Understanding of the equal sign is associated with early algebraic competence in the elementary grades and equation-solving success in middle school. Thus, it is important to find ways to build foundational understanding of the equal sign as a relational symbol. Past work promoted a conception of the equal sign as meaning "the same as".…

Given the significance of functional thinking as one of the main routes to foster early algebraic thinking, in this paper we describe how a current elementary mathematics textbook's unit titled "Pattern and Correspondence" was developed in the Korean context. The following four key instructional elements for fostering functional thinking…

Prior studies have identified the impact beliefs have on mathematics instructors' instructional practice, such as their choice to (or not to) lecture. However, the role of instructional context role in influencing beliefs and instruction has not been thoroughly researched. This paper explores how course context and beliefs could impact mathematics…

This study investigated the effects of (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…

This study investigated the effects of: (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…

We conducted two studies to investigate the extent to which brief, spaced, mastery practice on skills relevant to introductory physics affects student performance. The first study investigated the effect of practice of "specific" physics skills, each one relevant to only one or a few items on the course exam. This study employed a…

This study examined the relationship of learner profiles and the satisfaction of basic psychological needs among 109 undergraduate physics students participating in an online algebra training program. The study utilized latent profile analysis to identify groups of learner profiles and explored the role of students' perceived needs satisfaction in…

Algebra has been identified as a gatekeeper to careers in STEM, but little research exists on how algebra appears for practitioners in the workplace. Surveys and interviews were conducted with 77 STEM practitioners from a variety of fields, examining how they reported using algebraic functions in their work. Survey and interview reports suggest…

An increasing number of university faculty have become interested in alternative grading systems in recent years. While there is a growing body of research on such grading systems, implementation can be a challenge for instructors. Mastery-based testing is a grading system in which students learn from feedback and have multiple attempts to…

This study explores the potential of the large language model GPT-4 as an automated tool for qualitative data analysis by educational researchers, exploring which techniques are most successful for different types of constructs. Specifically, we assess three different prompt engineering strategies -- Zero-shot, Few-shot, and Fewshot with…

In this study, we look at student perceptions of a first course in linear algebra, focusing on two specific aspects. The first is the statement by Carlson that a fog rolls in once abstract notions such as subspaces, span and linear independence are introduced, while the second investigates statements made by several authors regarding the negative…

The authors discuss the status of college algebra and related offerings and their relationship to introductory statistics education. They also describe an innovative approach to college algebra that integrates a significant amount of statistical reasoning and concepts and statistical methods as natural applications of basic ideas that are part of…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…

In this paper, I propose a new construct named "analytic equation sense" to conceptually model a desired way of reasoning that involves students' algebraic manipulations and use of equivalent expressions. Building from the analysis of two existing models in the field, I argue for the need for a new model and use empirical evidence to…

As a follow-up to their article, "Emojis and Their Place in the Mathematics Classroom" (EJ1358586), the authors examine how emojis can be used as bridging representations to support student understanding of proof and algebra in upper primary school. They take a problem from reSolve, Level 3, (AAMT, 2020), look at it from the perspective…