A group of 24 14-year-old students were presented with sets of algebra tasks using the Leeds Modelling System (LMS), a computer-based modeling system. Four months later, these same students were given a paper-and-pencil test which covered comparable tasks set by LMS. In addition, certain students were given detailed diagnostic interviews. A…

This paper reports the results obtained with a group of 24 14-year-old students when presented with a set of algebra tasks by the Leeds Modelling System (LMS). These same students were given a comparable paper-and-pencil test and detailed interviews some 4 months later. The latter studies uncovered several kinds of student misunderstanding that…

Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics curriculum. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the…

This document deals with the observation of students in a direct translation scheme in the solution of word problems in a university freshman-level Intermediate Algebra class. It is felt that since successful problem solvers of algebraic equations often have as much difficulty in solving word problems as do other students in the classes, the…

A major goal of mathematics teaching is the involvement of students in the personal process of discovering mathematical ideas and formulating problems. The process of an inductive leap followed by a deductive argument is used in mathematics courses at Phillips Exeter Academy (New Hampshire). Mathematical problems are presented in which the givens…

The purpose of this study was to uncover information about and gain a greater insight into the extent to which students who are successful in a basic algebra course: l) demonstrate a reversibility of reasoning processes when solving algebraic problems; 2) demonstrate a flexibility of reasoning processes when solving algebraic problems; 3)…

This document focuses on Core Algebra, a course offered in the Hawaii State Department of Education's "Mathematics Program Guide." This algebra option is designed to be less theoretical and more application-oriented than Algebra IA and IB. The text opens with a list of twenty minimum learner objectives of the course. The next section presents an…

This document promotes computer symbolic mathematics and computer algebra as ideal instructional materials for mathematics, science, and engineering students. Further, computer algebra is viewed as appropriate for all students throughout the mathematics curriculum, by serving a vast area of mutual reinforcement and cross-motivation between…

This curriculum guide outlines the mathematics objectives of each of the grades K-8 under the headings of operations, sentences and problem solving, numbers and numeration, measurement, geometry, statistics, and applications. Examples of each of the objectives are given. High school minimal skills are listed. The sequence of mathematics courses…

A PROGRAMED ALGEBRA I COURSE WAS OFFERED FOR THE THIRD YEAR TO STUDENTS OF THE CLOUDCROFT, NEW MEXICO, HIGH SCHOOL. ALL FRESHMEN (15), 4 SOPHOMORES, 1 JUNIOR, AND 2 SENIORS WERE ENROLLED. A SCHEDULE WAS DEVELOPED WHEREBY EACH STUDENT COULD COMPLETE THE ENTIRE 73-CHAPTER COURSE IN A SCHOOL YEAR. TEACHER-MADE TESTS WERE GIVEN AT THE END OF EACH…

This longitudinal study is one of a series which is devoted to the task of evaluating new, secondary school mathematics curricula. This series of studies has involved ninth and eleventh grade teachers teaching a new mathematics curriculum (School Mathematics Study Group, University of Illinois Committee on School Mathematics, or Ball State…

Three instructional approaches on translating selected types of algebra word problems were investigated: direct translations, high imagery with materials, and high imagery with drawings. Participating were 366 seventh grade and 336 ninth grade students. Treatment effects by grade used multivariate analysis of covariance for student scores and…

Explains the constructivist theory of knowledge and discusses the theory's implications for teaching remedial college students. Analyzes student performance on a college placement test to highlight the differences between how novices and experts process scientific or mathematical materials. Suggests a radical change in introductory algebra…

Explores the problem of combining algebraic terms from the students' point of view and suggests changes in certain traditional teaching practices. (PK)

Argues that before topics are added to or deleted from the traditional mathematics curriculum, it should be determined how technology can be used to teach that content. (PK)