To help classroom teachers construct mathematics tests, nineteen general objectives, corresponding sub-objectives, sample test items, and answers are presented. In general, sub-objectives are arranged in increasing order of difficulty. The objectives were written to comprehensively cover three categories: (1) set theory; (2) numeration (Roman,…

A collection of 96 mathematics items are presented for state and local education agencies to draw upon in designing their own minimal competency tests. These items, part of the National Assessment of Educational Progress, have been reviewed in terms of their appropriateness for a minimal competency test for high school graduation. The items are…

The value of using inductive and deductive methods in instructing a mathematical principle and foreign language alphabet are tested with sample groups of sixth and eighth grade students in two separate educational experiments. In both cases, the instructional methods used were--(1) instruction in principle before application to examples, (2)…

The establishment of Research and Instructional (R and I) Units is discussed in terms of their utility and applicability for research needs. These units are said to provide a propitious setting for rigorous educational research. Two experiments in R and I units are described--one dealing with ways to implement feedback to students on their school…

Presents a study in which first grade students wrote about what they had learned or discovered at their math learning center. Suggests that students who learn actively by writing in a journal acquire ownership of the information, and that reflecting on information is more effective than transcribing and reciting. (JC)

This brochure highlights key concepts of the American Federation of Teachers (AFT) "Thinking Mathematics" courses. Citing adherence to No Child left Behind Act (NCLB) mandates, these courses are: (1) based on scientific research about how children learn mathematics; (2) designed to increase teacher mathematical knowledge; (3) provide a…

This report documents the process undertaken to produce scales in three cognitive domains: knowing, applying, and reasoning. Included are the final scales showing differences among countries, as well as within countries. TIMSS 2003 is the third and most recently completed round of IEA's Trends in International Mathematics and Science Study, a very…

Investigates the construction of understanding of the motion of an object down an inclined plane which takes place through the process of model building in an integrated algebra, trigonometry, and physics class. Discusses four major themes related to student learning through modeling that emerged from the results. Discusses implications for…

Investigates the characteristics of oral and written communication in a German third-grade mathematics class and theorizes how this knowledge might be applied to improve instruction. Develops several lessons incorporating communication skills into activities that illustrate fundamental mathematical concepts. Includes lesson transcripts, writing…

To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within…

A problem with interpretations of differences in mathematic achievement between students from Asian countries and those from the United States is the seemingly implicit assumption of the cultural homogeneity of Asian societies. Researchers rarely measure the effects of variables within cultures that are hypothesized to be related to differences…

This document describes the contributions of African peoples to the science of mathematics. The development of a number system is seen as related to need. Names of numbers, time reckoning, gesture counting, and counting materials are examined. Mystical beliefs about numbers and special meanings in pattern are presented. Reproductions of patterns,…

This book is for teachers of children in preschool through grade 4. It is designed to help teachers make important decisions about the mathematics curriculum and give them some effective ways to help children attain the mathematical power needed for everyday use and for future careers. Relevant research in each chapter provides a framework and…

This practicum addresses the need to organize a structured problem solving program for fifth and seventh grade students. The improvement of the students' problem solving skills and the enhancement of students' attitudes toward problem solving in mathematics were the main goals. The program implemented consisted of a structured problem solving…

This guide describes 47 number and numeration learning activities that can be used with elementary school students. These activities have been developed using the mathematics laboratory approach. This publication is designed to serve as a stimulant to encourage teachers to open their minds and employ their imagination in developing further…