Chapter 11: Teaching Mathematics With Problems: What One Teacher Learned Through Research

One key notion that mathematics teachers get from the NCTM Principles and Standards for School Mathematics (2000) is the value of using interesting and worthwhile problems to teach mathematical concepts to their students (see also Lampert, 2001). Unfortunately, finding worthwhile problems that one can use in teaching may not be as easy as it sounds. A worthwhile problem is not simply a problem that the students may see in their everyday life— it is a problem that gives them a fair chance to think about and explore mathematics. If a problem is to be usable for teaching something new, it also must push students to think beyond what they would do spontaneously. Some of these problems may lead students to work and think in novel ways. They may even require students to examine ideas that they later discover are completely wrong, but whose consideration illuminates a path towards a correct solution.