This program is designed to enable students to master the competencies and skills which reflect the learning goals and objectives developed by the Illinois State Board of Education. This document lists the learning objectives by grade level and reporting period for kindergarten through grade three. Topics included are arithmetic, measurement,…

Development of geometric congruence and motion was studied through tasks that tapped transformational imagery, correspondence matching, measurement operations, and transformation combinations. Results showed even the youngest children studied could generate strategies for verifying congruence. The dominant strategy in younger children was edge…

A questionnaire with 70 closed and 10 open questions was administered to 230 students enrolled in grades 9 through 12, the majority of whom were enrolled in Math 10 geometry courses. Aspects of the questionnaire dealt with: (1) attributions of success or failure; (2) students' comparative perceptions of mathematics, English, and social studies;…

This is the Teacher's Commentary for the Supplementary Units for Junior High School Students. Included in the Commentary are background material for teachers, suggestions for instruction, and answers to student exercises. Also included are comments on how to use the materials with different types of students and time needed for instruction. (RH)

This text was written under the auspices of the School Mathematics Study Group (SMSG) as a means for preparing teachers to teach the SMSG text Mathematics for Junior High School, Volume I. Included throughout are comments on suggested methods of presenting material to seventh graders. In this text, class exercises are interspersed throughout, with…

A particular shot on a pool table is analyzed using the concept of similar triangles, to introduce the equivalence of the "incident-reflection" principle and the "minimum-distance" principle. (CR)

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…

This research involved the observation and audio-recording of 30 ninth-grade mathematics students recommended as being outstanding by their mathematics teachers. Each student was presented with five different problem situations for which he or she was to make mathematical conjectures. During the interview, the students thought aloud and all of…

The application of the programmable calculator to evaluating complicated formulas is illustrated by considering the formula for finding the area of any triangle when only the lengths of the three sides are known. Other advantages of the programmable calculator are discussed such as freeing the student to explore more challenging problems and…

THE "DEMONSTRATION PROJECT" DESCRIBED IN THIS REPORT REPRESENTED A MAJOR PART OF THE ACTIVITY OF THE SYRACUSE UNIVERSITY-WEBSTER COLLEGE "MADISON PROJECT," BEGINNING IN SEPTEMBER, 1961, AND EXTENDING THROUGH THE SUMMER OF 1967. THE GOALS AS CONCEIVED BY THE MEMBERS OF THIS PROJECT WERE (1) TO CREATE EXPERIENCES IN MATHEMATICS…

TWO EXPERIMENTS WERE CONDUCTED TO ANALYZE THE SPECIFIC EXTERNAL FACTORS THAT CONTRIBUTE MOST SIGNIFICANTLY TO STUDENT LEARNING. THE THREE HYPOTHESES TESTED WERE--(1) LEARNING IS INCREASED WHEN AN EXPERIMENTER ACTIVELY AUGMENTS THE PROGRAM BY REPHRASING PROGRAM STATEMENTS AND BY BRANCHING THE STUDENT TO DIFFERENT PARTS OF THE PROGRAM WHEN THE…

This is a supplementary SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include sets, projective geometry, open and closed paths, finite…

This basic mathematics course is composed of eight lessons. Each lesson contains a pre-test and post-test, problems and examples oriented toward water and wastewater operations, suggested supplemental readings, and estimated time for completion. The topics of the lessons are: (1) numeration; (2) whole numbers; (3) fractions; (4) decimals; (5)…

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include points, lines, space, planes, segments, separations, angles, one-to-one correspondence,…