What patterns can be observed among the mathematical arguments above-average students find convincing and the strategies these students use to learn new mathematical concepts? To investigate this question, we gave task-based interviews to eleven female students who had performed well in their college-level mathematics courses, but who differed in…

The idea of a graphing portfolio and its implementation in two levels of traditional university calculus courses is described. The activity of graphing helps students to gain a broader and deeper understanding of the connection between a function and its graph.

Phyllis Whitin was interested in the role of communications in developing mathematical understanding among children. She designed a problem-posing explorations system, which encouraged children to think, question, solve problems and discuss their ideas, strategies and solutions.

The definition is an important language form in the register of mathematics. Students need to understand the structure of a definition so that they can make sense of the definitions they encounter and so that they can construct their own definitions as part of organising their thoughts about the concepts they have explored. This article suggests…

Japanese prefer odd numbers, whereas Westerners emphasize even numbers, an observation that is clear from the distribution of number-related words in Japanese and English dictionaries. In this article, the author explains why these two cultures differ by surveying the history of numbers, including yin-yang thought from ancient China, ancient Greek…

Though poetry and math may seem to be unrelated, there are parallels such as rhythmic language and language skills. Reading and writing poetry about math involves students with listening, speaking, reading, and writing in order to develop and demonstrate an understanding of mathematical concepts and relationships. This article features an…

Reading in mathematics classrooms needs to be an active part of the learning process. If it continues to be viewed as a passive way to gain information, then its benefit to the learning process will also continue to be under-utilised. The "Read--Think--Do (x2)" model, designed by these authors and described in this article, can be a support to…

Binary outcome data are common in research and evaluation. They are often analyzed using logistic regression, and results of these analyses are often reported in the form of odds ratios (ORs). However, ORs are not directly interpretable in the metric commonly used in policy-relevant discussions, which concerns probabilities. ORs are unfamiliar to…

All introductory statistics students must master certain basic descriptive statistics, including means, standard deviations and correlations. Students must also gain insight into such complex concepts as the central limit theorem and standard error. This article introduces and describes the Friendly Introductory Statistics Help (FISH) computer…

In this article, the author describes an individualized term project that is designed to increase student understanding of some of the major concepts and methods in multivariate calculus. The project involves having each student conduct a complete max-min analysis of a third degree polynomial in x and y that is based on his or her social security…

Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.

This paper describes a general education course that begins with proportion and logarithms (base 10), and that culminates in students' reading and presenting recent frontier research from a variety of disciplines. The theme of the course is that many disciplines use relative size to explain apparently unrelated phenomena. We provide a course…

In this article, the authors describe their efforts to assess prospective K-8 teachers' knowledge of proportional reasoning. Based upon their analysis of prospective K-8 teachers' work on a mathematics performance task, they discuss the implications for preparing prospective teachers to teach proportional reasoning to their students. In general,…

This paper examines the elasticity of demand, and shows that geometrically, it may be interpreted as the ratio of two simple distances along the tangent line: the distance from the point on the curve to the x-intercept to the distance from the point on the curve to the y-intercept. It also shows that total revenue is maximized at the transition…

The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…