Update: The crowdfunding campaign is now closed and the book is in the final stages. It should be headed to the printer soon. Check the Playing With Math homepage for publication and ordering information.

What do mathematicians do? We play with math. What are little kids doing when they’re thinking about numbers, shapes, and patterns? They’re playing with math. You may not believe it yet, but you can have fun playing with math, too.

— Sue VanHattum, editor

We had a discussion at the end of the club on how we are all confused now, but pleasantly so, and how important it is to rejoice in confusion and to be comfortable with it. Adults often strive very hard to get rid of any and all possible traces of confusion for kids, making things dreadfully boring.

— Maria Droujkova, after a math circle exploration of infinity

All it talkes to do mathematics is opportunity, a frustrating problem, and a bit of stubbornness.

— Ellen Kaplan, math circle leader

Our own school experiences can make it hard for us to teach without being tempted to “help them master” a concept that they may or may not be ready to master. What we never learned in school was the concept of playing around with math, allowing ideas to “percolate,” so to speak, before mastery occurs, and that process may take time.

Update: The crowdfunding campaign is now closed and the book is in the final stages. It should be headed to the printer soon. Check the Playing With Math homepage for publication and ordering information.

There’s a problem: Most people don’t like math. Why is that? Perhaps it has something to do with the way math is taught in school. As a teacher to my own kids and mentor to homeschooling parents, I’ve been fighting math anxiety for decades.

This book is one part of the solution.

Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers features more than thirty authors who tell delightful stories of learning to appreciate math and of sharing their enthusiasm with their communities, families, or students. After every chapter is a puzzle, game, or activity to get you and your kids playing with math, too.

You can read a couple of excerpts at PlayingWithMath.org:

Whether you love math and want to share it with your kids, or whether you fear and loathe math and need help getting over that hurdle so you won’t pass your fear on, Playing With Math will encourage you to see math more deeply and play with it more freely.

I’ve been waiting for this book for years, and I’m thrilled to see it finally come together. As I read the advance copy (review coming soon!), I am amazed at how many different ways there are to think about math. Each writer has a new perspective and unique insight, and my quotes journal is filling up with inspiration.

A Word from the Editor

The idea of crowd-funding may be new to you. Here’s how it works:

Today is the first day of our crowd-funding campaign. For a contribution of $25, we’ll send you a book as soon as it’s printed.

You can contribute anything from $1 to $5000 (with rewards at each contribution level) to help us pay for our illustrators, editors, page layout person, and printing. This is our way of asking for community support for this book as part of the production process. We hope to build lots of energy around the ideas in the book through this campaign.

Besides contributing, here’s another way you can help: Think of five friends who would enjoy this book.

Do you have friends who get frustrated helping their kids with math homework?

Or who teach young kids but don’t feel comfortable with math themselves?

Do you have friends who enjoy math?

Or who want ideas to share with the kids in their lives?

Do you know someone who might want to start a math circle?

Would you send them a quick message, to let them know we’re here?

I’m hoping for the power of exponential growth with this. Our outrageous goal is to change the way people all over this country, and maybe even the world, think about math. If you each send this to five friends who might enjoy the book, and each of them sends it to five friends, and each of them … Well, pretty soon we cover the world, right?

In fact, if we kept it going through eleven steps, that would make 5 to the 11th power, or over 40 million people. Does Sue dream big? Yep.

It’s a short book with plenty of great stories, advice, and conversation-starters. While Danielson writes directly to parents, the book will also interest grandparents, aunts & uncles, teachers, and anyone else who wants to help children notice and think about math in daily life.

You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.

You don’t need to love math. You don’t need to have been particularly successful in school mathematics. You just need to notice when your children are being curious about math, and you need some ideas for turning that curiosity into a conversation.

In nearly all circumstances, our conversations grow organically out of our everyday activity. We have not scheduled “talking math time” in our household. Instead, we talk about these things when it seems natural to do so, when the things we are doing (reading books, making lunch, riding in the car, etc) bump up against important mathematical ideas.

The dialogues in this book are intended to open your eyes to these opportunities in your own family’s life.

Do you enjoy math? I hope so! If not, browsing this post just may change your mind. Welcome to the Math Teachers At Play blog carnival — a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college.

Let the mathematical fun begin!

POLYHEDRON PUZZLE

By tradition, we start the carnival with a puzzle in honor of our 62nd edition:

An Archimedean solid is a polyhedron made of two or more types of regular polygons meeting in identical vertices. A rhombicosidodecahedron (see image above) has 62 sides: triangles, squares, and pentagons.

How many of each shape does it take to make a rhombicosidodecahedron?

Click for template.

My math club students had fun with a Polyhedra Construction Kit. Here’s how to make your own:

Collect a bunch of empty cereal boxes. Cut the boxes open to make big sheets of cardboard.

Print out the template page (→) and laminate. Cut out each polygon shape, being sure to include the tabs on the sides.

Turn your cardboard brown-side-up and trace around the templates, making several copies of each polygon. I recommend 20 each of the pentagon and hexagon, 40 each of the triangle and square.

Draw the dark outline of each polygon with a ballpoint pen, pressing hard to score the cardboard so the tabs will bend easily.

Cut out the shapes, being careful around the tabs.

Use small rubber bands to connect the tabs. Each rubber band will hold two tabs together, forming one edge of a polyhedron.

So, for instance, it takes six squares and twelve rubber bands to make a cube. How many different polyhedra (plural of polyhedron) will you make?

Can you build a rhombicosidodecahedron?

And now, on to the main attraction: the 62 blog posts. Many of the following articles were submitted by their authors; others were drawn from the immense backlog in my blog reader. If you’d like to skip directly to your area of interest, here’s a quick Table of Contents:

Homeschoolers, after-schoolers, unschoolers, or anyone else: if you’re a parent with kids at home, you need this book. If you work with children in any way (grandparent, aunt/uncle, teacher, child care, baby sitter, etc.) you need this book. Or if you hated math in school and never understood how anyone could enjoy it, you need this book!

Moebius Noodles is a travel guide to the Math Universe for adventurous families (and it has lots of beautiful pictures, too!) featuring games and activities that draw out the rich, mathematical properties of everyday objects in ways accessible to parents and children:

A snowflake is an example of a fractal and an invitation to explore symmetry.

Cookies offer combinatorics and calculus games.

Paint chips come in beautiful gradients, and floor tiles form tessellations.

When I first heard about Swagbucks, I figured there had to be a catch. How could they give away real money just for using their search engine? But over the past four years, I’ve collected nearly $600 worth of freebies, mostly for doing internet searches I would have done anyway.

I trade in my Swagbucks for Amazon.com gift certificates, with which I’ve bought Christmas gifts, printer ink, groceries, and (splurging on myself!) several math books, including Paul Lockhart’s new Measurement.

Would you like to earn free books, too? Check it out:

Swagbucks Search & Win
[To get a quick 50 Swagbucks, enter the code “SPRINGIN2SWAG” (for April 2013) when you sign up.]

I cleaned up the clutter on my other blog, and so I decided to make a page about my daughter’s book, which meant taking the time to pull out excerpts from her reviews. And since I hadn’t posted anything about her on this blog for a couple of months, I thought I’d brag a bit to you all, too.

Reviews of Banished

Banished is a captivating fantasy story with a well-thought-out plot that would be a credit to any writer. But it is especially remarkable coming from a thirteen-year-old student who has been homeschooled all her life.

Teresa Gaskins actually wrote this book as a project for the National Novel Writing Month program. One noteworthy thing about the book is that there is no sexuality or bad language (the euphemistic interjection “Blasted” is used once), so, other than those who object to the presence of any kind of magic in books, parents can let their kids read the novel with no reservations.

However, be forewarned. When you reach the final page and find the words, “Not the End…,” you will cry, “Oh! No!” The story does not resolve itself at the end and then pick up in a sequel. Rather, the plot is left hanging at the end and will continue in another book. I for one feel as if I simply can’t wait to read the next installment to find out what happens to Chris and his friends. It’s that good!

Who Killed Professor X? is a work of fiction based on actual incidents, and its heroes are real people who left their mark on the history of mathematics. The murder takes place in Paris in 1900, and the suspects are the greatest mathematicians of all time. Each suspect’s statement to the police leads to a mathematical problem, the solution of which requires some knowledge of secondary-school mathematics. But you don’t have to solve the puzzles in order to enjoy the book.

Fourteen pages of endnote biographies explain which parts of the mystery are true, which details are fictional, and which are both (true incidents slightly modified for the sake of the story).

I ordered Who Killed Professor X? from The Book Depository (free shipping worldwide!), and it only took 5 days to arrive here in the middle of the Midwest. My daughter Kitten, voracious as always, devoured it in one sitting — and even though she hasn’t studied high school geometry yet, she was able to work a couple of the problems.

After watching the video on the Amazon.com page, this book has jumped to the top of my wish list.

You may have read Paul Lockhart’s earlier piece, A Mathematician’s Lament, which explored the ways that traditional schooling distorts mathematics. In this book, he attempts to share the wonder and beauty of math in a way that anyone can understand.

According to the publisher: “Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living. Favoring plain English and pictures over jargon and formulas, Lockhart succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable.”

If you take any 4-sided shape at all — make it as awkward and as ridiculous as you want — if you take the middles of the sides and connect them, it always makes a parallelogram. Always! No matter what crazy, kooky thing you started with.

That’s scary to me. That’s a conspiracy.

That’s amazing!

That’s completely unexpected. I would have expected: You make some crazy blob and connect the middles, it’s gonna be another crazy blob. But it isn’t — it’s always a slanted box, beautifully parallel.

WHY is it that?!

The mathematical question is “Why?” It’s always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it.

So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems.

Banished is a captivating fantasy story with a well-thought-out plot that would be a credit to any writer. But it is especially remarkable coming from a thirteen-year-old student who has been homeschooled all her life.
…
However, be forewarned. When you reach the final page and find the words, “Not the End…,” you will cry, “Oh! No!”
…
I for one feel as if I simply can’t wait to read the next installment to find out what happens to Chris and his friends. It’s that good!

My 13-year-old daughter just released her first book on Kindle:

Banished (The Riddled Stone, Book One)
Falsely accused of stealing a magic artifact, Chris is forced to leave home, never to return. As he and three friends travel toward the border, however, they are warned of great danger approaching the land. They set out to solve an ancient riddle — but will they be able to save the kingdom, or will the quest cost them their lives?

[Update 7/6/12: The paperback book is now “In Stock” at Amazon (yay!). They are even including the book in their buy-3-get-1-free promotion for books and home/garden items.]

Teresa (also known as Princess Kitten) has done the NaNoWriMo Youth Program as part of her language studies for the past three years and has written many stories on her blog, but this is the first time we’ve followed through and published one of her books.

Of course I’m biased, but I think she did a pretty good job, as first books go. It’s clearly the beginning of a series, so she sets up more plot threads than she resolves — but I did convince her not to wait for this year’s NaNoWriMo to start Book Two. (I want to find out what happens next!)

Anyway, if you or your kids enjoy fantasy fiction and are interested in reading something written by a teenage homeschooler — and if you have a Kindle or Kindle Reading App — please download the sample chapters of her book and check it out. She would love to get some reviews!

Cat and Mice
Purrer has decided to take a nap. He dreams he is encircle by 13 mice: 12 gray and 1 white. He hears his owner saying: “Purrer, you are to eat each thirteenth mouse, keeping the same direction. The last mouse you eat must be the white one.”

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.

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.

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!

To celebrate their re-release of his classic puzzle books, the Dover Math and Science Newsletter featured an interview with Raymond Smullyan, as well as several extended excerpts from his books. (For my math club students: Professor Smullyan invented the Knights and Knaves puzzles.) Enjoy!

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.

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.

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! Here is a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college. Some articles were submitted by their authors, others were drawn from the immense backlog in my blog reader. If you like to learn new things, you are sure to find something of interest.

My math club had fun with several of these puzzles a few years ago, and the “Easy” ones (like the sample shown here) were just right for my 4th-5th grade students. One girl enjoyed them enough that she took home extra copies to share with her father.

It’s a thin book, just the right size for a stocking-stuffer. To see the full range of difficulty levels, look over the puzzles on Bogusia’s Daily Hexa-Trex page. To get your own copy of the book, read the giveaway instructions on Bogusia’s blog.

Object of the Puzzle

The object of the puzzle is to find the equation pathway that leads through ALL the tiles.

Forming Equations

Two or three (or four or five etc.) digit numbers are made up of the individual tiles in the particular order as the equation is read. For example 5 x 5 = 2 5 is correct, but read backwards 5 2 = 5 x 5 is incorrect.

The equation must be continuous (no jumping over tiles or empty spaces).

Each tile can be used ONLY ONCE.

Order of operations is followed. Multiplication and division comes before addition and subtraction.

The tile “-” can be used as both a subtraction operation or a negative sign in front of a digit, making it a negative number.

Kitten complained that some math programs keep repeating the same kind of problems over and over, with bigger numbers: “They don’t get any harder, they just get longer. It’s boring!”

So we pulled out the Counting lessons in Competition Math for Middle School. [Highly recommended book!] Kitten doesn’t like to compete, but she enjoys learning new ideas, and Batterson’s book gives her plenty of those, well organized and clearly explained.

Pizzas at Mario’s come in three sizes, and you have your choice of 10 toppings to add to the pizza. You may order a pizza with any number of toppings (up to 10), including zero. How many choices of pizza are there at Mario’s?

[The book said 9 toppings, but I was skimming/paraphrasing aloud and misread.]

What Leonardo did was every bit as revolutionary as the personal computer pioneers who in the 1980s took computing from a small group of “computer types” and made computers available to, and usable by, anyone. Like them, most of the credit for inventing and developing the methods Leonardo described in Liber Abbaci* goes to others, in particular Indian and Arabic scholars over many centuries. Leonardo’s role was to “package” and “sell” the new methods to the world.

The appearance of Leonardo’s book not only prepared the stage for the development of modern (symbolic) algebra, and hence modern mathematics, it also marked the beginning of the modern financial system and the way of doing business that depends on sophisticated banking methods.

* Leonardo of Pisa, also known as Fibonacci, used two b’s in the word “calculation” (abbaci) to distinguish his methods from the use of an abacus.

Can You Solve This Fibonacci Puzzle?

If you want a chance to win a personally signed copy of The Man of Numbers: Fibonacci’s Arithmetic Revolution, all you have to do is solve this riddle.

Do NOT give your answer as a comment here! If that email link doesn’t work for you, then copy my address by hand: lets play math [no spaces] at gmail dot com.

Here is the puzzle:

The Fibonacci sequence arises in the solution to a problem about a breeding rabbit population that Leonardo gave in Liber Abbaci.

But there is evidence that in another book he gave the problem in terms of different creatures. What were they?

[Hint: The answer is in the e-book, Leonardo & Steve. But this is a no-purchase-necessary contest: There are at least two places to find the answer online, if you search carefully.]

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 free gift card from Swagbucks.

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 page links from time to time). Download, print, enjoy!

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!

When you think of math do you think of a light-hearted fairy tale?

No? Then come and meet some of the delightful characters who live in Arithmetic Village.

Polly Plus collects jewels slowly and methodically, Linus Minus is carefree and loses his. Tina Times and King David Divide… well you’ll see.

The first book offers the overview of the math concepts. These are then demonstrated through the lives of each character. The books are designed to be supported by a manipulative kit [homemade: see video below] with 100 jewels, 10 golden bags, and a treasure chest…

Visit the Arithmetic Village website to read more about the books and explore the activity pages (links under each topic in the main page menu). Or check out Kim’s YouTube videos for activity 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.

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…

In the process of updating old book links (and otherwise cleaning up old posts), I’ve been spending more time than normal at the bookstore. I just noticed that Raymond Smullyan’s What Is the Name of This Book? is scheduled to come out this August — and it’s already available for pre-order. WooHoo!

Thanks to our insolvent state government, I need to go back and change all my book links. I never made much from the Amazon affiliate program, but it usually managed to cover Kitten’s school books. Oh, well, at least they haven’t closed the public libraries … yet …

Since I’m changing the old links anyway, I thought I’d give you all a chance to voice your opinions. Shall I continue to reference Amazon.com, or would you rather my book links took you to Barnes & Noble?

P.S.: For my rss subscribers, I apologize for the flood of old posts. Every time I make a change, it seems the feed releases the post anew. I’m afraid this will continue for a few weeks, since I’m using the affiliate mess as an excuse to do other long-neglected blog clean-up tasks as well. With 596 published posts, that will take awhile. I hate housecleaning!

You can see the publisher’s description of the book and read an excerpt here.

They also sent me a review copy, which I hope to write a blog post about sometime soon — though with our schedule this semester, I can make no promises. But from a quick flip through the book, I’ll give it a definite thumbs-up!

How to Enter the Giveaway

Remember, the book must be mailed to a U.S. address. If you live in the U.S., you have two ways to enter the contest:

Leave a comment on this post answering the question: What part of math do you find the hardest to understand or to explain to your children?

Post about the contest on your own blog (or on a homeschooling or parenting forum, if you don’t have a blog), then come here and add a comment with the link to your post.

You may do both, to double your chances — but please make sure your link is in a separate comment from your answer to the question, or I may forget to count it separately.

I will accept entries for a week and a half, through Friday, October 8th Monday, October 11th. (Extended due to family issues that made the weekend too busy!) After that, I will count up all the entries (numbered in order of their appearance in the comment section) and go to RANDOM.ORG to generate the winning number. I will email the winner to get your address, which I’ll then pass on to the publisher so they can send you your book.

Update

And the winner is . . . Lakshmi. Congratulations!

Thank you to everyone who participated in the giveaway. I enjoyed reading your comments, and you’ve given me several ideas for future blog posts.