Presents a program for the Apple II computer that teachers can use for exam questions and homework assignments. Prints out all cubic polynomials whose roots, maximum and minimum points, and points of inflection are all integers. (MVL)

Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)

Presents an interview with Dr. Constance Kamii on mathematics education. Based on her beliefs about the constructivist approach to elementary arithmetic, she advocates: reformulating goals and objectives, reconceptualizing the teacher role, de-emphasizing competition, eliminating workbooks, and relying instead on a curriculum made up predominately…

Presents the portion of a larger study of A-level British students understandings of calculus that deals with ambiguities inherent in the phrases "tends to,""approaches,""converges," and "limit." Responses to two questionnaires indicate that the four phrases generate everyday connotations that are at odds…

Highlights combinatorial problems appropriate for students aged 4 to 12 years that utilize manipulatives in a hands-on approach. Examines and identifies students' strategies and self-monitoring techniques that produce effective problem solving. (MDH)

Discussed is the importance of students being able to read and understand mathematics. The need for students to practice reading mathematics is emphasized. Discussions and homework are presented as examples of this needed practice. (KR)

The idea that studying part-whole number relationships can foster a better understanding of number concepts, addition, subtraction, fractions, decimals, ratios, and percentages depending on the age of the student is discussed. Activities that incorporate number relationships and representations are presented. (KR)

A study interviewed 6 grade-6 students after participation in 21 lessons on basic concepts of fractions and decimals to determine how different children construct rational number concepts. Discussed the formation of the key concept of equivalent fractions based on student responses to interview questions. (MDH)

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)

Describes a step-by-step procedure that enables teachers to develop lessons that effectively use software or special calculators in the classroom. Problem-solving strategies and questions are determined that correspond to the technology through which students are able to construct their own knowledge. Illustrates the procedure using spreadsheets,…

Explores the concept of extraneous roots in radical equations using an alternative to traditional algebraic methods. Using calculator- or computer-based graphs, accounts for extraneous roots by examining the four possible cases of systems of equations that can produce the solution to the radical equation. (MDH)

Examined gender differences in the mathematics performance of high-achieving fourth and sixth graders, noting the effects of ethnicity. Scores from 1996 California Achievement Tests indicated that students in both grades showed significant gender differences. There were no interaction effects of gender by ethnicity. There were inconsistent racial…

This article describes an approach to teaching linear equations using multiple representations in a highly motivating context. Connections among representations are made explicit to enhance understanding and empower students. (Contains 4 figures.)

The purpose of this study was to examine the effects of actively categorizing math problems on the math problem solving performance of students with and without attention deficit disorder (ADD). To this purpose, 52 fifth and sixth grade students were involved in actively categorizing or noncategorizing (control) tasks followed by two problem…

A postal survey was conducted regarding statistical techniques, research methods and software used in the workplace by 913 graduates with PhD and Masters degrees in the biological sciences, psychology, business, economics, and statistics. The study identified gaps between topics and techniques learned at university and those used in the workplace,…