In this article, the authors describe an algebra 2 class activity, called the Exponent Maze, that had students practice many mathematics problems, display their creativity, and work together collaboratively by creating their own mazes. The authors discuss how they introduced the activity, what the students created, and how creating mazes can be…

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…

This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

There is a dearth of empirical data to support the positive effects of problem solving (PS) combined with digital technology in the classroom, despite claims that these activities improve students' algebraic thinking abilities. Therefore, the purpose of this study was to evaluate how the teaching method known as Polya's problem solving with…

Jordan canonical form (JCF) is one of the most important, and useful, concepts in linear algebra. Mathematics, physics, biology, science and engineering undergraduates often find the first application of real JCF in the discipline of differential equations (continuous models) to solving systems of differential equations. In this work, we apply…

In this article, we explored Grade 11 learners' algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this…

Human-driven carbon emissions have resulted in increased levels of dissolved carbon dioxide in the Earth's oceans. This dissolved carbon dioxide reacts with water to form carbonic acid, which impacts ocean acidity as well as the solubility of carbonate-containing compounds, with far-reaching impacts on marine ecosystems and the human communities…

This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

In this article, the author will demonstrate how gestures--often used in combination with offloading information on scratch paper--can be used to help students with difficulties in mathematics succeed with secondary level algebra. The authors will provide key examples from three studies of the algebra learning of students with mathematics…

This scholarly inquiry critically examines the pedagogical aspects pertaining to the instruction and acquisition of Abstract Algebra within the realm of University Mathematics Education (UME). Drawing upon multiple lenses, including epistemological, cognitive, phenomenological, and institutional perspectives, this study investigates the formidable…

As students with autism spectrum disorder (ASD) participate in the general education setting at greater rates, they are expected to meet rigorous grade-level academic standards. Students with ASD typically struggle with problem solving, higher-ordered thinking, and mathematical reasoning. When students enter middle school, mathematics becomes more…

Parents and caregivers can use the activities in this report to help youth learn to solve algebra problems using different strategies. Knowing different strategies for solving algebra problems may help your child approach algebra problems with confidence. Children could apply the most appropriate strategy for a particular problem or could try a…