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)

Presents a mathematical game called the dinner-guest problem that deals with Steiner triple systems. (HM)

Examined are the problem similarity dimensions perceived by a student when classifying mathematical word problems as related and the relationship between a student's perception of problem similarity and performance on achievement tests. (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)

Problem-solving processes used by concrete- and formal-operational eighth-grade pupils were investigated through interviews. Formal-operational pupils used a larger variety of processes. Also, a larger variety of processes were used on more complex problems. (MP)

Proposes using the reform documents from the National Council of Teachers of Mathematics (NCTM), a theory-based multidimensional assessment framework, to help expand the scope of assessment in mathematics. Presents a framework using a context based on mathematical reasoning and components that comprise mathematical concepts, procedures,…

Describes a problem suitable for grades 1-6 where students utilize a hundreds chart and counters. Students cover any numbers that contain only the digit 1, then cover any numbers containing only the digits 1 and 2, and follow this pattern until they can determine how many digits are needed before the hundreds chart is half covered. (AIM)

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)

The cognitive effects of self-referencing in math word problems were studied in 100 third, fourth, and fifth graders solving compare-unknown and referent-unknown problems. In general, self-referencing (referring to "you") facilitated encoding processes in solving these problems. Self-referencing appeared to decrease the load on working…

Describes a study of 2 secondary students working problems over a 10-week period. Information on metacognitive awareness, confidence, and ability were collected through two videotaped sessions and questionnaires. Results suggest impulsiveness and perceived order of merit inhibit effective problem solving. (MTE)

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…

Presents a problem-solving investigation on coal mining that integrates science and mathematics with geology. Engages students in a scenario in which they play the roles of geologists and mining engineers. (NB)

Suggests use of the quadratic formula to build understanding that connections between factors and solutions to equations work both ways. Making use of natural connections among concepts allows students to work more efficiently. Presents four sample problems showing the roots of equations. Messy quadratic equations with rational roots can be solved…

Proposes a system to help at-risk students develop problem solving skills. Provides some teaching methods and evaluation ideas. (KHR)