Math Problem Solving books by George Lenchner

Creative Problem Solving in School Mathematics by George Lenchner.

and

Math Olympiad Contest Problems for Elementary and Middle Schools by George Lenchner.

Reviewed by Susan Richman

These books by George Lenchner, founder of the Math Olympiad for Elementary and Middle Schools, help your upper elmentary or junior high school students learn to solve tricky multi-step problems, the kind of problems your kids will later encounter when they take the SAT's.

The Creative Problem Solving book systematically teaches a repertoire of strategies to deal with math word problems. The Math Olympiad book gives you the actual problems from previous years, PLUS full solutions. A must for the family with a budding mathematician. Here's what Susan wrote in her reviews of each book.


Review of Creative Problem Solving in School Mathematics

by Susan Richman from Issue 27 (Spring 1989) of PA Homeschoolers newsletter.

George Lenchner, who began the Math Olympiad has written an excellent book, Creative Problem Solving in School Mathematics published by Houghton Mifflin Co. This book is one of the very best I've seen on problem solving, with clear format, specific examples all through, and suggestions for further problems of similar types. My kids especially appreciated the classifying of possible ways of going about solving problems-- trial and error, acting out a problem, using equations, making a diagram or chart, looking for a novel twist, and more.

Work at home with this books is a real help-- there are sample Olympiad sets from early years in the back, with solutions, and kids soon get to know the types of questions that are likely to be asked-- "Oh, that's another 'cryptorithm' one... aha! another painted cube problem... and there's one I could use that writing out an equation idea with." The problems become old friends in new disguises rather than frightening strangers.

Our own Math Olympiad group has just completed our last meet, and the children's scores have gone steadily up with each session...


Review of Math Olympiad Book

by Susan Richman

Many readers of PA Homeschoolers are well aware that one of my favorite programs for helping kids become top-flight young mathematicians is the Math Olympiad for Elementary and Middle Schools program. I first found out about this challenging yet very friendly math competition way back when our oldest son Jesse was in sixth grade, and I believe our little group of 8 homeschoolers was the very first homeschoolers' team in the world to take part. What a window into the excitement of really tough multi-step problem solving, unique non-routine problems, and the fun of working together with other kids on mathematics. Math became suddenly a social activity, a reason to get together regularly with friends, something to talk and share about and have a great time with. It has always been exciting somehow to us to know that over 80,000 kids all over the world are taking part in doing these same problems just like we are-- we feel part of a much larger community of young mathematicians. We've been coaching a team of homeschooled kids in the Math Olympiad ever since that first year, and I continue to feel it is the very best possible preparation for a really strong math program that you can give your kids. It's been so exciting to see how so many other homeschoolers have also taken part-- there must now be over a dozen Math Olympiad team among homeschoolers just in PA, and there are more all across the country.

So I was delighted to see that Dr. George Lenchner, the founder of the Math Olympiad, has just revised and expanded his excellent book Math Olympiad Contest Problems, containing all of the Olympiad problems from the last sixteen years. The book, aimed at students from 4th to 8th grades, also has many helps to problem solving, including a wonderful section of "hints" on how to get going on each problem in the book, followed by even more detailed solutions to all the problems-- and often several possible ways of going about a problem also. Parents can photocopy the Olympiad problem sets for their children too, and is nicely laid out for this purpose with the five problems from each set on their own page. The problems are very similar to the problems many of you have become familiar with through the excellent Figure it Out workbooks that we also sell in our catalog-- just a bit harder in general. This book is the real thing, the next step.

This is obviously an invaluable resource for a homeschool parent who is coaching an official Olympiad team, as you can let your team members practice with actual old problems sets. But the book would also be a great supplement for any upper elementary or middle school math program at home, and can be used over a number of years. I also wouldn't be at all surprised to see some high school homeschoolers who could benefit from these terrific problems-- they involve the same type of problem solving skills often tested on the SAT, in fact. I think homeschool dads in particular might really enjoy sitting down with several of the older children in an evening and working through a few of the problems for fun-- and I guarantee that Dad will find here many problems to really challenge his thinking also!

I hear from some parents who lament that their child just isn't "ready" for such tough problems, because basic computation is what they still really need to work on. And so they ignore problem solving altogether and only do drill, and drill, and drill, and more drill. And often their kids never get very good at math, even at that basic computation that they spend so much time on. I'd go for problem solving any day, myself, and let the child develop both their number sense and their computation skills while solving some intriguing real problems. Just today Hannah and her friend Becky were working cooperatively on a Math Olympiad homework set. In the course of their work they had to do long multiplication-- in fact their task was to find a number that when multiplied by itself would come closest to a given 4-digit number, so they actually had to do MANY calculations to gradually get closer and closer to the correct answer. They had to add up series of numbers, but in the context of seeing how many combinations of certain coins they could make given certain problem parameters. They had to multiply with fractions, use all basic operations, know basic math terms, and much more-- quite a plateful for a 4th and 6th grader, and they were also having a great time together to boot, because these problems just aren't like other math problems you come across in most textbooks.

So don't feel that computation practice will be missed by spending more time with more challenging word problems-- students are not allowed to use calculators on the Math Olympiad, and so need to continually work hard to develop sound computational strategies. And more importantly they develop their number sense. And in a given set of five problems your child will be asked to use a much wider range of computational procedures than in almost any math book.

It all reminds me of something I read once about a visitor from Germany who was touring American schools and was surprised to find so much emphasis on computation in isolation. He stated that in Germany they never were given mere pages of computations to do, but were always asked to work in the context of multi-step word problems, using the new computational strategies they had been learning in varied ways. Or it also reminds me of when I heard a person working for the math division of the PA Department of Education stating that if, after 12 years of schooling all a kid can do is basic computation, than we haven't helped the child become anything more than a cheap $3.00 pocket calculator. But to help a child use a growing range of math strategies and computational skills to solve real and challenging problems-- that's something that no calculator can do at all.

So I hope you try this book, and try the Math Olympiad. With supportive help from you as you work along side your kids to solve these problems, as you find yourself talking mathematics with your kids instead of just checking their work, you'll find your kids gaining a whole different feel for mathematics. This book can be an important step in making that transition.

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