Homeschooling – Page 24 – Denise Gaskins' Let's Play Math

Update: My Math Books

Posted on April 27, 2012May 13, 2022 by Denise Gaskins

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.

Nearly a year ago, I wrote:

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.

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PUFM 1.1 Counting

Posted on April 24, 2012September 29, 2023 by Denise Gaskins

Photo by Iain Watson via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.

Many things in mathematics need to be understood relationally — that is, in relationship to other concepts. But some things just need to be memorized. How do you know which is which? A homeschooling friend pointed out that one thing children definitely need to memorize is the counting sequence from 1-100 and beyond. While there are some patterns that make counting easier, one does just have to memorize which “nonsense sounds” we have attached to each number.

Another sort-of counting that young students should master is subitizing — recognizing at a glance how many items are in a small group. Children do this instinctively, but we can help them develop the skill by playing subitizing games.

[Aside: In writing this blog post, I ran into some nostalgia. Back when we first did these PUFM lessons, my daughter Kitten was only a toddler. I wrote, “I’ve tried to do lots of counting with my youngest, who hasn’t quite gotten beyond, ‘…eleven, twelve, firteen, firteen, nineteen, seven,…’ The numbers tend to start appearing randomly after she gets past 10.” Ah, memories.]

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PUFM 1.0 Preface

Posted on April 17, 2012September 13, 2023 by Denise Gaskins

Profound Understanding of Fundamental Mathematics (PUFM) is a phrase coined by Liping Ma in her landmark book, Knowing and Teaching Elementary Mathematics, to describe the deep, broad, and thorough understanding exhibited by several of the Chinese teachers she interviewed.

You gain PUFM the hard way: by teaching. The Chinese teachers with PUFM were the ones who had taught for years, taught multiple levels, and studied intensively the materials they taught. I doubt there’s any other way to do it. Home schooling is great for developing PUFM because you teach for years and teach multiple levels. The problem is, by the time you really understand the stuff, the kids are grown. Here are a few hints to help speed up the process a little bit:

Learn as much as you can, wherever you can, even when the topic doesn’t seem to relate to what your kids are studying now. Ask questions.
Pick up library books on math (510-519 on the Dewey Decimal shelves), some of which you’ll find helpful and some will bore you to distraction. Read the helpful ones and return the others — but try to get through at least 10 pages of a math book before giving up. You’ll learn a lot that way.
Always look for connections between topics. Think about how addition and subtraction are related, or addition and multiplication, or fractions and division. Think about how the different levels of understanding a topic are related. (Hint: Start by reading the lesson titles as well as the lessons themselves. Lay out a few years’ worth of math books and just read lesson titles, to see how it all goes together.)
Work on picking up the math vocabulary (distributive property, factors, sum, numerator, etc.) yourself and using it as you teach. Having the right words will help you hold ideas in your mind.

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PUFM 1.0 Introduction

Posted on April 9, 2012September 13, 2023 by Denise Gaskins

The Chinese teachers with PUFM didn’t get it automatically. It grew over many years of teaching several levels of elementary math and of studying their textbooks and teaching materials. They met weekly in teaching research groups to learn from each other’s experience, to find multiple ways to solve problems, and to broaden their mathematical understanding.

More than eight years ago, a group of homeschooling friends started a Yahoo “teaching research group” to discuss math in hope of deepening our own understanding and learning to better help our students. We had a good time, but the busy-ness of everyday life eventually won out. The group has mostly disbanded, though the archives remain. Now I’d like to bring that study to my blog, bit by bit, updated with things I’ve learned in the years since.

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Skit: Knights and Knaves Logic Puzzles

Posted on April 2, 2012May 13, 2022 by Denise Gaskins

photo by puuikibeach via flickr

Our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned. I planned to set up a static display showing some of our projects, like the fractal pop-up card and the game of Nim, but the students voted to do a skit based on the logic puzzles of Raymond Smullyan.

We had a small class (only four students), but you can easily divide up the lines make room for more players. We created signs from half-sheets of poster board with each native’s line on front and whether she was a knight or knave on the flip side. In the course of a skit, there isn’t enough time to really think through the puzzles, so the audience had to vote based on first impressions — which gave us a fair showing of all opinions on each puzzle.

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What I’m Reading: Fermat’s Enigma

Posted on March 5, 2012September 13, 2023 by Denise Gaskins

Homeschooling is much more than just doing school at home — it’s a lifelong lifestyle of learning. And thanks to the modern miracle of inter-library loan, even those of us who live in the middle of nowhere can get just about any book sent directly to our tiny home-town libraries.

As I mentioned in Math Teachers at Play 46, I’m trying to add more living books about math to our homeschool schedule, including my own self-education reading. So, a copy of Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem finally showed up at my library, and I am thoroughly enjoying it.

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Do You Teach Math to Young Children?

Posted on February 4, 2012September 13, 2023 by Denise Gaskins

Sue VanHattum is trying to convince the publishers that this excellent book would reach a wider audience if they made it available at a lower price. What do you think?

As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn ﬁrst? How hard should they work? Should they even “work” at all? Should we push them, or just let them be?

There are no correct answers to these questions, and Zvonkin deals with them in classic math-circle style: He doesn’t ask and then answer a question, but shows us a problem — be it mathematical or pedagogical — and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced.

This book is not a guidebook. It does not purport to show you how to create precocious high achievers. It is just one person’s story about things he tried with a half-dozen young children. On the other hand, if you are interested in running a math circle, or homeschooling children, you will ﬁnd this book to be an invaluable, inspiring resource. It’s not a “how to” manual as much as a “this happened” journal. … Just about every page contains a really clever teaching idea, a cool math problem, and an inspiring and funny story.

— Paul Zeitz
Introduction to Math from Three to Seven

Super Bowl XLVI Math Worksheet and Football Comic

Posted on February 1, 2012May 13, 2022 by Denise Gaskins

Lance Friedman of MathPlane.com has posted two bits of fun in honor of Super Bowl XLVI. (Click the images to go to Lance’s site.) And if you’re a homeschooler, Currclick is offering a Super Bowl Mini-Helper free this week.

NFL Math Quiz

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Free Math from Dover Publications

Posted on July 18, 2011May 13, 2022 by Denise Gaskins

I love Dover books, don’t you? They publish so-o-o-o-o many interesting titles at reasonable prices. I always have several Dover books on my wishlist, waiting for my next bit of extra cash.

But you don’t have to wait to enjoy free math from Dover books. Sign up for the Dover Sampler, and each week they will send an email with links to content from all sorts of books. Or try the Dover Children’s Sampler and Dover Teacher’s Sampler for coloring books, mazes, literature, and more. All the Dover samplers are completely free, and you can cancel at any time.

From Last Week’s Sampler

Last week’s email included a section on “Exploring Mathematics”:

And that’s only the beginning. Below, I’ve listed a wide variety of math-related links collected from past samplers. Though be warned: Dover does change its website from time to time, so these pages may disappear without notice.

Download, print, enjoy!

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Working on My Let’s Play Math! Books

Posted on April 25, 2011May 13, 2022 by Denise Gaskins

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…

Continue reading Working on My Let’s Play Math! Books