A module built around programing the computer is described. It recognizes the need of many children to have algebra introduced in a practical way and to give some concrete meaning to it. (MNS)

The roles of skills and meaning in mathematics are discussed, with concern expressed over the little time spent on developing understanding. Approaches to proportion are described, levels of meaning are proposed, and proportion as a unifying idea for geometry are among the topics discussed. (MNS)

Provided is an analysis of Turtle Geometry using van Hiele levels of development and understanding. The author also relates a language use framework, suggested by the work of Fry (1982), to the language activities of Turtle Geometry. Research supporting the analysis is discussed. (RH)

Described are responses of first-year college students to questions regarding acceleration. Responses regarding acceleration and possible reasons for student errors are discussed. (RH)

Describes a study comparing the assessment of student work by seven teachers with the assessment done by 20 secondary assessors. (PK)

Provides mathematical activities in reproducible formats appropriate for students in grades 7-12. The objective is to practice using area models in analyzing compound situations and calculating the expected value or long-term average. (PK)

Describes the development, implementation, advantages, and disadvantages of a mastery learning program for teaching mathematics to mixed ability classes. Indicates that the strategy provides a successful approach while taking account of the realities of group-based instruction, a fixed curriculum with fixed time, use of a textbook, and grading.…

Describes the characteristics of the five levels of thinking in the hierarchical sequence postulated by the van Hiele theory, as well as several properties associated with each level of thinking. Also discusses some implications of the theory for the planning of geometry instruction in the classroom. (JN)

A description is given of work with geometry students in Weston, Massachusetts. They were aided in thinking like geometers, with a curriculum based on conjecturing and problem posing, using the Geometric Supposer series of computer programs. (MNS)

Advantages and disadvantages of the modern definition of function, understanding the concept of function, procedures used in a study of the understandings of ninth graders, and detailed results of the study are discussed. (MNS)

Students were asked to make up a mathematics problem that would be difficult for a friend to solve: a subsample of 11- to 13-year-olds was interviewed as they solved the problems. Made-up problems were found to be a useful tool for studying mathematically talented children. (MNS)

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)

Using four activity sheets, students learn to identify fractions that are easy to use in estimation situations. (MNS)

Three theorems for Pythagorean triples are presented, with discussion of how students can amend their ideas about such numbers. (MNS)

Some limitations of computing with calculators and computers are described, with particular reference to typical computations which might be performed by senior secondary school students. Types of errors, the laws of number, and intermediate round-offs are each illustrated, with conclusions and implications. (MNS)