In this article, the authors focus on five instructional approaches with a strong evidence base for the teaching and learning of math: (a) plan, model, and practice: systematic and explicit instruction; (b) focus on the language of math; (c) use multiple representations, including number lines; (d) build fluency; and (e) provide word problem…

Fractions are an important concept used throughout advanced mathematical ideas and everyday life. Students need a solid understanding of fraction concepts, such as magnitude, equivalence, and operations. However, many students, including students with learning disabilities (LD) in mathematics, struggle with fractions. In this article, the use of…

Students encounter mathematics word problems as early as kindergarten and continue to see them throughout their schooling experience. Schema instruction with an attack strategy can support students to successfully navigate word-problem solving. Schemas help students categorize word problems by similar characteristics. To better support students…

Researchers have found that early math competencies are potent predictors of later student outcomes in math, reading, and executive functioning. This paper describes what early math instruction can look like and how some states have implemented evidence-backed strategies to teaching. Recommendations are given to State education leaders seeking to…

Too often, mathematics and science are taught in isolation from each other and from meaningful problems that matter to students. This book draws on the authors' experiences with teacher colleagues, including time spent in their classrooms co-developing and refining lessons. The core of their approach is to encourage learners to pursue solutions to…

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…

This Fast Five provides an overview of key evidence-based practices that should be considered as part of core mathematics instruction, as well as intervention settings to meet the needs of all students.

Research shows that when students engage with mathematical inquiry their problem-solving skills are strengthened. Demands in the revised Australian curriculum raised problem-solving of new senior secondary mathematics assessment, specifically in Queensland Problem-solving and Modelling Tasks (PSMTs). The challenge for Queensland was to scale…

The terms equity, inclusion, diversity, and belonging, often present an assumption that the dialogue will center around school climate, culture, and psychological safety. While these are critical components of equitable practices, the educational process of providing sound academic instruction and assessment cannot be lost in the conversation.…

We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.

There is a large body of research on how to improve student learning through active learning and metacognition. However, without well-structured guidelines, students do not tend to actively engage with the taught material, peers, and the instructor at a desirable metacognitive level (Deslauriers et al., 2019). To address this problem, a…

Faculty professional development is an important lever for change in supporting instructors to adopt research-based instructional strategies that engage students intellectually, foster learning-supportive attitudes and habits of mind, and strengthen their persistence in mathematics. Yet the literature contains few well-rationalized models for…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

Mathematical problem solving is a complex cognitive activity, which poses difficulties for students with and without disabilities in inclusive learning environments. With a variety of functions, Learning Management Systems (LMSs) have the potential to enhance personalized learning to meet the diverse needs of all students. This paper provides…

In this article, we focus on pairing instructional approaches with a strong evidence base in math with evidence-based practices for students with extensive support needs. To do so we draw on two sources. We use the 2021 Practice Guide from the Institution for Education Sciences (Fuchs et al., 2021). In addition, we use identified evidence-based…