When a professional engineer solves a mathematical problem using technology, he/she generally uses a single one-step "high-level" command of a readily available computer package to obtain the solution immediately. This should not happen during his/her learning cursus. In an engineering mathematics course, the educator should decompose the solution…

Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem…

In this paper, we describe the skeleton of two teaching units, based on a Model for teaching mathematics, Context Orientated Teaching (COT). The first teaching unit concerns the proof of a mathematical proposition, while the second one concerns the solution of an open problem. Both are taught in the 10th grade, under the specific conditions of the…

Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

College students were exposed to two pairs of mathematics assignments. Assignment Pair A included a high-effort assignment containing 18 long three-digit ? two-digit (3?2) multiplication problems with all numerals in each problem being equal to or greater than four and a moderate-effort assignment that contained nine long problems and nine…

Over the past two decades, calculus reformers have called for the use of alternative pedagogical techniques to promote student learning. Some mathematics instructors have responded by developing a set of student projects intended to hone thinking skills and improve the mathematical writing skills of calculus students. Drawbacks to this strategy…

What is a routine question? The focus of this paper is routine questions and time (in years) since a hitherto routine question was last attempted by the solver. The data comes from undergraduate students' work on solving two calculus questions. The data was selected for reporting purposes because it is well documented and because it threw up…

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

A traditional view of mathematics learning suggests that basic fact knowledge provides a cornerstone for success in problem solving. But possibly, for some children, automated basic fact responses may be disadvantageous for their problem solving success. The purpose of this study was to investigate the relationship between basic fact knowledge and…

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…

Researchers have noticed a gap between mathematics practice in school and mathematics practice in out-of-school situations. This study compares the out-of-school practice involving measurement of on-the-job carpet layers with the problem-solving strategies of ninth-grade students while engaged in measurement problems from the typical mathematics…

The purpose of this report is twofold. The first is to deliver an accurate portrayal of students' achievement in geometry and measurement as gleaned from the results of the 1986 Massachusetts Educational Assessment Program (MEAP). The second is to provide K-12 teachers of mathematics with activities that have proven to be helpful in encouraging…

If we are to say that mathematics deals only with numbers, then the assumption that having mathematics without language will undoubtedly be correct. To some extent this assumption is true but the main point that needs attention at this stage is how would it be ever possible to talk about mathematics without language. Language is the means of…

This publication was prepared to assist school personnel in strengthening their overall mathematics programs. These materials give an overview of a variety of teaching techniques for use in the first eight grades. The illustrative problems are concerned with those topics usually studied at the elementary school level. The problem-solving…

This document provides an overview of the 1980 and 1981 Illinois Inventory of Educational Progress (IIEP) in mathematics. Development of the IIEP is discussed, and results and analyses of the tests administered to students in grades 4, 8, and 11 are presented. Test items are included. Factor analysis identified two factors, "knowledge of…