Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…

In this research article, I present evidence of the existence of visual templates in pattern generalization activity. Such templates initially emerged from a 3-week design-driven classroom teaching experiment on pattern generalization involving linear figural patterns and were assessed for existence in a clinical interview that was conducted four…

In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

Presented is an example meant to enable students with a scant mathematical education to grasp the meaning of the limit of the binomial distribution. (Author/TG)

Argues that conventional dynamic modeling techniques divert attention from the importance of model structure and discusses various methods of system representation that are suitable for the analysis and improvement of model structure. (Available from IPC (America) Inc., 205 East 42 Street, New York, NY 10017; $46.80 annually.) (Author/JG)

This report describes the results of preliminary work by the Human Resources Research Organization to develop a comprehensive theory for structuring subject matter. The report focuses on the first three of five components that any comprehensive model of instruction should include: (1) a representation of the subject matter to be taught; (2) a…

Used software environment to examine algebra students' attempts to reformulate narratives using verbal and iconic lexical sets. Described how natural language text turns into a script of events and processes, how the qualitative graphic description of the script is sketched using iconic notations, and how the graph turns into a subject for…

Discusses the use of mathematical modeling. Describes types, examples, and importance of mathematical models. (YP)

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

A discussion is presented concerning variables associated with children's representation of certain addition and subtraction problems. Problem components are classified as physical, pictorial, sensual, verbal-spoken, verbal-written, symbolic, or internal. Problems are discussed as abstract (symbolic) or nonsymbolic. Three problem components are…

Reports a project that incorporated mathematical modeling into a college course. Reports evaluation of the course in terms of criteria derived from the stated aims: modeling performance, modeling framework, pedagogy assessment, and personal growth. Included are two sample problems. (YP)