Discusses concerns for mathematics education research on algebra and requestions methods that focus on the Piagetian concept of cognitive obstacles. Suggests the use of computer-based environments to develop the concept of variable and offers research findings indicating that experiences working with variables in LOGO influences student…

Analyzes a classroom lesson in which a student teacher was unsuccessful in providing a conceptually based justification for the standard division-of-fractions algorithms, focusing on the student teacher's beliefs about good mathematics teaching and learning to teach. Attempts to understand why the lesson failed, what it reveals about learning to…

Reports case studies using personal construct psychology and the logic of fuzzy sets to elucidate the content and organization of two elementary school teachers' knowledge of fractions and mathematical pedagogy. Results identified four personal constructions that affected classroom events; knowledge of fractions, general pedagogical knowledge,…

Discusses how technology can fit into a middle school curriculum. Highlights include examples of curriculum development; the Higher Order Thinking Skills program for math; instilling excitement in students; family involvement; the mission statement of the National Middle Schools Association; and a sidebar on early childhood education and school…

Presents the course outline and model of teacher change utilized by the Active and Reflective Teaching in Secondary Mathematics professional development program designed to introduce teachers to current developments in the teaching and training of mathematics. A case study is reported that illustrates and substantiates the initial process of…

Presents a series of five activities that introduce division of fractions through real-world situations. Discusses problems related to resurfacing a highway, painting dividing stripes on a highway, covering one area A with another area B, looking for patterns, and maximizing the result of a division problem. Includes reproducible worksheets. (MDH)

Presents an account of the historical evolution of the definition of variable and the way the concept is currently treated in textbooks. Shares activities to promote student discussion on the use of variables as constants, as quantities that vary, and as parameters. Provides a reproducible worksheet. (MDH)

This article is concerned with the learning of mathematics before the commencement of formal schooling. Describes the experiences of two students from four main sets of data: formal and informal measures of mathematics achievement, the learning environment in the home, and observations during teacher-led sessions concerned with mathematical…

Discusses how a single problem can be utilized to discuss mathematical skills and concepts at several different levels. Presents a problem involving fractions examined at the following four levels according to the abilities of the students: (1) finding solutions; (2) identifying methods for finding solutions; (3) exploring similar examples; and…

Describes activities that use the geometric construction capabilities of the Geometer's Sketchpad computer software to explore triangles. Topics investigated include angle measurement, the sum of the measures of the angles of a triangle and a five-pointed star, triangle classification, and area and perimeter of a triangle. (MDH)

Maintains that U.S. education should not be studied as a single entity. Interviews 44 students to understand how their learning experiences vary across the subjects of mathematics, science, English, and history. Finds that, although instruction revolves around the textbook, it is used differently in each subject. Discusses these patterns of use,…

Proposes three types of supplementary problems to develop students' skill in interpretation of graphically represented data. Eleven examples are presented and solved for the following types of problems: comparison of one quantity to another, comparison of two quantities that each depend on a common parameter, and reasonable data prediction. (MDH)

Presents activities for the K-2, 2-5, 5-6, and 5-8 levels that require students to analyze information graphically. Asks the students to discuss, describe, read, and write about the graphs and the information they contain. Supplies accompanying worksheets. (MDH)

Investigates effects of a manipulative instructional approach and traditional instruction on the achievement of subtraction facts for 4 African-American and 26 white second graders in a rural North Carolina school. Greater gains in achievement of subtraction basic facts occurred with the manipulative instruction approach. Implications for…

Examines the issue of how calculators and computers can best be used in mathematics education. Contends that practicing a procedure is noncognitive and does not produce learning. Suggests utilizing customized computerized tools in schools for getting answers to algorithmic problems instantly, thus allowing teachers to explain and students to…