Pre-Service Mathematics Teachers Attention to Tasks Affordances While Analyzing and Designing Tasks

The objective of this collective case study is to comprehend how pre-service mathematics teachers (PMTs) attend to mathematical and pedagogical affordances in task analysis and how their attention reflects their original task-design. To achieve this, we acquired data from written reports analyzing their selected tasks, instructor notes, and the designed tasks of five PMTs over four phases. PMTs conducted an analysis of a task during Phase 1, revised their analysis in Phase 2, had the opportunity to observe a task implementation provided by the course instructor in Phase 3, and designed an original task during Phase 4. As a result of being prompted to identify the mathematical elements of the activities, PMTs described more mathematical and pedagogical aspects of the tasks. Based on the instructor's notes, PMTs have a belief that quality tasks require intricate procedures, leading to critical instructional phases being overlooked during implementation. Furthermore, the PMTs, who paid attention to the instructional questions, appropriately designed tasks with a higher level of cognitive demand. Therefore, PMTs require assistance in evaluating and designing original tasks with regards to their mathematical and pedagogical elements.