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Olympiad Book Reviews
Math Olympiad Contest Problems for Elementary
and Middle Schools by Dr. G. Lenchner.
Math Olympiad Contest Problems for Elementary
and Middle Schools by George Lenchner. Glenwood Publications (now MOEMS), 2154 Bellmore Avenue , Bellmore , NY 11710
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,
Creative Problem Solving in School Mathematics
by Dr. George Lenchner.
From:
The Arithmetic
Teacher, March, 1984
(The National
Council of Teachers of Mathematics)
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
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,
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,
“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