Teaching practices for differentiating mathematics instruction for middle school students

Abstract

Three iterative, 18-episode design experiments were conducted after school with groups of 6-9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction.As the experiments proceeded, this definition of DI emerged: proactively tailoring instruction to students' mathematical thinking while developing a cohesive classroom community. Analysis of 10 episodes across experiments yielded five teaching practices that facilitated DI: using researchbased knowledge of students' mathematical thinking, providing purposeful choices and different pathways, inquiring responsively during group work, attending to small group functioning, and conducting whole class discussions across different thinkers. The latter three practices, at times, impeded DI. This study is a case of using second-order models of students' mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students' thinking are at the heart of differentiating mathematics instruction.

Students’ solution of arrangement problems and their connection to Cartesian product problems

“…As these models are developed, refined, and extended, they can serve as powerful instruments to support teachers and researchers to engage students in productive interactions (Author, 2014b). Moreover, attending to how students who use different multiplicative concepts reason about similar situations can serve as a basis for researchers and teachers to differentiate instruction in ways that are rooted in differences in student reasoning (Hackenberg, Creager, & Eker, & Lee, 2016). Differentiation of instruction helps researchers and teachers make informed decisions about how to adjust to students who bring different resources to the classroom.…”

Differentiating Instruction: Development of a Practice Framework for and with Secondary Mathematics Classroom Teachers

“…Consequently, classroom teaching (at least in developed and developing regions) became focussed on the idea that opportunities for meaningful learning can be achieved by establishing what students already know and then presenting new information in such a way that students can create their own meanings (Bada, 2015;Brooks & Brooks, 1999). This idea is reflected in the modern secondary mathematics classroom, where differentiated instruction is considered as proactively adapting instruction to suit the mathematical thinking of students while concurrently developing a cohesive classroom environment (Hackenberg et al, 2020).…”

“…In the secondary mathematics classroom, as in classrooms more generally, differentiated instruction is a vital component of inclusive education-all students are considered mathematical thinkers and receive the instruction needed for learning (Tomlinson, 2017). A differentiated mathematics classroom is cohesive, where the students work closely with the teacher and celebrate the diversity within, and where the teacher adapts instruction, posing to students the problems and challenges that are aligned with, and at the edge of their thinking (Hackenberg et al, 2020). The remainder of this article describes the development of a practice-based approach, including a practice framework constructed to assist secondary mathematics teachers in developing and implementing effective and sustainable strategies for differentiated instruction.…”

Investigation of the Contribution of Differentiated Instruction into Science Literacy

“…In addition, there are various studies which concluded that during the teaching and learning process with differentiated instruction the students experienced a sense of success, participated in cooperative tasks, took on responsibilities, showed metacognitive and problem solving skills and developed good peer relationships (Decovsky, 2012;Demir, 2013;Gault, 2009;Hackenberg, Creager, Eker, & Lee, 2016;Moyle, 2012;Munro, 2012;Samms, 2009;Sondergeld & Schultz, 2008;Westbrook, 2011). There are also some studies on the contribution of differentiated instruction to the self-efficacy of the students and teachers (Affholder, 2003;Dixon, Yssel, McConnell, & Hardin, 2014;Wan, 2015).…”