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<p>The action of comparing solution strategies fosters strategy flexibility in equation solving. Implementing comparison in the classroom, however, is challenging: Teachers find it difficult to integrate it into their lessons. Therefore, in professional development (PD) programs on comparing, teachers need to learn how to integrate tasks that promote comparing in their classroom. For example, teachers can use worked example pairs with self-explanation prompts comparing the two worked-out solutions to introduce and discuss multiple strategies. They can also use metacognitive practice problems (e.g. “solve 17(<i>x</i> – 3) = 34 efficiently”) that require students to plan and evaluate multiple potential strategies before solving the given equation. We hypothesized that the number of worked example pairs and metacognitive practice problems that teachers provided in class after attending a PD program would predict the improvement in students’ achievement. We tested this hypothesis by analyzing two PD programs and a control condition in a randomized implementation study. Both PD programs introduced comparing solution strategies, but only one program additionally introduced orchestrating productive classroom discussions. The results partially confirmed our hypothesis: the number of worked example pairs and metacognitive practice problems offered in class mediated effects of the PD program on students’ achievement, but this mediation effect depended on the type of task and whether the PD program introduced orchestrating productive classroom discussions.</p>

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Tasks as mediators for advancing strategy flexibility in equation solving

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月6日

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  • Christian Rüede,
  • Maurus Küttel,
  • Sog Yee Mok,
  • Fritz C. Staub

摘要

The action of comparing solution strategies fosters strategy flexibility in equation solving. Implementing comparison in the classroom, however, is challenging: Teachers find it difficult to integrate it into their lessons. Therefore, in professional development (PD) programs on comparing, teachers need to learn how to integrate tasks that promote comparing in their classroom. For example, teachers can use worked example pairs with self-explanation prompts comparing the two worked-out solutions to introduce and discuss multiple strategies. They can also use metacognitive practice problems (e.g. “solve 17(x – 3) = 34 efficiently”) that require students to plan and evaluate multiple potential strategies before solving the given equation. We hypothesized that the number of worked example pairs and metacognitive practice problems that teachers provided in class after attending a PD program would predict the improvement in students’ achievement. We tested this hypothesis by analyzing two PD programs and a control condition in a randomized implementation study. Both PD programs introduced comparing solution strategies, but only one program additionally introduced orchestrating productive classroom discussions. The results partially confirmed our hypothesis: the number of worked example pairs and metacognitive practice problems offered in class mediated effects of the PD program on students’ achievement, but this mediation effect depended on the type of task and whether the PD program introduced orchestrating productive classroom discussions.