Reports that students entering an urban state college still had high remedial placement rates even though they successfully completed college preparatory math and English courses in high school. Discusses the "chain of blame" and concerns regarding the rigor of high school programs. (Contains 45 references.) (AUTH/NB)

Describes changes that are being made in mathematics teachers' subject studies in order to provide students with sufficiently deep knowledge of mathematics and science and with present-day expertise in their profession as teachers. Provides an abstract algebra course as the ultimate example of a pedagogical experiment where co-operative learning…

Presents seven mathematics games, located on the World Wide Web, for elementary students, including: Absurd Math: Pre-Algebra from Another Dimension; The Little Animals Activity Centre; MathDork Game Room (classic video games focusing on algebra); Lemonade Stand (students practice math and business skills); Math Cats (teaches the artistic beauty…

Much of modern mathematical research requires a serious level of commitment and ability on the part of the researcher and, as a natural consequence, precludes any real involvement by undergraduate mathematicians. However, to put it crudely, Computer Algebra Systems, can make experts of us all. With the use of such systems even the average…

This article describes a unit of instruction designed to promote a conceptual understanding of area in sixth-grade students. Students used benchmarks to estimate the areas of real houses and calculated the areas of houses based on building plans. (Contains 7 figures.)

A three-stage model for algebraic word problem solving is developed in which students' understanding of the intrinsic logical structure of word problems is strengthened by connecting real-life problems and formal mathematics. (Contains 3 figure.)

This article discusses relationships between the development of an understanding of algorithms and algebraic thinking. It also provides some sample activities for middle school teachers of mathematics to help promote students' algebraic thinking. (Contains 11 figures.)

This article describes three engaging introductions for topics on a Cartesian graph and the distributive property. (Contains 3 figures.)

In early algebra students often struggle with equation solving. Modeled on Streefland's studies of students' own productions a prototype pre-algebra learning strand was designed which takes students' informal (arithmetical) strategies as a starting point for solving equations. In order to make available the skills and tools needed for manipulating…

A key element in educational reform has been to increase mathematical proficiency. We look at how five urban high schools with virtually all low-income, minority, and immigrant students have arranged for students to take algebra I, and we examine the course enrollments and grades of these student in the core college prep courses. Both preparation…

This article addresses the enhancement of the learning environment by using Java applets in the mathematics classroom. Currently, the first year mathematics program at the United States Military Academy involves one semester of modeling with discrete dynamical systems (DDS). Several faculty members from the Academy have integrated Java applets…

Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

The paper's aim is to note a remarkable (and apparently unknown) relation for right triangles, its generalisation to arbitrary triangles and the possibility to derive these and some related relations by elimination using Groebner basis computations with a modern computer algebra system. (Contains 9 figures.)

A mathematician's work consists of proving theorems, calculating, and making mathematics understandable. An assistant for all three components is a Computer Algebra System. We describe and discuss various CAS-assisted processes for proving theorems, and discuss the constraints which can appear regarding efficiency, confidence in the result and…

This paper extends and develops theories of mathematical learning to provide a framework for the analysis of classroom video data of students working at a computer in a task aimed at increasing understanding of multiple representations of quadratic functions. Student interactions are coded using novel software tools in the process of analysis, and…