Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying…

P. Maguire, B. Devereux, F. Costello, and A. Cater discussed the Gagne and Shoben (1997) CARIN theory of conceptual combination and, after presenting a sample drawn from the British National Corpus and comparing the two corpora, concluded that the Gagne and Shoben corpus is too small and unrepresentative. They then discussed the mathematical model…

What is the time course of visual attention? Attentional blink studies have found that the 2nd of 2 targets is often missed when presented within about 500 ms from the 1st target, resulting in theories about relatively long-lasting capacity limitations or bottlenecks. Earlier studies, however, reported quite the opposite finding: Attention is…

The utility of an "ecologically rational" recognition-based decision rule in multichoice decision problems is analyzed, varying the type of judgment required (greater or lesser). The maximum size and range of a counterintuitive advantage associated with recognition-based judgment (the "less-is-more effect") is identified for a range of cue…

In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the…

This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

This article considers some issues in designing a course focusing on statistical concepts rather than memorizing formulae.

This paper identifies several serious problems with the widespread use of ANOVAs for the analysis of categorical outcome variables such as forced-choice variables, question-answer accuracy, choice in production (e.g. in syntactic priming research), et cetera. I show that even after applying the arcsine-square-root transformation to proportional…

Mechanics has never been the most popular subject in A-level mathematics, the UK's public examination for 16-18-year olds, either with students, teachers or educators. The attempts to popularize mechanics have failed and it is conceivable that the subject will be dropped from the A-level syllabus in the foreseeable future. This article argues the…

In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaputa's belief in a Science of Need to motivate and direct the development of tasks and tools for engaging students in…

The aim of this paper is to present a shortened version of the SIS (support intensity scale) obtained by the application of mathematical models and instruments, adopting special algorithms based on the most recent developments in artificial adaptive systems. All the variables of SIS applied to 1,052 subjects with ID (intellectual disabilities)…

A PUBMED search for "mathematical models in medicine" shows more than 15,000 articles covering almost every field of medicine. We designed a course with the goal of developing the students' skills in computerized data analysis and mathematical modelling, as well as enhancing their ability to read and interpret mathematical data analysis. The study…

The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…

Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge…

In this paper, we examine the development of pre-service mathematics teachers' use of multiple representations during teaching in technology-rich environments. The pre-service teachers took part in a preparation program aimed at integration of technology into teaching mathematics. The program was designed on the basis of Technological Pedagogical…