This material is designed to examine the research on how children acquire basic addition and subtraction concepts and skills. Two major lines of theories of the development of basic number concepts, called logical concept and quantification skill approaches, are identified. Major recurring issues in the development of early number concepts are…

This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…

It is noted that there are some integrals which cannot be evaluated by determining an antiderivative, and these integrals must be subjected to other techniques. Numerical integration is one such method; it provides a sum that is an approximate value for some integral types. This module's purpose is to introduce methods of numerical integration and…

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 teacher's guide is designed to aid in the incorporation of programable calculators in the school mathematics program for pupils in grade 11. Warnings include the need for care in modifying the curriculum so that students are not punished in the process. The concept of "black boxing," of letting the computer or calculator take charge…

This teacher's guide is designed to aid in the incorporation of programable calculators in the school mathematics program for pupils in grade 12. Warnings are given, including the need for care in modifying the curriculum so that students are not punished in the process. The concept of "black boxing," of letting the computer or…

Teachers in elementary schools, supervisors of instruction, and other educational practitioners are the primary audience for this publication. The paper presents philosophical, psychological, and practical reasons for including a problem-solving approach in elementary school instruction. It draws on the writings of John Dewey, Jean Piaget, James…

Seventeen research reports related to mathematics education are abstracted and analyzed. Five of the reports deal with aspects of learning theory, three with teacher education, two with testing, three with children's knowledge and understanding of various mathematics-related concepts, and one each with errors in solving linear equations, classroom…

This module, concerned with fractional parts, contains 15 activity sheets, 12 of these involve students in making fractional parts and discovering the relationships of less than, equal to, and greater than, between different fractional parts. The last three sheets are for extending and enriching experiences with fractional parts. Teaching…

STUDY OBJECTIVES WERE DEVELOPED AROUND THE IDEA THAT DELIBERATE AND PLANNED TEACHING OF FORMAL SYMBOLIC LOGIC WILL BENEFIT THE STUDENT AT ANY AGE BY ENLARGING HIS SCOPE AND PROVIDING FOR A DEEPER AND MORE PENETRATING STUDY OF MATHEMATICS AND OTHER DEDUCTIVELY FORMULATED DISCIPLINES. IT WAS HYPOTHESIZED THAT THE ABLE STUDENT IN ELEMENTARY SCHOOL IS…

This document notes that arithmetic disabilities can occur with an otherwise normal intelligence level. Two models of explanation are given. The first emphasizes the conditions under which children learn mathematics, the second views the identification of a number of factors in the "structure of intelligence" that appear to be strongly…

This is one of a series of reports summarizing the results of the second mathematics assessment conducted by the National Assessment of Educational Progress (NAEP). Nine, 13- and 17-year-olds were assessed during the 1977-78 school year. The assessment measured achievement in various content areas at four levels of cognitive processes (knowledge,…

Three addresses by internationally renowned mathematics researchers and a fourth paper on the role of research are presented. Each of the addresses focuses on the learning process, but from different points of view. Heinrich Bauersfeld provides an analysis of the miscommunication inherent in many teacher-student interactions. Four deficient areas…

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 investigation was performed to test the hypothesis that male high school students of high discrepancy score on self-concept would be less able to apply principles of dynamics to new situations than male high school students of low discrepancy score. The discrepancy score was the difference between self-concept and ideal self as calculated…