This qualitative exploratory case study delves into learners' understanding of differentiation through the first principle and power rule. The study adopted the action, process, object, and schema (APOS) theory as a lens to track learners' understanding of these concepts using the activities, classroom discussion, and exercise (ACE) teaching…

Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…

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…

In this paper we review selected significant developments in the use of digital technology in the teaching and learning of mathematics over the last five years. We focus on a number of important topics in this field, including the evolvement of STEAM and critical making as well as the process of redefining learning spaces in the transformation of…

This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around…

A design experiment with 18 students in a regular seventh grade math class was conducted to investigate how to differentiate instruction for students' diverse ways of thinking during a 26-day unit on proportional reasoning. The class included students operating with three different multiplicative concepts that have been found to influence rational…

Worked examples and collaborative learning have both been shown to facilitate learning. However, the testing of both strategies almost exclusively has been conducted independently of each other. The main aim of the current study was to examine interactions between these 2 strategies. Two experiments (N = 182 and N = 122) were conducted with…

Problem Statement: Algebra, which is one of the basic principles of mathematical learning, still maintains its importance in mathematics programmes. However, especially starting from the primary school years, algebra represents a complex mathematical factor in the operational stage for many students. In this scope, a differentiated teaching…

Concern about students' math achievement is nothing new, and debates about the mathematical training of the nation's youth date back a century or more. In the early 20th century, American high-school students were starkly divided, with rigorous math courses restricted to a college-bound elite. At midcentury, the "new math" movement sought,…

One of the many challenges teachers face is trying to differentiate instruction so all students have equal opportunities to participate, learn, and engage. To provide guidelines for differentiated instruction in mathematics, staff from the Madison Metropolitan School District in Wisconsin created a pedagogical framework for teaching called…

Many African American students have different learning styles than their Caucasian and Asian American counterparts. This distinction makes differentiated instruction a vital teaching strategy, as it allows teachers to tailor curriculum and teaching to meet the needs of individual students, especially those with different learning styles. This…

In "Educating English Learners," Joyce W. Nutta and her colleagues offer practical tools for helping schools and teachers successfully integrate English learners into mainstream classrooms. Drawing on the One Plus model presented in their award-winning book, "Preparing Every Teacher to Reach English Learners," the authors now…

The study investigated whether online professional development courses with different levels of support have different impacts on teacher outcomes. Variations of an online course for middle school algebra teachers were created for four experimental conditions. One was a highly supported condition, with a math education instructor, an online…

Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…

The algebraic concepts and major ideas that govern Newton's laws of motion can often be a challenge for the majority of ninth-grade students. Therefore, to make learning these concepts less task-oriented and more enjoyable, the author developed lessons that allow students to construct and express their understanding of these ideas through…