Math Olympiad Contest Problems for Elementary and Middle Schools by George Lenchner. Glenwood Publications (now MOEMS), 2154 Bellmore Avenue, Bellmore, NY 11710, (516) 781-2400

Many readers of this journal have had their students participate in various mathematics contests over the years. The Math Olympiad, an interschool competition that is held five times during the school year at monthly intervals beginning in November, is one of the better-known competitions. In this book Lenchner provides 400 challenging problems, puzzles, and mathematics topics from sixteen years of Math Olympiads.

Intended for use in elementary and middle schools, this volume is not just another book of brain teasers. The introduction concisely reviews many problem-solving strategies. The appendixes are a resource of mathematics concepts, including fractions, factors, and exponents. For teachers looking for certain types of problems to supplement their lessons, a guide breaks down the book into problem types from “addition patterns” and “algebra” to “volume” and “work backward.”

The main body of the book contains eighty Olympiads of five questions each, hints for each question, answers, and detailed solutions. The book includes a glossary and an index.

Many books are available that offer problems, brain teasers, and puzzles for your students, but this one is so complete, concise, and well done that it really should be part of your professional library. – Jeff Hoyle, Dartmouth Middle School, Dartmouth, MA 02747

NEW - 2nd Edition

From:

The Arithmetic Teacher, March, 1984

(The National Council of Teachers of Mathematics)

 (Review of the first edition)

Creative Problem Solving in School Mathematics. George Lenchner. Houghton Mifflin Co.. One Beacon St.. Boston, MA 02108

This is an excellent professional resource book for teachers of elementary school mathematics. The organization and quality of materials are outstanding! Problem solving is initially defined and characterized via Polya’s How to Solve It. An excellent description of the standard heuristics for problem solving is provided with accompanying mathematical examples.

     A large portion of the text is devoted to seven common curricular themes of elementary school mathematics. Each theme has from four to eight categories of problems for investigation by students. Arriving at solutions to these problems will truly necessitate your students’ use of their problem-solving skills.

     The last section of this important book provides very complete and clearly stated solutions to the problems. This book is an excellent resource from stem to stem.

FROM:

CURRICULUM REVIEW                  FEBRUARY 1984

 (Review of the first edition)

Creative Problem Solving In School Mathematics

George Lenchner

Creative Problem Solving in School Mathematics helps elementary and middle school teachers improve each student’s ability to solve problems. Its emphasis is on teachers “learning by doing” — trying out new approaches and techniques. Through these experiences, mathematics teachers should gain fresh insights and ideas for their classroom teaching.

     The content falls into three major sections on teaching techniques, problem-solving strategies, and relating problem solving to standard topics of the school mathematics curriculum. A special section on resource problems follows.

     The resource problems consist of 20 problem sets (100 problems) written by the author for use in Mathematics Olympiads for Elementary Schools (MOES). These Olympiads are interschool mathematical competitions instituted by the author and held five times during each school year. The 20 problem sets may be used by teachers wishing to conduct an Olympiad Competition in their schools.

     While problem solving has received considerable attention recently, George Lenchner points out that the “ultimate goal of school mathematics at all times has been to develop students’ abilities to solve problems.”

     He distinguishes between an exercise, where the procedure is known, and a problem, where the solution strategy is unknown, thereby requiring some creativity on the part of the problem solver. He discusses in considerable detail the four-step method advocated by George Polya: understanding the problem, planning how to solve the problem, carrying out the problem, and looking back. In addition, he devotes considerable attention to planning how to solve a problem through such strategies as drawing a picture or diagram, finding a pattern, making an organized list, making a table, solving a simpler problem, trial and error, experimenting, acting out the problem, working backwards, writing an equation, and using deduction.

     The topics in the problem solving section cover number patterns, factors and multiples, divisibility, fractions, geometry and measurement, clocks and things, and logic. The topics are presented as examples for teachers to experiment with and to use in preparing their own problem sets for pupils. Numerous line drawing, diagrams, illustrations, tables, and pictures reinforce the activities. The solutions to these problems are more than routine answers, they give detailed explanations and helpful suggestions for each problem set.

     Creative Problem Solving in School Mathematics should be an excellent resource book for elementary and middle school teachers. Some sections also have applications for the secondary school level. Moreover, the book would be helpful in inservice courses.

     This carefully prepared and mathematically sound resource book should stimulate teachers’ interest in problem solving and encourage them to approach problem solving as a creative aspect of mathematics teaching. The book will make a significant contribution to the available literature dealing with elementary school mathematics teaching.

Wilbur H. Dutton, Ed.D.— Professor Emeritus of Elementary Mathematics, University of California, Los Angeles.

Letters to Dr. Lenchner:

“Your book, Creative Problem Solving in School Mathematics, is the best I’ve seen for upper elementary grades.”

Rachel C. Hopkins, Norfolk Academy VA

“The layout, content, and problems are all really terrific. I’m teaching a 4 session course on problem solving … and I included your book as number 1 on my bibliography. I have recommended it highly to those people taking the course.”

Sandy Cohen, Oceanside NY

During Math Olympiad practice sessions, I used Creative Problem Solving in School Mathematics as a source book for problems. The students found the problems both challenging and interesting. I have also used many of the problems in the undergraduate course, which I teach for prospective elementary teachers. I am interested in providing inservice instruction for other teachers who are teaching problem solving in their classrooms.

Margaret Bangs, Fullerton CA

“Your enthusiasm and love for mathematics jump out of every page. … Not only are all my students deriving special benefits from your book but I too have improved my ability to solve math problems. Your method of working out challenging problems through an organized approach has enabled all of us to confront mathematics without fear. In the past you have inspired me to teach mathematics in a creative and thoughtful way. Your new book serves to reinforce your previous insights into the learning process.”

Florence Shapiro, Valley Stream NY