Mathematical problem posing: Types of tasks & frameworks for analysis of responses

Abstract

Mathematical problem posing has been defined as the generation of problems or the re-formulation of existing ones. Research studies on students posing problems have received increasing attention elsewhere but have not been explored systematically in the local context. This paper reports the initial stages of a study in progress. This paper aims to do three things. Firstly, it aims to survey the literature to document and classify types of mathematical problem posing tasks for use in future research. This will clarify the multiple meanings associated with the phrase ‘problem posing tasks’. A taxonomy to classify problem posing tasks will be presented. Secondly, the paper aims to document and compare previous frameworks used to code written responses to problem posing tasks. These frameworks as well as one developed for the present study are used to analyze written responses of secondary one students. The strengths and weaknesses of these frameworks will be discussed. Thirdly, this paper aims to describe the Nodal Framework, which is developed to analyze mathematical problem posing responses. The theoretical principles underlying the framework will be presented.