This paper is a discussion of algebraic factoring. It is suggested that factoring is frequently presented in textbooks and by teachers without specifying one of the great values of this technique; that is, finding some of the factors of any number that can be generated by a particular polynomial. Concrete examples can help students understand the…

Tracing the history of algebra within the U.S. secondary curriculum requires at the same time a review of the various reform movements relevant to secondary education, an acknowledgement of the sociological, political, and psychological perspectives driving these reforms, and most importantly, the perceived role of mathematics in the education of…

This document was initiated with the collection of 150 questions in telephone interviews of a national sampling of junior high school and high school teachers. A Mathematics Consultant Panel reviewed the questions, and selected topics were developed, for which there were research bases for answers. The material covers: (1) Effective Mathematics…

Three sequences of coursework are detailed in the curriculum development guidelines provided in this document. The 4-year sequence, structured around problem-solving, applications, and the acquisition of theory, is designed for the college-bound student who plans to enter a mathematics-based field of study. The 3-year sequence is designed for…

This textbook is first in a series of three volumes presenting a mathematics course for junior high school and six-year high schools. This volume covers arithmetic related to home, store, farm, industry, and bank; intuitional and constructive geometry; and introduces algebra. [For Book II, see ED623225. For Book III, see ED623226.]

This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…

In Experiments 1 and 2 subjects read a series of standard algebra story problems, and were asked to recall each problem. In Experiment 3, subjects were asked to construct problems based on certain situations (such as "train leaving stations"). Results indicated that "relational propositions" (such as "the rate in still…

To determine the effects of videotape supplements to the programmed instruction used in developmental mathematics at Danville Community College (Virginia), videotapes and supplements (study time record, instructions, flow chart, prefatory information, index of tapes, objectives, exercises, and summary) were produced for four units of Algebra I.…

This publication is the teachers' manual, level 9, of the Instructional Support Systems (ISS) Program, which was developed by the Community School District 18 of New York. The curriculum was designed to fulfill the requirements established by the New York State Board of Regents for the Algebra I course. Two sequences of modules are suggested, for…

This research addressed itself to the development of a novel teaching-learning scheme for non-trivial, first-degree equations in one unknown, based on an analysis of the notions and misconceptions of junior high students. The approach was tried in a "teaching experiment" involving six case studies of students of various abilities in…

THIS IS A SOURCE MANUAL TO ASSIST TEACHERS OF PROGRAMED ALGEBRA IN PROVIDING FOR INDIVIDUAL DIFFERENCES AMONG STUDENTS. THE MATERIAL WAS INTENDED FOR ASSIGNMENT TO SELECTED STUDENTS WHO REQUIRE ADDITIONAL MATERIALS TO SATISFY VARIOUS ABILITIES AND TALENTS. IN ADDITION TO REFERENCE LISTS ON FILMS AND FILMSTRIPS, PRINTED BIBLIOGRAPHIES WERE PREPARED…

Freshmen at a large suburban high school were given a questionnaire about their attitudes toward tracking or ability grouping. From the 867 students, 50 were randomly selected from each of four levels in the tracking system: honor algebra, regular algebra, fundamentals of algebra, and general mathematics. The majority of students at each level…

The focus of this paper is on the use of frames in achieving understanding of learning and problem solving in school mathematics. The paper seeks to illustrate the use that has been made of frames and frame-like conceptions and to add to the case for the usefulness of such conceptions. Results reported are: (1) those related to more sequential…

Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra I. Topics covered include: sets; vocabulary; linear equations; inequalities; real numbers; operations; factoring; fractions; formulas; ratio, proportion, and…

A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…