Mathematical Problem Solving: Beliefs, Values, and Implications for Teaching and Teacher Education

Abstract

Problem solving has become a central objective of mathematics education in many countries, yet instructional practice often continues to equate success with the rapid production of correct, well-presented answers. This perspective argues that an emphasis on correctness is insufficient to account for the nature of mathematical problem solving as an intellectual and cultural practice. Drawing on research in mathematics education, the paper highlights the crucial roles of beliefs and values in shaping learners’ engagement with non-routine tasks, their willingness to persist in the face of uncertainty, and their views of what it means to “do mathematics”. Beliefs about mathematics, learning, and self-capability interact closely with educational values such as whether speed or depth, outcomes or processes, and competition or collaboration are prioritised in classroom practice. These orientations influence not only how students approach problem solving but also the kinds of learners they become. The article further discusses how teachers and teacher education can support learners in thinking and working more like mathematicians, and illustrates how innovative pedagogical approaches - such as comics-based mathematical tasks - can integrate motivation, values education, and problem solving. It is argued that while correctness remains a necessary condition in mathematics, the cultivation of resilient, reflective, and humane ways of thinking through problem solving should be recognised as a key educational goal.