This study examines the correspondence between a representation of subject-matter structure and a representation of the cognitive structure in students as a result of instruction. Eighty-seven eighth-grade students were assigned randomly to experimental and control treatments. The experimental students (N = 43) studied from a programmed text on…

Decision-theoretic testing is used to explore whether students can improve their realism, i.e. congruence between reported and true probabilities. Randomized sets of math problems were presented at computer terminals to 49 seventh graders from two classes (high/low achievers) over a period of three weeks. The subject assigned values to each of…

This book is a sequel to MATHEMATICAL CHALLENGES, which was published in 1965. In this sequel are 100 problems, together with their printed solutions. The problems range from those that are quite simple to those that will challenge even the most ardent problem solver, and they include examples from algebra, geometry, number theory, probability,…

This booklet is part of a series of four pamphlets, each intended to stand alone, which provide problems in probability and statistics at the secondary school level. Twelve different real-life examples (written by professional statisticians and experienced teachers) have been collected in this booklet to illustrate the ideas of mean, variation,…

The first part of the teachers' guide for "Finding Models" briefly describes the mathematical background necessary for the student, lists the substantive areas touched on by the problems in the pamphlet, suggests classroom uses for the booklet, and gives background information for the individual chapters. The second part provides complete…

The 1959 Royaumont seminar "New Thinking in School Mathematics," having agreed on the need for modernization, recommended that a second group of experts work out detailed synopses of the entire subject matter of secondary school mathematics. This book is the report of the second seminar and contains the Dubrovnik Program which stimulated…

Behavioral objectives for geometry, algebra, computer mathematics, trigonometry, analytic geometry, calculus, and probability are specified for grades 10 through 12. General objectives are stated for major areas under each topic and are followed by a list of specific objectives for that area. This work was prepared under an ESEA Title III…

Description of the characteristics and mechanics of the Delphi technique of identifying the likelihood of occurrence of specified future events precedes suggested uses for the technique in research, planning, and teaching. The procedure involves obtaining individual predictions, aggregating results, presenting results to the individuals, and…

A distinction is made between reliability of measurement and reliability of classification; the "criterion-referenced reliability coefficient" describes the former. Application of this coefficient to the probability distribution of possible scores for a single student yields a meaningful way to describe the reliability of a single score. (Author)

A test of mental arithmetic skills was developed and normed for children in grades one to six. Statistical techniques were used to predict the probability correct for each item and to rank order the items. Students in a given grade took only one level of the test and inferences were made of their performance on those tests which they did not take.…

College Level Examination Program (CLEP) Tests were normed on a national basis, administering the test to nationwide samples of subjects. Norms appear in the booklet, CLEP Scores: Interpretation and Use, and consist of the test score means for groups of students receiving grades of A, B, C, D, and F in the relevant course, the proportion of…

Referring to several examples, the author argues that more time should be spent developing statistical concepts such as randomness and independence before developing mathematical models for statistical computations. (SD)

Analyzing the effects of tilting a probability board can be an effective method of introducing a discussion of models in a probability class. (SD)

Describes the electronic circuitry which can be used to demonstrate the buildups of Poisson distributions with very high precision. Analysis of the data obtained is included in the paper. (CP)

Activities involving rolling dice and recording results in diverse ways introduce children to a variety of basic mathematical concepts. Several games and activities are described. (SD)