Küttel Maurus, Rüede Christian, Staub Fritz C
Pädagogische Hochschule Luzern, Frohburgstraße 3, 6002 Luzern, Schweiz.
Pädagogische Hochschule FHNW, Hofackerstraße 30, 4132 Muttenz, Schweiz.
J Math Didakt. 2025;46(2):11. doi: 10.1007/s13138-025-00262-y. Epub 2025 Aug 18.
In secondary mathematics education, students are expected to apply procedures not only correctly but also flexibly, for example when solving quadratic equations. Tasks that deliberately stimulate cognitive and metacognitive processes support the development of such flexibility. The aim of this paper is to investigate the relationship between students' learning gains and the activation potential of the tasks provided. To this end, prompts included in tasks on solving quadratic equations based on a sample of 39 classes. In parallel, the learning gains of = 739 students in these classes were measured over the course of an instructional unit on rule-based solving of quadratic equations.Linear regression analyses showed that (a) the development of strategy flexibility and procedural knowledge depends on the number of tasks that prompt students to compare worked-out solutions; (b) the development of strategy flexibility and conceptual knowledge depends on the number of tasks with metacognitively activating prompts; and (c) a high number of tasks with prompts that prescribe a specific procedure tend to hinder the development of strategy flexibility. These findings indicate that the activation potential of task prompts is a significant predictor of learning gains in solving quadratic equations.
在中等数学教育中，期望学生不仅能正确而且灵活地应用解题步骤，例如在解二次方程时。刻意激发认知和元认知过程的任务有助于培养这种灵活性。本文旨在研究学生的学习收获与所提供任务的激活潜力之间的关系。为此，基于39个班级的样本，分析了二次方程求解任务中包含的提示。同时，在一个关于基于规则解二次方程的教学单元中，对这些班级中739名学生的学习收获进行了测量。线性回归分析表明：（a）策略灵活性和程序性知识的发展取决于促使学生比较已解出的答案的任务数量；（b）策略灵活性和概念性知识的发展取决于具有元认知激活提示的任务数量；（c）大量具有规定特定步骤提示的任务往往会阻碍策略灵活性的发展。这些发现表明，任务提示的激活潜力是解二次方程学习收获的一个重要预测指标。
