For the mathematics experience to be liberating, the curriculum must share how and why mathematical knowledge is developed, with special emphasis on its grounding in belief, intuition and subjectivity, and facilitate our understanding of the world in which we live and create and the beliefs we act upon. (Author)

Five exploratory activities arising from work by sixth-grade students are described. They concern geometric ideas and number concepts, including fractions. Illustrations are included. (MNS)

A one-to-one teaching session with a student is described and analyzed in an attempt to communicate how student attempts at discovery in mathematics can be thwarted by teachers who do not allow room for creativity. (MP)

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)

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…

Examines the use of spreadsheets for solving equations by the method of iterations. The combination of the spreadsheets and graphical representation is shown to be appropriate both for teaching and learning the method of iterations and for investigating properties of equations. (Author)

Presents an alternate form of assignment, called "Special Problems," that incorporates writing in journals into the mathematics classroom. The method requires students to provide process narratives to accompany selected homework exercises. Allows the teacher to monitor the student's thought processes and development. (MDH)

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)

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)

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)