An approach to teach with variations: using typical problems

  • Ban Heng Choy Nanyang Tecnological University
  • Jaguthsing Dindyal Nanyang Tecnological University


Mathematics teachers ubiquitously use typical problems from past examination papers and textbook exercises to develop procedural skills. Can these typical problems be used otherwise? In this paper, we focus on the affordances that an experienced teacher, John, perceives in typical problems and how he uses these affordances to enhance students’ learning by harnessing the idea of teaching with variations or bianshi. Drawing on data from a larger qualitative design-based research on investigating teacher noticing, we present snapshots of John’s classroom practices to highlight what he noticed about the variations afforded by typical problems and how he used these problems with students to promote both procedural skills and conceptual understanding. Our findings suggest that it is worthwhile to support teachers in harnessing variations of typical problems, which have important implications for teacher education and professional development.