We describe highly generative and affectively powerful classroom activity structures that are made possible by applying new levels of connectivity across diverse hardware platforms. Based on teaching experiments involving core topics in basic algebra (slope-as-rate, linear functions, simultaneous conditions), we examine 3 kinds of activity…

There is a significant gap between theories of general psychological functions on one hand (e.g., memory) and theories of mathematical content knowledge on the other (e.g., content of algebra). To better guide the design of ground breaking and demonstrably better mathematics instruction, we need instructional principles and associated design…

Described is the notion of multiple alternative representations of mathematical reasoning, particularly as they relate to algebraic notation and the potential of computers to change representations. Features of a desirable notation for algebraic problem solving are described. This is followed by a description of the RAND Corporation's intelligent…

A study of approximately 600 University of Arkansas remedial algebra students divided into seven control and seven experimental group sections substantially confirms John Saxon's findings that mathematics achievement can be improved by using Saxon's incremental approach to mathematics instruction. (JBM)

The concerns of two teachers at a school where computer-integrated instruction was being used in five second-year algebra classes were studied. High levels of personal and management concerns, coupled with low refocusing concerns, were found. Both teachers were judges as mechanical users of computer materials. (MNS)

Examines the potential of technology for an algebra curriculum. Provides examples of technology in use in examining families of functions, fitting a curve to a data set, and observing and analyzing patterns. Discusses exemplary software and calculators for the algebra curriculum. (MDH)

Virtual Reality (VR) is a computer generated, multi-dimensional, inclusive environment that can build axioms of algebra into the behavior of the world. This paper discusses the use of VR to represent part of the algebra curriculum in order to improve students' classroom experiences in learning algebra. Students learn to construct their knowledge…

The problem-of-the-week (POW) and problem-solving class openers are exemplified as methods for the integration of course-relevant problem solving into a first-year algebra classroom without sacrificing time spent on developing skills and learning concepts. Illustrated examples, as well as problem sources, are included. (JJK)

Examines the potential role for Computer Algebra Systems (CAS) when teaching courses as functions, calculus, and linear algebra to students with low prerequisite algebra skills. A study reports the rationale, planning, and implementation of a functions course integrating Maple CAS into instruction. (MDH)

Intelligent tutoring systems (ITS) aim to improve upon previous computer-aided instruction programs by embedding much of the expert knowledge that good human teachers possess. While ITS research has a practical goal of developing programs that assist students in learning, there is little data on their instructional effectiveness. This paper…