A generative computer-assisted instruction system is being developed to tutor students in analytical geometry. The basis of this development is the thesis that a generative teaching system can be developed by establishing and then stimulating a simplified, explicit model of the human tutor. The goal attempted is that of a computer environment…

Reported are the results of a study which investigated the effect of temporal position of review through two experiments. Experiment I involved one review; Experiment II involved two reviews. In Experiment I, eighth grade students were pretested, presented with the learning task (four rules from algebra and geometry), and randomly assigned to one…

These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics K-6. In view of the experiences of other curriculum groups and of the general discussions since 1963, the present report initiates the next step in evolving the "Goals".…

This guidebook on minimum course content presents a study of the nature and methods of proof, using Euclidean geometry as a model. A more rigorous and formal course than usually offered, it is intended for the student who plans to study advanced mathematics. Overall course goals are specified, a course outline is provided, performance objectives…

This bulletin suggests teaching procedures for a tenth-grade geometry course. An introduction states general objectives and discusses the nature of inductive and deductive thinking. Lesson outlines follow which give a statement of objectives and a plan for development. Major lesson groupings are congruent triangles, parallel lines, quadrilaterals,…

The purpose of the study was to demonstrate that by altering or modifying homework assignments for slow-track high school geometry students, various intellective and emotive variables could be improved without any significant decrease in achievement. Two intact Geometry B classes were randomly assigned to a no-homework treatment where all problems…

This guide provides a structured program for the slow learner in mathematics grades 6-11. Suggestions for implementing the program are included. The guide is divided into the following major areas of mathematical competency: Fundamental Operations, Geometry, Measurement, Graphing, Algebra, Probability and Statistics, and Logic. Recreation is the…

The purpose was to evaluate the effectiveness of a geometry course for preservice elementary teachers and, at the same time, to validate the assumptions that the arrangement of categories in Bloom's "Taxonomy" is hierarchical and cumulative. Sixty-two preservice elementary education majors took an investigator-constructed achievement…

Outlined are the minimum requirements for a quinmester course intended to strengthen a student's experience in a first algebra course, prior to entry to high school geometry and the second algebra course. After a brief description of overall goals and strategies, further details are presented in eight sections. Each section gives performance…

The purpose was to develop a system to describe the extent to which geometry teachers seek to elicit high levels of student thought and to teach the nature of proof. Also investigated was the relationship between a teacher's questioning behavior and the performance of students on a geometry test. A total of 35 tape recordings were made of 15…

This document is the report of a curriculum writing session, and covers three activities: (1) a textbook for grade seven, written using the outlines produced the previous year (SE 012 735), was reviewed and criticized; (2) the outlines for grades eight and nine, also produced the previous year, were completed in greater detail; and (3)…

This is a collection of 24 papers presented or prepared by participants of the Comprehensive School Mathematics Program (CSMP) International Conference in 1970 covering a wide range of topics in mathematics and geometry education. Conference recommendations are summarized, including the use of geometry to lead into other branches of mathematics…

This is a set of 8 x 11-inch cards containing ideas for manipulative materials, generally inexpensive household items, for use in the elementary classroom. The cards are tab-indexed into seven categories: sets (which is subdivided into set recognition and set operations), number-numerals, geometry, measurement, probability, number theory, and…

Three approaches used in the analysis of semantic differential data to determine similarity in meaning between profile ratings on concept pairs are discussed. These approaches are: (1) to compute mean scores on each scale for each concept and to compare concepts on a scale-by-scale basis; (2) to form mean scores on each dimension for each concept…

This booklet describes a one year college course for students in the lower half of the mathematics ability range. The main aim of the course is to "provide the students with enough mathematical literacy for adequate participation in the daily life of our present society." A second aim is remedial, to allow a student to continue with…