Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

Provides several problems and their solutions for a descriptive statistics course. Included are problems related to measurement, data collection, sample construction, applications, and computation. Discusses the misleading nature of statistics. (YP)

Discusses geometric construction problems. Presents four ways to construct a regular octagon using different conditions. Provides drawings showing the constructions. (YP)

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

Suggests that, although questions are often used to help students or stimulate student thinking, questions can also be used to help evaluate student thinking and attitudes about problem solving. Sample problems and questions are given. (PK)

How children give meaning to problems solved by multiplying or dividing is considered. After showing two cases of children's understanding of multiplication problems, six recommendations for classroom practice are presented. (YP)

From 1984 through 1988, the authors worked with teachers using an inquiry approach to teach high school geometry courses with the aid of the "Geometric Supposers." Problems are a critical component of the approach because they focus attention and energy and guide students in the application, integration, and extension of knowledge.…

The "General Mathematics" series is intended to introduce students to basic mathematic principles and concepts as well as to the opportunity to apply those principles and concepts. This color coded module, one of six in the series, will allow students to build or increase their level of understanding of whole numbers and will help…

The "General Mathematics" series is intended to introduce students to basic mathematic principles and concepts and to provide the opportunity to apply those principles and concepts. This module, one of six in the series, will allow students to build or increase their level of understanding of decimals and percents, and will help students…

This book is written for coaches of secondary school students involved in mathematics contests. Benefits, of contests and suggestions for coaching mathematics contests are described. Sample questions are presented for the following contests: (1) Open categories, written competition; (2) Identified topics written competition; (3) Eight-person team…

This report attempts to discover how students think about and use mathematics in open-ended questions. Part I, "Open-ended Questions in Mathematics," describes the rationale for adding open-ended questions to the grade 12 mathematics test of the California Assessment Program (CAP). Part II describes the findings from students' responses…

This monograph provides activities for beginning algebra students to develop an understanding of the meaning and use of letter symbols, to show applications of algebra in their own lives, and to develop an understanding of mathematical processes through investigation. The activities included were developed by considering the students' mathematical…