Tuesday, June 21, 2011

Math Teachers at Play #39

Check it out, over at Let's Play Math.

I like 39 because it's part of the first fraction that can be simplified, but isn't obvious ... 39/52.

Denise gave us these puzzles:
  • Easy: Can you make 39 with four 3s?
  • Tricky: Can you make 39 with four 4s?
  • Really tough: Can you make 39 with this year’s digits, keeping the numbers in order (2, 0, 1, 1)?

For the 'tricky' one, it may help to know that decimals are allowed (so you can use things like .4). I can't imagine how the 'really tough' one is possible.

Next month's Math Teachers at Play blog carnival, Number 40, will be here on July 15.

Sunday, June 12, 2011

The Book: Playing With Math is Ready for the Reader Response Team

Artwork by Linda Palter.
Playing With Math: Stories from Math Circles, Homeschoolers, and the Internet - a book by 35 authors - is almost ready. I've collected some great blog posts and posts from email groups; I've transcribed speeches and talks, and solicited chapters written especially for the book. All of these authors have collaborated with me to put together a book full of the vibrancy and joy of people who love math (and a few who don't). After every chapter is a puzzle or game, designed to pull the reader into our world. It's pretty exciting.

The manuscript is getting tighter every day. At this point, it really needs more eyes. So here's the idea Maria Droujkova, founder of Natural Math (my publisher), came up with:
If you'd like an early peek at the book and the glory of being in the acknowledgements, you can sign up to be a part of the Reader Response Team. You'll get 3 to 5 chapters a week to read (starting this Wednesday). We don't need close editing for grammar and spelling at this point. What we need is your opinions as reviewers: What works? What doesn't? What's missing? And a rating for each chapter (Keep, Toss, or Wow!).

You'll make a commitment to review the chapters within the week; it will take 11 weeks to read through the whole book. (Or you can pick the Summer Speed Reading option, and get the whole manuscript all at once.) Each week, discussions among the Reader Response Team will bring new depth to the already wonderful writing.

We are especially looking for people who love to read and do not like math. You are our acid test of the book!

To join the Reader Response Team, comment here with your email address or email me at mathanthologyeditor at gmail. The first 30 volunteers are in. Those of you who have a chapter in the book are welcome to get a manuscript from me, but we'll let other folks be on the Reader Response Team.

If you'd like to contribute in any other way, let me know. Any questions?

Friday, June 10, 2011

On Refusing Testing: Fiction & Facts

The Fiction
I just read a kid's book that I really enjoyed, titled The Report Card, by Andrew Clements. It's about Nora, a 5th grade girl who's a genius, but has been hiding it from her family and everyone else. Some of the book is quite unrealistic, but I loved the campaign she and her 'average' friend Stephen initiate at school to get all the kids to refuse to participate in testing. I think the book cops out at the end, but it raises some great issues.

The Facts
While I was trying to find the information I wanted for my previous post, I stumbled on a great article about teachers refusing to administer standardized tests.Yeay for British teachers!!
Teachers refuse to give standardized tests to kids

By Valerie Strauss

Maybe there is a lesson in this for American teachers.

Saying that they are sick and tired of forcing kids to take standardized tests, thousands of teachers in England are refusing to administer high-stakes standardized tests in reading writing, spelling and math this week.

British newspapers, including the Daily Telegraph, are reporting that as many as half of the estimated 600,000 primary school students due to sit for tests will not take them because their teachers have decided to take a stand against them.

Read the rest on the Washington Post site. (Valerie Strauss writes regularly on issues I care about. I've added her column to my Google Reader.)

Vi Again, with the Best Response Yet to Facebook's Silly Math

I bet most of you have seen the silly thing that was going around Facebook. It was a poll which asked: 6 ÷ 2(1+2) = ? It didn't seem worth even commenting on, because it dealt with such a silly issue. But it adds to math's bad reputation, and I loved Vi Hart's response, which is at the end of this video. (She saw a different problem floating around,  48÷ 2(9+3), which addresses exactly the same issue.)

The first part of her video is fun too. I bet she's lying about not knowing what 6x7 is, but that's ok by me. Maybe she can help the hopelessly honest among us (like me) learn to lie a little bit more. It seems pretty important to develop a culture of questioning instead of answering among math teachers and students, and that might just help.

Thursday, June 9, 2011

Seymour Papert...

... wrote Mindstorms: Children, Computers, and Powerful Ideas. For years and years, I kept hearing about it, and thinking I should read it. Why did it take me until last year to do that? I think I didn't expect it to be as deep as it was. Maybe I thought it would focus on computers too much. It doesn't. It's more about how we learn. I was so excited when I read it, I immediately bought another book of his, The Children's Machine, also excellent (though Mindstorms was better, I think).

I blogged about Mindstorms just after reading it last year. Maybe it's time to re-read it. Unfortunately, my copy is lent out to a friend. But now I can get a daily dose of Papert from The Daily Papert. Upon discovering the Daily Papert, Pat pointed out a conversation between Papert and one of my heroes, Paulo Freire. What a delight!

If you prefer your reading in more concentrated doses than the Daily Papert provides, you can just go to this archive of articles Papert has written.

Seymour Papert was in a tragic accident in December 2006. While in Hanoi for a conference, he was hit by a motorbike and suffered a severe brain injury. There is hope he will eventually recover, but he hadn't yet as of July of 2008. Here's the news article from then. (Nothing more recent online.)  I'm wishing him well.

Wednesday, June 8, 2011

Communicating Mathematics

This paper by William P. Thurston is officially titled  On Proof and Progress in Mathematics, but what interests me most are his insights about how we communicate math, and how it's learned.

Here are a few excerpts:
The transfer of understanding from one person to another is not automatic. It is hard and tricky. Therefore, to analyze human understanding of mathematics, it is important to consider who understands what, and when.

Mathematicians have developed habits of communication that are often dysfunctional. Organizers of colloquium talks everywhere exhort speakers to explain things in elementary terms. Nonetheless, most of the audience at an average colloquium talk gets little of value from it. Perhaps they are lost within the first 5 minutes, yet sit silently through the remaining 55 minutes. Or perhaps they quickly lose interest because the speaker plunges into technical details without presenting any reason to investigate them. At the end of the talk, the few mathematicians who are close to the field of the speaker ask a question or two to avoid embarrassment.

This pattern is similar to what often holds in classrooms, where we go through the motions of saying for the record what we think the students “ought” to learn, while the students are trying to grapple with the more fundamental issues of learning our language and guessing at our mental models. Books compensate by giving samples of how to solve every type of homework problem. Professors compensate by giving homework and tests that are much easier than the material “covered” in the course, and then grading the homework and tests on a scale that requires little understanding. We assume that the problem is with the students rather than with communication: that the students either just don’t have what it takes, or else just don’t care.

Outsiders are amazed at this phenomenon, but within the mathematical community, we dismiss it with shrugs.


There is another effect caused by the big differences between how we think about mathematics and how we write it. A group of mathematicians interacting with each other can keep a collection of mathematical ideas alive for a period of years, even though the recorded version of their mathematical work differs from their actual thinking, having much greater emphasis on language, symbols, logic and formalism. But as new batches of mathematicians learn about the subject they tend to interpret what they read and hear more literally, so that the more easily recorded and communicated formalism and machinery tend to gradually take over from other modes of thinking.


We mathematicians need to put far greater effort into communicating mathe- matical ideas. To accomplish this, we need to pay much more attention to com- municating not just our definitions, theorems, and proofs, but also our ways of thinking. We need to appreciate the value of different ways of thinking about the same mathematical structure.
We need to focus far more energy on understanding and explaining the basic mental infrastructure of mathematics—with consequently less energy on the most recent results. This entails developing mathematical language that is effective for the radical purpose of conveying ideas to people who don’t already know them.

There's lots more to chew on in the article, check it out.

Sunday, June 5, 2011

A Very Simple Poll

Shawn, at Think Thank Thunk,  is doing a poll. I think getting results separately for different groups would be helpful and I'd really like to see these results, so I've replicated his poll here.

Please vote. Thanks!

(And if you'd like to set up the same poll question on your blog, it only takes about 5 minutes to set up a free account at polldaddy.com, write the poll, and embed the code in a blog post.)

Saturday, June 4, 2011

Book: The False Promises of Constructivist Theories of Learning

Does this title sound like one of those conservatives who thinks we ought to lecture? It's not. The critique is from ... something more like the far left. Left of Paulo Freire?! Yep. But left is probably the wrong word for it...

The False Promises of Constructivist Theories of Learning: A Global and Ecological Critique, by C.A. Bowers, is part of a series called Complicated Conversation.

Here's a bit from the introduction:

At $27, I'm not sure I can afford it, but Friere has been one of my heroes, and I'm intrigued by this critique. Some of the other books in the series look interesting also. Hmm, I wonder if UC Berkeley's library will have it. [Added on 7-16: As pointed out in the comments, you can read C.A. Bowers shorter articles online at his website; this article [pdf] seems to cover some of the same ground this book does. I just communicated with the author by email, and he's involved with Eco-Justice Press. They've published some books on similar issues; you can get the ebooks for $11.]

Wednesday, June 1, 2011

A Free Calculus Text

R. Wright mentioned this text, Calculus in Context, in the comments at dy/dan's. I had a copy of this book shortly after it came out, and I didn't know what to do with it. I think it might be great, but I couldn't use it back then.

I remember wanting to use groups and projects, and not knowing how. Maybe I'm a particularly slow learner, but I think most people have deeply imprinted on the classes they were students in, and use those as models for their teaching.

I'd like to try to get a print copy and see if I can use it now. Does anyone here have any experience with this text? What do you think?


I posted this too soon. I'm reading the pdf, and I'm so intrigued. This text uses a radically different organization than the standard course, so I don't know if I could use it at my school. But I definitely want to read the whole thing now.

Here's a quote from the Handbook for Instructors:
If you ask typical students what mathematics is about, they are likely to deny that it is about anything. They perceive mathematics as existing in a world of its own, with its own rules, having little to do with any questions they might be interested in. The so-called “applications” that are provided, almost always after the mathematics has been completely worked out, are often transparently artificial and do little to convince skeptical students that mathematics has anything to say about the world in which they live. We feel much of the low regard the general public currently has for mathematics arises from treating mathematics as a strictly technical discipline, responsive only to its own internal logic and structure.

Historically, though, much of calculus arose as a tool to explore questions in the sciences—including, of course, other branches of mathematics. Our students need to see this connection throughout as they learn the material, not just as an optional afterthought appended to the mathematics.

What Money Can Buy

I took a course in college that taught students how to follow the money trails, as we did research on issues of interest to us. I never quite got the hang of it. Susan Ohanian and Rachel Tabachnick sure did.

I was raised in Grand Rapids, Michigan, home to the DeVos and VanAndel families (and Gerald Ford). It never occurred to me when I was young that their money would be a significant factor in how the whole country is run.

The decades-long campaign to end public education is propelled by the super-wealthy, right-wing DeVos family. Betsy Prince DeVos is the sister of Erik Prince, founder of the notorious private military contractor Blackwater USA (now Xe), and wife of Dick DeVos, son of the co-founder of Amway, the multi-tiered home products business.

By now, you've surely heard of the Koch brothers, whose behind-the-scenes financing of right-wing causes has been widely documented in the past year. The DeVoses have remained largely under the radar, despite the fact that their stealth assault on America's schools has the potential to do away with public education as we know it.

And there's the Gates Foundation...
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