This paper investigates the challenges faced by secondary school teachers and pupils in the teaching and learning of algebraic linear equations. The study involved 80 grade 11 pupils and 15 teachers of mathematics, drawn from 4 selected secondary schools in Mufulira district, Zambia in Central Africa. A descriptive survey method was employed to…

Script writing by learners has been used as a valuable pedagogical strategy and a research tool in several contexts. We adopted this strategy in the context of a mathematics course for prospective teachers. Participants were presented with opposing viewpoints with respect to a mathematical claim, and were asked to write a dialogue in which the…

This study offers a new method to measure navigation disorientation in web based systems which is powerful learning medium for distance and open education. The Needleman-Wunsch algorithm is used to measure disorientation in a more precise manner. The process combines theoretical and applied knowledge from two previously distinct research areas,…

In this present study, it was aimed to investigate whether the hierarchical structure of mathematics emerged in university students' minds or not, considering the concepts of limit, continuity derivative and integral from the perspective of students in the department of secondary school mathematics teacher training and the department of…

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of…

A critical numeracy examination of Benford's Law suggests that our understanding of the integers is faulty. We think of them as equally likely to turn up as the first digit of a random real world number. For many real world data sets this is not true. In many cases, ranging from eBay auction prices to six digit numbers in Google to the…

In this paper we introduce a new collaborative technique in teaching and learning the epsilon-delta definition of a continuous function at the point from its domain, which connects mathematical logic, combinatorics and calculus. This collaborative approach provides an opportunity for mathematical high school students to engage in mathematical…

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

As teachers, we want to encourage our students to ask searching questions on topics like how old the Universe is, how much of the Universe we can actually see and how far away the cosmic microwave background radiation is. But how many of us can honestly say we know the answers? And, even if we know the answers, how are we going to respond to the…

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

In this note, we introduce sequence factorial and use this to study generalized M-bonomial coefficients. For the sequence of natural numbers, the twin concepts of sequence factorial and generalized M-bonomial coefficients, respectively, extend the corresponding concepts of factorial of an integer and binomial coefficients. Some latent properties…

We consider an oblique approach to cutting regions out of a flat rectangular sheet and folding to make a maximum volume container. We compare our approach to the traditional approach of cutting out squares at each vertex of the sheet. (Contains 4 figures.)

In the author's eighth year of teaching, she hit a wall teaching percent change. Percent change is one of the few calculations taught in math classes that shows up regularly in the media, and one that she often does in her head to make sense of the world around her. Despite this, she had been teaching percent change using textbook problems about…

What does "to be a mathematician" mean? What is implied, and what image is created of "a mathematician"? Are "mathematicians" members of an exclusive club? Are mathematicians different to "other people"? Are mathematicians different because they are able to mathematize? These might not be the most oft asked questions, but are they questions to…

This article reports findings from an investigation of precalculus students' approaches to solving novel problems. We characterize the images that students constructed during their solution attempts and describe the degree to which they were successful in imagining how the quantities in a problem's context change together. Our analyses revealed…