The Comprehensive School Mathematics Program (CSMP) is described as a complete elementary mathematics curriculum that provides a natural place for probability and statistics. The CSMP approach of innovative, pictorial techniques is summarized here, with emphasis on methods and activities seen as proven successful through the enthusiastic reception…

This work studies the difficulties children have solving two-step word problems of a given structure (e.g., 7 lollypops/2 chocolate bars X 6 chocolate bars). Thirty-six children between the ages of 9 and 14 years were individually observed solving problems of the above type. Other tasks, repetition of the problem and model recognition, were used…

The effects of negative instances on the acquisition of the mathematical concepts of commutativity and associativity were examined. Also investigated were possible transfer effects that might result from the use of negative instances. For 64 ninth-grade subjects, results favored the treatments containing mixed instances and supported the transfer…

This article is a continuation of SE 514 442. The use of learning hierarchies in analyzing and planning changes in the teaching of mathematics is discussed. (SD)

Noting that ratios can be used to great advantage in scoring informal reading tests, such as the cloze procedure and the informal reading inventory, this paper explains the procedures for calculating cross-ratios and percentages when computing scores for informal reading assessments. Examples are provided for using ratios to determine scores for…

A group is viewed to be one of the simplest and most interesting algebraic structures. The theory of groups has been applied to many branches of mathematics as well as to crystallography, coding theory, quantum mechanics, and the physics of elementary particles. This material is designed to help the user: 1) understand what groups are and why they…

This paper, presented at the 1979 meeting of the American Educational Research Association (AERA), investigates student errors in high school mathematics. A conceptual framework of hypothetical information-handling processes such as procedures, frames, retrieval from memory, visually-moderated sequences (VMS sequences), the integrated sequence,…

Instructors in 14 Navy electronics "A" schools (12 basic core and 2 advanced) were presented with a list of 70 mathematical skills and asked to indicate: (1) how important they were to successful school performance, and (2) whether they were prerequisite, reviewed, or taught in the "A" schools. They were also asked to state the number and type of…

This paper reviews literature related to two questions: (1) How do preschoolers acquire numerical concepts? (2) What range of basic numerical knowledge do beginning kindergarteners possess? The first section briefly highlights main ideas of learning theories. The second section discusses Piaget's concept of conservation of number and how young…

The Materials in this bulletin indicate suggested teaching procedures needed to implement the teaching of "mathematics, 9th Year" as outlined in Curriculum Bulletin No. 3, 1958-59 series, Course of Study Mathematics 7-8-9. Whereas the course of study suggests the application of mathematical principles such as commutativity,…

Information is provided on the methods, rationale, and tests used by PMDC investigators to obtain data on the status of first and second graders during the first five weeks of the school year. Instruments to assess general intelligence, cognitive mathematical concepts and skills, socioeconomic status, and school environment of students from seven…

In Fall 1975, PMDC investigators administered a battery of tests to 185 first graders and 152 second graders to assess children's progress in acquiring mathematical concepts and skills during the beginning school years. Two tests were constructed by PMDC and this document reports item statistics and results from these tests; copies of the tests…

This document contains 15 case studies developed by the group teachers during a teaching experiment. Background information on each second grader, behavior and achievement characteristics, and analyses of the evaluation interviews are presented. (MS)

The author investigates elementary school students' performance when solving selected open distributive sentences in relation to three factors (Open Sentence Type, Context, Number Size) and identifies and classifies solution methods attempted by students and students' errors in performance. Eighty fifth-grade students participated in the…