The role of task classification and design in curriculum making for preservice teachers of mathematics

Abstract

This paper reports on a research project undertaken with a group (n = 19) of Irish preservice student teachers (PSTs) during the third year of a five-year undergraduate education course. A series of workshops were carried out on the classification and design of mathematics tasks. The research is presented as a case study using mixed methods to gather data at three points, before the workshops, after the workshops, and two years later, when PSTs were in their final year. We argue that task classification and design are curriculum-making activities for mathematics teachers. Through critically classifying and designing mathematics tasks, PSTs developed skills of evaluating the cognitive demand of tasks and showed evidence of using these skills in curriculum making. Through using frameworks to classify tasks, the PSTs demonstrated a capacity to take a more critical role in curriculum making. Our data show that the development of skills in these areas has lasting effects on PSTs' practices and willingness to engage meaningfully with the curriculum in mathematics. The research highlights the need for PSTs to work on evaluating and designing tasks. How frameworks can support and enhance PSTs' capacity to make curricular decisions is evidenced.

Preservice Mathematics Teachers’ Knowledge about the Potential of Tasks to Promote Students’ Mathematical Reasoning

“…This study shows that the activity of selecting and adapting a task, although less demanding than the design of a new task which may prove to be very difficult for prospective teachers (Leavy & Hourigan, 2020), can still provide them with important reflection and knowledge about its potential to promote students" MR. It also reinforces the recognized relevance of the discussion of theoretical frameworks for the recognition of specific characteristics of mathematical tasks in teacher education (Dempsey & O"Shea, 2020), such as the principles explored in the instructional unit. The possibility of implementing in practice the mathematical task they had developed was a key element in the development of the PTs" knowledge about the potential of the task to promote their students" MR. On the one hand, the feedback they derived from the activity in the two classes allowed them to realize aspects of the task that needed to be modified to ensure that the students were, in fact, involved in MR processes.…”

“…In addition, Lee, Lee and Park (2019) suggest exploring noticing-oriented activities with PTs, including examples of students" work on the tasks, to develop their ability to better modify mathematical tasks, as this process is connected to a progressive understanding of their related mathematical and pedagogical elements as well as of their limitations (Liljedahl et al, 2007). Providing and discussing theoretical frameworks to increase the recognition of specific characteristics of mathematical tasks to achieve outlined objectives can be an essential first step for PTs acquire knowledge to select and modify tasks according to those goals (Dempsey & O"Shea, 2020).…”

“…Some recent studies have focused on PTs" conceptions and knowledge to select, modify, and enact mathematical tasks, particularly problems and inquiry tasks, that is high-level cognitive demand tasks (Dempsey & O"Shea, 2020;Kilic et al, 2017;Leavy & Hourigan 2020;Lee, Lee, & Park, 2019;Magiera & Zambak, 2020). To analyse or evaluate PTs" conceptions about those tasks and their ability to recognize the tasks" potential and to elaborate and modify them, these studies identify different aspects PTs need to attend and integrate into the tasks.…”

“…They also value its importance in preparing mathematical tasks and, by complementing it with the assessment of students" learning after its implementation, develop perceptions about the potential of tasks (Kilic et al, 2017). However, in most studies the tasks evaluated or designed by the PTs do not consider the classroom situation, thus research still highlights the need to consider further investigation of how PTs implement cognitively complex mathematical tasks in the classroom (Dempsey & O"Shea, 2020;Leavy & Hourigan, 2020;Oliveira et al, 2021), particularly those targeting students" RM.…”

Investigating the presence of mathematics and the levels of cognitively demanding mathematical tasks in integrated STEM units

“…This guide can be found in mathematics methods course textbooks. Notably, mathematics education journals report its use in supporting the development of mathematical reasoning and problemsolving skills (Boston & Smith, 2011;Dempsey & O'Shea, 2020). The lowest level demand ("memorization") involves reproducing previously learned rules or formulas, for example, requiring students to recall the formula for two-and three-dimensional shapes.…”