The authors discuss the question, "What is mathematics education research at the university level?" They go on to consider "Making progress in tertiary mathematics education research: pushing the field forward." This includes a discussion of basic concepts and theoretical frameworks used. Further, they consider who does such research and how one…

I present a theoretical distinction that may prove useful in conceptualizing mathematics teacher education (and graduate education) and research on mathematics teacher education. Further, the distinction can contribute to developing frameworks on the design of mathematics curricula. The distinction between empirical activity and…

New information technologies can act as a Trojan horse offering activities that will require major changes in the teaching-learning process. Computer aided learning applications are able to offer advanced students the opportunity to improve their skills and to maintain their motivation. In the spirit of "learning by doing", they are…

On the occasion of having to design an introductory course of mathematics for the University (UNGS, Buenos Aires, Argentina) we took into account the perspective of mathematical modelling. In this article we present the theoretical framework that we elaborated on to design our course. This framework allowed us to adapt the generic perspectives of…

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore…

This article presents an in-class Monte Carlo demonstration, designed to demonstrate to students the implications of multicollinearity in a multiple regression study. In the demonstration, students already familiar with multiple regression concepts are presented with a scenario in which the "true" relationship between the response and…

This article defines "higher level mathematical skills" and details an important class: that of "constructing instances" of mathematical objects satisfying certain properties. Comment is made on the frequency of higher level tasks in undergraduate work. We explain how such questions may be assessed "in practice" without the imposition on staff of…

Gateway tests provide a means of assuring that students in reformed precalculus and calculus courses acquire the algebraic and computational skills needed in courses following these, while allowing the focus of the course to be on the conceptual understanding intrinsic to the reformed courses. However, logistical difficulties plague the…

This report describes how journaling and email were used to benefit both the teacher and her students on a college campus in Georgia. The report outlines how decisions were made about the content of the journals, submission deadline considerations, and concerns about the e-journal process. Benefits to the teacher/professor are enumerated and…

Most research in the area of Computer Algebra Systems (CAS) has been designed to compare the effectiveness of instructional technology to traditional lecture-based formats. While results are promising, research also indicates evidence of the steep learning curve imposed by the technology. Yet no studies have been conducted to investigate this…

When students are working with hand held technology, such as graphics calculators, we usually only see the outcomes of their activities in the form of a contribution to a written solution of a mathematical problem. It is more difficult to capture their process of thinking or actions as they use the technology to solve a problem. In this paper we…

We report on a study of the relationship between calculator technology and student learning in two introductory statistics class sections taught by the same instructor at the University of Texas at San Antonio. At the introduction of hypothesis testing and confidence intervals, one class section (A) was given graphing calculators capable of…

This study investigated introductory statistics students' conceptual understanding of the standard deviation. A computer environment was designed to promote students' ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an…

This paper describes two classroom activities and a project that supplement a Liberal Arts Mathematics course's coverage of logic and reasoning. The first classroom activity introduces the writing of inductive and deductive arguments, and the second activity involves analyzing a guest speaker's arguments. The project consists of using logic and…

The Statistical Reasoning Assessment or SRA is one of the first objective instruments developed to assess students' statistical reasoning. Published in 1998 (Garfield, 1998a), it became widely available after the Garfield (2003) publication. Empirical studies applying the SRA by Garfield and co-authors brought forward two intriguing puzzles: the…