Centre for Research in Mathematics Education Seminar Series 2019/20
75 years have passed since George Pólya introduced the idea of heuristic strategies, rules of thumb for effective problem solving, in his classic book How to Solve It. What do we know now that we didn’t know then?
Pólya was right – the strategies work – if you know how to use them. They are more complex than we thought and there are more of them to consider. Issues of self-regulation and students’ beliefs can cause problems.
The bigger question is: How do we create learning environments in which students learn to be effective problem solvers? This involves a shift of frame, moving our focus from what the teacher does (which is still vitally important) to how the student experiences the classroom environment. I will discuss the Teaching for Robust Understanding (TRU) framework and what it means for our teaching.
Biography: Alan Schoenfeld is a leading figure in mathematics education research, receiving the ICMI Felix Klein Medal for lifetime achievement in 2011. A professor at the University of California, Berkeley, he has worked on a series of collaborative projects with the Shell Centre team at Nottingham, where he is an Honorary Professor. His work ranges widely across thinking, teaching, and learning in mathematics but he has focused successively on three major areas: problem solving, models of teaching, and impact-focused work to improve classrooms.
On problem solving, he made the first empirical study of how far mathematics undergraduates tackling non-routine problems can use the strategies set out in George Polya's reflections on how he solved problems. Schoenfeld's study found that the strategies alone are weak, and need to be strengthened by complementary domain-specific tactics. He has worked with the Shell Centre team on projects to develop tools for teaching and assessment, culminating in the Mathematics Assessment Project. Complementing this he developed a theoretical framework, Teaching for Robust Understanding (TRU) – a model of classrooms in which productive learning is likely to occur.