Research in mathematical problem solving has produced significant results in trying to understand what people do to solve problems. An important part of the solution process is the presence of both cognitive and metacognitive strategies. This paper documents the extent to which 13 ninth grade students are able to recognize the basic structure of a…

Fifth grade children's (n=16) understandings of simple fractions such as 1/2, 1/3, and 1/4 were investigated. The study identified three alternative conceptions of fractions: (1) 1/"N" is one of "N equal" parts, (2) 1/N is one of "N equal" parts, and (3) parts must fit together to form the whole. In addition, many…

Students need in-school mathematical experiences to build on and formalize the mathematical knowledge they gain in out-of-school situations. This paper presents illustrations from research that was conducted to better understand how mathematics practice and problem solving in everyday work situations compared to secondary students' solutions of…

This booklet explains the background, rationale, and issues addressed in the NCTM Curriculum and Evaluation Standards. A detailed vignette of a classroom lesson is presented as an example of what is envisioned for the future. A comparison of the differences between the reform urged by the Standards and the efforts of the "New Math"…

It was hypothesized that receiving a problem of the day would result in higher mathematics scores on the Ohio Ninth Grade Proficiency Test. An experimental group consisting of 19 students received a problem of the day treatment every day during the 5 month period. The 19 students in the control group received no special treatment. Test scores of…

This publication is designed to educate high school students about the problems and challenges of transportation. The parent project was conceived as a mathematics curriculum project, but developed into an interdisciplinary project to ensure that students would become well informed regarding the transportation decisions they make. In the…

This report summarizes the mathematical and pedagogical content of the Square One TV library (155 programs) after three seasons of production, relating that content to the three goals of the television series. It also provides a rundown of the shows, with a complete specification of each segment's show number, content, description, format, length,…

The game of chess is recommended as a school activity. In addition to requiring that individuals become actively involved in a mentally demanding competition, its effects are stimulating, wholesome, and healthy. Several benefits accrue from the teaching and promoting of chess in schools. Chess limits the element of luck (teaching the importance of…

Literature in mathematic problem-solving suggests that learners store information in memory which helps them solve stereotyped algebra word problems. Cluster analysis has been used as an exploratory tool to infer the types of problems which have common representations in memory. This study compares the results of a hierarchical cluster analysis of…

Suggests activities that promote consciousness of consumer economics in children while they learn problem solving and mathematical skills and develop useful consumer attitudes. (ED)

Intuition in mathematics is essential but it must be based on good knowledge of mathematics. An example related to velocity, time, and area is presented and discussed, with models, visual approaches, and geometric arguments noted. (Author/KM)

We show a new approach, based on the utilization of Mathematica, to solve gas permeation problems using membranes. We start with the design of a membrane unit for the separation of a multicomponent mixture. The built-in Mathematica function, FindRoot, allows one to solve seven simultaneous equations instead of using the iterative approach of…

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

We investigated the properties of the distribution of human solution times for Traveling Salesperson Problems (TSPs) with increasing numbers of nodes. New experimental data are presented that measure solution times for carefully chosen representative problems with 10, 20, . . . 120 nodes. We compared the solution times predicted by the convex hull…