A DESCRIPTION IS GIVEN OF ITEM SAMPLING, OR "PSYCHOMETRIC-STATISTICAL INFERENCE," AN APPROACH TO GATHERING AND USING EDUCATIONAL DATA THAT ALLOWS STATISTICAL INFERENCES TO BE MADE SIMULTANEOUSLY WITH PSYCHOMETRIC INFERENCES. THIS IS A PROCEDURE IN WHICH BOTH PEOPLE AND ITEMS ARE SAMPLED AND THE DATA FROM A SAMPLE OF PEOPLE TAKING A SAMPLE OF ITEMS…

A HETEROGENEOUS SAMPLE OF 246 FOUR-YEAR COLLEGES AND UNIVERSITIES REQUIRED ALL ENTERING FRESHMEN TO FILL OUT A SHORT INFORMATION FORM WITH REGISTRATION MATERIALS. THE 76,015 MALES AND 51,100 FEMALES GAVE INFORMATION ON FATHER'S OCCUPATION, FATHER'S EDUCATION, AND HIGH SCHOOL GRADE AVERAGE. A STUDY OF THE DATA SUGGESTS THAT THREE INFLUENCES, IN…

In 1979-80, the Arkansas minimum competency tests were administered to a sample of 5,000 students in grades 3, 6, and 8. To determine how well test objectives matched the curriculum, their teachers estimated how many of the four items per objective a randomly selected student would answer correctly. Because chi square test comparisons of teacher…

This teacher's guide to probability and statistics contains three major sections. The first section on elementary combinatorial principles includes activities, student problems, and suggested teaching procedures for the multiplication principle, permutations, and combinations. Section two develops an intuitive approach to probability through…

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the history of the number pi; (2) what's new about pi; (3) the number pi; (4) pi and probability; and (5) from the…

This is volume three of a three-volume set for teachers using SMSG junior high school text materials. Each unit contains a commentary on the text, answers to all the exercises, a copy of the questionnaire used for evaluating the material, and a summary of comments by the teachers using the text. Unit topics include: (1) what is mathematics; (2)…

This booklet, one of a series, has been developed for the project, A Program for Mathematically Underdeveloped Pupils. A project team, including inservice teachers, is being used to write and develop the materials for this program. The materials developed in this booklet include (1) the meaning of probability, (2) counting outcomes, (3) mutually…

This publication is a response to the need expressed by elementary teachers for a concise introduction to intuitive probability concepts and how they may be presented. Instruction is divided into five concept groups including: (1) basic understandings; (2) the probability of simple events; (3) the probability of compound events; (4) counting; and…

Models proposed by Cleary, Thorndike, Cole, Linn, Einhorn and Bass, Darlington, and Gross and Su for analyzing bias in the use of tests in a selection strategy are surveyed. Several additional models are also introduced. The purpose is to describe, compare, contrast, and evaluate these models while extracting such useful ideas as may be found in…

This guide is the sixth in a series of publications to assist teachers in using a laboratory approach to mathematics. Twenty activities on probability and statistics for the elementary grades are described in terms of purpose, materials needed, and procedures to be used. Objectives of these activities include basic probability concepts; gathering,…

The true state of the system described here is characterized by a probability vector. At each stage of the system an action must be chosen from a finite set of actions. Each possible action yields an expected reward, transforms the system to a new state in accordance with a Markov transition matrix, and yields an observable outcome. The problem of…

To determine if Rasch Model procedures have any utility for equating pre-existing tests, data from the equating phase of the Anchor Test Study (ATS) were reanalyzed. This management report summarizes the work completed in the project, describes the differences in this project and that of the ATS, and presents recommendations and conclusions to the…

In some educational research studies--particularly longitudinal studies requiring a probability sample of schools and spanning a wide range of grades--it is desirable to so select the sample that schools at different levels (e.g., elementary and secondary) "correspond." This has often proved unachievable, using standard methods of selecting school…

One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…

Digraphs, graphs, and task analysis were used to map out the content structure of a programed text (SMSG) in elementary probability. Mathematical structure was defined as the relationship between concepts within a set of abstract systems. The word association technique was used to measure the existing relations (cognitive structure) in S's memory…