Describes an activity that addresses some fundamental principles of scaling, a technique that provides a mathematical basis for explaining many biological differences between small and large organisms. (WRM)

This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation, were taught according to their historical development, and the students tried to follow the…

A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…

This paper explores the idea of thinking skills approaches as tools for pedagogical inquiry and in so doing seeks to develop the link between the promotion of inquiry-based learning, which is a central tenet of thinking skills, and inquiry-based teaching as an approach to professional development and school improvement. The first part of the paper…

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers.…

This article presents a constructivist approach for teaching mathematics to prospective elementary school teachers in USA. This approach employs a model of a "mathematical situation," a set of physical operations and a physical language to reason about students' mathematical doings. One of the primary goals of this approach is to promote a…

This submission contains the Proceedings of the 2010 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Simon Fraser University in Burnaby, British Columbia. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims…

This study investigates whether or not the factor structure of reading comprehension is invariant across large, nationally representative samples of 14-year-old students from four different countries. The data from French-speaking Belgium, Hungary, Italy, and the United States were collected as part of the Reading Literacy Study of 1990-91,…

The concept of Arithmetic Story Grammar is introduced. Arithmetic Story Grammar maintains that any equation containing a single operand tells, in and of itself, a complete story with a setting, plot, theme, and resolution. Multiple-operand equations differ from their single-operand siblings only in the number of actions undertaken and the number…

This study investigated the extent to which log-linear smoothing could improve the accuracy of common-item equating by the chained equipercentile method in small samples of examinees. Examinee response data from a 100-item test (the Advanced Placement Examination in United States History) were used to create two overlapping forms of 58 items each,…

It has previously been shown by M. Beller (1990) that an additive tree (Addtree, a hierarchical tree representation of similarity data developed by S. Sattath and A. Tversky in 1977), may be useful for representing the structure between tests and items through the similarity among them as measured by their intercorrelations. In this study, the…

Standard errors and bias of unidimensional and multidimensional ability estimates were compared in a factorial, simulation design with two item response theory (IRT) approaches, two levels of test correlation (0.42 and 0.63), two sample sizes (500 and 1,000), and a hierarchical test content structure. Bias and standard errors of subtest scores…

It is argued that analysis of variance (ANOVA) and related methods should be taught using a general linear model (GLM) approach, rather than a classical ordinary sums of squares approach. The GLM approach emphasizes the linkages among conventional parametric methods, emphasizing that all classical parametric methods are least squares procedures…

The empirical performance of the technique proposed by P. O. Johnson and J. Neyman (1936) (the JN technique) and the modification of R. F. Potthoff (1964) was studied in simulated data settings. The robustness of the two JN techniques was investigated with respect to their ability to control Type I and Type III errors. Factors manipulated in the…

The performance of the following four methodologies for assessing unidimensionality was examined: (1) DIMTEST; (2) the approach of P. W. Holland and P. R. Rosenbaum; (3) linear factor analysis; and (4) non-linear factor analysis. Each method is examined and compared with other methods using simulated data sets and real data sets. Seven data sets,…