Using general-mathematical and content-specific elements to assess the quality of prospective mathematics teachers’ problems in a problem-posing context

Abstract The open-ended nature of problem-posing tasks causes a serious diversity in learners’ responses. This diversity presents a variety of difficulties in assessing the quality of the problems posed. This study aimed to assess the quality of problems that prospective mathematics teachers’ (PMTs) posed about linear graphs through a combination of general-mathematical and content-specific elements. Additionally, this study concentrated on the PMTs’ declarations about their difficulties in posing problems on linear graphs. In this study, the data sources were PMTs’ problems, their own solutions to them, and reflection papers. The results revealed that integrating general-mathematical and content-specific elements in assessing the quality of problems provided a better understanding of PMTs’ problem posing performances. In terms of general-mathematical elements, posed problems were mostly solvable, situated in a real-world context, and linguistically precise. However, the problems mostly failed to reflect content-specific elements related to key mathematical ideas about linear graphs. Moreover, the results showed that the mean score for general-mathematical elements was significantly higher than the mean score for content-specific elements in the problems. In their written explanations, PMTs also said that task-related components (like prompts and situations) and teacher-related components (like lack of experience, weakness in subject knowledge, and pedagogical content knowledge) made it challenging for them to pose problems about linear graphs. It was concluded that the inclusion of both general-mathematical and content-specific elements in evaluating the quality of the posed problems paves the way for future empirical and theoretical studies that seek to develop a systematic approach to problem assessment.