On the basis of a substantial, robust, and well-replicated cognitive science research literature, interleaving has been recommended across a range of professional pedagogical works as an evidence-based strategy for mathematics teachers. This report first notes the conflation of interleaving and spacing effects underpinning those recommendations…

Learning mathematics is difficult for many students, especially students with mathematics learning disabilities MLD. To improve the academic achievement for students with MLD, educational legislations (IDEA 2004; ESSA 2015) mandate that schools must use evidence-base core curricula. Textbooks conveys the intended values and principles for…

Effective and data-driven math instruction can maximize student learning and achievement. This Spotlight will help analyze best practices for developing math word problems; explore how showing students both the correct and incorrect solutions can improve their understanding; investigate math 'fact fluency' and strategies for strengthening it;…

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…

In this paper we present the results of a survey of research studies on the learning of multivariable calculus in a wide geographic spectrum. The goal of this study is to describe what research results tell us about students' learning of calculus of two-variable functions, and how they inform its teaching. In spite of the diversity of cultures and…

At the commencement of 2022 there was an opportunity to be engaged in a curriculum development project focused on reimagining mathematics learning in primary schools. Schools were seeking new experiences to support engaging students and teachers in mathematics learning. Laburnum Primary School participated in the project with Monash University,…

A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children's Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) non-traditional…

One of the most fundamental strategies in mathematics instruction is practice problems because teachers know that practicing a skill improves performance. At the same time, teachers also know that just because students can correctly answer practice problems does not mean they fully understand the concept or how to apply a formula--especially not…

Algebra is the foundational mathematics course that students take as they begin their high school career and is often difficult for the average learner. In order for students with disabilities and those with mathematics difficulties to meet the high expectations of future mathematical courses, providing quality instruction by implementing…

Students who have difficulty with mathematics may have trouble understanding underlying concepts of numbers and operations. The concrete-representational-abstract (CRA) instructional sequence of instruction provides a way for teachers to help students gain meaning from numbers and the mathematical concepts those numbers represent. This study…

In recent years, attention has turned to the development of evidenced-based learning progressions/trajectories as a means of identifying the likely paths learners might take in developing a deep, well-connected understanding of key aspects of mathematics. However, the extent to which this work influences what happens in mathematics classrooms…

Children are innately mathematical and explore mathematical concepts through play. However, educator beliefs about mathematics can impact the inclusion of mathematics in early childhood education (ECE). Recent research has suggested that spatial reasoning is a key concept which forms the foundations of mathematics learning. The theoretical…

To make complex mathematics concepts accessible to students, teachers often rely on visual representations. Because no single representation can depict all aspects of a mathematics concept, instruction typically uses multiple representations. Much research shows that multiple representations can have immense benefits for students' learning.…

Understanding fractions has been a pervasively difficult skill for struggling math learners, yet it is essential for success in secondary level mathematics skills. The present systematic review examined the evidence base of fraction interventions for elementary level students identified as struggling math learners. Twelve studies met inclusion…

I present my perspective on the design process in this article, arguing for a focus on student learning and "slow design" that stems from knowledge of mathematics and their support system in the learning process. I have a question about the design process academization and task design research direction. Numerous examples from my work at…