IMSA Math Journal

Mathman

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Fall, 1992

Dear Friends of Mathematics:

It is with great pleasure that the Illinois Mathematics and Science Academy distributes to you our first IMSA Math Journal, designed to serve as a resource and an invitation to mathematical inquiry and engagement.

As the mathematical community knows only too well, our nation is focused on enhancing the achievement of our students in mathematics and science. In his most recent book, The Unschooled Mind, Howard Gardner cites, "The surprising fragility of mathematical understanding," in our nation's children.

In Illinois, I believe our commitment has been to design mathematical communities, learning communities in classrooms and schools that foster mathematical exploration, conjecture, and logical reasoning that develop mathematical power and self-confidence, that immerse students in the beauty, elegance, imagination, and symbolic language of mathematics, and that enable students to view mathematics as an essential language and discipline through which they can better understand the relationships, patterns, and symmetries in our universe.

This inaugural IMSA Math Journal is an attempt to invite you to share the fascinating world of mathematics and mathematical thinking. As our editors note, we invite your comments and your creative ideas. Please join us as we strive to encourage the growth of mathematical communities in classrooms across our state and the nation.

Stephanie Pace Marshall, Ph.D.
Executive Director
Illinois Mathematics and Science Academy

The Illinois Mathematics and Science Academy is proud to share the first issue of the IMSA Math Journal with mathematics teachers and students throughout the state of Illinois - and beyond. As the editors have stated, this journal is presented as a resource "to open the door to new ideas for exploration and discovery."

We believe that the effective learner of mathematics is someone who is actively engaged in doing mathematics and who, therefore, constructs meaning from his or her experiences rather than passively receiving it. We also believe that mathematics is both inherently interesting and fun to do. Both the interest and the fun are enhanced when the individual gains a sense of "mathematical power" by discovering and extending patterns, by looking for and seeing connections among the various branches of mathematical thought, by applying mathematical processes to problems in other disciplines as well as to "real life" experiences, and by exploring "elegant" or "clever" methods for solving problems. The intent is to have you develop or deepen your "mathematical habits of mind" as you read and work with the ideas presented.

The editors of the IMSAMJ are all members of the IMSA mathematics faculty. Several of the articles contained in this premier issue present problems or ideas developed or expanded for use in the IMSA math program. Many have been presented at professional meetings and student seminars. We ncourage teachers and students from other schools to use these ideas and to share their interesting problems and explorations with us through submissions for future issues.

Sue Eddins
Curriculum Team Leader, Mathematics

LETTER FROM THE EDITORS:

Welcome to the first issue of the IMSA Math Journal, an official publication of the Illinois Mathematics and Science Academy. The journal is supported by IMSA's Alliance office (now known as The Center @IMSA --ed), the office that coordinates the dissemination of IMSA progams and services to other schools in Illinois. This first school year will have two issues, the second to be published in February/March of 1993 (this second issue was never published --ed). The purpose of the IMSAMJ is to communicate through mathematics with students and their teachers. Some of our goals include:

• Publishing student written work.
• Presenting teaching insights, lessons, problems, connections, etc.
• Sharing mathematical ideas, observations, approaches, extensions and generalizations of interest to students and mathematics educators.
• Featuring math contest-level problems and solutions.
• Discussing the use of technology, especially calculators and computers, and technology's role in mathematics learning.

We look forward to hearing from both students and teachers about the IMSAMJ. Please give us feedback on what you liked, what you found to be useful and what additional items would be helpful and interesting to you. We welcome your constructive criticisms. The last page has a convenient response form for you to use.

Teachers are encouraged to make copies of the IMSAMJ, or its articles, for students' use provided the name of the author and the IMSA logo are included. We would like to incorporate student articles, solutions to proposed problems and other works in the next issue. See the front cover for guidelines. Any submissions become the property of the IMSAMJ and are subject to editing and abstraction. None will be returned, so please keep a copy for yourself. Submissions must be received at least 60 days prior to publication in order to be considered for the next issue. Responses to this issue should be returned to us by January 15, 1993. Be sure to include your full name, affilation, mailing address and status (teacher, student, . . .). If you are responding to a problem or particular article, make specific reference to the title, page and issue. We hope you will find enjoyable and worthwhile materials in our publication.

Titu Andreescu, Charles Hamberg, George Milauskas
Illinois Mathematics and Science Academy

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