New educational technologies that utilize students' interaction data and visualizations provide a means to expand our understanding of learning processes. In this study, we apply two advanced and novel data visualization techniques, called the "Indivisualizer" and a "Sankey diagram," to explore how middle school students (N =…

New educational technologies that utilize students' interaction data and visualizations provide a means to expand our understanding of learning processes. In this study, we apply two advanced and novel data visualization techniques, called the "Indivisualizer" and a "Sankey diagram," to explore how middle school students (N =…

Evidence-based instructional strategies in mathematics provide critical support related to academic achievement for students with disabilities. Data from national achievement assessments suggest that students with disabilities' academic growth in mathematics stagnates at the secondary level. Given that the majority of previously researched…

Mathematical modelling has acquired relevance at all educational levels in the last decades since integrating this activity in instruction provides significant contexts for improving students' learning, including in linear algebra courses that have a notable presence in many undergraduate courses from different fields, including engineering and…

This research is motivated by a linear equations system, which is the basis for studying necessary linear algebra materials, such as rank, range, linear independent/dependent, linear transformations, characteristic values and vectors. There are still prospective mathematics teachers who have difficulty solving linear equations system and…

Critical thinking (CT) is a type of convergent thinking explored when students learn mathematics. This study aims to obtain a comprehensive representation of students' mathematical Critical Thinking (CT) abilities, based on the mathematical ability level. Data were obtained from 35 students using CT skills tests and semi-structured in-depth…

By focusing on food and a pervasive contaminant, this experiment engages student interest and effort while providing essential instruction and experience. As institutions are challenged by existing and emerging budgetary constraints, this experiment offers a determination approach employing commonly available instrumentation, the graphite furnace…

In this paper, we make a case for the importance of teaching secondary school level algebra to students with learning disabilities (LD). Furthermore, we illustrate how they struggle and present best-practices on how they are best supported. We demonstrate effective ways of how teachers can show students with LD how to solve challenging algebra…

This article explains how explorations into the quadratic formula can offer students opportunities to learn about the structure of algebraic expressions. In this article, the author leverages the graphical interpretation of the quadratic formula and describes an activity in which students derive the quadratic formula by quantifying the symmetry of…

This paper describes a study that used a novel method to investigate conceptual difficulties with mathematical induction among two groups of undergraduate students: students who had received university-level instruction in formal mathematical induction, and students who had not been exposed to formal mathematical induction at the university level.…

Many students do not have a deep understanding of slope. This paper defines what a deep understanding of slope is in terms of mathematics-education theory. The various factors which help explain why such a deep understanding is difficult to acquire are then discussed. These factors include the following: the different representations for slope;…

This article investigates how the recent implementation of programming in school mathematics interacts with algebraic thinking and learning. Based on Duval's theory of semiotic representations, we analyze in what ways syntax and semantics of programming languages are aligned with or divert from corresponding algebraic symbolism. Three examples of…

Preferences for solution methods have an important implication teaching and learning mathematics and students' mathematical performances. In the domain of learning mathematics, there are two modes of processing mathematical information: verbal logical and visual-pictorial. Learners who process mathematical information using verbal logical and…

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…