Discusses how American and Canadian Indians created mathematical connections and the first numeration systems used north of Mexico. A listing of various tribes, their locations, and how their simple or complex methods of computing may have originated from establishing a correspondence between different parts of the body and quantities they wished…

Demonstrates how mathematics is a changing science through an in-depth look at the history of the development of logarithms. Serves as a reminder to continue to remember and appreciate the efforts and contributions of past mathematicians. (KHR)

This article focuses on understanding the teaching and learning of division from a constructivist perspective. An overview of constructivism is provided, followed by a discussion of division in the context of both computation and word problem solving. Suggestions are provided for teaching students with learning disabilities using a constructivist…

Reviews the use of chi-square statistics for goodness of fit. Examines how to help students relate their earlier work with independence to the use of chi-square statistics. (KHR)

Describes how open-ended writing prompts provide a window into student understanding and mathematical thinking. (YDS)

Presented is a script for a classroom presentation introducing weighted means and geometric means to students who are already familiar with arithmetic means. Frequent questioning is included to keep the students mentally active and involved in the development of this new idea. Typical student responses to these questions are provided. (CW)

Discussed is the tendency of students to equate the concepts of continuity and connected graphs based on their lack of an understanding of such concepts as limit points, closed sets, and connected sets. Included is a theorem with three lemmas with their proofs. (KR)

Discussed is the problem of inscribing a rectangle of maximum area in a given right triangle. Answered is whether there is an advantageous orientation and whether a corner of the rectangle of maximum area can lie on the midpoint of a leg of the triangle. (KR)

Describes how to get equations for parabolas, ellipses, and hyperbolas from conic sections. Provides diagrams both in perspective and in cross-section for each case. (YP)

The main features of the theoretical framework of French research in didactical mathematics are presented. An example is given that presents the rationale for the construction of a didactical situation and its analysis. (CW)

Discusses when to use the computer, paper-and-pencil, or mental-computation procedures. Provides examples of solving problems dealing with roots of polynomial using computer graphing and other strategies. Suggests implications for curricular planning. (YP)

Describes an activity for developing an understanding of the unit rates associated with a proportional relationship. Provides the material, objectives, directions, four worksheets, and answers of the activity. (YP)

Discusses the use of mathematical modeling. Describes types, examples, and importance of mathematical models. (YP)

Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)

There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)