Constructing Written Arguments for Developing Mathematical Reasoning for Students With Learning Difficulties in the Elementary Grades

Introduction

Mathematical reasoning and communication involve a combination of mathematical practices and language ability for successful learning (Ball & Cohen, 1990; Boaler, 2016; National Council of Teachers of Mathematics [NCTM], 2000). To engage students in developing their mathematical reasoning, scholars recommend constructing written arguments and critiquing peers' reasoning to facilitate students' learning (Casa et al., 2016). Meta-analyses of studies conducted in the United States and other countries have strong evidence to suggest that supporting students' mathematics learning by constructing written arguments in academic contexts enhances learning for students who are 6 to 18 years old in primary, secondary, and post-secondary classrooms (Bangert-Drowns et al., 2004; Graham et al., 2020). Although embedding writing activities has shown to be an empirically effective instructional practice to enhance mathematics learning, few empirical studies have investigated the effects of using written arguments for developing mathematical knowledge and reasoning of students with learning difficulties (Hacker et al., 2019; Kiuhara et al., 2020; Kiuhara, Levin, Tolbert, Erickson et al., 2023; Kiuhara, Levin, Tolbert, O'Keeffe et al., 2023).

This chapter will begin with a brief overview of the language and mathematics difficulties students with learning challenges may encounter when engaging in activities that use writing to learn mathematics. Next, a brief overview of the evidence supporting the genre of argumentative writing to develop students' mathematical reasoning will be presented. Finally, to illustrate how argumentative writing can be used to develop students mathematical reasoning, especially for students with learning challenges, an instructional model will be presented that embeds the explicit teaching of both argumentative writing and mathematical reasoning targeted for students with learning challenges who are 9 to 12 years old and represent Grades 4 to 6 in the United States (Hacker et al., 2019; Kiuhara et al., 2020; Kiuhara, Levin, Tolbert, Erickson et al., 2023; Kiuhara, Levin, Tolbert, O'Keeffe et al., 2023). The mathematics content focuses on learning part-whole and partitioning fractions and foundational concepts, such as comparing the magnitude of two fractions between 0 and 1, equivalence, and measure (Charalambous & Pitta-Pantazi, 2007; Wu, 2011), which aligns with the Common Core State Standards for Mathematics (2010) adopted by many states across the United States. Moreover, combining mathematical practices, such as making sense of problems and preserving when solving them, within an evidence-based instructional framework engages students in the processes of constructing written arguments when learning foundational fraction concepts, supports the learning and attention needs of students with learning challenges, develops their strategic competence and productive dispositions toward learning mathematics, and shows promise for developing the quality of their mathematical reasoning and their fraction knowledge (Hacker et al., 2019; Kiuhara et al., 2020; Kiuhara, Levin, Tolbert, Erickson et al., 2023; Kiuhara, Levin, Tolbert, O'Keeffe et al., 2023).