Modeling data behavior is differentiated from statistically determining a best-fit regression function, as it allows students to develop functions that hold certain attributes in respect to a set of data. Three techniques for developing polynomial models are demonstrated that afford students optional methods for determining appropriate polynomial…

Based on seminal work by Lord and Hambleton, Swaminathan, and Rogers, this article is an analytical, graphical, and conceptual reminder that item response theory (IRT) parameter invariance only holds for perfect model fit in multiple populations or across multiple conditions and is thus an ideal state. In practice, one attempts to quantify the…

The origin of the function concept is usually traced to Galileo's work on motion. We argue that specific proto-function concepts appeared in the work of Tartaglia a century before the publication of Galileo's Two New Sciences. The study of Tartaglia's ideas can be used in the classroom as a historical introduction to various function concepts,…

In this research paper we discuss how some multiple-choice questions may be used to improve understanding, to develop and to assess modelling capabilities and as an aid to teaching.

This article proposes a general latent variable approach to discrete-time survival analysis of nonrepeatable events such as onset of drug use. It is shown how the survival analysis can be formulated as a generalized latent class analysis of event history indicators. The latent class analysis can use covariates and can be combined with the joint…

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.)

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…

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…

This white paper focuses on the integration and enhancement of the computing experience for undergraduates throughout the chemical engineering curriculum. The computing experience for undergraduates in chemical engineering should have continuity and be coordinated from course to course, because a single software solution is difficult to achieve in…

The paper discusses an elementary spring model representing the motion of a magnet suspended from the ceiling at one end of a vertical spring which is held directly above a second magnet fixed on the floor. There are two cases depending upon the north-south pole orientation of the two magnets. The attraction or repelling force induced by the…