Mathematical Approaches and Strategies

Introduction

There is a need in the United States to improve students’ mathematics performance. For longer than a decade, the majority of eighth grade students nationwide has been performing below proficient, and recent national test data continues to show little change (U. S. Department of Education, 2013). However, the cause of students’ low performance is unclear. Some point to the data from comparative studies examining differences in mathematics instruction between the United States, Japan, and China that has identified differences in teaching methods and student outcomes. For example, findings from studies including the Trends in International Mathematics and Science Studies (TIMSS) show an emphasis in the United States on procedural methods, repetition, and individualized work, rather than conceptual methods and contextualized in-depth group problem solving (Hiebert et al., 2005; Jacobs et al., 2003; Ma, 1999; Stigler & Hiebert, 2009). While others point to potential sources to explain students’ lack of progress, such as teacher quality (Akiba, LeTendre, & Scribner, 2007; Kersting, Givvin, Thompson, Santagata, & Stigler, 2012), inadequate teacher knowledge (Ball, Hill, & Bass, 2005; Hill & Ball, 2004), and instruction with low cognitive demand (Stein, Smith, Henningsen, & Silver, 2009). Though the reason for students’ poor performance is unclear, most agree that reform is necessary (Darling-Hammond, Wei, Andree, Richardson, Orphanos, 2009; Desimone, Smith, & Phillips, 2013; President’s Council of Advisors on Science and Technology, 2010). In an effort to shift mathematics instruction, reform efforts initiated through induction of the Common Core Standards places an emphasis on mathematical practices to leverage a balance between conceptual and procedural practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [CCSSO], 2010).

With many students working below proficiency levels in mathematics, pre-service teachers K-12 need research-based approaches and strategies to differentiate for students’ learning. Research has shown that student with math difficulties struggle with both conceptual understanding and procedural fluency (Gersten, Jordan, & Flojo, 2005). Oftentimes, struggling students require multiple ways to learn a single concept; however, differentiation should not consist of “tricks,” or ways to memorize procedures alone, but rather differentiation should examine and strategize appropriate methods to confront the underlying misconceptions rooted in students’ thinking (Powell, Fuchs, & Fuchs, 2013). As well, pre-service teachers need to know the best approaches to developing and fostering students’ procedural knowledge. Overall, teachers must recognize that the design of the learning experience influences students’ engagement, access to content, and expression of understanding and flexibility is needed in providing support in a variety of ways (Jiménez, Graf, & Rose, 2007; King-Sears, 2009). Therefore, pre-service teachers must know how to employ effective teaching methods and provide strategies to differentiate for all students’ needs while also being able to closely examine, monitor, and assess student thinking.