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…

The Department of Mathematics and Computer Science at Adelphi University engaged in a year-long program revision of its mathematics major, which was initiated by a longitudinal study and the publication of the 2015 Curriculum Guide by the MAA's Committee on Undergraduate Programs in Mathematics. This paper stands as a short story, so to speak, of…

The purpose of this work is to explore alternative geometric pedagogical perspectives concerning justifications to 'fast' multiplication algorithms in a way that fosters opportunities for skill and understanding within younger, or less algebraically inclined, learners. Drawing on a visual strategy to justify these algorithms creates pedagogical…

Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and to what extent, productive failure methods may be used to enhance the learning of procedural skills. A typical productive failure study focuses on a single, complex concept;…

The researcher conducted a qualitative case study of two sessions of a preservice teacher tutoring a student with a learning disability on Algebra 1 content. In this study, the focus was the tutor's use of gestures overlaid on the students' offloaded work on paper to help the student make sense of the problems. The student also demonstrated how…

This study aims to find out the dominant factors that cause students' difficulties in learning abstract algebra. The factors investigated in this study focused on attitude, motivation, prior knowledge, lecturer performance, learning methods, as well as teaching materials. This study is a descriptive research using a survey method. We involved 30…

The appropriateness of guess and check as a problem-solving strategy has been debated. This qualitative study examines the use of guess and check by middle-grades students to solve linear systems of equations. Students' reasoning is examined within the number sequences framework, which is based in part on students' units coordination. Only…

Responding constructively to unexpected events during a lesson is a particularly challenging facet of teaching. This study aimed to investigate how a secondary school mathematics teacher responded to learners' unexpected or unplanned offers in the teaching of algebra. A total of three sequential lessons were video recorded and the quality of the…