Over the past 25 years, performance measurement has gained salience in higher education, and with the explosion of structured data and the impact of business analytics and intelligence systems, there are new angles by which big volumes of data can be analyzed. Using traditional analytical approaches, pairs of reciprocal cohorts are considered as…

The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…

Trigonometry is one of the topics in mathematics that the students in both high school and pre-undergraduate levels need to learn. Generally, the topic covers trigonometric functions, trigonometric equations, trigonometric identities and solving oblique triangles using the Laws of Sines and Cosines. However, when solving the oblique triangles,…

A portion of all students in introductory or developmental undergraduate mathematics courses find themselves at an unfortunate tipping point: the border between passing and failing. These high-stakes courses often come with high enrollments, and a recurring problem: high failure rates. The measure of success used at the author's institution, the…

The K-W-L method of teaching is a simple method that actively engages students in their own learning. It has been used with kindergarten and elementary grades to teach other subjects. The authors have successfully used it to teach physics at the college level. In their introductory physics labs, the K-W-L method helped students think about what…

Textbooks, like many other resources teachers have at hand, are meant to be an aid for instruction; however there is little research with textbooks or on their potential to develop metacognitive knowledge. Metacognitive knowledge has received substantial attention in the literature, in particular for its relationship with problem-solving in…

This Ontario-based qualitative study examined secondary school and college textbooks' treatment of trigonometric representations in order to identify potential sources of student difficulties in the transition from secondary school to college mathematics. Analysis of networks, comprised of trigonometric representations, identified numerous issues…

The purpose of this study was to: (a) investigate the effects of email to enhance learners' use of self-regulation strategies; (b) examine different effects between email list and individually addressed notes on the enhancement of self-regulation; (c) observe and record changes in self-regulation and self-efficacy; and (d) explore the…

In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the derivative of the exponential functions and the derivative of their inverses, the logarithmic functions. I extend this approach to generate formulae for the…

The question is addressed of choosing four points on the circumference of an ellipse so that the quadrilateral formed has maximum area. (MP)

An identity for sin x/x is proved. Rate of convergence, a geometric interpretation, and an application from physics are discussed. (DT)

An examination problem and solution gives rise to the question of whether there actually exists a theorem concerning the minimal period of the sum of certain periodic functions. The author discusses such a theorem and uses the situation to support mathematical education as opposed to the teaching of mathematics. (MN)

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

A computer program is presented that generates problem sets involving sketching graphs of trigonometric functions using graphical addition. The students use calculators to sketch the graphs and a computer solution is used to check it. (MP)

Described is the construction of a computerized test bank to generate and score tests in college algebra, trigonometry, and intermediate algebra; including a discussion of uses, advantages and disadvantages of computerized testing. (JLH)