From Problem-Solving to Reflection: Activating Diverse Metacognitive Skills in Mathematics
摘要
This study explores what types of metacognitive skills (MS) (planning, monitoring and evaluation) are activated with students in three age cohorts by a mathematical problem-solving task and reflective prompts. The study is also interested in determining possible age-based differences in students’ MS. The data consisted of material from 225 Finnish comprehensive school students from the sixth, seventh and ninth grades. The students participated in an individual in-person interview with a researcher, at the beginning of which they solved a closed problem-solving task. Employing theory-guided content analysis complemented by quantitative analyses, the findings revealed a strong emphasis on planning skills, with some significant differences observed across grade levels regarding planning and evaluation skills in favour of ninth graders compared to sixth graders. However, in most cases, MS were not activated without reflective prompts. This suggests that reflection is not inherently embedded in the design of closed mathematical problems. While the problems themselves can initiate reflection, prompts significantly enhance the activation of MS. Thus, in the context of mathematics education, it is crucial to embed structured reflective prompts within problems to effectively support students’ metacognitive development. The findings highlight the need for further research on how various types of tasks influence the activation of MS across different age groups. Such insights are essential for designing mathematics tasks that not only foster proficiency in mathematical problem-solving but also stimulate students’ metacognitive processes critical for mathematical learning.