Excerpts a student-teacher discourse from a 4th-grade mathematics classroom to illustrate how discourse helps students construct algebraic thinking. Discusses the implications of the discourse method of collaborative inquiry for teaching. (JPB)

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of…

T-algebra is a project for creating an interactive learning environment for expression manipulation tasks of elementary algebra. Our main didactical principle has been that all the necessary decisions and calculations at each solution step should be made by the student, and the program should be able to understand the mistakes. This paper…

Using symbolic algebra to represent and solve linear equations is one of the expectations within the "Algebra" content standard for the 6-8-grade band in the National Council of Teachers of Mathematics (NCTM) "Principles and Standards for School Mathematics" (2000). Students' understanding of these concepts, even before a formal algebra course,…

Although the myth of public education as the "great equalizer" is alive and well in the minds of many, the reality is that the notion of public schools as the savior of the less fortunate is fundamentally compromised when institutional decision making does more to suppress low-income and minority students through low expectations…

This study examined practices of teachers in Wake County Public Schools (WCPSS) high school Algebra I classes. Regression analyses of standardized state testing results allowed for identification of the most effective and least effective Algebra I teachers and schools. The study used surveys, observations, and focus group interviews to compare and…

The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…

A study was conducted at the Community College of Allegheny County, in Pennsylvania, to compared the level of preparedness in an intermediate algebra course for students who placed directly into the course and those who had tested into and completed a basic algebra course. Placement test scores, algebra course grades, and repeat status were…

This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…

Over the past 3 years, the Mathematics Department of Grossmont College, in California, has examined the issues of course standards, instructor grading variability, and course placement. In 1990, a study was conducted to determine if the Elementary Algebra instructors with lower pass rates had higher standards, and if their students had a higher…

This document offers instructional materials for a 60-hour course on math operations involving decimals, fractions, proportions, statistics, probability, measurement, geometry, and linear algebra as applied in the workplace. The course was part of a workplace literacy project developed by Mercer County Community College (New Jersey) and its…

The 13 leading mathematics educators who made up the task force that prepared this report were thoroughly acquainted with every major report on math education produced within the last decade. They were also thoroughly acquainted with the realities of instruction in the K-12 classrooms. Their aim, therefore, was to make appropriate compromises…

This collection of four papers deals with problem solving and the measurement of problem solving. "Climbing Up the Competence Ladder: Some Thoughts on Meaningful Assessment of Problem-Solving Tasks in the Classroom" by K. C. Cheung uses the metaphor of a competence ladder to represent the problem-solving continuum with progressive…

This report offers details of the results of basic skills testing of the entering freshman class in New Jersey's public colleges. Levels of proficiency in verbal skills, computation, and elementary algebra are estimated from performance on the New Jersey College Basic Skills Placement Test. For the 48,568 students tested in the fall of 1990, 24%…