This exploratory study investigated the behaviors and content of onscreen calculator usage by a nationally representative sample of eighth-grade students who responded to items from the 2017 National Assessment of Educational Progress mathematics assessment. Meaningful features were generated from the process data to infer whether students…

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…

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…

We compared students' learning gains in authentic seventh-grade classrooms (N = 144) in 4 different interventions that incorporated a computer game that aims to teach players to solve linear equations. Significantly higher learning gains were measured in the implementations that were specifically designed to mediate the attribution of algebraic…

Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the…

Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We…

To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students…

Although policy documents promote teaching students multiple strategies for solving mathematics problems, some practitioners and researchers argue that struggling learners will be confused and overwhelmed by this instructional practice. In the current exploratory study, we explore how 6 struggling students viewed the practice of learning multiple…

This study investigated whether an intervention including an online game contributed to 236 Grade 6 students' performance in early algebra, that is, solving problems with covarying quantities. An exploratory quasi-experimental study was conducted with a pretest-posttest-control-group design. Students in the experimental group were asked to solve…

This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms,…

In a small-scale, 8-month teaching experiment, the author aimed to establish and maintain "mathematical caring relations" (MCRs) (Hackenberg, 2005c) with 4 6th-grade students. From a teacher's perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…

The purpose of this study was to examine the effects of a schema-based instructional strategy that emphasizes prealgebraic conceptualization of multiplicative relations on solving arithmetic word problems with elementary students with learning disabilities or problems (LP). Introducing symbolic representation and algebraic thinking in earlier…

Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which…