Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)

Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (MDH)

Discusses prerequisites that help students develop multiple strategies for solving problems as recommended in the National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards." Presents two examples of activities involving addition, subtraction, and permutations that promote multiple strategies. Suggests ways to…

Reports results of interviews in which students were asked to illustrate three interpretations of fractions: a unit subdivided into equal-sized parts; a set subdivided into equal-sized parts; and a ratio. Two areas of difficulty in giving reasonable representations are discussed. Proposes teaching suggestions to overcome these difficulties. (MDH)

Discusses "connectionism," an alternative learning model wherein meaning resides in the function of the whole state of a network, rather than being localizable in certain symbols or areas. Topics discussed include integration with other learning models; the culture of the mathematics classroom; and characteristics of alternative…

Interviewed six students from each of four secondary mathematics teachers to investigate the influence of teachers' views concerning error making in mathematics on the children's image of mathematics. Results indicated strong links between teachers' images and the images of their students. (15 references) (MDH)

Discusses the use of the computer software MINITAB in teaching statistics to explore concepts, simulate games of chance, transform the normal variable into a z-score, and stimulate small and large group discussions. (MDH)

Describes the use of three computer tools used to enhance the teaching and learning of algebra: the spreadsheet, LOGO, and computer algebra tools. Examines the strengths of each tool and presents practical considerations for their use. (MDH)

Discusses the surprising result that the expected number of marbles of one color drawn from a set of marbles of two colors after two draws without replacement is the same as the expected number of that color marble after two draws with replacement. Presents mathematical models to help explain this phenomenon. (MDH)

Describes the Microworld Chance, a simulation-oriented computer environment that allows students to explore probability concepts in five subenvironments: coins, dice, spinners, thumbtacks, and marbles. Results of a teaching experiment to examine the effectiveness of the microworld in changing students' misconceptions about probability are…

Reviews chapters of this book on probability in mathematics education. Topics discussed in the chapters include a historical perspective of probability, an epistemological perspective of probability, an overview of the psychological research on probability learning, computers in probability education, and an analysis of the probability curriculum.…

Discusses a methods course for preservice mathematics teachers that addresses the affective side of learning mathematics. Students are encouraged to reflect on their experiences in relation to themselves as learners, teachers, and mathematicians. (MDH)

Discusses a pedagogical approach to calculus based on the question: What kinds of problems should students be able to solve? Includes a discussion of types of problems and curriculum threads for such a course. Describes a projects-based calculus with examples of projects and classroom activities. (Author/MDH)

An examination of constructivist learning and teaching theory and its current popularity looks at previously popular theories, implementation problems, classroom experiments using constructivism, and the roles of teacher and learner under this approach. Discussion is confined to mathematics instruction and the mathematics classroom. (Author/MSE)

Describes a three-day course offered by British consultants to train key education officers and teacher advisor-trainers in Botswana in observational and interaction skills as part of an effort to improve primary education in the country. Details the instructional content of each day of the course devoted to ice-breaker activities, math…