Number lines can benefit students in learning an array of mathematical concepts. An area of mathematics where number lines are visibly underused is in teaching measurement concepts. For students in upper elementary grades, accurate measurements require the use of mathematical precision and coordination, including skills in fractions and decimals,…

In this paper, we explore the following research questions: How do first-grade students define even and odd numbers? What types of justifications do they use to support their generalizations using these definitions? We report the ways in which first-grade students define even and odd numbers and how they justify generalizations that use their…

The purpose of this study was to examine the relationship between students' engagement with Legends of Learning's Math Basecamp (MBC) and students' math achievement at the elementary school level in Rialto Unified School District (RUSD) in California. Researchers examined the association between MBC usage and student achievement scores on the…

There is growing evidence that the ability to perceive structure is essential for students' mathematical development. Looking at students' structure sense in basic numerical and patterning tasks seems promising for understanding how these tasks set the foundation for the development of later mathematical skills. Previous studies have shown how…

Recent solar eclipses provide relevant real-world contexts for learning about the scientific phenomena of the lunar phases. News coverage of the phenomenon may have raised questions such as, "Why does the Moon look different at different times, and sometimes as if it is not there?," and "What patterns can be found in the lunar…

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 paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…

The many studies with coin-tossing tasks in literature show that the concept of randomness is challenging for adults as well as children. Systematic errors observed in coin-tossing tasks are often related to the representativeness heuristic, which refers to a mental shortcut that is used to judge randomness by evaluating how well a set of random…

In many schools across the world, students experience mathematical concepts as ideas empty of wisdom and possibility. In this paper the authors analyze a philosophical conversation in which fifth-grade students were caught up in the animacy of the concept of space. Challenging the common view of mathematics as dealing with absolute truths and…

One of the most difficult types of arithmetic word problems in primary school is compare problems. Among these problems, the most problematic are those in which the relational term is not consistent with the arithmetic operation required for the solution. This study investigates how 10-11-year-old primary school pupils' read and interpret compare…

Repeating patterning proficiency predicts students' later mathematical proficiency. A comparative multi-case design enabled the present study to compare patterning success and strategy use for repeating patterns of 75 Norwegian 6-year-old grade 1 students. We provided the students with duplicate, extend, transfer, and unit isolation activities in…

Reimagining elementary mathematics pedagogy using a three-step process--See It, Say It, Symbolize It--author Patrick L. Sullivan provides a guide for developing a dynamic and flexible understanding of numbers and operations. By helping students develop a language that is consistent across concepts and connecting it to what is seen and symbolized,…

Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to…

Instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) have shown to support students' development of reasoning about covarying quantities. However, research often neglects how this development occurs from the student point of view during the interactions with these artifacts. An analysis from this lens…

In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…