What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable…

Recent research into students' reasoning about variation refers specifically to notions of distribution that emerge. This paper reports on research where written responses, from tertiary introductory statistics students, were coded according to the level of consideration of variation. A hierarchy of reasoning about distribution is proposed, based…

The paper is based on research carried out on secondary school students and students commencing their university studies in mathematics. The basic purpose of the research was to investigate the understanding of the concept of a sequence and to determine the sources of the formation of revealed conceptions. To achieve the objectives an expanded set…

Ana De Carvalho and Tania Cabral write here that they think the learning process rests heavily on the ability of speech, so they recommend placing students more and more in the position of speaking. Not happy with prompt, correct answers, they confront their students with further related questions trying to establish if they have fairly consistent…

In this article and part 2, the author focuses on how an individual appropriates notions from the socially-sanctioned body of knowledge called mathematics. Specifically, the author is concerned with how students, to a greater or lesser extent, internalise mathematical ideas that exist in the social world (on the chalkboard, in textbooks, in the…

In this work we show some activities designed with a First Year group of the Mathematics Degree to give the graphic register back its mathematical status and promote its use on the part of the students. In particular, we have chosen the topic related to improper integration to reinforce the use of this register by the students. [For complete…

There has been growing concern about the mathematical skills and understanding of undergraduates entering higher education to study mathematical sciences. In spite of this, as in other disciplines, the classifications of degrees awarded in mathematical sciences have risen. The research described here uses statistical analyses of data collected by…

This paper presents an assessment tool which can be used during the first weeks of calculus to measure students' visual thinking skills. We have developed and applied this instrument in classes for the last three years, tabulating results and interviewing students on a regular basis. We discuss our findings and provide hints to using the…

The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…

This article describes a sophomore transition-to-advanced-math course taught via a modified Moore method at Lebanon Valley College.

This article describes both the process and products of a cooperative inquiry project between two educational researchers--one from literacy education and one from mathematics education. The collaboration took place in an undergraduate, inquiry-based mathematics classroom in which the researchers sought to develop a shared vision of learning and…

Contemporary mathematics education is at a crossroads. It has become exposed to forces, both static and dynamic, that pose a challenge to its traditional place in academia. Mathematics has a long-established status as perhaps the most critical foundation for analytical knowledge. But the manner in which mathematics instructors choose to respond to…

Simple examples are really encouraging in the understanding of rearrangements of infinite series, since many texts and teachers provide only existence theorems. In the absence of examples, an existence theorem is just a statement and lends little confidence to understanding. Iterated sums of double series seem to have a similar spirit of…

This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…

In the first decade of the 21st century, the nation, the states, and colleges and universities began to grapple with the challenges of globalization, changing demography, the implications of the digital era, and of a less expansive public sector. Although not a transformative period for higher education, the decade saw significant innovations in…