Some Theoretical References Related to Advanced Mathematical Thinking

Abstract

Background: In Mathematics Education, the theoretical reference of Advanced Mathematical Thinking has contributed to some research. However, others opt for a different but somehow related theoretical reference. Identifying the similarities and differences between those references can elucidate the researcher’s motivations when adopting one or another reference. Objective: to synthesise three studies involving Mathematical Creativity, Advancing Mathematical Activity and Advanced Mathematical Knowledge, respectively, and to illustrate possible contributions of those theoretical references in the analysis of a written production. Design: the research is qualitative and theoretical and speculative so that theoretical relationships were carried out and used later in the analysis of the written production. Setting and Participants: the research involves a participant with a degree in mathematics with whom the researchers had a virtual interaction to present the questions. Data collection and analysis: the procedures performed in the resolution of questions prepared based on the OBMEP question bank are analysed and, with the support of this example of analysis, possible contributions of each reference in the analysis of a written production are discussed. Results: none of the references covers all the thinking mobilised in the activity, but each one favours the focus on specific aspects that were verified in the written production of the research participant, in line with the similarities and divergences emphasised in the theoretical appreciation of each reference. Conclusions: the knowledge of different theoretical frameworks provides the teacher with foundations to exercise their teaching practice and the researcher with options for an adequate choice for their research.