Mathematical Reflections to Enhance Learning
The Standards for Mathematical Practice ask students to make sense of problems and persevere in solving them. Metacognitive strategies allow students to engage in this sense-making, focus on their process, and deepen their understanding of key concepts by reflecting on their thinking. This collection explores the importance of encouraging students to reflect on their mathematical processes, and offers research-supported practices as described in the IES Practice Guides Improving Mathematical Problem Solving in Grades 4 Through 8 and Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools.
In the first video, Monitoring Progress While Solving Problems, the University of Georgia's Sybilla Beckmann demonstrates how students can reflect on their thinking by asking themselves questions such as “what do I know and what do I want to know?” Reflecting on reasoning can help students make sense of challenging problems and to examine their problem solving in the moment. The second video, an interview with Mark Driscoll of the Education Development Center, explains how prompts and tools such as sentence frames can build the habit of reflective thinking and reasoning. Driscoll stresses the importance of continual use of analytic prompts as students work on a task. The Monitoring the Problem-Solving Process audio interview encourages prompting students to consider the “why?” of a challenging problem, rather than just plugging in numbers to find an answer.