Two experiments examined identification and bisection of tones varying in temporal duration (Experiment 1) or frequency (Experiment 2). Absolute identification of both durations and frequencies was influenced by prior stimuli and by stimulus distribution. Stimulus distribution influenced bisection for both stimulus types consistently, with more…

This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of…

A simple car following model based on the solution of coupled ordinary differential equations is considered. The model is solved using Euler's method and this method of solution is itself interpreted as a mathematical model for car following. Examples of possible classroom use are given. (Contains 6 figures.)

This paper deals with a prey-predator model incorporating a prey refuge and harvesting of the predator species. A mathematical analysis shows that prey refuge plays a crucial role for the survival of the species and that the harvesting effort on the predator may be used as a control to prevent the cyclic behaviour of the system. The optimal…

The existing vector formalism method for thermodynamic relationship maintains tractability and uses accessible mathematics, which can be seen as a diverting and entertaining step into the mathematical formalism of thermodynamics and as an elementary application of matrix algebra. The method is based on ideas and operations apt to improve the…

This article presents the results of two studies on using an innovative pedagogical strategy in teaching mathematical modelling and applications to engineering students. Both studies are dealing with introducing non-traditional contexts for engineering students in teaching/learning of mathematical modelling and applications: environment and…

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an…

This paper explores the public awareness that there presently exists a crisis in mathematics education and a "dumbing down" of the curriculum, examines the nature of this crisis and argues that there has been a lowering of cultural, pedagogical and cognitive expectations with respect to most learners. The notion of cognitive development in…

The goal of this paper is to demonstrate the infrastructural nature of many modern conceptual technologies. The focus of this paper is on conceptual tools associated with elementary types of data modeling. We intend to show a variety of ways in which these conceptual tools not only express thinking, but also mold and shape thinking. And those ways…

In current curriculum materials for middle school students in the US, data and chance are considered as separate topics. They are then ideally brought together in the minds of high school or university students when they learn about statistical inference. In recent studies we have been attempting to build connections between data and chance in the…

This paper provides a microanalysis of one Algebra I teacher's instruction to explore the advantages that are afforded us by coordinating two perspectives to document and account for the teacher's mathematical understandings. We use constructs associated with Stein, Grover and Henningsen's domain of mathematical didactics and Realistic Mathematics…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

Prior work has proposed different theoretical mechanisms to explain students' course-taking patterns in schools. On the one hand, there are oversocialized accounts that claim that rules, social background factors, and supply-side factors shape observed career patterns. On the other hand, there are undersocialized accounts that claim that the…

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…