Examination of mathematics teachers’ strategic flexibility in solving mathematical problems

Abstract

One of the fundamental skills teachers aim to impart in mathematics education is problem-solving. Developing and sustaining this skill is only possible if teachers possess strategic flexibility. Assessing the current level of teachers’ strategic flexibility is crucial, as it also plays a key role in their professional development. The research aims to explore the strategic flexibility of mathematics teachers in solving mathematical problems–both routine and non-routine problems. Using a qualitative research methodology, specifically the case study design, this study engaged a cohort of 12 mathematics teachers who were actively teaching during the autumn semester of the 2022–2023 academic year. These participants represented various educational levels, possessed different postgraduate qualifications, and had diverse years of professional experience. Data collection tools include a Problem Solving Flexibility Test with four math problems and semi-structured interviews to gather teachers’ perspectives on routine and non-routine problems. The semi-structured interviews aimed to reveal all the strategies that teachers use or can use when solving problems. In the initial stages of data analysis, the distinct strategies employed by each participating teacher in addressing the problems were classified. In the context of intra-task strategic flexibility, teachers often used different strategies simultaneously while solving a problem. Teachers were able to switch strategies or use a different strategy because they were able to tackle routine difficulties more readily. The most commonly favoured problem-solving approaches among participants was “Reasoning” and “Make a Drawing or Diagram”. Interestingly, strategies like “Look for a Pattern” and “Simplifying the Problem” were predominantly employed in non-routine scenarios, which is a significant finding of the research. It was found that teachers’ inter-tasks strategic flexibility paralleled their teaching experience and postgraduate education status. In summary, this study investigates how mathematics teachers adapt their problem-solving strategies when faced with different types of mathematical challenges, highlighting the prevalence of specific approaches in routine and non-routine contexts.