This document is a progress report on the implementation of the recommendations of the Commission on Mathematics regarding the teaching of mathematics in secondary schools. Data were obtained from a survey of about 38,000 students who represented more than 7,500 secondary schools in the United States and who took College Board Achievement tests…

This document is a reprint of the geometry section from the 1954 syllabus Mathematics 10-11-12, An Integrated Sequence for the Senior High School Grades. The text outlines a tenth year geometry course integrated with arithmetic, algebra, and trigonometry, which progresses from an informal to a formal level. The topics suggested include definition,…

Two approaches to teaching college algebra were evaluated to determine their effectiveness in achieving the objectives of college algebra in the industrial technology curriculum. The null hypothesis of no significant difference in the effectiveness of the traditional approach to teaching college algebra and an experimental approach was…

This basic guide to a complete secondary mathematics curriculum is designed to ensure that each student will be presented uniform mathematical concepts and principles, geared to his individual needs, abilities, and interests. The guide is not planned for use with a particular textbook; instead, it is to serve as a core around which each teacher…

Strategies for problem solving are discussed in the first chapter in Unit 10 of this SMSG series. The second chapter covers the following algebra topics: solving simple equations and inequalities, simplifying expressions, solving fractional equations and solving inequalities involving fractions, factors whose product is zero, and factoring. See SE…

This study was undertaken to test the findings of Dienes and Jeeves concerning the strategies used by students to learn mathematical structures. The study also proposed to determine whether students are consistent across structures and embodiments in the strategies they use and the evaluations they give. One hundred adolescent girls were given…

The second in a series of three workbook texts on beginning algebra. Designed primarily for use by lower ability mathematics students, the texts have been used by average ability students as supplementary materials. Volume 2 contains material on operations, variables and phrases, equations, exponents equivalent phrases, terms, and adding like…

Twenty-six structural variables were defined and investigated using a set of algebraic word problems solved by 96 college students. The study attempted to identify a small independent well-defined set of arithmetic, linguistic, and algebraic structural variables which account for a maximum amount of the variance of the observed probability correct…

The aim of this report is to suggest aspects of mathematics education that should be incorporated into curricula rather than to outline specific courses of study. General recommendations are made regarding curriculum, instructional methods, and textbooks. The suggestion that graphs and relations to be used as a unifying theme is followed by…

The purpose of this study was to confirm or deny Carry's findings in an earlier Aptitude Treatment Interaction (ATI) study by implementing his suggestions to: (1) revise instructional treatments, (2) improve the criterion measures, (3) use four predictor tests, (4) add time to criterion measure, and (5) use a theoretical model to identify relevant…

This is the second volume of a series produced by the State Education Department of the University of the State of New York. Mathematics objectives and sample items included were originally developed by four local school districts and are not intended to be official or comprehensive, but an aid to teachers in constructing curricula and making…

This is the third volume of a series produced by the New York State Education Department. Originally developed by four local school districts, the mathematics objectives and sample items included were not intended to be official or comprehensive but rather to be used as an aid to teachers in constructing curricula and in making classroom goals…

This is volume five of a series produced by the New York State Education Department. Originally developed by four local school districts, the mathematics objectives and sample items are not intended to be official or comprehensive, but to be an aid to teachers in constructing curricula and in making classroom goals clear and precise. The document…

This eleventh unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 9. First a general overview of the entire FIRST COURSE IN ALGEBRA (Units 9 and 10) is provided. Then, a time allotment for each of the chapters in Unit 9 is suggested. For each of the chapters in Unit 9, the goals for that chapter are discussed,…

This twelfth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 10. For each of the chapters in Unit 10 the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are provided, the answers to exercises are listed, and sample test questions for that chapter are suggested.…