Investigates the convergence of three measures on a representation of cognitive structure and examines the correspondence between these representations and the representation of subject matter structure. (Author/DEP)

This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit…

This study focuses on the mental processes used during estimation. This research: (1) developed an operational definition of estimation; (2) created an instrument to identify exceptionally good estimators; (3) collected performance level data on 1187 subjects; (4) constructed interview problems and developed protocols to identify the thinking…

The approach to teaching group theory used in this report was to give students many different kinds of examples of the concept being taught. The functions of models and examples in terms of student preferences and the psychology of the learning experience are discussed. Six representations of the tetrahedral group were developed as test materials.…

Refinements of work with calculator algorithms previously conducted by the author are reported. Work with "chaining" and the doing/undoing property in addition and subtraction was tested with 24 third-grade students. Results indicated the need for further instruction with both ideas. Students were able to manipulate the calculator keyboard, but…

This paper describes an approach to task analysis which seeks to identify potential sources of difficulty in the self-discovery of improved procedures by students who have been taught simpler procedures. The approach considers novices' procedures in terms of the changes needed to produce an expert procedure; the knowledge required to make those…

The described learning module is designed for teachers at the middle school level who wish to improve specific basic mathematics teaching skills. The contents of the module are outlined, and activities and resources involved in its use are described. Ordering information for materials is included, and a critique of the module is provided. (JD)

Investigated were concepts of conservation (number and length), cardination, one-to-one correspondence, and counting ability, and the role of these concepts in learning first-grade mathematics. A Piagetian-type number concept test was developed and administered at the end of the school year to a sample of 38 entering first-grade students selected…

This is the report of a teaching experiment designed to teach the concept of equality as an equivalence relation to a group of first graders. The rationale, design, selected samples of the instructional materials, summaries of students' performances during the instructional program, analyses of students' performances on a series of evaluations…

Children's understanding of mathematical concepts, written symbolization of these concepts, and a specifically defined readiness factor were investigated. Thirty-eight first graders were classified as ready or not ready according to scores on a readiness test. Students were paired, with 11 pairs of not-ready and 8 pairs of ready students; one…

This report presents the results of a teaching experiment which investigated (1) the role of mathematical experiences on the development of counting, addition, subtraction, mental arithmetic, classification, and other arithmetical topics and (2) the role of quantitative comparisons and class inclusion as readiness variables for learning the…

An exploratory investigation designed to gain insights into children's mathematical formulation of observed actions upon objects is presented. Eight episodes in which first and second graders were asked to interpret, in terms of number sentences, a sequence of actions with unifix cubes are also presented. Results of analysis of the videotaped…

Intended as an instructional aid for teachers of general business and other secondary school business courses, this annual bulletin discusses the following four general economic concepts: Opportunity costs, supply and demand, industrial organization, and marginal analysis. For each concept, principles are developed which can often be applied in…

Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 54th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education are covered. Three reports concern the effects of differing presentations of mathematics, four are related…

This brief text was written to provide more extensive treatment of descriptive statistics than is ordinarily available in modern statistics textbooks. It is intended for use in conjunction with any college level text. The booklet consists of an introduction, three content oriented chapters, and four appendices devoted to computer programming…