This book reinforces the outstanding work done by the National Council of Teachers of Mathematics (NCTM) in developing curriculum standards for students in kindergarten through fourth grade by discussing the 13 strands of mathematics and their implications for teachers and parents who work with students. It also provides some suggested resources…

A method of generating common statistical tables using canned statistical computer software is presented. This method allows instructors to provide statistical tables for their students, tailored to their needs. The four most common tables used in elementary college statistics courses are z (standard normal), t, F, and chi square. Specific…

The Course Placement Service of the American College Testing Program (ACT) uses logistic regression to model the relationships between outcomes in standard college courses and placement test scores. The logistic regression results are used together with empirical test score data to obtain estimates of validity statistics (e.g., proportion of…

Taguchi methods are methods of product quality improvement that analyze major contributions and how they can be controlled to reduce variability of poor performance. In this approach, knowledge is used to shorten testing. Taguchi methods are concerned with process improvement rather than with process measurement. This manual is designed to be used…

The relationships among types of errors observed during probability problem solving were studied. Subjects were 50 graduate students in an introductory probability and statistics course. Errors were classified as text comprehension, conceptual, procedural, and arithmetic. Canonical correlation analysis was conducted on the frequencies of specific…

Three methods of factor analyzing dichotomously scored item performance data were compared using two raw score data sets of 20-item tests, one reflecting normally distributed latent traits and the other reflecting uniformly distributed latent traits. This comparison was accomplished by using phi and tetrachoric correlations among dichotomous data…

Mathematical modelling activities related to everyday situations (e.g., traffic lights) can be used to develop probability concepts. (SD)

This study examined how the practice of prepublishing prompts used on the writing section of the Graduate Record Examinations® (GRE®) General Test impacts test-preparation behavior, test performance, test validity, and examinee perceptions of the value of prompt prepublication. Researchers imposed modest experimental control over how participants…

The general question examined by this study was whether the tendency of subjects to ignore the known score in giving the best guess for a sample mean was due to a descriptive heuristic such as representativeness or to a mechanistic one such as active balancing. Two experiments were conducted. In Experiment 1, subjects estimated: (1) the mean of a…

Five sets of activities for students are included in this document. Each is designed for use in junior high and secondary school mathematics instruction. The first is concerned with the use of models in mathematics. The second contains a variety of activities involving polygonal numbers. The third set of activities includes a variety of games for…

The National Assessment of Educational Progress (NAEP), like most large national surveys, employs a complex stratified multistage unequal probability sample. The design provides a rigorous justification for extending survey results to the entire U.S. target population. Developments in the analysis of data from complex surveys which provide a…

The problem of spurious significance in multivariate exploratory research is discussed. When a very large number of statistical tests are performed, many tests will be significant on the basis of chance alone. To counter this problem, the use of two sign tests to analyze sets of results has been suggested; the chance expectation [CE test] assesses…

Few phenomena in psychology have been studied more than reaction time. However, while response latency now provides the basic data for research in many areas of cognitive psychology, little work has been done on the problem of incorporating response latency in the measurement of individual differences. A solution to this problem requires the…

This document contains three modules. The first of these examines applications of algebra to geometry. It is designed to teach students how to algebraically characterize points which may be constructed with a compass and straight edge, and how to use this characterization to obtain classical geometric nonconstructibility results. The second unit…

Decisions to terminate training for subjects involved with discrete trial experiments in discrimination learning should utilize a probability criterion rather than a deterministic criterion. Furthermore, these decisions should be based upon the number of correct and error responses made by the subject, with the decision made to terminate training…