This essay examines some aspects of the teaching of mathematics and its applications in three of the principal sixteenth century Spanish universities (Salamanca, Valencia and Alcala) and in other institutions sponsored by the monarchy, such as the "Casa de la Contratacion" (House of Trade) of Seville and the so-called Academy of…

Understanding the effects of additive and multiplicative constants on basic statistical procedures provides the important groundwork necessary for a thoughtful and logical understanding of more complex methods. This paper explores the effects of additive and multiplicative constants on the mean, standard deviation, skewness, kurtosis, and…

We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of…

Within the set of points in the plane with integer coordinates, one point is said to be visible from another if no other point in the set lies between them. This study of visibility draws in topics from a wide variety of mathematical areas, including geometry, number theory, probability, and combinatorics.

In this study, we explore six students' conceptions of Z[subscript n] in an effort to understand students' conceptions of quotient groups in general. We discovered that there were three different ways our students thought about Z[subscript n], namely as infinite sets, element-set combinations, and representative elements. We explore how…

As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.

This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…

This paper focuses on the developments experienced by natural philosophy and mathematics in Bologna during a period of rapid change in the relationship of the various disciplines in the faculty of Arts and Medicine. Insisting that university science was characterized by a greater vitality than the traditional historiography usually concedes, this…

Triangular numbers are used to unravel a new sequence of natural numbers here-to-fore not appearing on the Encyclopedia of Integer Sequences website. Insight is provided on the construction of the sequence using "buildings" as a viewable model of the sequence entries. A step-by-step analysis of the sequence pattern reveals a method for generating…

Mathematics lecturers have long expressed concern about their students poor mathematical background and the effect this has on performance in first mathematics courses at university level. This article explores a similar concern about students' numeracy in a statistics course for psychologists.

Supplemental Instruction (SI) incorporates collaborative learning in small, peer-led, group settings in order to integrate instruction in learning and reasoning skills with course content. Several meta-analyses speak to the efficacy of SI but fail to address selection bias due to ability/motivation and gender. In this study, SI was paired with a…

Although variability is of fundamental concern and interest to statisticians, often this does not get communicated to students who are taught instead to view variability as a nuisance parameter. A brief survey of a few case studies, as well as a recounting of some history, shows that variability is worthy of study in its own right, and examination…

For the past two years, Achieve, Inc. has worked with the Transition Mathematics Project (TMP), a collaborative project of K-12 schools, community and technical colleges, and baccalaureate institutions within the state of Washington, as it developed mathematics standards that "define the core knowledge and skills expected of students entering…

Due to a poor module evaluation, mediocre student grades and a difficult teaching experience in lectures, the Data Analysis section of a first year core module, Research Methods for Social Sciences (RMSS), offered at the University of KwaZulu-Natal in South Africa, was completely revised. In order to review the effectiveness of these changes in…