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.

A structural equation modeling approach to scale reliability evaluation can be employed to estimate generalizability theory indexes in settings where sampling of subjects and conditions is carried out. In one- and two-facet crossed designs, it is demonstrated how this method can be used to obtain estimates of relative generalizability…

Researchers often have one or more theories or expectations with respect to the outcome of their empirical research. When researchers talk about the expected relations between variables if a certain theory is correct, their statements are often in terms of one or more parameters expected to be larger or smaller than one or more other parameters.…

Two experiments used a magnitude estimation paradigm to test whether perception of disfluency is a function of whether the speaker and the listener stutter or do not stutter. Utterances produced by people who stutter were judged as "less fluent," and, critically, this held for apparently fluent utterances as well as for utterances…

Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…

In this article, the author discusses the Soroban (Japanese abacus) in the age of computers and its structure. Since the advent of computers, the Soroban has started to shift from being used purely as a calculating device to being a useful tool in general mathematics education. The beauty of the Soroban is that it represents numbers exactly as you…

While attending a Postgraduate Certificate in Education (PGCE) course, this author was provided with the time and encouragement to try out different activities, styles, and strategies of teaching. She used this time to develop numeracy starter lessons with Y7 students, spending two weeks with each of four sets of students. She decided from the…

If larger and larger samples are successively drawn from a population and a running average calculated after each sample has been drawn, the sequence of averages will converge to the mean, [mu], of the population. This remarkable fact, known as the law of large numbers, holds true if samples are drawn from a population of discrete or continuous…

The sequence 1, 1, 2, 3, 5, 8, 13, 21, ..., known as Fibonacci sequence, has a long history and special importance in mathematics. This sequence came about as a solution to the famous rabbits' problem posed by Fibonacci in his landmark book, "Liber abaci" (1202). If the "n"th term of Fibonacci sequence is denoted by [f][subscript n], then it may…

For 137 years Markovnikov's rule has been extensively used in organic chemical education and research to describe the regioselectivity in electrophilic addition reactions to alkenes and alkynes. When the structures of the final reaction products are used as reference, the rule requests that certain polar addition reactions be termed…

This study examined the concurrence between proxy generated estimates of physical activity via diary recordings and accelerometer generated estimates of physical activity for 37 adults with intellectual disability living in supported group homes. Specifically, the following questions were addressed: (a) to what extent did the proxy estimates agree…

In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as…

An analytical approach was employed to compare sensitivity of causal effect estimates with different assumptions on treatment noncompliance and non-response behaviors. The core of this approach is to fully clarify bias mechanisms of considered models and to connect these models based on common parameters. Focusing on intention-to-treat analysis,…

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer…

An adapted alternating treatments design was used to evaluate and compare the effects of two procedures designed to enhance math fact accuracy and fluency in an elementary student with low cognitive functioning. Results showed that although the cover, copy, compare (CCC) and the taped problems (TP) procedures both increased the student's math fact…