This article focuses on the didactic transposition of the homomorphism concept and on the elaboration and evaluation of an activity dedicated to the teaching of this fundamental concept in Abstract Algebra. It does not restrict to Group Theory but on the contrary raises the issue of the teaching and learning of algebraic structuralism, thus…

In this paper, we identify, from historical vantage points, the following six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalised arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of…

This study aims to explore undergraduate mathematics students' difficulties in their initial encounter with the subgroup test, and in particular in the proof of closure under operation. Subgroup test is one of the first results in an introductory course of Group Theory where students need to cope with the characteristic, for novice students, high…

In this paper, we explore algebra students' mathematical realities around fractions and division, and the ways in which students reinvented mathematical productions involving fractions and division. We find that algebra students' initial realities do not include the fraction-as-quotient sub-construct. This can be problematic because in algebra,…

This paper is written in honor of Zoltan Paul Dienes, an internationally renowned mathematician and educator, who passed away in January 2014. It is an attempt to describe, analyze and apply Dienes' theory on how mathematical structures can be taught by applying his four principles of learning upon which he believed a teacher can base concept…

The cubic polynomial with real coefficients has a rich and interesting history primarily associated with the endeavours of great mathematicians like del Ferro, Tartaglia, Cardano or Vieta who sought a solution for the roots (Katz, 1998; see Chapter 12.3: The Solution of the Cubic Equation). Suffice it to say that since the times of renaissance…

A growing number of Introductory Physics for Life Sciences courses have been developed to prepare biology, premedicine, and prehealth majors for cross-disciplinary connections between physical principles and biological systems. Many students find it challenging to apply idealized algebra-based general physics to more complex biological systems. A…

In this article, we present the results of a classroom action study that was done in the course of advanced algebra and analytic geometry at Huaiyin Institute of Technology. Specifically, we identify and analyze the students' difficulties in learning the course of advanced algebra and analytic geometry, put forward three visual strategies to…

We examine the case of a lesson planning session within the context of professional development for dialogic instruction, and the lesson enacted following this session, which was intended to provide opportunities to 11th and 12th grade algebra students to explore polynomial functions in terms of their roots and linear factors. Our goal was,…

Background: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical learning. The South African curriculum proposes that learners work with and understand the logic of a pattern, but this important idea has largely been neglected in classroom texts and in…

This project describes a way to help students recognise that the expressions on both sides of the equals sign are the same. It was developed to support teachers in disadvantaged communities to help their students make sense of mathematics.

Algebraic reasoning is foundational to all mathematical thinking. This is no less the case in the early years of school, where the capacity to recognise the structure of mathematical processes enables students to acquire deep conceptual understanding. It is through algebra, therefore, that students are able to explore and express mathematical…

We build on research connecting teaching assignments to teacher effectiveness by examining the characteristics of secondary grades mathematics teachers with more course preparations--both the unique number of courses taught and courses never taught before--and by assessing whether additional course preparations predict teacher value-added.…

Remedial/developmental and introductory university mathematics courses have a long history of high attrition rates. Recently, university administration and mathematics departments have been considering technological solutions, and one such solution is computer-adaptive-instruction (CAI). In fact, CAI has been touted as a "silver bullet"…

Enrollment in eighth-grade algebra doubled from the 1990s to 2012 (National Center for Education Statistics, 2013) as research demonstrated that Algebra I operates as a "gateway" to advanced mathematics courses in high school (Adelman, 2006), and that students who succeed in Algebra I in middle school have more success in mathematics…