Curves are considered to have the same shape when they are related by a similarity transformation of a certain kind. This paper extends earlier work on parallel curves to curves with the same shape. Some examples are given more or less explicitly. A generalization is used to show that the theory is ordinal and to show how the theory may be applied…

This study compared four instructional treatments which differed in the degree of individualization and personalization in a computer assisted instructional unit designed to teach the concept of function. The researcher developed two units and adapted the second for four types of feedback: two levels of individualization to incorrect responses and…

This is the second of the six guidebooks on minimum course content for first-year algebra; it includes the ordered field properties of the real number system, solution of linear equations and inequalities, verbal problems, exponents and operations with polynomials. Overall goals for the course are stated; performance objectives for each unit, a…

This is the fourth of six guidebooks on minimum course content for first-year algebra; it includes first degree equations involving absolute value, radicals, various approaches to solving quadratics, and problem solving with quadratics. After course goals are stated, a listing of performance objectives, a course outline, textbook references, and…

This is the first of six guidebooks on minimum course content for first-year algebra; it introduces the language of sets, the fundamental operations and properties of the real number system, the use of variables, and the solution of simple linear equations and inequalities. Overall goals for the course are stated; then performance objectives, a…

Unit 10 in the SMSG's secondary school mathematics series is a student text covering the following topics in Algebra I: factors and exponents, radicals, polynomial and rational expressions, truth sets of open sentences, graphs of open sentences in two variables, systems of equations and inequalities, quadratic polynomials, and functions. (DT)

This twenty-fourth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 23. For each of the chapters in Unit 23, a time allotment is suggested, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, and answers to exercises are provided. In the appendix is a…

Graphs of exotic functions which can be defined using algebraic operations are discussed. (SD)

Examples of the presentation and solution of variations on a common projectile trajectory problem are presented. (BB)

The best predictor for success in Algebra I was found to be the grade in eighth grade math. (KR)

The patterns of the coefficients in the expansion of (x + y +z)n are discussed, and a recursive property is developed as a generalization of the Pascal triangle. (MP)

An alternative development of the quadratic formula via paper squares and rectangles is presented. A physical model is constructed to demonstrate the constant term needed to complete the square. (MP)

An algebra test was constructed within a Piagetian framework. Results of a selection of the test items are given and discussed. (MP)

Difficulties encountered when drawing the graphs of linear equations are discussed. Programs are developed to overcome these and worksheets are given for further practice. (MP)

Allowing students to discover a winning strategy for this game is suggested as a way to introduce modular arithmetic. (MP)