Teach learners to recode semantically incongruent representations by comparing strategies and studying the problem's deep structure¶

Strategy · All strategies
Evidence · 4 claims (4 for) · 1 study (1 theoretical), q2 · 0 of 1 report an effect size · 4 claims rest on one study

Description¶

This strategy addresses the crucial step learners struggle with: recoding a semantically incongruent initial representation. The article defines recoding as the process by which, when the initially encoded interpreted structure cannot be translated into an appropriate, tractable algorithm, "a new representation can be abstracted by recoding the interpreted structure". In the training studied, children were instructed to compare the two strategies, identify their initial semantic representation, and were shown a visual representation of the deep structure to help them recode their initial encoding.

Design Implications¶

Context¶

Requirements¶

• Learners must be able to identify their initial semantic representation
• Training must focus on the mathematical relations between the described entities and the deep structure of the problems

Constraints¶

• The recoding process is described as costly and one that does not systematically happen

Target Learners¶

• 4th and 5th grade students solving arithmetic word problems

Target Learning Goals¶

• adopting more efficient solving algorithms on problems whose world semantics misalign with the required mathematical semantics

Affordances¶

• Seco Semantic Congruence Model

Claims¶

• Transfer of a permutation algorithm succeeds for objects-assigned-to-people problems but fails for people-assigned-to-objects problems [+W]
• Training on the deep structure of problems increases 4th and 5th graders' use of the shorter 1-step algorithm on unordered-entity problems [+W]
• Minor rewording of structurally identical change problems raises children's success from 36% to 55% [+W]
• A superordinate structuring term such as “bouquet” increases use of the factorization algorithm in isomorphic multiplication problems [+W]

Related Strategies¶

• Schema-Based Instruction
• Productive Failure

Examples¶

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Key Sources¶

• 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