Structure varied exercises so that repetitive practice supports sense-making¶

Strategy · All strategies
Evidence · 1 claim (1 for) · 1 study (1 theoretical), q1 · 0 of 1 report an effect size · 1 claim rests on one study

Description¶

The paper points to structuring varied exercises as a way to embed discovery opportunities in practice, citing work on variation in mathematics education: “For one comparison, see Watson and Mason (2006), on the pedagogical benefit of structuring varied exercises in mathematics education.” The strategy is to design exercise sequences whose variation invites learners to see exercises as instances of a single object.

Design Implications¶

Context¶

Requirements¶

• Exercises must be deliberately varied rather than identical, so that repetition carries explorative potential.

Constraints¶

Target Learners¶

• Mathematics students

Target Learning Goals¶

• Procedural fluency combined with sense-making during practice

Affordances¶

• Bernstein Repetition Without Repetition

Claims¶

• Direct instruction and discovery are complementary rather than opposite, linked by repetitive yet explorative practice [+W] (the argument the strategy comes from: repetitive yet explorative practice)

Related Strategies¶

• Variation theory: contrast, generalization, and fusion as necessary conditions for discerning aspects of an object of learning: variation theory, which explains why structured variation lets learners discern what stays the same

Examples¶

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Key Sources¶

• Trninic, D. (2018). Instruction, repetition, discovery: restoring the historical educational role of practice. Instructional Science, 46(1), 133–153. doi:10.1007/s11251-017-9443-z