This article details how certain mathematical "discoveries" that Cavazos' fourth graders made were recorded throughout the year. Cavazos invited a math professor, a biologist, a literacy professor, a chemist, a statistician, and an engineering student, as well as their school principal and computer lab technician, both of whom are…

This article outlines a series of investigations in graph theory which simultaneously gives exercises in visualization. It is argued that one of the advantages of classroom investigations is that students can be lead to an intuitive grasp of advanced mathematics. (PK)

Explores families of parabolas that result from the graphs of quadratic functions. Computer software allows students to quickly depict a series of graphs and make conjectures about emerging patterns. Discusses cases in different parameters in the quadratic are varied to produce different effects in which the parabolas. (MDH)

Student research projects are open-ended questions or sets of questions intended to give undergraduate students experience doing introductory mathematical research. Proposed is an investigation of a Faro shuffle that is performed by cutting the deck exactly in half and then perfectly interleaving the cards of the two halves. (Author/JJK)

Describes an activity in which geometry and trigonometry are studied using pyramids. Identical model pyramids are constructed from card stock, along with pyramids of different proportions and cuboids to use as controls. Also includes an investigation of some apparently non-scientific claims. (DDR)

Gives an example of an open exploration using trigonometric relationships in which the law of cosines can be deduced from the law of sines. Discusses the characteristics and value of the exploration process. (MDH)

Discusses the use of the computer software MINITAB in teaching statistics to explore concepts, simulate games of chance, transform the normal variable into a z-score, and stimulate small and large group discussions. (MDH)

Describes the Microworld Chance, a simulation-oriented computer environment that allows students to explore probability concepts in five subenvironments: coins, dice, spinners, thumbtacks, and marbles. Results of a teaching experiment to examine the effectiveness of the microworld in changing students' misconceptions about probability are…

Presents a worksheet on graph paper that allows students to determine the perpendicular bisectors of given segments by folding the paper. Students then determine the slopes of the perpendicular bisectors and use inductive thinking to discover the relationship between the slopes of perpendicular lines. (MDH)

This review features new examples of using the computer relative to college-level mathematics to enhance pedagogy, solve problems, and model real-life situations. Included is a LOGO program that can be used to create and to stimulate subsequent investigations of spirolaterals, those figures generated by repeatedly drawing basic loops. (JJK)

Explores the use of dialogue and dramatization to reconstruct the formation of mathematical concepts. An appendix provides the synopsis of a 6-scene play that portrays the rise of negative numbers over a period of 300 years. (MDH)

Focusing on how expert writers in various disciplines convey complex ideas, this paper shows how the techniques used by the mathematician, Clark Kimberling, in various writings can (1) be transferred to other disciplines, (2) show learning taking place, and (3) provide models for students to re-enact learning in all subject areas. The paper…

Discusses possible approaches to solving the problem of how many different triangles can be formed on an n x n geoboard and the different geometric concepts utilized to formulate a solution. Approaches include counting strategies, writing a computer program, and using difference equations. (MDH)

Presents two worksheets that ask students to count and classify the triangles that can be formed with a given total number of toothpicks or a given number of toothpicks for one side of the triangle. A third worksheet asks students to identify patterns observed during the investigations. Provides reproducible worksheets. (MDH)

Highlights combinatorial problems appropriate for students aged 4 to 12 years that utilize manipulatives in a hands-on approach. Examines and identifies students' strategies and self-monitoring techniques that produce effective problem solving. (MDH)