A two-part communication model for teaching elementary mathematics is proposed. Part I delineates symbols commonly used in teaching arithmetic. Parts of mathematical language (mathematical objects, relations, operations, expressions, and sentences) are compared to analogous parts of the English language. Part 2 is a conceptualization of strategies…

A set of 11 teacher-prepared Learning Activity Packages (LAPs) in beginning algebra, these units cover sets, properties of operations, operations over real numbers, open expressions, solution sets of equations and inequalities, equations and inequalities with two variables, solution sets of equations with two variables, exponents, factoring and…

Methods of instruction and organization are discussed in the first chapter, including critiques of the Winnetka plan and the Dalton plan. The next author argues that algebra is a method of thinking and explains some mental processes involved. The following three chapters are concerned with the functional concept. Using function as a unifying…

Mastery learning is an approach to learning whereby students are expected to demonstrate competence of one level, or unit, of learning objectives before advancing to the next level. Most junior college instruction is group-paced, with the instructor determining the rate with which units are presented. One compromise between existing instruction…

Design techniques for generative computer-assisted-instructional (CAI) systems are described in this report. These are systems capable of generating problems for students and of deriving and monitoring solutions; problem difficulty, instructional pace, and depth of monitoring are all individually tailored and parts of the solution algorithms can…

The programs in these three booklets are designed to demonstrate how the computer can be applied to the problems of many disciplines. The problems and the corresponding computer programs are, for the most part, quite simple and are designed to be "jumping-off points" for students from the high school level up. Programs include one or more from…

Argues that the use of computer technologies in secondary schools should change the nature of mathematics education. Urges the rethinking of the uses of traditional paper-and-pencil computations. Suggests some computer applications for elementary algebra and for problem solving in arithmetic and calculus. (TW)

Reports on the progress of a project designed to establish both a research agenda for mathematics education and a conceptual framework for such an undertaking. Describes four conferences which have been organized to consider teaching problem solving, effective teaching, teaching and learning algebra, and middle school number concepts. (TW)

This study investigated the predictive validity of the Descriptive Tests of Mathematical Skills (DTMS) and the SAT-Mathematics (SAT-M) tests as placement tools for entering students in a small, liberal arts, historically black institution (HBI) using regression analysis. The placement schema is four-tiered: for a remedial algebra course, college…

We studied experts' solving methods and analyzed the nature of mathematical knowledge as well as their efficiency in algebraic calculations. We constructed a model of the experts cognitive functioning (notably teachers) in which the observed automatisms were modeled in terms of schemes and instruments. Mathematical justification of transformation…

This research examines students' ability to work with algebraic variables and their notations as a result of the type of instruction they received, and places their work on scales that illustrate its location on the continuum from arithmetic thinking to algebraic reasoning. It presents data from pre- and post-instruction clinical interviews…

There is evidence that structured cooperative logic is an effective way to introduce or reinforce mathematics concepts, explore thinking processes basic to both math and science, and develop the important social skills of cooperative problem-solving. This book contains a number of cooperative logic activities for grades K-4 in order to improve…

Mastering mathematics has become more important than ever in the United States. Students with a strong grasp of mathematics have an advantage in academics and in the job market. The eighth grade is a critical point in mathematics education. Achievement at that stage clears the way for students to take rigorous high school mathematics and science…

The goal of this series of guides is to show Texas educators what components of the Texas Essential Knowledge and Skills (TEKS) curriculum are eligible for testing on the Texas Assessment of Academic Skills (TAAS) and end-of-course tests. This guide contains information for the end-of-course tests administered for the following subjects: Algebra…

This report examines performance differences between Asian, Black, Hispanic, and White students in Delaware on the mathematics portion of the Third International Mathematics and Science Study-Repeat (TIMSS-R). Data analyses show that the mathematics performance gap across ethnic groups is significant. The lowest 100 Black and White performers were…