Uses Muybridge's sequence of photos of a moving cat to examine how one might picture changes in the cat's velocity. Classroom implications include building on personally enacted physical experience and recognizing uncertainty as fundamental. Concludes that carefully examined case examples are essential in teaching students to learn and reason…

Describes the habits of mind that would be most desirable for students to develop. In high school for example, content-specific habits would include geometric habits of mind that support the mathematical approaches, and algebraic ways of thinking that complement the geometric approaches. (AIM)

Addresses the early stages of children's introduction to the use of variables in formal algebraic notation. Describes a teaching approach that aims to situate the use of formal notation in meaningful contexts. Presents a study of a teaching sequence based on children working with this approach using graphical feedback in problem solutions. (AIM)

Covers a project conducted by the Freudenthal Institute in which observation of student behavior supported the premise that the graphics calculator can stimulate the use of realistic contexts, the exploratory approach to mathematics, a more integrated view of mathematics, and more flexible behavior in problem solving. (AIM)

Examines the self-directed activity of two students who learned about molecular structure by writing computer programs. The programs displayed the solution of a mathematics problem, then the programs were extended to represent several classes of organic molecules. Different ways to enhance mathematical connections to chemistry education are…

Discusses the relevance of teaching algebra to all students. Issues examined include the desperate need for reform in the algebra curriculum, developing a curriculum for a broad range of people, and rethinking how mathematics courses are structured and taught. Concludes that teaching algebra to students previously unsuccessful in mathematics will…

Attempts to examine the place of mathematics in terms of the goals within education and in particular to seek reconsideration regarding who has the right to make such decisions. Stresses that there is no one answer because many influences change over time, and students may decide they do not wish to learn a subject. (AIM)

This study examines the assessment beliefs and practices of four middle school mathematics teachers implementing a reformed mathematics curriculum for the first time. The constraints on change in assessment include time available to develop, implement, and interpret alternative assessments, as well as parent and student beliefs about what it means…

Describes one possible approach to solving the following problem: given a pentagon ABCDE in which triangles ABC, BCD, CDE, DEA, and EAB all have area=1, is the area of the pentagon determined? (AIM)

Begins with a description of the research paradigm and the theoretical perspective. The following two sections are a consideration of some points from the literature and a description of the evolution of a genetic decomposition of the limit concept. Concludes with some suggestions for instruction that relate to how the limit concept can be…

Presents a perspective on the nature of the use of proofs in high school geometry. Compares three currently used approaches to the geometry curriculum: (1) traditional geometry with no explanation of the axiomatic system; (2) hands-on geometry with no proofs until the end of the course; and (3) experimental geometry with no proofs. (DDR)

Profiles a middle school mathematics teacher and examines her use of two problems from a pilot version of a 6th grade unit developed by a mathematics curriculum project. Reports that problem-solving-oriented curricula provide opportunities for students to make mathematics connections and leads to student confusion and uncertainty. Contains 35…

The technique of using "seed problems" involves starting with a simple problem and seeing how far it leads. It may inspire different, related problems, or it may be approached with varied tools. Problems related to points and lines, pyramids, Pythagorean quadruples, and regular pentagons are discussed. (MNS)

Discussed is changing from the lecture-and-demonstration approach to teaching which treats learning as primarily the transfer of information. The approach used in a school in New Jersey is described in detail. (MNS)

Discussed are the range and balance of learning activities in the classroom, including discussion of the various roles of the people involved. The analysis is based on records of observations of 174 mathematics lessons with students aged 12-14; microcomputer use was integrated as a teaching aid. (MNS)