Mathematical representation includes the process of transforming problems or ideas into new forms, including changing pictures or physical models into symbols, words, or sentences that can facilitate students in solving mathematical problems. Pythagorean Theorem material is widely used in analytic geometry, so this material becomes important for…

Mathematics requires thinking but also pattern recognition. Recent research indicates that perceptual learning (PL) interventions facilitate discovery of structure and recognition of patterns in mathematical domains, as assessed by tests of mathematical competence. Here we sought direct evidence that a brief perceptual learning module (PLM)…

The main goal of the Learning and Teaching Geometry (LTG) project is to build professional development (PD) materials that provide opportunities for teachers to engage in learning about geometric similarity through the use of video cases, in which specific and increasingly complex mathematical ideas are presented within the dynamics of classroom…

The assumption that is most important to the hypothesis testing procedure of multiple linear regression is the assumption that the residuals are normally distributed, but this assumption is not always tenable given the realities of some data sets. When normal distribution of the residuals is not met, an alternative method can be initiated. As an…

Data transformations are commonly used tools in quantitative analysis of data. However, data transformations can be a mixed blessing to researchers, improving the quality of the analysis while at the same time making the interpretation of the results difficult. Few, if any, statistical texts discuss the tremendous influence a distribution's…

The present investigation developed power curves for two parametric and two nonparametric procedures for testing the equality of population variances. Both normal and non-normal distributions were considered for the two group design with equal and unequal sample frequencies. The results indicated that when population distributions differed only in…

The relative difficulty ratio (RDR) is used as a method of representing test difficulty. The RDR is the ratio of a test mean to the ideal mean, the point midway between the perfect score and the mean chance score for the test. The RDR tranformation is a linear scale conversion method but not a linear equating method in the classical sense. The…

The utility of a non-linear transformation of the criterion is established. The Pythagorean Theorem is used as the example to demonstrate the point. The functional relationships may be such (as in the Pythagorean Theorem) that an R-squared of 1.00 cannot be found without making a non-linear transformation of the criterion. The goal of…

In this paper it is argued that the characterization of mathematical justifications as inductive or deductive is incomplete. Promoting in classrooms the development of and discourse about a third type of reasoning, transformational reasoning, which considers the results of operations on a set of objects, may contribute to mathematics learning in…

This study examined the links students are able to make between formal expressions and situations to which they might refer. Students' understanding of a basic set of transformational rules in elementary algebra sign changes in addition and subtraction expressions with parentheses was assessed, exploring: (1) informal intuitive understanding of…

Most of the multivariate statistical techniques rely on the assumption of multivariate normality. The effects of non-normality on multivariate tests are assumed to be negligible when variance-covariance matrices and sample sizes are equal. Therefore, in practice, investigators do not usually attempt to remove non-normality. In this simulation…

This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…

Using raw-to-scaled-score conversions derived from test-score equating to link item-parameter estimates from the one-parameter (Rasch) and three-parameter logistic models, this study evaluated an indirect method for converting item response theory estimates to a common scale. Data were taken from Petersen's Scholastic Aptitude Test (SAT) scale…

This paper examined the rank transformation approach to analysis of variance as a solution to the Behrens-Fisher problem. Using simulation methodology four parameters were manipulated for the two group design: (1) ratio of population variances; (2) distribution form; (3) sample size and (4) population mean difference. The results indicated that…

Two experiments investigated children's strategies for solving geometric matrices that were correctly or incorrectly completed and that varied in number of elements and number of transformations. Examining the relationship between working memory and item complexity, the first experiment tested 90 boys and girls of 7, 10, and 13 years of age for…