Data distributions can be represented using different external representations, such as histograms and boxplots. Although the role of external representations has been extensively studied in mathematics, this is less the case in statistics. This study helps to fill this gap by systematically varying the representation that accompanies a task…

The notion that undergraduates are capable of making profound and original contributions to mathematical research is rapidly gaining acceptance. Undergraduates bring their enthusiasm, creativity, curiosity, and perseverance to bona fide research problems. This article discusses some of the key issues concerning undergraduate mathematical research:…

This dataset contains the results of a quasi-experiment, testing Karl Pearson's "drunkard's walk" analogy for an abstract random walk. Inspired by the alternate hypothesis that drunkards stumble to the side of their dominant hand, it includes data on intoxicated test subjects walking a 10' line. Variables include: the…

This study examined student indicators for success in entry-level college calculus. An attitude toward mathematics inventory, course performance, readiness assessment, and student interviews were used to determine characteristics and behaviors of students who succeeded in the course. In addition to student indicators, difficult topics and…

As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a "pre-brief, teaching, and debrief" process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the…

As computing becomes ubiquitous, software correctness has a fundamental role in ensuring the safety and security of the systems we build. To design and develop software correctly according to their formal contracts, CS students, the future software practitioners, need to learn a critical set of skills that are necessary and sufficient for…

Students experience difficulty learning and understanding chemistry at higher levels, often because of cognitive biases stemming from common sense reasoning constraints. These constraints can be divided into two categories: assumptions (beliefs held about the world around us) and heuristics (the reasoning strategies or rules used to build…

The author studied how math anxiety, motivation, and ability group interact to affect performance in college math courses. This clarified the effects of math anxiety and ability grouping on performance. It clarified the interrelationships between math anxiety, motivation, and ability grouping by considering them in a single analysis. It introduces…

A system was developed for automatic generation of problems and solutions for examinations in a university distance course in discrete mathematics and tested in a pilot experiment involving 200 students. Considering the success of such systems in the past, particularly including automatic assessment, it should not take long before such systems are…

Validating proofs and counterexamples across content domains is considered vital practices for undergraduate students to advance their mathematical reasoning and knowledge. To date, not enough is known about the ways mathematics majors determine the validity of arguments in the domains of algebra, analysis, geometry, and number theory--the domains…

University mathematics education (UME) is considered, in this paper, as a kind of "didactic practice"--characterised by institutional settings and by the purpose of inducting students into "mathematical practices." We present a research programme -- the anthropological theory of the didactic (ATD)--in which this rough…

This article presents a historical defense of liberal arts education--a philosophy that is commonly claimed among Christian colleges and universities--in order to provide an understanding of liberal education to skeptics and subscribers alike. A subsequent discussion of the role of mathematics in the liberal arts tradition contends that…

This paper describes a collaboration between a mathematician and a compositionist who developed a sequence of collaborative writing assignments for calculus. This sequence of developmentally appropriate assignments presents peer review as a collaborative process that promotes reflection, deepens understanding, and improves exposition. First, we…

Unit conversion need not be boring. If students see that the skill is necessary, both their motivation to learn and their appreciation of the process can be enhanced. As a result, students become actively engaged and construct understanding and computational skills that they will retain over time. The activity described here makes use of scale…

In this paper, we report a pilot study on engaging a group of undergraduate students to explore the limits of sin(x)/x and tan(x)/x as x approaches to 0, with the use of non-graphic scientific calculators. By comparing the results in the pretest and the post-test, we found that the students had improvements in the tested items, which involved the…