Presents a model for teaching reasoning using technology in the contexts of algebra and geometry. (MKR)

This material shows how to use basic techniques, principles of counting, and geometry to count squares on geoboards. The methods are elementary in that the proofs are easily conceptualized. A discussion of other approaches illustrates that easily stated problems may lead to very difficult and sophisticated methods. (MP)

Materials designed to promote student investigation of factoring quadratic polynomials over the integers through using a physical model are presented. Pupils are expected to discover regularities that will permit them to factor such polynomials at the symbolic level. Worksheet masters designed for classroom use are provided. (MP)

Presents two methods for solving equations. An asymmetric approach works backward from a number by reversing operations performed on a variable. A symmetric approach views the equation as a scale and performs inverse operations on both sides of the balance to solve for the variable. (MDH)

This paper discusses the overall design of the PIXIE Intelligent Tutoring System, and more specifically a series of recent enhancements. The original system has been implemented to involve three separate phases: the offline, or model generation phase; the online, or tutoring, phase; and the analysis phase. The offline phase, which is completed…

This competency analysis profile contains eight lists of mathematics skills that have been identified by employers and verified by math-certified instructors as being core competencies for eight groups of occupational areas. Each list is organized into subsections dealing with the following: numbers and number relations, measurement, data analysis…

Six studies discussed in this paper compared error-specific or model-based remediation (MBR) with reteaching in algebra. MBR points out, and highlights as incorrect, errors specific to the student's solution before reteaching the correct procedures. Reteaching shows the student the correct procedure without addressing specific errors. Three of…

This paper provides an overview of the four major aspects of the PIXIE Intelligent Tutoring System: the field work undertaken to determine how teachers diagnose and remediate in introductory algebra; the set of experiments run to determine the relative effectiveness of Model-Based-Remediation (MBR) and Reteaching; systems work carried out to…

The implementation of the program used in this study, TPIXIE, was predicated on the assumption that acquiring the skill to diagnose student errors was important for teacher trainees. The TPIXIE system (part of the PIXIE family of intelligent tutoring systems) was designed to present users with a series of task-student-answer pairs (where the…

Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…