Drawing from research and observations at Lansing Community College (Michigan) (LCC), this paper argues that typical arithmetic courses do little to prepare students to master algebra, and proposes an alternative set of arithmetic skills as actual prerequisites to algebra. The first section offers a description of the algebra sequence at LCC,…

Precalculus and Discrete Mathematics (PDM) is the sixth and final course in the secondary mathematics curriculum developed by the University of Chicago (Illinois) School Mathematics Project. During the 1989-90 academic year, a formative evaluation of the third field-trial edition of PDM was conducted among a volunteer sample of 9 high schools with…

A study was conducted to test the hypothesis that the ability to comprehend in reading has no effect on mathematical problem solving ability of seventh grade students. Two seventh grade classes were administered a standardized test of reading comprehension and knowledge of mathematical concepts and application at the beginning of a school year.…

Two studies were conducted to compare experimentally the effects of teacher-led instruction and seatwork on acquiring mathematical concepts. In the first study, 255 fourth graders were assigned to groups to be taught a 15-minute teacher-led lesson only, a 15-minute lesson plus 12 minutes of teacher-led follow-up, or a 15-minute lesson plus 12…

An instructional method using flow-chart symbols to make mathematical abstractions more concrete was implemented for a year in a technical mathematics course. Students received instruction in computer applications and programming in the BASIC language in order to increase motivation and firm the mathematical skills and problem-solving approaches…

Using arrays of dots and grids many numerical concepts can be illustrated for students. (SD)

One of the most important provisions of Act 750 of the 1979 Louisiana Legislature is the mandated development and establishment of statewide curriculum standards for required subjects for the public elementary and secondary schools. The 1986 revision of the Louisiana standards for mathematics recognizes the need to move from minimum to…

Research on computational estimation and mental computation has received a considerable amount of attention from mathematics educators during the past decade. These proceedings resulted from a meeting to explore dimensions of number sense and its related fields. The participants came from three groups: mathematics educators actively pursuing…

Students come to the classroom with theories that they have actively constructed from their everyday experiences. However, some of these theories are incomplete half-truths. Although such misconceptions interfere with new learning, students are often emotionally and intellectually attached to them. Some common mathematical misconceptions involve:…

This activity book stresses the integration of measurement with all phases of mathematics and other school curricula. It emphasizes: activities that teach basic measurement skills; techniques for understanding small and large numbers; learning devices that improve measurement understanding; strengthening measurement vocabulary through…

This material is a supplement to existing mathematics programs for young learners. The activities presented are based on assumptions about the young problem solver which are difficult to address in standard mathematics texts. In these pages it is assumed that each learner brings to the problem-solving effort a very personal experience base and a…

This paper discusses the development of the mathematical experiences which make up the three-term sequence of mathematics courses taken by participants in the Elementary Mathematics Project (EMP), a longitudinal study of change in preservice teachers' perceptions and beliefs about mathematics. For the mathematics courses, both content and teaching…

Difficulty in comprehending mathematical concepts is a consequence of the system of knowledge acquisition prevailing in schools, and more specifically, of the typical pattern of classroom interaction. In the common task-setting/task-solving pattern, the teacher divides the subject matter into segments. Students are involved interactively in…

This resarch identified K-6 children's (N=1202) and teachers' (N=54) perceptions of what constitutes doing or using mathematics. Perceptions were documented by a questionnaire which included items reflecting the six major strands of the K-6 syllabi and explicit and implicit use of numbers and operations as both facilitating and distracting…

This document is a collection of activities designed to use children's literature to introduce, reinforce or broaden mathematics skills and concepts. The mathematical topics that are addressed include: time; problem solving; logic; measurement; comparison; sets; one-to-one correspondence; fraction concepts; division; counting; averages; infinity;…