“Is It Valid or Not?”: Pre-Service Teachers Judge the Validity of Mathematical Statements and Student Arguments

Zulfiye Zeybek Simsek

doi:10.30935/scimath/10772

Abstract

There is a wide recognition that reasoning abstractly, constructing arguments, or critiquing arguments should be an important educational goal in the mathematical experiences of all students in the standards for school mathematics. Seeing these standards as an essential element for developing deep mathematical understanding; however, call for a strong knowledge of proof for teachers. Thus, the purpose of this study is to investigate how pre-service middle school teachers (PSMTs) decide whether a presented mathematical statement is true or false and how they verify student arguments presented for these statements. 50 PSMTs participated in the study. Individual interviews were conducted with 7 PSMTs to further delve into the verification processes of the PSMTs. The results of the study demonstrated that meeting the expectations of the current standards is not an easy feat by documenting that most of the PSMTs struggled with evaluating mathematical tasks and constructing arguments.

Highlights

Standards for school mathematics have increasingly focused on the importance of student reasoning abstractly, constructing viable arguments, critiquing others’ reasoning, and attending to precision across their K-12 experience (Ministry of National Education [MEB], 2018; National Governors Association Center/Council of Chief State School Officers [NGA/CCSSO], 2010; National Council of Teachers of Mathematics [NCTM], 2000; Stylianides, Bieda, & Morselli, 2016)
13 pre-service middle school teachers (PSMTs), who recognized that the task was not always true, were able to provide a valid counterexample that refuted the task while 1 PSMT failed to provide a valid counterexample
There has been a strong emphasis in various policy documents for the inclusion of constructing and critiquing mathematical arguments in all grades (MEB, 2018; NGA/CCSSO, 2010; Stylianides & Stylianides, 2017)

Summary

Introduction

Standards for school mathematics have increasingly focused on the importance of student reasoning abstractly, constructing viable arguments, critiquing others’ reasoning, and attending to precision across their K-12 experience (Ministry of National Education [MEB], 2018; National Governors Association Center/Council of Chief State School Officers [NGA/CCSSO], 2010; National Council of Teachers of Mathematics [NCTM], 2000; Stylianides, Bieda, & Morselli, 2016). While there has been a strong emphasis in various policy documents for the inclusion of constructing and critiquing mathematical arguments in all grades, these documents are generally thin in describing how to teach proofs in this vision and what this requires for teachers. The place of proof in mathematics classrooms is far from that vision (Buchbinder & McCrone, 2020). Seeing these standards as an essential element for developing deep mathematical understanding and making it a crucial element of students’ mathematical experiences obviously call for a strong mathematical knowledge for teachers (Buchbinder & McCrone, 2020; Lesseig, 2016; Mata-Pereira & da Ponte, 2017). Teachers are expected to decide what conjectures proposed by students or textbooks are worth pursuing, to judge whether students have the requisite background such as key definitions or Zeybek Simsek

Objectives

Results

Conclusion