Wise mathematicians are never satisfied with merely finding the answer to a problem. If they decide to put effort into solving a math puzzle, then they are determined to milk every drop of knowledge they can get from that problem. When mathematicians find an answer, they always go back and think about the problem again.
Is there another way to look at it?
Can we make our solution simpler or more elegant?
Does this problem relate to any other mathematical idea?
Can we expand our solution and find a general principle?
Our childhood struggles with schoolwork gave most of us a warped view of mathematics. We learned to manipulate numbers and symbols according to what seemed like arbitrary rules. We may have understood a bit here and a bit there, but we never saw how the framework fit together. We stumbled from one class to the next, packing more and more information into our strained memory, until the whole structure threatened to collapse. Finally we crashed in a blaze of confusion, some of us in high school algebra, others in college calculus.
As you may know, I’ve been working hard on my Let’s Play Math! books, and I’m still hoping to get at least couple of them out this summer. (Though if I keep thinking of more sections to add, I may never get them done!) I’m also finishing up the editing on my daughter’s novel and plan to release it soon.
One of the most useful resources I’ve found for self-publishing information is Joel Friedlander’s blog, The Book Designer. The last time I published my books, a dozen years ago, I made nearly every one of the mistakes he mentions in Amateur Hour Books and 5 Book Design Mistakes to Avoid.
My favorite playful math lessons rely on adult/child conversation — a proven method for increasing a child’s reasoning skills. What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?
As soon as your little ones can count past five, start giving them simple, oral story problems to solve: “If you have a cookie and I give you two more cookies, how many cookies will you have then?”
The fastest way to a young child’s mind is through the taste buds. Children can easily visualize their favorite foods, so we use mainly edible stories at first. Then we expand our range, adding stories about other familiar things: toys, pets, trains.
Are you a homeschooler? Are you happy with your current curriculum, or would you like to break out of the textbook mold and explore math through “living” books and activities? Whether you hope to replace your math program or just to supplement it, I can show you ways to turn math into a learning adventure for the whole family. Your children will build a stronger foundation of understanding when you teach math as a game, playing with ideas.
This blog originally grew out of my books, and now it’s coming full circle: New, expanded editions of my long-out-of-print books are ripening on the vine, growing out of the blog. To bring them to harvest, I’m going to need your help.
It has taken much longer than I had hoped to whip the manuscripts into form. My new goal is to publish ebook editions, since I will be able to sell them for about half what the original books cost twelve years ago. I’m hoping that I can finish at least a couple of the ebooks by mid-summer.
Someone mentioned one of my old books on the Living Math forum, which made me curious how the used copies were doing at Amazon.com. These are simple little books, 100 loose pages comb-bound together. I have seen ridiculous prices before, but this one takes the cake.
I am still at work revising (and greatly expanding) the old books so I can publish new editions. If you haven’t voted yet in my “What Do You Want from a Math Book?” survey, I’d love to hear your opinion!
As I continue to polish the manuscript for my math games book, I’ve been looking for short quotations to put at the beginning of each chapter. I’ve gathered a lot of math quotations over the years, from my own reading and from quote-collection websites. But there’s a problem with using most of these in a book, since to do it right I would have to dig up the original source of each quote and then write a letter to the publisher for permission to use it. And pay a fee that, depending on the publisher’s sense of self-importance, can run into the hundreds of dollars. Bother!
So I went digging around my rss reader to see what sort of inspiration I could find. Bloggers love to be quoted, right? And most of them are happy to give permission via email, which makes my job ever so much easier.
Here are some of the gems I’m considering. I’d love to hear your favorite quotes from math bloggers, too — or favorite passages from your own blog. Please comment!
It’s amazing that this vision of math as “getting to the right answer on your first try” even exists. I have to make, unmake, remake so many mistakes to get where I’m going. I think all mathematicians work that way.
Somehow, a big part of the experience of math is trouble. Frustration is the status quo. But when you get something—the thrill!
This blog originally grew out of my books, and now it’s coming full circle: New, expanded editions of my long-out-of-print books are ripening on the vine, growing out of the blog. To bring them to harvest, I’m going to need your help.
The Books
I’m working on the games books first because I think they will be the most helpful supplements to any math program.
Let’s Play Math! Number Games for All Ages
This book will include games like Tens Concentration and Hit Me, as well as tips for teaching negative numbers, the times table, and more. Never before published, because it was planned as the fifth book in my earlier how-to-teach-homeschool-math series, but my self-publishing experiment ended after book four.
Gotcha! Strategy Games for Math and Logic
This will include games like Math Club Nim and Avoid Three, as well as a lesson about logic and some Lewis Carroll puzzles. An earlier edition is currently available on Amazon for such an exorbitant price that I can’t recommend it to anyone.
Others to be announced, if I ever get the first two done…
Denise Gaskins' Let's Play Math 