5th graders using factorization and expansion algorithms on florist problems. Problems without the structuring term were solved by factorization by "44% among 5th graders"; no effect size is printed.

"were less often solved using factorization (44% among 5th graders) than problems identical in every aspect except for the presence of a superordinate structuring term such as “a bouquet”"

Hippolyte Gros 2020 (2)¶

Hippolyte Gros, Jean-Pierre Thibaut, Emmanuel Sander. (2020). Semantic Congruence in Arithmetic: A New Conceptual Model for Word Problem Solving. Educational Psychologist. https://doi.org/10.1080/00461520.2019.1691004

q2 · i? · theoretical · r3

The article reports, citing Coquin-Viennot and Moreau (2003), that the bouquet-worded version of the same problem was solved by factorization by "68% among 5th graders". The percentages are descriptive; no statistical test or effect size is printed.

"“For a prize-giving, the florist prepares for each of the 14 candidates a bouquet made up of 5 roses and 7 tulips.” (68% among 5th graders)."

Discussion¶

Related Claims¶

• Training on the deep structure of problems increases 4th and 5th graders' use of the shorter 1-step algorithm on unordered-entity problems — related
• Larger numerical values shift adults' solving strategy from the grouping algorithm to the more economical sequential algorithm