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…

The applicability of the identical elements (IE) model of arithmetic fact retrieval (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994) to cued recall from episodic (image and sentence) memory was explored in 3 transfer experiments. In agreement with results from arithmetic, speedup following even minimal practice recalling a missing word from an…

Some potential contributions of invariants, heuristics, and exemplars to the perception of dynamic properties in the colliding balls task were explored. On each trial, an observer is asked to determine the heavier of 2 colliding balls. The invariant approach assumes that people can learn to detect complex visual patterns that reliably specify…

In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as…

This paper indicates that prospective teachers' familiarity with theoretical models of students' ways of thinking may contribute to their mathematical subject matter knowledge. This study introduces the intuitive rules theory to address the intuitive, "same sides-same angles" solutions that prospective teachers of secondary school mathematics come…

The purpose of this study was to compare the isolated effects of cover-copy-compare (CCC) with the combined effects of CCC and two types of performance feedback (i.e., digits correct and incorrect per minute) on sixth grade students' mathematics fluency and accuracy. An alternating treatments design was employed to compare treatments across 16…

Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…

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…

Some of the different approaches to standard setting are discussed. Brief comments and references are offered concerning strategies that rely primarily on the use of expert judgment. Controversy surrounds methods that use expert judges, as well as those using test groups to set scores empirically. A minimax procedure developed by H. Huynh, an…

Contingency tables, and their associated statistical tests, are frequently used in educational and social research. Popular statistical tests used in contingency table analyses include the Pearson chi-square test and the likelihood ratio chi-square test. These two tests are chi-square distributed under large sample conditions. However, when a…