This paper presents an analysis of high school and starting college students' work with algebraic expressions and problems involving parameters. We suggest that parameters should be considered as general numbers that are used to make second order generalizations. The Three Uses of Variable model (3UV model) is then used as theoretical framework to…

This paper consists of a learning unit for college algebra in which the problem presents three different payment plans for a tuition plan to pay for college expenses. The details of each payment plan are presented, each followed by several exercises so that comparisons of the results can be made across payment plans. (MM)

This paper presents a developmental model of students' acquisition of competence in quantitative and algebraic problem solving. A key notion underlying the developmental model is a distinction between grounded and abstract representations. Grounded representations, like story problems, are more concrete and familiar, closer to physical objects and…

An analysis is made of overall probabilities of juries making the correct decisions when the juries vary in size from two to beyond five. (DT)

Solution of, and commentary on, a problem suitable for use in the secondary school mathematics classroom. Topics from arithmetic, algebra, and number theory appear in a unified way. (FL)

Procedures to help algebra students solve problems more efficiently are discussed, using linear programing graphs. (MNS)

A computer program that uses determinants to solve simultaneous systems of equations is presented. The purpose is to show teachers how to use topics from algebra, geometry, and programing to lead pupils to appreciate the beauty and unity of mathematics. (MP)

Four problems are given and discussed involving reflection about a line or the reflection properties of conic sections. Solutions are given. (MP)

Forty second-year algebra students were interviewed while solving eight problems. Data from the interviews included frequencies of problem-solving processes and scores on the test. Conceptual knowledge accounted for 50 percent of the variance. (MP)

The transfer between problems having related structures was investigated. The results indicated that transfer occurred for both algebraic and puzzle problems, and significant transfer resulted when the generalization was solved first. (MP)

Presents selected responses to the question "The Farmer's Dilemma" that represent the thinking of sixth-, seventh-, and eighth-grade students. Indicates that by being given the freedom to use a variety of methods, most students found at least one solution or demonstrated an understanding of the restrictions set by the problem. (ASK)

As times change, so has the role of algebra in the educational program. The Interactive Mathematics Program (IMP) offers secondary students an opportunity to learn algebra in a college preparatory sequence that combines basic skills, problem solving, and conceptual understanding while integrating algebra into a problem-based program. Designed for…