Monday, September 6, 2010

Books and Math: Parts 1 & 2

As I'm trundling along, doing the posts for this resource extravaganza faire, I'm amazed at what I got myself into. Truly, we live in a blessed age for learning at home - learning anywhere, actually. There is an abundance of resources available to us and I think the tricky part (and the reason we've keep buying new bookshelves every couple of years at my house) is that it's so hard to weed through what's really fine and what's just average.

It's my goal to share with you what I think is really fine. And then you can have a chance to look through these things and decide for yourself whether or not you'd like to explore what's listed here. I've also provided links to a few sites that have lists and lists of math related books that you can peruse. I've looked at many books from these lists and I've been very happy with most of what I've seen. Our local library may have around 70% of the books listed. You can request for them to bring in new-ish books (I believe the rule is that it has to be within two years of the publication date). You can also see if it's possible to get an interlibrary loan. Some books may be out-of-print and  you can find these books at AbeBooks online for a reasonable cost.

Part 1: For You - Thinking about Math Learning

The books I'll suggest for you, the parent, aren't books that have anything to do with you learning math. Phew. I heard that. They do, however, ask you to think about how humans learn and some of them, in particular, ask you to think about how human's learn mathematics.

What Do I Do Monday? by John Holt.

John Holt was a master of observing children learning. His insights have helped so many of us discard old ways of thinking about how children learn and move on to the realization that learning happens all the time, with or without adult direction (usually without).

In this book, he specifically talks about some of his observations about children learning math and gives some ideas about how to work with children in the area of math learning. The other book of his that has a nice section on math is Learning All the Time (my favourite John Holt book).

If you read only one book about the true nature of learning, this is the book to read.

The Book of Learning and Forgetting by Frank Smith

Frank Smith is my personal hero. He's a psycholinguist, born in Britain, who started his career as a newspaper reporter and ended up with a Ph.D. in psycholinguistics from Harvard. He writes things like this: "The first is that all children know how to learn. The brain of a child is a superbly efficient and instinctive learning device, so much a part of any normal living creature that it functions automatically. The task of education is not to create or even develop the ability to learn, but to understand and respect its nature, thereby facilitating its operation. Children are not empty vessels into which teachers pour selected skills and nuggets of knowledge. Rather, if is in the child’s nature to express and develop innate intellectual capacities, integrating all experience into an intricate view of life that includes hopes and fears, loves and hates, beliefs and expectations, and attitudes towards other people and towards himself." from Comprehension and Learning

The Glass Wall: Why Mathematics Can Seem Difficult by Frank Smith

Frank Smith carries on his remarkable observations about math learning in this book, The Glass Wall. For those of us who may have any residual mathematical misgivings as adults, it's important for us to take a look at how we got there and why. It's so easy to pass on our fears and concerns about something to our children, even without intending to. Reading books like this one (and like the next one listed), we can come to the origins of our math anxieties (no matter how slight) and change our perspective.

Math: Facing an American Phobia by Marilyn Burns

Marilyn Burns has single-handedly started a revolution about how mathematics is taught in schools. Unfortunately, the only folks who have listened thus far are some scattered elementary school teachers, but at least that's something. In this book, Burns looks at the root of the "phobia" and explains how we got here and what we can do about it. It's a very accessible book and is good if you'd like to understand your own math education (and how to not replicate that with your kids!).

Raising Lifelong Learners: a Parent's Guide by Lucy Calkins

Lucy Calkins has been my pedagogical role model for many years. As a public school teacher, her books were on my pile of resources that explained and rationalized why I did what I did every day in my learner-centered classroom.

She has taken the basic ideas out of her books for teachers and compiled them in this very lovely book about supporting children's learning and it has a specific chapter on math learning that's quite good. NOTE: her children go to school so this is not a book about homeschooling. However, it is a book about truly seeing and respecting children's learning. I love it and highly recommend it to all parents of kids 10 and younger.

Part 2: For the Kids

There are tons and tons and tons of books related to Math learning that are not textbooks. Tons.

I cannot list them all. I can't even list all the ones on my own shelves as I've pulled  together quite a collection over the years. I will list the ones that I personally like the most. And I will point you to other places you can find lists (I'll do that first):

Julie Brennan's Living Math

Julie Brennan's Living Math site is a thing of beauty. She's been working on it for years and it just keeps evolving. This link leads you straight to her Math Literature page, where she has lists of books according to specific concepts. It's a fantastic resource and many of these books are worth strewing around your house or using to supplement a text-book based program.

Mathematical Fiction

These are really interesting (and sometimes quirky) lists of books where math is present - either purposefully (as in the Sir Cumference books or The Number Devil) or as a part of the story's milieu (as in Madeleine L'Engle's A Wrinkle in Time). I particularly like the list for books that aren't written to "teach" math but the author clearly enjoys math so much, he or she just can't leave it out of the story.

Hoagies Gifted Education

Don't let the word "Gifted" turn you off. Yes, this is a site pulled together by someone who feels that's an important designation. And it's a well of fabulous resource ideas. This link goes directly to their page of Math books for kids. It's a long list, separated out only by age groups (rather than topic) so it should keep you busy for some time. Have fun. :)

Our Favourites

Grandfather Tang's Story by Ann Tompert

Before you get this book, make sure you have a set of tangrams at  your house. Yes, this is a story book, but during the story, a girl and her grandfather play with their tangrams. You can make your own tangrams out of construction paper (and there is a pattern for this in the book). We have both plastic and wooden tangrams at our house and we played with them a lot when my son was younger. It's great fun to make the images in this book at the same time you read the book. My son and I would actually race to see who could get their tangram built first (his idea). There is a great amount of geometry involved in translating a tangram on the page to a physical one in front of you. Add to that a charming story, and this is a great mathematical adventure.

The King's Chessboard by David Birch

A dear friend recommended this book to me when my son was quite young -- not as a math book, though. It's simply a great story. A man does a favour for a  king and can name his reward. The man places a grain of rice on a chess board and asks that each day, the amount of rice given to him is doubled for as many days as there are squares on the chess board. This book is a powerful way to look at number and quantity.

Math for All Seasons by Greg Tang

Greg Tang has a number of engaging puzzle books that use pictures and riddles to tell math stories. These books definitely are math-focussed (with a right answer) but they provide kids with the opportunity to start thinking about how to solve math problems on paper.

The Cat in Numberland by Ivar Ekeland

Written by a professor at UBC, this is a story based on infinity. From the book description: "How can a hotel always have room for more, even when all the rooms are full? It can if it's Hotel Infinity on the faraway planet of Numberland. While their cat looks on in growing confusion, hotel proprietors Mr. and Mrs. Hilbert manage feats of hospitality impossible anywhere else in the galaxy -- with some help from Zero. Based on the concept of infinity as described by mathematicians Georg Cantor (1845-1918) and David Hilbert (182-1943), Ivar Ekeland's lively text and John O'Brien's charmingly imagined illustrations bring Hotel Infinity and its guests, the Numbers, to life for mathematicians of all ages."

The Adventures of Penrose the Mathematical Cat by Theoni Pappas

For children who love to explore the language of mathematics, I can think of no better guide than Theoni Pappas. Pappas has written a number of wonderful books on math concepts that are above and beyond what a child would encounter in a typical math class. It does help for a child to have some understanding of basic mathematical ideas, but her books are still quite accessible. This is the best one to start with. You can do a search on Amazon to find her other titles. Her Joy of Mathematics books are quite wonderful for older children.

G is for Googol by David M. Schwartz

David M. Schwartz writes great math books for kids. His How Much is a Million is a classic and he has others in that same vein. A book we quite like is his math alphabet book, G is for Googol. We've had lots of fun playing with the different math-related words in this book and it has introduced new concepts to us as well.

Our favourite bedtime routine for many years as been: "I love you. " "I love you, too." "I love you three!" "I love you [and so on...]" "I love you googolplex!" "Well, I love you infinity!"

The I Hate Mathematics Book by Marilyn Burns

We're back at Marilyn Burns, this time for kids. Marilyn was a pioneer in writing math books for kids that bring forward the beauty and ultimate coolness that is mathematics. The book is full of riddles and puzzles that are fun to figure out. And if you like this one, you'll want to check out the companion volume, Math for Smarty Pants.

These books are good for kids 9+.

The Man Who Counted by Malba Tahan

This is a book for the older child (and parent) who is interested in mathematics and also loves story. The Man Who Counted is a tale of a journey, full of puzzles and mathematical lore.

From "Here's a delightful little book that combines the joys of mathematical recreation with some fine storytelling. It follows the Arabian adventures of a man with remarkable mathematical skills, which he uses to settle conflict and give wise advice. The tales of his travels involve the solving of mathematical puzzles and sharing insights from the minds of some of history's great mathematicians. In reading it, you can almost smell the spices and feel the desert wind. You just don't find this kind of atmosphere in books about mathematics."

Murderous Maths by Kjartan Poskitt

These books are funny. Seriously funny. Trust the Brits (and their Maths) to come up with a series of books about math concepts (pre-algebra and up) that are actually entertaining and interesting.

My son was quite young when I landed these, but he read them for the funny bits. Even though he was too young to really be interested in the concepts, he still is making connections between real world conversations and information he pulled out of these books (even from the funny bits).  We're big fans and I heartily recommend them.

They are a tad hard to get a hold of. I had a local bookshop order them in for me. You can also get them online line from Fun Books or from Horrible Books.


Parts 3 and 4 of Books and Math coming soon!