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)

Algebridge, the first phase of a University of Arizona project (PRIME) to promote higher education among minority middle school students, makes algebra more accessible by smoothing students' transition to abstract thinking and pinpointing potentially frustrating concepts. The program helps at-risk youngsters dispel their fear of math and clear the…

Most mathematics anxiety has its roots in the teaching and teachers of mathematics. Because people generally are not math anxious before going to school, an examination of the previous statement proves to be well founded. This article reviews the literature and discusses different ways that teachers may help to prevent their students from becoming…

Small group instruction was assessed in a naturalistic study involving 206 observations of mathematics periods in 33 classrooms of grades 4, 5, and 6 in 21 schools. Six types of group instruction were identified, and teachers' use of such groups was explored. (SLD)

The costs, effects, and utility of mathematics instruction assisted by microcomputer presentations were compared with those of conventional classroom approaches, using 79 students in grades 3 and 5. Results indicate that grouping students for instruction on microcomputers in classrooms is cost effective. (SLD)

Nineteen special educators implemented Curriculum-Based Measurement with a total of 36 learning-disabled math pupils in grades 2-8 to examine the effects of goal line feedback. Results indicated comparable levels and slopes of student performance across treatment conditions, although goal line feedback was associated with greater performance…

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)

Presents the framework for a chemical engineering course using ordinary differential equations to solve problems with the underlying strategy of concisely discussing the theory behind each solution technique without extensions to formal proofs. Includes typical class illustrations, student responses to this strategy, and reaction of the…

Seven secondary teachers of 57 students with learning disabilities used a videodisc program to teach fractions. Teacher and student reactions were very positive, almost two-thirds of the students reached or exceeded criterion performance, and teaching styles of participating teachers subsequently became more interactive. (JDD)