This publication is a collection of eleven manuscripts which deal with research in mathematics education. Each of the first ten papers is concerned with one or more of the following areas: (1) significant research efforts in mathematics education; (2) the need for both "information-oriented" (basic) and "product-oriented" (applied) research; (3)…

The author seeks to clarify the aims and values of status studies, such as the IEA Study of Mathematics Achievement, which deals primarily with administrative variables. He states the value of such a study is in providing administrators with a basis for decision making. (Author/CT)

This study was designed to determine whether (1) rules are more easily memorized when stated in mathematical symbolism or when stated verbally, and whether (2) the ability to use constituent symbols correctly, assuming mastery of the underlying grammar, is a necessary and/or sufficient condition for applying a learned rule statement. Twenty-four…

The purpose of this report was to test the hypothesis that extra-scope transfer depends on the extent to which a statement of strategy may be viewed as a restriction of a more general strategy. Sixty-six high school students were taught a restricted statement of one of three strategies of varying generality. Twenty-two of these students served as…

The author's theories concerning the learning of mathematical concepts are outlined. (SD)

The research reported in this paper was designed to analyze the incidence of use of higher-order rules by students solving geometric construction problems. A carefully selected set of construction problems was subjected to rigorous a priori analysis by mathematics educators to determine what basic and second-order rules might be used by able high…

This report describes research conducted regarding the development of a precise scientific language called the "Set-Function" Language (SFL) which was formulated in terms of sets and functions. The SFL retains many of the basic aspects of cognitive formulations but also provides more rigor than most of the other scientific languages. The SFL…

Piagetian and other tasks involving basic processing skills judged relevant to learning mathematics were used to establish baseline data on the capabilities of young children entering school. Some of the problems that involve specific attempts to improve such basic abilities were discussed. (JP)

This study is one of several conducted by the authors in their investigation of the use of "higher order rules" in the solution of problems. The focus of the current experiment was determination of the compatibility of identified rules with the knowledge of average teenagers, and of the extent to which instruction in higher order rules…