The practical use of such concepts as sets, probability and statistics are considered by many to be vital and necessary to our everyday life. This student manual is intended to familiarize students with these concepts and to provide practice using real life examples. It also attempts to illustrate how the insurance industry uses such mathematic…

This study investigated young children's ability to solve probability problems and studied the cognitive processes proposed by Piaget and Inhelder as necessary to solve probability problems. The effects of tutorial and self-discovery training were measured and discussed. Results from 168 first-graders in five training conditions indicated that:…

These materials are intended to provide meaningful mathematical experiences for pre-algebra students. These experiences emphasize the development of computational skills, mathematical concepts, and problem-solving techniques. This bulletin may be used as the basis for the first term of a one-year course. The complete course is divided into 12…

This document contains three papers from the Methodology Project of the Center for the Study of Evaluation. Methods for characterizing test accuracy are reported in the first two papers. "Bounds on the K Out of N Reliability of a Test, and an Exact Test for Hierarchically Related Items" describes and illustrates how an extension of a…

Multiple matrix sampling of three subscales of the California Psychological Inventory was used to investigate the effects of four variables on error estimates of the mean (EEM) and variance (EEV). The four variables were examinee population size (600, 450, 300, 150, 100, and 75); number of subtests, (2, 3, 4, 5, 6, and 7), hence the number of…

This bibliography is an effort to sort through the mathematical literature that is available. It categorizes the books into the main strands found in most elementary mathematics curricula or scope and sequence charts. Those strands are: sets and numbers; measurement and geometry; and graphs, functions, and probability. These are supplemented in…

THE THEME OF THIS PROGRAM WAS THE USE OF PROBABILISTIC MODELS AS MEASUREMENT TOOLS FOR EXPERIMENTAL DESIGN IN TEST CONSTRUCTION AND FOR ANALYSIS OF TEST DATA. SOME CENTRAL ISSUES IN THIS FIELD ARE DISCUSSED AND RESOLVED IN THE FIRST FOUR CHAPTERS OF THE REPORT UNDER THE FOLLOWING TITLES--(1) CONTRIBUTIONS TO ITEM SELECTION, (2) CLUSTERING…

Presented is a description of the experimental first-year algebra materials "Algebra Through Applications"; a description of the procedure used in evaluating these materials; and recommendations for changes in the materials, implementation, evaluation, and funding. The evaluation indicates that these materials can be effectively used in a variety…

This yearbook is intended to be primarily a highlighting of the essential elements of those basic mathematical understandings which should be continually developed and extended throughout the entire mathematics curriculum. An attempt is also made to illustrate training in mathematical modes of thought, sometimes labeled problem solving or creative…

The question of whether test factor structure is indicative of the test item hierarchy was examined. Data from 1,000 subjects on two sets of five bivalued Law School Admission Test items, which were analyzed with latent trait methods of Bock and Lieberman and of Christoffersson in Psychometrika, were analyzed with an ordering-theoretic method to…

This paper explores the effects of item choice on ability estimation when using a tailored testing procedure based on the Rasch simple logistic model. Most studies of the simple logistic model imply that ability estimates are totally independent of the items used, regardless of the testing procedure. This paper shows that the ability estimate is…

As an alternative to a classical test theory basis for criterion-referenced test construction, it is proposed that a strict item-sampling model be used. The computer's role in such a model is outlined. The assumptions of the model are carefully defined and its properties reviewed. The relationship between mastery criteria and such sampling plans…

Digraphs, graphs and task analysis were used to map out the content structure of a programed text (SMSG) in elementary probability; mathematical structure was operationally defined as the relationship between concepts within a set of abstract systems. The word association technique (WA) and paragraph construction technique (PC) were used to…

A flexilevel test is found to be inferior to a peaked conventional test for measuring examinees in the middle of the ability range, superior for examinees at the extremes. Throughout the entire range of ability, a flexilevel test is much superior to any conventional test that attempts to provide accurate measurement at both extremes. See also ED…

Individualized instruction programs have imposed an increased reliance on tests as a means of selecting and routing students through sometimes complex programs. Testing which occurs within the training sequence is particularly vulnerable to inefficient use of both trainee and instructor time, but computer-based instruction system can provide a…