A inquiry-based approach called the "modelling discussion" is introduced for structuring beginning modelling activity, teaching new mathematics from examining its applications in contextual situations, and as a general classroom management technique when students are engaged in mathematical modelling. An example which illustrates the style and…

This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…

The question of how to estimate school and teacher contributions to student learning is fundamental to educational policy and practice, and the three thoughtful articles in this issue represent a major advance. The current level of public confusion about these issues is so severe and the consequences for schooling so great that it is a big relief…

The CODE Theory of Visual Attention (CTVA) is a mathematical model explaining the effects of grouping by proximity and distance upon reaction times and accuracy of response with regard to elements in the visual display. The predictions of the theory agree quite acceptably in one and two dimensions (CTVA-2D) with the experimental results (reaction…

This note describes a large-scale modelling activity involving geometry that can be solved with the help of uni-variable calculus. More specifically, it introduces and proves the following theorem: given any non-equilateral triangle, there exist infinitely many mutually non-congruent triangles with the same area and the same perimeter as the given…

Methodological implications of a person-oriented, holistic-interactionistic perspective in research on individual development are outlined, desirable properties of a mathematical model of a phenomenon are discussed, and selected methods for carrying out person-oriented research are briefly overviewed. These methods are: (1) the classificatory…

An adapted alternating treatments design was used to evaluate and compare the effects of two procedures designed to enhance math fact accuracy and fluency in an elementary student with low cognitive functioning. Results showed that although the cover, copy, compare (CCC) and the taped problems (TP) procedures both increased the student's math fact…

In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…

In this article, the authors present the results of a research study in which they used two national datasets to construct and examine a model that estimates relative faculty instructional costs for specific undergraduate degree programs and also identifies differences in these costs by region and institutional type. They conducted this research…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

Learning styles encapsulate the preferences of the students, regarding how they learn. By including information about the student learning style, computer-based educational systems are able to adapt a course according to the individual characteristics of the students. In accomplishing this goal, educational systems have been mostly based on the…

In tasks as diverse as stock market predictions and jury deliberations, a person's feelings of confidence in the appropriateness of different choices often impact that person's final choice. The current study examines the mathematical modeling of confidence calibration in a simple dual-choice task. Experiments are motivated by an accumulator…

The dataset presented here illustrates to students the utility of logistic regression. Its analysis results in a fit that explains much of how senators vote on a particular bill, and allows for quantification of the effects of ideology and money on the vote. A number of interesting quantitative interpretations follow from a good fit. A successful…

One of the objectives of the process technology curriculum at Wageningen University is that students learn how to design mathematical models in the context of process engineering, using a systematic problem analysis approach. Students find it difficult to learn to design a model and little material exists to meet this learning objective. For these…

This paper shows how inequalities can be utilized in reducing dimensionality of problems associated with the partition of unit fractions into the sums of two, three, and four like fractions. The need for such a reduction in this context stems from using a spreadsheet as a modelling tool. Activities described in this paper are grounded in standards…