This study, firstly, aimed at investigating the various types of the multiple math representations and transitions among them in the 8th grade math textbook, and secondly, teachers' use of these representations in teaching. The current study employed the content analysis approach to investigate the multiple mathematical representations and…

Understanding how mathematics preservice teachers (M-PSTs) learn about issues of equity is essential to addressing the inequities that persist in mathematics education. In this article, we use (Gutiérrez, in: Herbel-Eisenmann, Choppin, Wagner, Pimm (eds) Equity in discourse for mathematics education: theories, practices, and policies, Springer,…

The purpose of the reported study was to investigate the social science students' concept images and concept definitions of anti-derivatives. Data were collected through asking students to answer 10 questions related to anti-derivatives and also by interviewing them. The theory of concept image and concept definition was used for data analysis.…

Algebra problem solving is one of the most difficult areas in the mathematics curriculum for secondary students with learning disabilities (LD) due to the higher-order reasoning demands and strategic thinking required. The purpose of this review is to examine how effective algebra problem-solving interventions conceptualize the cognitive processes…

Patterns pervade our everyday life and are natural and familiar to children. Exciting new research in the field of Early Algebra describes the development of young children's algebraic thinking through the meaningful study of patterns. This paper contributes to this research by reporting on a case study of two primary schools in South Africa and…

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set…

Students' ability to reason for themselves is a crucial step in developing conceptual understandings of mathematics, especially if those students are preservice teachers. Even if classroom environments are structured to promote students' reasoning and sense-making, students may rely on prior procedural knowledge to justify their mathematical…

This study explored the mental constructions displayed by pre-service mathematics teachers (PMTs) when applying Cramer's rule. The aim was to reveal the character of mental constructions made around the nature of the solution set of equations and the role of parameters in the solution of equations with parametric coefficients. These mental…

Inspired by the entering of computer algebra systems (CAS) in the Danish upper secondary school mathematics program, this article addresses, from a theoretical stance, what may happen when traditional procedures are outsourced to CAS. Looking at the commands "solve" and "desolve," it is asked what happens when such CAS…

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve…

This descriptive causal-comparative study examined differences between ACT mathematics subtest scores for students taught using an integrated mathematics curriculum (Integrated Math 1-2-3) and students taught using a traditional mathematics curriculum (Algebra 1-Geometry-Algebra 2). The study also controlled for gender and aptitude. The results of…

Systems of equations are an important topic in school mathematics. However, there is limited research examining productive ways of supporting students' understandings of systems of equations. In this paper, we first present a conceptual analysis of potential ways students may leverage their quantitative and covariational reasoning to graph systems…

This study investigated preservice secondary mathematics teachers' difficulties with and understanding of graphs of two-variable inequalities with the lens of the APOS theory. The analysis showed that most teachers understood inequality graphs as actions, at best, and used informal rules to construct graphs. They also had difficulty justifying…

The research reported in this article explored the methods by which concept maps served as formative assessment by capturing changes in the ways preservice mathematics teachers represented their understanding of algebra. The participants were enrolled in a course on high school algebra for teachers and created the maps on the first and last day of…

Chemical engineering problems often involve the solution of systems of nonlinear algebraic equations (NLE). There are several software packages that can be used for solving NLE systems, but they may occasionally fail, especially in cases where the mathematical model contains discontinuities and/or regions where some of the functions are undefined.…