As a learning theory, constructivism describes knowledge as being in flux--where an individual internally constructs knowledge through social and cultural mediation. Constructivist learning theorists contend that social activity and discourse must play important roles in order for understanding to occur. This paper describes how the social…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 6-8, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, exponents, fractions, pre-algebra, algebra, geometry, number theory, set theory, ratio, proportion, percent, probability,…

This paper illustrates a different conception of arithmetic, an arithmetic with reasons as well as rules. This arithmetic includes making connections between different representations and making sense of rules as well as using them. It provides a foundation for "Algebra the Web of Knowledge and Skill" in the sense that algebra can be…

Discusses social and intellectual factors in medieval Italian algebra; problems and methods, including operating on the unknown, quasi-equation problems, and giving-and-receiving problems; and the scope of algebraic methods. Considers implications for teaching. (43 references) (MKR)

Discusses features of the Algebra Project, whose goals include a minimum standard of mathematical literacy for minority students and strong community involvement. (MKR)

This report describes the success of the LaHarpe (Illinois) Community Unit School District in raising student math scores on the Illinois Goal Assessment Program (IGAP). Low IGAP test results and faculty dissatisfaction with scores precipitated the school district to modify the content and delivery of math instruction based on student needs…

Introduces the use of the game Battleship to study the system of equations and the distance formula. (ASK)

These excerpts from the National Council of Teachers of Mathematics (NCTM) Standards support the Third International Mathematics and Science Study (TIMSS) Resource Kit by offering some context for discussing the teaching of algebra and geometry seen in the videotapes that are also part of the kit. The Standards describe the mathematics content…

This volume contains the full text of 2 plenary papers and 26 research reports. In addition, brief, usually one-page, reports are provided for 6 discussion groups, 10 technology focus groups, 7 symposiums, 7 oral presentations, and 17 position sessions. The two full plenary reports are: (1) "Problems of Reification: Representations and…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for curriculum…

Reports on progress in incorporating equity indicators into curriculum development and program-evaluation design with specific reference to the completed program evaluation of the Hawaii Algebra Learning Project. Contains 18 references. (DDR)

Explains the cooperative learning technique of jigsaw. Details the use of a jigsaw lesson for explaining complex numbers to intermediate algebra students. Includes copies of the handouts given to the expert groups. (Author/ASK)

Presents examples of word problems that can be used to illustrate the distributive property for preservice teachers. Includes examples involving extended sums, volume, area, prealgebra, place value, long multiplication, fractions, decimals, and algebra. (MDH)

This collection of four papers deals with problem solving and the measurement of problem solving. "Climbing Up the Competence Ladder: Some Thoughts on Meaningful Assessment of Problem-Solving Tasks in the Classroom" by K. C. Cheung uses the metaphor of a competence ladder to represent the problem-solving continuum with progressive…

Described are the difficulties in translating word sentences between English and Algebra. Two classic sentences that typically produce student errors are presented with explanations that can be shared with the students on overcoming these translation difficulties. (MDH)