Solutioning

Abstract

The theory that is presented below aims to conceptualise how a group of undergraduate students tackle non-routine mathematical problems during a problem-solving course. The aim of the course is to allow students to experience mathematics as a creative process and to reflect on their own experience. During the course, students are required to produce a written ‘rubric’ of their work, i.e., to document their thoughts as they occur as well as their emotions during the process. These ‘rubrics’ were used as the main source of data. Students’ problem-solving processes can be explained as a three-stage process that has been called ‘solutioning’. This process is presented in the six sections below. The first three refer to a common area of concern that can be called ‘generating knowledge’. In this way, generating knowledge also includes issues related to ‘key ideas’ and ‘gaining understanding’. The third and the fourth sections refer to ‘generating’ and ‘validating a solution’, respectively. Finally, once solutions are generated and validated, students usually try to improve them further before presenting them as final results. Thus, the last section deals with ‘improving a solution’. Although not all students go through all of the stages, it may be said that ‘solutioning’ considers students’ main concerns as they tackle non-routine mathematical problems.