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[The Role of Task Prompts in Fostering Strategy Flexibility, Procedural, and Conceptual Knowledge when Solving
Maurus Küttel1, Christian Rüede2, Fritz C Staub3
1Pädagogische Hochschule Luzern, Frohburgstraße 3, 6002 Luzern, Schweiz.
Journal Fur Mathematik-Didaktik
|August 21, 2025
Summary
The study found that task prompts encouraging solution comparison and metacognitive thinking boost strategy flexibility and knowledge in secondary math students. Prescriptive prompts, however, can impede flexibility when solving quadratic equations.
Area of Science:
- Mathematics Education
- Cognitive Psychology
Context:
- Secondary mathematics students often struggle with flexible application of procedures, particularly in solving quadratic equations.
- Developing cognitive and metacognitive processes through task design is crucial for enhancing procedural and conceptual flexibility.
Purpose:
- This study investigates the relationship between the activation potential of task prompts and student learning gains in secondary mathematics.
- The research specifically examines how different types of prompts influence the development of strategy flexibility and knowledge in solving quadratic equations.
Summary:
- Learning gains in strategy flexibility and procedural knowledge were positively correlated with tasks prompting students to compare worked-out solutions.
- Strategy flexibility and conceptual knowledge development were linked to tasks featuring metacognitively activating prompts.
- Conversely, an abundance of tasks with prompts prescribing specific procedures appeared to hinder strategy flexibility.
Impact:
- Task prompts significantly predict learning gains in solving quadratic equations, highlighting the importance of instructional design.
- Findings suggest that educators should prioritize tasks that encourage critical thinking and metacognition over rote procedural instruction to foster mathematical flexibility.
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