Presents a study that analyzed errors made by randomly chosen fourth grade students (25 of 57) while using the division algorithm and investigated the effect of remediation on identified systematic errors. Results affirm that error pattern diagnosis and directed remediation lead to new learning and long-term retention. (MDH)

Presents the results of a survey of 922 Alabama secondary mathematics teachers' perceived needs for in-service training. Factor analysis produced six factors, with the factors New Knowledge, Teaching Marginal Students, and Computer Use and Knowledge containing the eight most significant needs. The most significant need was for more parent-student…

Presents suggestions for developing algebraic concepts beginning in the early grades to develop a gradual building from informal to formal algebraic concepts that progresses over the K-12 curriculum. Includes suggestions for representing relationships, solving equations, employing meaningful applications of algebra, and using of technology. (MDH)

Describes the three components of an enrichment program developed in Port Angeles, Washington, to improve mathematics and science instruction: (1) classroom instructional units conducted by a certified teacher, (2) teacher inservice sessions to develop teacher skills, and (3) Family Learning Nights to encourage parental involvement. Enrichment…

Describes the Secant Method, a numerical method to approximate solutions to equations for which symbolic solution methods do not apply. Illustrates the method using the EXCEL spreadsheet program. Discusses instructional implications of utilizing this method. (MDH)

Discusses the mathematical pedagogy changes that reflect the constructivist approach exemplified in the National Council of Teachers of Mathematic's "Professional Standards for Teaching Mathematics." As part of the change process, recommends that teachers (1) reflect on their present practices, (2) risk making changes in classroom…

Presents a model of the tutoring process that takes into account the evolving tutor/student relationship and the subject matter concerns that the tutor is helping the student master. Reports illustrative data from case studies from which the model is derived. (15 references) (MDH)

Reports a study to test the hypothesis that intermediate grade teachers (n=96) will reflect an expectation of male success in the scores they assign to students' work in mathematical problem solving. MANOVA involving the variables of student gender, teacher grade level, and teacher gender indicated no gender bias on the part of teachers. (MDH)

Discusses teachers' knowledge and beliefs about mathematics and how mathematics is best taught and learned. Considers interrelationships between beliefs and teachers' classroom practices. Argues that instruction is shaped by teachers' knowledge and beliefs and that meaningful change in instruction will entail fundamental changes in what teachers…

Presents examples of questions and answers arising from a hands-on and exploratory approach to discrete mathematics using cuisenaire rods. Combinatorial questions about trains formed of cuisenaire rods provide the setting for discovering numerical patterns by experimentation and organizing the results using induction and successive differences.…

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

Examined 6 widely used grade-8 standardized tests for content, required processes, and level to determine their alignment with the 5-8 NCTM "Curriculum and Evaluation Standards." Concluded that these tests inadequately covered the 5-8 standards. A follow-up study examined items from newly developed and foreign tests to demonstrate the…

Presents two teaching ideas for mathematics instruction. The first employs "mind maps" as a method to help students learn, record, and recall mathematical information. Provides examples for solving quadratic equations and complex numbers. The second discusses two ways to find the average speed during a trip employing differing constant…

Responds individually to Shoenfeld's objections that Ohlsson, Ernst, and Rees' model is unclear; that the hypotheses about learning are unjustified; that the models have not been tested against extant data; and that it is unclear whom the model models. (MDH)

Discusses problem-solving evaluation methods and describes the development of an instrument to evaluate an individual's problem-solving processes. Provides an example of the instrument. (MDH)