Use brief inversion-problem activities before associativity instruction to increase shortcut use¶

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

Description¶

The article suggests that brief activities in which learners solve 'a + b – b' inversion problems before encountering 'a + b – c' associativity problems can increase their willingness to use associativity shortcuts. In all three studies, learners "who first solved inversion problems (e.g. 'a + b – b') were more likely than controls to then use associativity on 'a + b – c' problems." The activity is brief (about 4 minutes 30 seconds of paper-based problem solving) and does not explicitly prescribe strategies, which the authors argue may better preserve strategy flexibility than explicit demonstrations.

Design Implications¶

Context¶

Requirements¶

• Learners should solve 'a + b – b' inversion problems (not 'a + b – a' or two-term problems) as the pre-activity, since only that format was expected to activate all three mechanisms

Constraints¶

• The effect was demonstrated on self-reported shortcut use on a single test problem; it did not significantly increase problems solved or attempted on a timed problem-solving measure, and the effect may depend on how conducive the test problems are to shortcuts

Target Learners¶

• adult undergraduates in mathematics-related courses

Target Learning Goals¶

• willingness to apply associativity shortcuts on three-term arithmetic problems
• easing the transition to algebra

Affordances¶

• Three Mechanisms Inversion Promotes Associativity

Claims¶

• Solving inversion problems increases adults' self-reported use of associativity shortcuts on three-term problems [+W]
• Inversion intervention did not significantly increase problems solved or attempted on a timed problem-solving measure [~W]
• Solving only 'a + b – b' inversion problems replicates increased self-reported associativity shortcut use in a new sample [+W]
• Self-reported shortcut users solve substantially more conducive problems than non-users, validating the problem-solving measure [+W]

Related Strategies¶

Examples¶

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Key Sources¶

• Joanne Eaves, Nina Attridge, Camilla Gilmore. (2018). Increasing the use of conceptually-derived strategies in arithmetic: using inversion problems to promote the use of associativity shortcuts. Learning and Instruction. https://figshare.com/s/230ee9491e0b67d9d3f3