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…

Little-to-no research examines the provision of targeted mathematical interventions to students struggling with mathematics in a virtual environment. And yet, the global pandemic of 2020--extending into 2021--found schools in such a scenario. This article reports two studies in which researchers explored the intervention package of explicit…

This study investigated the effects of Plickers use on rural students' learning outcomes through two case scenarios. In the first case scenario, the study adopted a preexperimental study method with a focus on comparing Plickers with traditional testing to examine rural students' learning attitudes toward Plickers. The participants were 24…

This study examined the impact of the levels of fidelity of teacher implementation of a research-based middle school mathematics program, implemented systemically across a district, on student achievement benchmarks. By examining the systemic implementation based on the level of fidelity to the written curriculum, this quantitative study sought to…

The purpose of this evaluation was to examine the impact of i-Ready Personalized Instruction on math achievement, as measured by SBA scores. We compared students in schools using i-Ready Personalized Instruction school-wide (Treatment students) and students who only received i-Ready Diagnostic assessments and who were in schools only partially…

Mathematical paradoxes often produce awe and wonder in the mathematics classroom. In this classroom episode, I share a paradoxical task, based on Simpson's Paradox, and its power as an intervention for a child diagnosed with ADHD. The Paradox leveraged his strengths to help him build understandings in proportional reasoning.

As institutions strive to improve teaching and learning for all, educators must consider equitable instruction. This includes equitable distributions of authority and agency among students. The authors define distribution of authority as shared opportunities for decision-making in enacting mathematical tasks and agency as the power to carry out…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…

In this study, we explored teachers' attention to and flexibility with referent units as well as how teachers' understanding of referent units is related to their performance on other fraction concepts and their professional background. By using data collected from 246 U.S. mathematics teachers in Grades 3-7 where fractions are taught, we found…

Background: Educational video games are increasingly used in classrooms because they can offer meaningful contexts for problem solving. However, educational video games bring together two historically disparate activities: school mathematics and video games. How these two activities complement, compromise, or contradict each other influences how…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

In this article we show how students' productive struggle on a mathematical task can lead to collective mathematical creativity. We use observable (co)actions and interactions from a video record that features three Grade 6 students in a problem-solving session to document the emergence of collective creativity leading to a solution. We discuss…

In this article the authors provide an overview of the Interdisciplinary Mathematics and Science project conducted in Grades 1 to 6 in four Australian schools. The project teachers implemented an enquiry-based pedagogical model through 12 interrelated topics. This paper details how a range of mathematics and science concepts can be effectively…

Many students may find math word problems uninteresting; therefore, lacking the motivation to solve them. The content in most math word problems in use today is outdated, deliberately generic, and does not fully engage students. The development of technologies that personalize math word problems seeks to improve the engagement of students.…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…