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…

Simplifying equations via assumptions is integral to the "engineering method." Algebraic scaling helps in teaching the engineering skill of making good assumptions. Algebraic scaling is more than a pedagogical tool. It can create a solution where one was not possible before scaling. Scaling helps in engineering proper design…

Solving word problems is a large part of algebra coursework and statewide testing. However, solving secondary mathematics word problems is difficult for most students and extremely challenging for students with specific learning disabilities (SLD). In recent meta-analyses, two problem solving strategies emerged as effective for secondary students…

The overwhelming presence of a procedural meaning of equality and equations reported in previous research has led to a call for suitable pedagogical interventions to nurture a relational meaning of these concepts. This paper is a response to that call. Drawing on the theory of objectification, the first part deals with the configuration of a Grade…

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…

This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…

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…

Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further.

Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…

The ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci…

In agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians' mathematics ('scholarly mathematics'). One main result is that the mathematics taught, too often taken for granted by curriculum…

We present a type of arithmetic called Proportional Arithmetic. The main properties and objects that emerge with this way of operating quantities are exposed. Finally, the antiderivative and the indefinite integral are defined in order to calculate the primitive of [equation omitted] in the Proportional context.

Incorporating open-ended real-world tasks enhances students' access to mathematical and real-life knowledge and maximizes learning experiences. This article examines how a secondary mathematics teacher used an open-ended problem on distributing pay raises to teach mathematical concepts and fairness to students. The teacher's actions exemplify…

The research reported in this article sought to develop a taxonomy of grade 11 students' levels of understanding in algebraic problem-solving tasks. The student sample was from high schools in the province of Ontario in Canada. Problems from four areas in algebra namely, variables, expressions, equations and word problems were chosen to be…