Covariational reasoning, essential for understanding functions and modeling dynamic situations, is traditionally introduced in secondary education. This paper proposes introducing covariational reasoning in primary school settings through an artifact, the Tracer. Previous studies investigate a covariational approach to functions with younger…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

This study investigates the characteristics of Japanese primary school mathematics lessons that adopt a problem-solving approach. We argue that these characteristics are reflected in three key aspects: collective teaching and learning, the lesson as a "drama" (i.e., its structured flow), and the focus on mathematical knowledge. In this…

In this convergent mixed methods design study, single-subject and qualitative data were collected concurrently to provide an in-depth picture of the impact of a modified schema-based instructional intervention. The intervention was delivered using instructional trials embedded across general education math lessons and a modified…

Developmental Education in Mathematics (DEM) according to Zankov's model, or "Russian mathematics", has been in use in Norway since 2009 in an increasing number of schools (about 100 elementary schools in 2024). There has been relatively little research into the implementation of this teaching method in a Norwegian context. In this…

Children are having fewer embodied social interactions outside (Haidt, 2024). Thus, there is a need to create embodied activities that turn students' attention to each other and nature (Barwell et al., 2022) and that build from their interests (Frankenstein & Powell, 2023). Using a socio-ecological framework that centers on relationships among…

The number line is a powerful tool for supporting students' understanding of fraction magnitude. Fractions are a critical component of mathematics instruction in the elementary and intermediate grades. More specifically, understanding fraction magnitude is central to mathematical development. Yet, fractions are challenging for many students,…

At the beginning of the 21st century, "number sense" was listed as one of the core words in the mathematics curriculum of compulsory education in China, and it has now become one of the core competencies of primary school mathematics. It is necessary to determine the development of number sense of first-grade primary school students (6-7…

Background and Aims: Students with intellectual disability benefit from high-quality instruction in reading and mathematics. Methods: This Theoretical Paper outlines the need for effective, evidence-based instructional practices for this population and the potential for observation research to inform such advancements. We report our systematic…

Traditional mathematics teaching approaches result in inequitable outcomes for students outside the dominant community. One reason for this is a school system that prioritises overly narrow ways of knowing, being and doing. One example of this is a teaching approach that prioritises very specific learning goals and highly structured lessons that…

This study investigates the types of instruction multilingual learners (MLs) experience in the general education classroom in upper-elementary school. Using the Early Childhood Longitudinal Study, Kindergarten Class of 2010-2011 (ECLS-K) we examine the types of instructional practices MLs experienced in reading, math, and science in fourth and…

Typically, vocabulary instruction is associated as part of reading instruction. However, vocabulary instruction is also a necessary component of mathematics instruction. In fact, state and national standards (e.g., Common Core State Standards) require elementary students to communicate about mathematics to provide clear explanations, construct…

The paper presents findings from a study that examined, through the lens of the Image Having layer of the Pirie-Kieren model, the qualitative characteristics of the images that different children formed when engaging with eight, novel partitive quotient tasks. The Image Having layer is the first point of abstraction within the Pirie-Kieren model.…

This study identifies characteristics of polygon class learning opportunities for 8-9-year-old children during the whole-class instruction. We consider the interplay between the geometrical tasks demanding different ways of reasoning, features of children's geometrical thinking, and the teacher's moves to identify characteristics of learning…

Analysis of consistent Zearn Math users and a comparable group of non-users in a large Southern district shows that students who used Zearn Math had higher levels of academic growth than similar students with no usage. This analysis used the quasi-experimental method, Coarsened Exact Matching (CEM), to examine the impact of Zearn Math across 1,111…