The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

Through individual interviews with remedial and precalculus university students, five characteristics of the student were identified that influence whether a diagram is used in solving a problem and whether its use is successful. The interviews also suggested a set of subskills that contribute to the overall ability to draw effective diagrams.…

Provided are 121 mathematics activities for children aged 3 to 6. Sections include: (1) "Introduction" (describing how to use the book, how to communication with parents, what materials are needed, and how to begin, and also indicating cross-curriculum areas); (2) "Shapes" (describing 20 activities that provide children with an awareness of…

This book presents activities designed to promote students' understanding of important mathematical ideas as well as to provide learning experiences intended to let students practice and refine their skills. Chapter topics include: (1) understanding and using numbers; (2) computation; (3) problem solving; (4) calculators; (5) fractions and…

Results of the most recent administration of the National Assessment of Educational Progress (NAEP) suggest that the majority of secondary students believe in the independence of random events. In the study reported here, a high percentage of high school and college students answered similar problems correctly. However, about half of the students…

There has been much recent discussion concerning the content of the standard calculus course for students majoring in mathematics and the sciences. Some of this discussion has focused on the available textbooks. One weakness noted in some of these books involves the definitions of limit and continuity for functions of several variables. A…

This curriculum guide lists mathematics topics and concepts, learning outcomes, and sample learning objectives (in three columns) for these secondary school mathematics courses in Alaska: (1) general mathematics; (2) consumer mathematics; (3) pre-algebra; (4) algebra I; (5) algebra II; (6) geometry; (7) trigonometry; (8) precalculus; and (9)…

An English-Vietnamese math dictionary for Vietnamese high school and college students is presented. The dictionary was developed for students within the Vietnamese-speaking refugee community in Australia, many of whom are advanced in mathematics but are held back by their unfamiliarity with English terminology. The first column in the dictionary…

This document contains final versions of papers that were conference contributions. This second conference, held in September 1978, was attended by 70 participants from 11 countries. Lectures were presented under the following five main sections: (1) Acquisition of Arithmetical Concepts; (2) The Learning of Generalization and Proof; (3)…

This document presents five activities which represent a part of the Comprehensive School Mathematics Program (CSMP) curriculum. The package is primarily designed to: (1) introduce instructors to one or more of the three non-verbal languages used in the CSMP elementary curriculum in such a way that teachers would want to pursue the possibility of…

This is the third in a series of documents designed to supplement the statistics training of social science students studying applied statistics. The intent is to present selected proofs and derivations of important relationships or formulas that students typically do not find available and/or comprehensible in journals, textbooks, and similar…

Through a mathematical analysis, Piaget's grouping concept can be formally interpreted as being a hybrid between the mathematical concepts of a group and a lattice. Some relevant pedagogical models are presented. Activities with Cuisenaire Rods, Dienes Blocks, and Papy's Minicomputer are shown to take place in groupings. (LS)

Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 56th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education is covered. Ten reports deal with problem solving, four are concerned with instructional methods, three…

Research supported by U.S. Public Health Grant No. 293-60 to D.O. Hebb and Grant No. 298-3980 of the Medical Research Council of Canada to Virginia I. Douglas. Part of a PhD thesis submitted to McGill University (Friebergs, 1965).

This module considers ordinary linear differential equations with constant coefficients. The "complex method" used to find solutions is discussed, with numerous examples. The unit includes both problem sets and an exam, with answers provided for both. (MP)