Barriers to learning can affect educators and students in achieving learning objectives. One of them is the epistemological obstacle caused by the limited context used when a concept is first learned. The purpose of this study was to explore the epistemological obstacles of mathematics students in the concept of limits and functions during online…

Many mathematics teachers, at one time or another, have exclaimed that "I really didn't understand mathematics, until I had to teach it." Secondary mathematics teachers' knowledge, both subject matter and pedagogical content, plays an important role in their teaching of the subject. Teacher education programs are, therefore, designed to…

Translation skills are very important possessed by students, but currently, there are still many students who have difficulty in translating between representations. The purpose of this study is to analyze students' errors in translating from symbolic representations to verbal and graphic representations. This research was descriptive study with…

A task-based written survey was administered to 69 pre-service teachers (PSTs) at a large Midwestern University in the USA to examine their recognition of examples/non-examples of [one-fourth] presented in various forms of the area model, their perceived mathematical key points in identifying examples/non-examples, and their instructional…

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…

In this article, we use a case study to explore the views of first-year university students on the differences between mathematics at school and at university, and on the changes to their study methods as they make the transition to university mathematics. We also consider their views on the differences and affordances of tasks that they encounter…

One way to develop a cross-curricular lesson is to select the most common mathematical formulas used in science and carefully develop and implement tasks that allow students to make connections between the mathematical representations and theoretical/physical science concepts. The slope-intercept formula, which is used to study relationships…

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;…

Mathematical connections play an important role in achieving mathematical understanding. Therefore, in this article, we report research whose objective was to identify mathematical connections that pre-university students make when they solve problems that involve the derivative and the integral. In this research, we consider a mathematical…

In this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques;…

Our research with Grade 9 learners at a school in Soweto was conducted to explore learners' understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners' transition from whole numbers to rational numbers enabled…

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…

"The limits of my language are the limits of my mind. All I know is what I have words for" (Wittgenstein). When learning something completely new, we connect the unknown term to an already existing part of our knowledge. We can only build new ideas and insights upon an existing conceptual foundation. In the field of statistics, we…