Spatial reasoning is a skill that needs to be developed in students as it is important in geometry for determining total surface areas and volumes of 3-dimensional shapes (Liedtke, 1995). Simply teaching children the formulae, in this case for finding total surface areas, can limit them in understanding mathematics conceptually (Bonotto, 2003).…

The author and his first-year algebra students explored the quadratic behavior behind the parabolic shape of fountains at the local family splash park. This hands-on discovery project has three main parts: (1) gathering data by experimenting with and photographing the fountains; (2) analyzing the photographs to obtain numerical data; and (3)…

Introduction: In the present-day didactic process of transition from natural numbers to integers, a certain kind of measure is involved which is neither easy nor appropriate to integrate into the familiar numerical systems. We refer to measures and comparisons for which we need a third numerical system--what we will call "relative…

The "Cognitive Tutor[R] Algebra I" curriculum, published by Carnegie Learning, is an approach that combines algebra textbooks with interactive software. The software is developed around an artificial intelligence model that identifies strengths and weaknesses in each individual student's mastery of mathematical concepts. It then…

A simple algorithm for computing the partial fraction expansions of proper rational functions with multiple poles is presented. The main idea is to use the Heaviside's cover-up technique to determine the numerators of the partial fractions and polynomial divisions to reduce the multiplicities of the poles involved successively, without the use of…

This paper proposes a methodology using graph theory, matrix algebra and permanent function to compare different architecture (structure) design of intelligent mobile learning environment. The current work deals with the development/selection of optimum architecture (structural) model of iMLE. This can be done using the criterion as discussed in…

Identities for many and varied combinations of binomial coefficients abound. Indeed, because of the wide range of interrelationships it is possible that a great deal of mathematical effort has been wasted in proving essentially equivalent formulae. As well as proving identities these methods can be used to rule out closed form solutions (at least…

Prior research has demonstrated gaps in the academic success of college student subgroups defined by race/ethnicity, income, and gender. We studied trends over time in the success of students in these subgroups in particular first-year college courses: English Composition I, College Algebra, social science courses, and Biology. The study is based…

It is well known that e-squared is irrational: this note presents a simple proof of it. The arguments stay within the realms of a first proof course in mathematical analysis offered for undergraduates.

A little known property of determinants is developed in a manner accessible to beginning undergraduates in linear algebra. Using the language of matrix theory, a classical result by Sylvester that describes when two polynomials have a common root is recaptured. Among results concerning the structure of polynomial roots, polynomials with pairs of…

Define the centre of a parallelogram to be the intersection of its diagonals. It was shown in an earlier paper that the intersection of arbitrarily many parallelograms with the same centre is the unit disc about that centre in a metric defined using ideas from Linear Algebra. In this note, it is shown that this characterizes compact, convex sets,…

Understanding the meaning of rational numbers and how to perform mathematical operations with those numbers seems to be a perennial problem in the United States for both adults and children. Based on previous work, we hypothesized that giving students more time to practice using rational numbers in an environment that enticed them to apply their…

In recent years, a considerable number of teachers in Spain have been using DERIVE to teach math subjects in High Schools and Universities. This software has been used by the authors of this work as a support tool in Mathematics courses for Engineering. Since Texas Instruments does not support DERIVE, we were faced with finding an alternative…

The purpose of this research is to determine the effect of concept cartoons on the students' perception of their levels of self-efficacy towards mathematics. The research has been designed as the pre-test post-test with quasi experimental control group. The research participants are composed of 94 7th grade students attending an elementary school…

Getting high school students to enjoy mathematics and to connect concepts to their daily lives is a challenge for many educators. The Mathematics of Skateboarding demonstrated innovative and creative ways to engage students in content and skills mapped to state requirements for high school students in Algebra and Geometry.