Traditional college algebra courses focus almost exclusively on power functions such as y = x[superscript 2] and y = x[superscript 3] rather than the more general y = x[superscript p]. However, it is the more general form that is the basis of the mathematical models that arise throughout the natural sciences in a host of unexpected and highly…

Students' understanding of functions is a topic that has been researched extensively. In this qualitative study, five university students of varying mathematical backgrounds were interviewed to reveal strategies and misconceptions as they struggled with graphical and analytical tasks relating to sum functions. Weaker students are seen to rely…

Here we give an example of a problem that could be beneficially investigated by AS/A level students. It is a geometry problem that they can profitably tackle by geometric (especially geometry software) and algebraic means. Such problems naturally lead students to the need for proof--an essential part of mathematics that is often lacking in current…

The paper discusses an elementary spring model representing the motion of a magnet suspended from the ceiling at one end of a vertical spring which is held directly above a second magnet fixed on the floor. There are two cases depending upon the north-south pole orientation of the two magnets. The attraction or repelling force induced by the…

Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.

This paper examines the work of students who, when reasoning about real analysis, do so almost exclusively by means of verbal and algebraic reasoning, and tend not to incorporate visual images into their work. It examines the work of students from two parallel courses of introductory real analysis, whose reasoning ranges from those who introduce…

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

This article presents a project that introduces compositions and inverses of functions, using a method that compliments the learning styles of Native American students.

The study was aimed at characterizing the exact algebraic structure of the love schema in order to trace possible changes in the conceptualization of love throughout the adult life cycle, notably as regards the weight attributed to the three components of love: passion, intimacy, and commitment. The methodological framework was the Functional…

Sfard and Kieran [Kieran, C., Educational Studies in Mathematics 46, 2001, 187-228; Sfard, A., Educational Studies in Mathematics 46, 2001, 13-57; Sfard, A. and Kieran, C., Mind, Culture, and Activity 8, 2001, 42-76] have developed a methodological framework, which aims at characterizing the students' mathematical discourses while they are working…

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a…

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

Painting the Cube is commonly used in middle and high school mathematical courses as a mathematically rich problem, wherein the exposed faces of the large cubes are painted after being assembled from small unit cubes. The problem perfectly combines algebraic as well as geometrical aspects and helps students to study and understand various linear,…

In this article I discuss the factors that led me to implement study groups in the teaching of mathematics. An important influence in this decision began with an experimental study conducted with two College Algebra classes in which students were randomly assigned to treatment groups. While there was no statistical difference between the study…