Pre-service Mathematics Teachers’ Reflections on Cognitively Demanding Tasks and the Characteristics of Algebra Tasks They Developed

Abstract

This study aims to investigate pre-service mathematics teachers’ (PMTs) reflections on the 2018-2020 High School Entrance (HSE) exam questions and the characteristics of the algebra tasks developed by the PMTs after participating in an intervention that involves examining and categorizing algebra questions. It also examines the degree to which PMT-generated tasks are cognitively demanding and consistent with the characteristics of HSE exam questions. A case study was employed in this study as a qualitative research design. The study was conducted in the 2020-2021 Spring semester as part of the Methods of Teaching Mathematics in Middle Schools II course offered in the 3rd year of a 4-year teacher education program in a public university. A total of 29 PMTs enrolled in the course, and they were asked to work in groups. The study intervention took place during the course, and one of these groups was focused on during the intervention. The data were collected through two algebra tasks that the group produced at the end of the intervention, four PMTs’ individual responses to a written form, and their semi-structured individual interviews about reflections on HSE exam questions. All the collected data were qualitatively analyzed using content analysis. Both existing categories in the literature and new emergent categories were used in this process. Four categories emerged from PMTs’ reflections on HSE exam algebra questions: algebra objectives, use of algebra, use of context, and cognitive demand after participating in the intervention. The findings about the characteristics of the tasks developed by PMTs indicated that they were capable of developing cognitively demanding algebra tasks, which were mostly consistent with PMTs’ reflections on the characteristics of HSE exam questions. The implications of the findings for PMTs’ reflections on HSE exam questions and the tasks they developed were also discussed.