Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to…

This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and…

This is a step-by-step guidebook that is designed to help students on the quantitative section of the SAT. This guidebook produces an understanding of key mathematical concepts as the various topics are covered by the text, and, unlike other SAT guides, lists skills and capabilities, that if mastered will result in well-prepared students. More…

This study was designed to investigate whether the implementation and integration of the use of the Explorer Calculator into the curriculum influenced students in grades three through six. The sample consisted of approximately 440 students who were assigned to the treatment group or the control group. Achievement scores from the Iowa Test of Basic…

Outlines two mathematics teaching strategies: the exploration/discovery approach to mathematical concepts, and the use of pair group problem-solving. These require teachers to shift from the traditional role of lecture/demonstrator to a role demanding new skills in planning and facilitating student work. Includes 10 references. (MD)

Presents research on cognitive skills demanded by elementary and secondary school mathematics textbooks, based on an original 10-level classification of thinking activities; reports a general decline both in the amount of material demanding student involvement and in the percentage of that material requiring higher-order thinking. (MCG)

The purposes of this paper are: (1) to investigate the effects of SQUARE ONE TV on children's problem-solving behavior and their attitudes toward mathematics and (2) to indicate some connections between the result and the National Council of Teachers of Mathematics (NCTM)'s Curriculum and Evaluation Standards for School Mathematics. This paper…

This document has been prepared to help teachers and administrators in New York plan and execute a mathematics program for grade eight. The syllabus is designed to improve the problem solving abilities of students, while continuing a natural development of mathematical skills and concepts. Problem solving situations are emphasized in each of seven…

As momentum for change in U.S. education continues to grow, questions about the nature and goals of mathematics education take on increasing urgency. This report proposes a framework for reform of school mathematics mainly through reshaping of the mathematics curriculum. Chapters included are: (1) "A Rationale for Change," describing changing…

This document contains a list of recommended essential mathematical skills and outcomes developed for Arizona students from primary through secondary grades. These skills have been developed by using a spiral structure of individual clusters of objectives that are taught at an initial level and then retaught at higher levels as students progress…

The call for educational reform has caused mathematics curriculum, instruction, and assessment to come under both professional and public scrutiny. The three elements contesting for leadership in assessment reform are the conventional testing agencies, reformers led by the National Council of Teachers of Mathematics (NCTM), and political agencies…

Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…

One of the strengths of the Pennsylvania Council of Teachers of Mathematics (PCTM) is that it gives mathematicians and mathematics educators the opportunity to exchange and contribute to each other's professional growth. The topic for each yearbook is chosen to coincide with the annual PCTM meeting. This 1986 yearbook contains 17 articles related…

One of the strengths of the Pennsylvania Council of Teachers of Mathematics (PCTM) is that it gives mathematicians and mathematics educators the opportunity to exchange and contribute to each other's professional growth. The topic for each yearbook is chosen to coincide with the annual PCTM meeting. This 1987 yearbook contains 14 articles which…

This publication contains reference materials and activities for teachers in a staff development program in New York City, teaching grades 3 and 6. The program combines content and methodology. Sections in the publication include: (1) Student Verbalization Resources; (2) Manipulative Resources; (3) Probability, Statistics, and Graph Resources; (4)…