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…

Understanding increased achievement as a dynamic relationship between student engagement and mathematical understanding, we designed an intervention to address both factors. Our intervention was the instructional routine number strings, led by an undergraduate tutor. In this paper, we provide a case study of the development of a fourth-grade…

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…

In the present study, researchers used problem-posing instruction to examine elementary students' understanding of multiplication. Students in fourth and fifth grade classrooms (n = 24) from a rural school district participated in a semester-long study. The focus of this study was examining student solutions to two specific lessons with problems…

We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's "spontaneous" additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses…

The aim in the current study is to examine the conceptualizations of zero in arithmetic operations among students with learning disabilities (LD) and no learning disabilities (N-LD). The similarities and differences in the understandings of students with LD and N-LD of zero in arithmetical operations will be discussed. The study is a multiple case…

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…

Unitizing, a cognitive support for number sense, describes how students conceptualize quantities in terms of units. Given the importance of this skill, a formative assessment tool was developed for array multiplication problems, including arrays that model the distributive property found in typical classroom curricula. Video of 77 fourth grade…

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…

In the current study, it is aimed to determine the activities that need to be done to eliminate the mistakes made by primary school fourth grade students in multiplication and division operations and to present solution suggestions for eliminating these mistakes. The study employed action research, one of the qualitative research methods. The…