This study examined a 6-week intervention in which fourth grade students either played fluency games or used pictorial flashcards to develop fluency with their basic multiplication facts. Students who played fluency games showed more growth than the pictorial flashcards, but an analysis of variance showed that there was no statistically…

Incremental rehearsal (IR) has consistently been shown to improve students' math fact retention and fluency (Maki et al., Journal of Behavioral Education 30:534-558, 2021). However, less is known about how intervention modifications may support longer-term skill maintenance. The purpose of this study was to compare traditional IR with a modified…

How can students achieve an understanding of multiplication that allows them to go beyond recall to explain their thinking? Author and mathematics education professor Juli Dixon introduces a program that teachers can seamlessly integrate into existing mathematics instruction. Learn six tactics to help you shift from an anxiety-producing,…

Math facts are foundational for later math skill development, but many students demonstrate difficulties with math facts in early schooling. Drill-based interventions have been shown to effectively target foundational academic skills; however, there is limited research examining drill-based interventions for teaching math facts compared to basic…

This study presents the results of a series of design experiments that aimed to engage twelve fourth-grade students in mathematical activity exploring the volume of right prisms and cylinders as a dynamic sweep of a surface through a height, an approach that is referred to as Dynamic Measurement for Volume (DYME-V). This article describes this…

The shift from additive to multiplicative thinking is challenging for students. A professional learning program was developed that focused on an identified area of need by teachers, namely multiplicative thinking. Program content focused on concepts underpinning multiplicative thinking, pedagogical approaches, challenging tasks, and application to…

Making connections within and between different aspects of mathematics is recognised as fundamental to learning mathematics with understanding. However, exactly what these connections are and how they serve the goal of learning mathematics is rarely made explicit in curriculum documents with the result that mathematics tends to be presented as a…

The current study examined digits correct per minute (DCPM) growth using explicit timing procedures across varying instructional set sizes (ISSs) and dose. Specifically, the study used a randomized group design to compare DCPM growth within three different ISSs (9, 18, and 36 multiplication facts) across three different levels of dose (2-, 4-, and…

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

Mathematical fluency supports maintenance of mathematical skills (Shurr et al., 2019). Multiple interventions support fluency, including the use of games. However, limited research exists exploring games as a means of increasing student fluency in mathematics. In this single case design study, researchers examined the relation between four…

This qualitative descriptive study was designed to address the deficiency in early math literacy skills, specifically those related to multiplication fact fluency, in early elementary students. More specifically, this study was designed to gather research and data to provide understanding of the mathematical curriculum instruction used in…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning…

The low performance of Grade 4 learners in the mathematical concept of word problems involving multiplication remains a concern for many researchers in mathematics education. Several studies conducted have largely focused on improving learners' performance on bare problems involving multiplication, with little focus on contextual problems. The…