Teaching through Mathematics Problems: Re-designed for a Focus on Mathematics

Recent research on problem solving explores its potential as a pedagogical practice. This emphasis rejuvenates the interest in problem solving as a learning activity. This paper presents the practice of using a selected problem together with its variants in a single lesson. The practice was implemented in middle school classroom settings with gifted students and with mixed ability students as well as in teacher education classrooms. Experiences from practice are used to illustrate that the use of a set of closely related problems is likely to make students more eager to share their solutions, to generate several solution strategies, and to show various connections among the ideas involved. The shift toward exploring multiple math strategies and representations, and big ideas is at the center of innovative and successful approaches to teaching mathematics. The paper is guided by an evaluation of literature that considers teaching through problem solving and of literature on complex professional tasks