6th Annual Math Circle Summer Teacher Training Institute at Notre Dame

This is the most math fun I've ever had. I went three years in a row, and then decided I had to branch out, and do something else with my summer. (I went to Maria Andersen's fabulous tech training that year.) I missed the Institute so much I found a way to go back the next summer. And I am now officially going this summer! I can't wait to meet all the new people who will be there. My buddy JD2718, for one.

Why come?

• Math - There will be at least one problem you never saw before, I betcha.
• Very good food (I don't think it's organic, but it's amazingly good, and there's so much to choose from!)
• Math - Morning math circles will get your brain humming, and introduce you to a style of teaching and learning that makes me smile all over.
• Walking all over Notre Dame's huge campus - You'll be tired, but happy.
• Math - Amanda brings lots of cool books and math toys. I'll be once again trying to make the origami thing that takes 30 or so sonobe units.
• Great companions - besides our fearless leaders, there's me and JD2718, and Dan Goldner. And you'll meet other great people there, I just don't know who they'll be yet.
• Math - You'll get to (have to?) run your own math circle session with local kids. I'm a slow learner, and didn't feel like I got it right until my fourth attempt, last year. You also get to watch other people run theirs. It makes it all real.
• Swimming pools and other gym stuff - I love swimming in the early morning, when I'm still half asleep, because it's 4am here in California. Oh yeah.
• Math - You can even do math in the evening. We've had some great problem sessions in our dorm in the evenings.
• Here's what I had to say about the previous years: (I hadn't started my blog yet for the first year), year two, year three, year four, year five.

Are you dying to know the details?

• Sunday, July 7 to Saturday, July 13
• $850 includes accommodations and food
• To apply, email Bob and Ellen Kaplan (kaplan@math.harvard.edu)
• Official Info on The Math Circle Site

Here's something that bears repeating:

The participants range from folks whose math skills had me intimidated (I am so over that now!) to people who are just beginning to discover the joys of math. We all worked together, and no one expected you to know things you didn't.

Please join us.

My First App Review: Dragonbox

I just got my very first smartphone. First app I bought was DragonBox. I've heard lots of good things about it, and I think I played around with a free online version a while back (although it doesn't seem to exist now).

It is fun to play with, even though I know my algebra. I still need to test it with kids who haven't learned algebra yet, to see how much sense it makes to them, and how well it transfers to paper-and-pen(cil) algebra.

I did find a few bugs, and I hope the makers will set up some sort of program to get users to report bugs, so they can fix them.

Bug #1 (minor):

Here's the screen. I wanted to subtract a/5 from both sides, but that's not possible. I had to multiply both sides by 5, subtract a, and then divide both sides by 5.



Bug #2 (minor):
I was penalized for changing c+c to 2c. Not sure why.



Bug #3 (bigger):

I divided both sides by x, and got x = 1/3. Dreambox said that was right. But that leaves out the other possible answer, which is x = 0. Yikes! I think dividing by x needs to be a wrong step in the game.



I bought the version for age 5 and up ($5.99) by mistake. I'm looking forward to checking out the version for age 12 and up ($9.99), too.

Even with bugs, this game is great. I'm impressed.

Book Review: Measurement, by Paul Lockhart

In 2002, Paul Lockhart wrote A Mathematican's Lament, a 25-page exploration of much that is wrong with math education. I liked it, but I'd rather explore how to do math education right. Last year he came out with Measurement, a 398-page exploration of mathematics itself. It is delightful, and I want to recommend it to all my students in pre-calculus, calc I, and calc II. I think anyone who has some experience with geometric and algebraic reasoning can enjoy this book.

His publisher, Harvard University Press, put out a short video of Lockhart explaining the difference between math and science questions and why he thinks of math as one of the arts, with the help of a nice geometry problem. The video will give you a small taste of what's in store for you in the book.




If you watch the whole video, you'll notice that he never offers an answer for the puzzle he poses (though he suggests that there are many answers). That would be like telling the surprises from the end of a movie. He doesn't give many answers in the book either.  He does give lots of hints, and shows lots of strategies and techniques. He knows that the joy of math comes from figuring things out for yourself, so he shows us some of his favorite problems and asks us if we'd like to solve them. But he went beyond a mere compendium of puzzles, and connected the problems he shows, taking his readers on a delightful journey though size and shape (part one) and time and space (part two).

Many of the problems posed are familiar to those who study math, like this one:

And many are less familiar, like this one:

All of them are presented in the context of the larger story Lockhart tells.

You'll find the book enjoyable, even if you're not feeling up to solving these puzzles. But the more often you put down the book and pick up your pen or pencil and paper, the more fun you'll have. I only did a fraction of the problems he posed, so I'm looking forward to lots more fun the second time I read it.

Calculus Teacher Extraordinaire: Bowman Dickson

I don't usually do this, and maybe everyone who reads my blog (and cares about calculus) already reads Bowman's blog, and knows how amazing he is. But I've been quietly filing away about half of his posts, and today I just had to tell the world - Bowman Dickson rocks!

I don't save the posts about using whiteboards, even though that's cool, or the ones about review strategies, though you might find something great there. I save the projects (I already do one like this, but am eager to compare to Bowman's experience), models (I want to build these), and cool problems (I used this last week).

I can't find years on his blog, but he's been posting good stuff for at least four years now. You could play around in his archives for hours. His main blog is Bowman in Arabia (he teaches at a boarding school in Jordan). He started a new blog, Bowmanimal180, in September, on which he posts "a picture and a few sentences about every day of class for a whole year." Both are fabulous repositories of great ideas.

I cannot do his blogs justice (got to get on to grading and prep), so do yourself a favor and check them out.

Bowman, I wish my high school math teachers would have been more like you!

Moebius Noodles is Now Available!

Delta Stream Media will soon be publishing my book, Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers, as part of their series of playful math books. The first book in the series is now out:

Moebius Noodles: Adventurous Math for the Playground Crowd, by Yelena McManaman and Maria Droujkova, illustrated by Ever Salazar, is a gift to parents and kids everywhere. The book is full of ways to grow mathematical eyes, with very accessible activities.

I wrote about Maria's crowd-funding campaign back in 2011. She raised $6200 back then, and is sending out lots of books to the funders. (Can't wait to get my copy!) If you didn't join in then, you can still buy a copy for $15. If you have anyone in your life with young children, I think they'll love it.

If you're just as comfortable reading your books online, you can get a pdf at whatever price you choose to pay (from zero to infinity). I like this model. When I wanted to read Little Brother, by Cory Doctorow, I downloaded the free copy.I had already bought a copy for my nephew the previous xmas, and wanted to know how good it was before spending any more money on it. I loved it, and didn't hesitate to buy a paper copy of another of his books, Makers. (Also available for free.) I've bought lots more of Cory Doctorow's books than I would have if the free copies weren't available. So we're both happy. And I believe Moebius Noodles will work out the same way. You can download the pdf for free to get a taste. And, if my guess is right, you'll be eager to fork over the $15 for a print copy that's easy to share with little ones.

...watching for a package...

Presenting Mathematics Through Dialogue and Story

Susan Jane Colley has written a review of both Math Girls and Manga Guide to Linear Algebra for the College Mathematics Journal. (Unfortunately, it's only available to MAA members.) I liked it and want to share a few thoughts. After sharing a dialogue from Math Girls, she wrote:

Passages such as this make me think Galileo was right to explain his cosmological theories in a dialogue between actual characters. Maybe we should routinely present mathematics as a conversation between two people striving for understanding rather than as persona-free perfection.

Well, now I'll have to see if the Galileo is worth reading. (I just checked using google books, and it's not too hard to read. The misogyny bugged me, but the opinions about "the Pythagoreans" were interesting. Perhaps the math will be too. Ahh, history.)

I agree with Susan Colley that presenting math as conversations is a good pedagogical device. I'd like to try it. One benefit of writing this way is that it's possible to explore a problem more fully without giving away any punchlines. Of course, it also adds interest.

Would any of my readers be interested in writing short dialogues on selected topics?

Summer's coming, and I like to think during summer about topics in my upcoming courses that need a better introduction than what I have available so far. I'll be looking for other people's goodies online, and I'll be thinking about how to create my own.

I'll be teaching pre-calculus, calculus I, and linear algebra in the fall. My long handout for finding the derivatives for sine and cosine went over like a bag of cement. I might be able to enliven that with a dialogue. And I'm thinking some of the first topics in linear algebra might do well with this treatment.

Exemplars
Besides Math Girls and Math Girls 2, I only know of a few other shining examples of this genre:

Check out The Cat in Numberland (a delightful retelling of the Hotel Infinity story), in which the storyline, more than the dialogue, helps the reader understand infinity more deeply.

I also loved working through some deep mathematics in the book Surreal Numbers, by Donald Knuth, which has more of the style of Math Girls. Alice and Bill are lightly sketched characters, exploring mathematical ideas together on a secluded beach.


 Are there other books you know of which present math through dialogue or story? Would you like to write a short story or dialogue with math at its core? Let's form a math writing group this summer!

Now Affordable: Math from Three to Seven, by Alexander Zvonkin

Last year I ran a poll to see how many people would buy this book if the price were reduced. The publisher, AMS (American Mathematical Society) publishes mainly scholarly works, and originally priced it at $50, in line with the prices of their other books. (Yikes!) 96 people said they would buy this book if it were $20 or less, and now it is!

I loved reading Math from Three to Seven. Zvonkin worked with his young kids and some of their friends, and documents his successes and failures with them. He had lots of great ideas for getting very young children to think about deep math. When I read it last year, I had access to an online copy. I have just now ordered a real book, so I can turn down my favorite pages and find them again quickly.

The people at the Math Circle Library have been working with the folks at AMS to change the pricing structure for the math circle books. The prices of seven of the twelve books in the Math Circle Library series have been reduced to $18.75*. I ordered Math from Three to Seven, Math Circle Diaries (aimed at grades 5 to 7), and Invitation to a Mathematical Festival.


More about the book... Paul Zeitz, who edited the English translation of this book (originally published in Russian), said in his introduction:

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.

If you buy it, let me know what you think.




_____
*The pricing on the AMS site may be a bit confusing. They show a list price and a lower price for "all individuals". If you haven't set up an account, the price will initially show up as the $25 list price. Once I logged in, it changed to $18.75.

Inspirations video

You've probably seen links to this lovely video by Cristóbal Vila before, but I had trouble finding it this morning, and I'm hoping I'll find it more easily the next time if I post about it. This video inspired parts of the design of the book cover for Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers. I'm hoping we'll have the book out by summer. (But I have guessed wrong so many time before, I must emphasize that this is only a hope.)





INSPIRATIONS from Cristóbal Vila on Vimeo.

Vila has written about the math in the video here.  

Happy Mathy Day

I copied Denise's sign, with minor modifications, and got this..

We're both writing in response to David Coffey's post, What's the Point? And all three of us are using the easy peasy sign generator made by a teacher at the real Roosevelt Middle School in Oakland, California.

Why play? Because every day can be a math day.

Wouldn't it be cool if a different math lover made a Happy * Day sign every day for the rest of this month?

Who will do a sign tomorrow?

Pi Day Puzzle Party - Join in, a bit late...

My friend Sharon invited me to head over to the city (San Francisco) on Thursday evening to meet her at a Pi Day Puzzle Party, sponsored by Ask a Scientist. Contestants could form teams of up to 6 people or work alone. The venue was a fascinating spot. SOMA Streatfood Park is an open lot with a pre-fab metal building in the center, surrounded by food trucks (some gourmet, some not so much), buried in a very industrial part of the city. It made me think of a gypsy camp.

I arrived first and grabbed us a (picnic) table. Sharon arrived soon after and we got food from the Peruvian food truck. When the party started, there were about 40 teams, with about 100 people packed into the cozy space.

We were handed the first question face down, and the MC, Wes Carroll, read it it to us all. Then we could turn it up and work on it for ten minutes, before getting the next question. There would be seven questions in all.

Question 1: There is a rare disease, called Anti-Mathitis (AMI for short), that afflicts 1 person in 10,000. There's a 90% accurate test that tells whether you have AMI. This means that 90% of the people who have it test positive and 90% of the people who don't have it test negative. You have just found out that you tested positive. What are the chances that you have the dreaded AMI?

Well, I knew all about this from teaching statistics. Back in the nineties, the state of Illinois required an HIV blood test for people applying for a marriage license. It turned out not to be as helpful as expected, along with being a big expense.

My teammates were working away together, while I wrote out what I needed. Sharon had emailed us messages about how she wasn't sure her 8-year-old friend Pai would like it, because we would be working hard at solving the puzzles and not slowing down to explain. So I knew ... winning was our goal, and my new buddies would be ok with me jumping in to explain my answer. Pai did come, and didn't mind our intense focus at all. We named our team The Pai Team.

Explaining my method showed me my arithmetic mistakes. (No calculator, oh no!) As I was cleaning those up we were handed the next question:

Question 2: There are 100 ants in a line on a 1 meter log. They are all walking on the same straight line. When one reaches the end of the log, it falls off. If two collide, they immediately reverse direction and continue on their way. Each is going at the speed of 1 centimeter per second. How long until all of them are guaranteed to have fallen off the end?

I knew I had seen one like this before, but had no idea how to proceed. I knew I needed to think about making the problem simpler, though... I suddenly had a flash of insight. This time, I waited until my team had finished discussing other ideas before I threw my idea in the ring.

And before we had time to take a breath, we were on to the next:

Question 3: Pat calls out 4 consecutive integers. Chris divides each by her age (a whole number), and notes the remainder each time. She adds the remainders and gets 40. Now Chris calls out 4 consecutive integers, Pat divides each by his age (a different whole number), and notes the remainder each time. He also adds the remainders and also gets 40. What are their ages?

This ended up being my favorite problem. I'd never seen one like it. We were still explaining it to one another when we got the crazy logic problem ...

Question 4: Stuck on an island there are 100 people with blue eyes, 100 people with brown eyes, and one guru with green eyes. Each of these people is a perfect logician, and will figure out their own eye color as soon as it is possible. They cannot speak, or communicate in any way, except for the one time the guru makes a statement. Nor can they find any way to see their own eye color. They each can easily see the eye color of every other person on the island. Each night at midnight, a good fairy comes and takes away anyone who has figured out their own eye color. One day the guru says, "I see someone with blue eyes." Does anyone leave the island? If so, who and when?

We got it...

Then came the red, white, and blue balls. I thought this problem would be our downfall...

Question 5: We have 6 balls that are visually identical except for color. There are two of each color, red, white, and blue. One of each color is heavier and one is lighter weight. All the lightweight balls weigh the same, and all the heavy balls weigh the same. We also have a balance scale. We need to determine which is which with only two weighings.

 We came up with lots of good ideas, but they all ended up requiring three weighings. We had to leave #5 blank on our answer sheet and go on to #6...

Question 6: In the picture at right the square has area 64, and the triangle is equilateral. What is the diameter of the circle?

Hew got us started on this one, and we worked feverishly on the algebra. We got it... (At the end, the MC shared with us all another  way to solve it that requires no algebra. This other way is elegant and beautiful.)

One last question... (Although I think they're out of order...)

Question 7:  You have a pile of coins. Ten of them are heads up, and the rest are tails. You are blindfolded and cannot see them, but you can flip as many of them as you'd like. Can you put them into two piles, so that there are the same number of heads in each pile?

I had heard of this problem before, and probably heard the answer. But I have a terrible memory, and remembered nothing. As we worked on it, nothing made sense. Finally, I saw what needed to happen. And they were giving us twenty more minutes to work on our answers! Back to those dratted balls. I scribbled out my final asnwer just as we were asked to pass our answer sheets to a neighboring team to check. They took my scribbles along with our answer sheet. Whew!

The MC gave the first answer. It was different than ours. I had explained ours so carefully to the rest of our team, I was sure we were right. And the team whose answers we were checking had the same answer. So I raised up my hand, and the MC said, "Ahh, we have some dissent." He called me up to the microphone. Of course, there was a chance I was wrong, and I was shaking with nervousness.  But I explained my thinking to him, and he agreed, and there were cheers. (When have I ever been cheered before for the answer to a math problem?)

We answered all 7 questions correctly, as did the team sitting right next to us. It turned out they and we were the only two teams to get them all correct. So our two teams were asked to send a representative up front for a tie-breaker question. We had to stand on chairs to be seen by the crowd. The MC warned us that a wrong answer would give the other person plenty of time to think.

The Final Tie-Breaker Question: What is the smallest prime factor of 3¹⁷+5²³?

I saw the answer, said "I know it", and won the contest for our team! I was stoked. I have never done a math competition before, and I'm not particularly fast, so I hadn't dreamed that we'd win. My teammates came up, and photos were taken. It was quite a scene.

I asked the other team if they had recognized any of the questions. No, they hadn't. I told them they had really won then. Even so, we were full of the thrill of victory as we made our way homeward, and delighted to have shared it with 8-year-old Pai. None of our questions had had any relation to the number pi, so we were very satisfied to hear about her part in the  Pi Day parade at the Exploratorium. Pai and her mom held up the 95th and 96th digits of pi, both 1's.

Celebrate Pi Day a bit late, and answer these 8 puzzle questions. (Please, no answers in the comments.) I'll send a fun math book to the first person to get all 8. (No fair using Google. You are on your honor.) Teams are fine. Send your answers to mathanthologyeditor on (use the letter after f, along with mail). Your last puzzle is to make sense of my email, that I'm hoping to keep away from the scambots.