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

Abstract

The use of tasks to promote mathematical reasoning (MR) in teaching practice is essential to meet curricular goals. However, that practice is often a huge challenge for teachers, and particularly for prospective teachers and thus it is essential to highlight it as a goal for initial teacher education. This study focuses on preservice mathematics teachers’ (PTs) knowledge about the potential of mathematical tasks to promote students’ MR, in a teacher education course. Results show that PTs were able to justify their option for a mathematical task with potential to promote students’ MR, and through its implementation in one 8th grade classroom they have deepen their knowledge and gave greater meaning to task design principles and acknowledging their students’ knowledge. Thus, the activity of selecting and adapting a task, although less demanding than the design of a new task, can still provide PT with important reflection and knowledge about its potential to promote students’ MR. The study stresses the relevance for initial teacher education of considering four domains associated with the recognition of the potential of tasks to promote MR.

Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education

“…The tasks prepared by Sílvia and her colleagues, with the support of the facilitators, intended to foster the use of different solving strategies and representations, with questions with different degrees of challenge, as in Oliveira and Henriques (2021). In particular, the task proposed for the first lesson just focused on justifying solving strategies.…”

“…The teaching approach and the way the lesson is structured are also important factors in the promotion of students' reasoning (Oliveira & Henriques, 2021). They need to understand the task before setting to work on it, as well as having the opportunity to solve it autonomously, in small groups, before sharing their ideas with the class.…”

“…Indeed, it is crucial that prospective teachers reflect on their own practice so that they are able to recognize "important transversal issues in teaching, such as the need for careful planning and the value of reflection" (Ponte et al, 2017b, p. 301), which implies that they have the opportunity to observe and teach lessons. It is through these classroom experiences that they can understand how their actions influence students' learning (Buchbinder & McCrone, 2020;Oliveira & Henriques, 2021). Also, an in-depth analysis of lesson situations are important moments for prospective teachers to be able to foresee and define strategies to improve their practice (Ponte et al, 2017b;Ramos-Rodríguez et al, 2017).…”

“…Research has been moving forward intending to support teachers and prospective teachers to overcome this challenge (Buchbinder & McCrone, 2020;Davidson et al, 2019;Mata-Pereira & Ponte, 2017Oliveira & Henriques, 2021). However, further research is still needed on how prospective teachers can develop their knowledge about students' reasoning and also on how this reasoning can be promoted through teachers' actions and the tasks they propose in the classroom (Buchbinder & McCrone, 2020;Oliveira & Henriques, 2021).…”

Supporting Spatial Reasoning: Identifying Aspects of Length, Area, and Volume in Textbook Definitions

“…Prospective teachers experience spatial reasoning and measurement-related practices, along with many other topics, in mathematics content courses required as a part of their preparation for teaching. Tasks and experiences, in classroom interactions and in homework completed outside the classroom, impact prospective teachers' informal reasoning about spatial measurement concepts (e.g., Kabael & Akin, 2018;Oliveira & Henriques, 2021;Ozturk, Demir, & Akkan, 2021;Yackel & Cobb, 1996). This study focuses on textbooks written for these mathematics content courses because, even though implementation varies across classrooms (Tarr et al, 2008), textbooks play an important role in what teachers teach, the opportunities they present for mathematical sensemaking (Stein et al, 2007), and their profound impact on K-12 and university classroom instruction (McCrory et al, 2009).…”