Recent applications and extensions of the research technique of interviewing in teaching experiments are discussed. An experiment to reveal the constructive mechanisms used by children in learning numeration, addition, and subtraction is reported. (MSE)

Recent applications and extensions of the research technique of interviewing in teaching experiments are discussed. An experiment to reveal the constructive mechanisms used by children in learning numeration, addition, and subtraction is reported. (MSE)

Results from the data analysis show that children learn mathematical concepts for clear cases, and that an analysis of attributes common to examples of a given concept is not a prerequisite to concept formation. The protocol findings provide information as to why this may be happening. (Author/PN)

Too many approaches to mathematics instruction at the elementary level focus only on the production of correct answers rather than on the development of mathematical thinking skills. Author urges encouragement of children's own thought processes. (Author/PGD)

Dialog from a filmed lesson that uses graphing to explain positive and negative numbers is presented. The material highlights the responses of children. The work was also presented to a class of low, mixed-ability pupils since the filming, and the work of two pupils from this group is noted. (MP)

Details are given of a university course that utilizes computer programing to help students explore aspects of number theory. The course is thought to provide acceleration of the discovery process to the point where pupils can study a full range of topics. (MP)

Evidence is presented that many primary-age children are good at solving word problems. The data comes from three years of observation of about 100 pupils from grades one through three. It is noted that instances of total failure were relatively rare. The individual interview method is recommended to teachers. (MP)

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)

Examples and nonexamples of geometric concepts are discussed. Four guidelines for selecting and using geometric examples and nonexamples are presented. (MK)

A list of heuristics for elementary school children is provided. Two examples which are viewed to demonstrate the conscientious and creative use of problem-solving strategies by fourth graders are detailed. Suggestions for teachers on how to help pupils develop their problem-solving abilities are included. (MP)

Reviews common place-value errors in addition and subtraction and describes a classroom-tested instructional model using the diagnostic-prescriptive approach for remediation of these errors. The method is considered appropriate for introducing the concept of regrouping. (Author/DB)

Offers a definition of computational estimation and discusses the poor performance of most pupils on tests or exercises measuring this skill. Several suggestions are offered for teaching computational estimates. Difficulties associated with measuring estimation skills are discussed, and some practical ideas are proposed for testing computational…

The history of probability from ancient times is presented. The relationship between the mathematical and experimental definitions of probability are detailed. (MP)

Cardinal infinities, the superrational numbers, and intuitions of infinity in limiting processes are discussed. (MP)

A renewal of the study of the philosophy of mathematics is encouraged and a search is made for a philosophy better attuned to the present state of the subject. (MP)