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.”

feature photo above by Junya Ogura via flickr (CC BY 2.0)

A couple of weeks ago, James Tanton launched a wonderful resource: a free online course devoted to quadratic equations. (And he promises more topics to come.)

Kitten and I have been working through the lessons, and she loves it!

We’re skimming through pre-algebra in our regular lessons, but she has enjoyed playing around with simple algebra since she was in kindergarten. She has a strong track record of thinking her way through math problems, and earlier this year she invented her own method for solving systems of equations with two unknowns. I would guess her background is approximately equal to an above-average algebra 1 student near the end of the first semester.

After few lessons of Tanton’s course, she proved — within the limits of experimental error — that a catenary (the curve formed by a hanging chain) cannot be described by a quadratic equation. Last Friday, she easily solved the following equations:

and:

and (though it took a bit more thought):

We’ve spent less than half an hour a day on the course, as a supplement to our AoPS Pre-Algebra textbook. We watch each video together, pausing occasionally so she can try her hand at an equation before listening to Tanton’s explanation. Then (usually the next day) she reads the lesson and does the exercises on her own. So far, she hasn’t needed the answers in the Companion Guide to Quadratics, but she did use the “Dots on a Circle” activity — and knowing that she has the answers available helps her feel more independent.

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.

I love math, but had forgotten why I developed a love for math in the first place. This book made me realize how experiences in my childhood lit a spark in me … Denise Gaskins shows us how we can ignite this fire in our own children.

I believe her suggestions are invaluable for homeschoolers, but essential for the many parents whose children are learning to dislike math in school.

If you’ve wavered on whether to pick up my math book, be warned: This is the last month for the introductory sale price. In January, the price will go up to $5.99 — which is still much less than what the original edition sells for, used.

You don’t need a Kindle to read an Amazon.com ebook. You can access it on your computer, tablet, or smart phone using Amazon’s Kindle Cloud Reader or a Kindle Reading App.

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!

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.

Update: Giveaways are over. Congratulations to the winners!

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.

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.

Update: I received a wide variety of answers to the Fibonacci riddle, including sheep, mice, donkeys, kittens, chambered nautilus, spiders, cow, dog, fox, sunflowers, humans, and an amoeba. Honeybees were by far the most popular wrong answer. Seven people managed to discover the correct creature. (No, I’m not telling! The answer is in the e-book, and it’s an interesting story to read.) Our official winner is Ken. Congratulations! I’ve sent you an email.

Math History E-book: Leonardo & Steve

When teachers share stories from the history of math, we help students build a mental picture of the ebb and flow of ideas through the centuries: how men and women wrestled with concepts, made mistakes, argued with each other, and gradually developed the knowledge that today we take for granted.

I taught my Math Club to use a medieval counting board, but still I have trouble imagining the historical setting. What was it really like to work and think in Roman numerals, and then to suddenly learn this new way of calculating? In Leonardo & Steve, Keith draws a parallel between Leonardo’s work and the personal computer revolution — and having lived through the latter helps me understand what it was like when the Hindu number system changed the world.

To the reader today, Leonardo’s text describes something we have been familiar with since our early childhood math classes, but at the turn of the thirteenth century, elementary arithmetic was entirely unknown. When Leonardo was writing his mammoth work, the information it contained was as new to him as to his future readers. In many cases he was working out the examples for the first time ever. He was working them out for himself as much as for his later readers.

In addition to the title characters’ stories in Leonardo & Steve, I found the mystery of the abbacus books interesting. These were small math instruction books for the lay reader, like the Treviso Arithmetic. Hundreds, perhaps thousands, of people across Italy published abbacus books (at first handwritten, later printed) in the years after Leonardo wrote Liber Abaci. And then the books disappeared from history, until scholars rediscovered and began to write about them in the 1960s.

The abbacus books were not written by people doing original mathematics, but by people who learned the new way of working with Hindu-Arabic numbers, found it exciting, and wanted to share it with others. [Sort of like math teacher blogs?]

It would have made sense if the abbacus books had been copied from Leonardo’s Liber Abbaci — but they weren’t. So where did this flood of arithmetic books come from? Keith tells a story of historical forensics, as modern-day literary detectives sift clues to find the original source of the abbacus writings.

Despite the fact that medieval authors copied freely from one another all the time, hardly any of the abbacus books contained any passages from Liber Abbaci. The vast majority of abbacus books, including all the known early ones, had almost nothing in common with Leonardo’s masterpiece. Clearly, the authors of those early abbacus books found their material elsewhere than in the dense pages of Liber Abbaci.

For a chance to win a copy of the e-book Leonardo & Steve (in your choice of format), you have two ways to enter the contest:

Scroll down and leave a comment on this post answering one (or both) of these questions: What is your favorite math history resource, or favorite math story?
Do you use math history in your teaching — and if so, how?

Post about this contest on your own blog, tweet about it, or otherwise share the news, and then come here and leave a comment telling me about your link.

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

Update: Omitting the comments by Keith Devlin and the blog carnival pingbacks, we had 34 entries in the e-book giveaway. Congratulations to Judy, Katie, Penney, Rachel, and Charlotte. I will forward your email addresses to Keith, and you should be receiving a download code for your e-book soon. Thank you all for participating!

Would You Buy Math History for the Price of a Latte?

If you don’t win the giveaway, Leonardo & Steve is available at Barnes & Noble or Amazon or Smashwords for a mere $2.99. Keith would like to hear your reaction to the book:

As an author, the short, cheap, e-book format is new to me, and I think this is the first ever popular mathematics e-book. So please let me know what you think. In addition to knowing your views of the content, I’m eager to know your reaction to the format and the price. Many fascinating stories about mathematics can be told in 15,000 words, so if authors like myself can get it right, this could be a major part of the future of popular mathematics writing.

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.

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.