Perplexity

On January 11, Internet celebrity and Stanford grad student Dan Meyer worked with the Math Dept at the Urban School, plus a handful of members of Escape from the Textbook! He presented his thoughts about how to design and present modeling problems, but in fact his ideas have broader applicability.

I had already seen Dan's TED talk, and heard him give a keynote presentation at an NCTM institute. (See some notes I took about the latter here.) So I more or less knew what to expect. Still, it was a very worthwhile afternoon, as I collected some important and powerful ideas, which will help me as I teach and design curriculum.

The biggest idea for me was that when we map out problems, and more generally lessons, we should give them a three-act dramatic structure.

Act 1 is largely about generating perplexity. It is often visual -- the words and numbers come later. A successful Act 1 yields many student questions. (Hopefully, the main questions are the ones you intend to tackle.) The example he used with us was a photo of a museum exhibit where the walls were entirely covered with dollar bills. This triggered many great questions, and obviously the main one was how much money was there. If students are genuinely curious, they will be much more engaged, and more likely to learn something from the lesson. (To quote myself: "you cannot answer questions they don't have.")

Act 2 involves building a strategy to solve the problem: figuring out what information will be needed, and using it on the way to a solution.

Act 3 is an opportunity to debrief, figure out what was learned, and perhaps to pursue some extensions.

This is to some extent the structure of many of the lessons I have created over the years. For example, in Algebra: Themes, Tools, Concepts, many of the lessons are launched with an Exploration, which is intended to be worked on with the book closed. The rest of the lesson typically offered some scaffolding to help students head to a solution, after they have grappled with the problem on their own, in groups, or in a whole-class discussion. In that book, my Act 3's were strong on extensions, but weak on making the mathematical structures and techniques explicit.

Later, in Geometry Labs, I came up with a strong structure for Act 3 (the Discussion Questions), but many of the labs were weak on Act 1, and directly plunged into strongly guided activities. Guiding too much and too early ("by the nose") is the Achilles' heel of guided discovery, the curriculum style I usually favor.

More generally, organizing lessons from whatever source into the 3-act structure is likely make them more effective. Learn more about this: Dan Meyer's workshop is archived here.

Break a leg!

--Henri

PS: One other thing to think about, also raised by Dan in his workshop, is whether paper is the best medium for all math lessons. He points out that for some activities, there are benefits to putting the computer at the center. Doing so allows the use of video (and of course, math software), and moreover it gives us the possibility of making more data available off the Web and other sources.

Summer workshops

I posted detailed info about my summer workshops on my Web site.

This summer, the geometry workshop expands to four days, to make room for the abundance of ideas I'd like to share. In particular, I'm expanding to include a little more computer-based activities, while keeping the workshop as a whole centered on hands-on activities with manipulatives.

On the other hand, the algebra workshop shrinks back to its three-day incarnation, to make room for a new workshop on "reimagining high school math." The latter is intended to help trigger reflection and discussion on how to break the stranglehold of traditional pedagogy and curriculum in the program of so many schools -- public, parochial, and private. So much is known about the limitations of the traditional approaches, but so little is done to try new things. I have many years of experience on that front, and hope for a rich conversation with colleagues, young or old, whether they have been on this path for a long time, or are just starting to think about it.

As always, much of what we'll do in all three workshops is based on material that is readily available on my Web site, but it is always more powerful to explore these ideas collaboratively and in person. I hope I'll meet some of you this summer!

Of course, I'm happy to answer questions, either here or via e-mail.

--Henri

Dan Meyer live stream

The Center for Innovative Teaching is hosting two events with Dan Meyer on January 11 at the Urban School of San Francisco. Both events are sold out, but they will be streamed live (and archived) at:

    http://www.livestream.com/urbanschool

From 12:00 noon to 2:30 (Pacific Time), Dan will be working with the Urban School Math Dept and a few guests from Escape from the Textbook!

From 3:00 to 4:00 p.m. (Pacific Time), he will speak to the entire Urban School faculty, plus 60 or so educators in all disciplines, about "Capturing, Sharing and Resolving Perplexity". Here is the description of this presentation:

"Given the infinite smorgasbord of tools and technology to try out in the classroom, how do you decide what's worth your and your students' time? Without some kind of criteria guiding our selection, we'll spend years building up a dusty closet of tools that looked good, promised a lot and didn't deliver. 
With that in mind, join us for a lively hour (free!) with math educator, TED speaker and Stanford University doctoral candidate Dan Meyer, who will describe 'perplexity,' one of the scarcest resources in the classroom. Dan will show educators why perplexity is key to engaging students in the classroom, and how to pick tools and technology to maximize it."

--Henri

ATTC upgrade

Algebra: Themes, Tools, Concepts (ATTC) is an algebra textbook I co-authored with Anita Wah in the early 90's. It was ground-breaking in some ways, and includes many extraordinarily effective approaches to the teaching of algebra. In fact, ATTC features powerful lessons on many parts of secondary school math, which are used by teachers in grades 7 to 12.

On the other hand, ATTC is not particularly easy to use as a textbook, and never became a best-seller. Thus, the publisher decided to declare it out of print, and the copyright reverted to the authors. It is now available absolutely free, on my Web site, for your non-commercial use.

Thanks to Google digitization, I have been able to post searchable, full-color copies of ATTC and its Teacher's Edition, in addition to the files that have been there for a while. Check it out:

• ATTC on line
• ATTC downloads
• ATTC Teacher's Edition
• ATTC Teacher Resources
• Sample lessons

--Henri

Geometry Labs

My book Geometry Labs is now available for free download on my Web site.

Whew! It was a bit of work to get it ready.

--Henri

PS: In addition to the book itself, I'll be adding links to revisions and extensions of the labs. So far, a revision of the rep-tile lab, and an extension of the soccer angles lab. I'm happy to post other people's revisions and extensions there.

Everything I Know

On December 1st, I was a guest presenter at the UC Berkeley School of Education, for a student-initiated course about teaching practice.

My past experiences in working with preservice teachers (at NC State in 1992, and at USF in 2006) had been rather unsuccessful. Both times I taught a course for undergraduates who were future math teachers, and both times they were very resistant to my approach, especially the idea that they should try to get more depth of understanding of high school math -- something they felt they already knew. Thus, when I used some of the activities I always do very successfully with both students and teachers, they were resentful, and I was clueless about how to help them shift their perspective.

Given this, I was worried about the December 1st presentation being a disaster. Luckily, I had a 3-hour workshop I had done at the California Association of Independent Schools Retreat for Beginning Teachers every year from 1991 to 2005. That workshop had invariably gone well, so I decided to do an abbreviated version for the Berkeley group.

The full version of that workshop had included these activities and discussions:
- the polyomino perimeter exploration (which can be found in my Geometry Labs book, as well as here and here. It is an activity I've done successfully with students of almost every age, with teachers at every level of experience, and even with parents.)
- Heterogeneous Classes
- Group Work
- Technology
    Make These Designs (Teacher Notes)
    Super-Scientific Notation
- manipulatives
    Scaling Supertangrams
    The 10cm Circle
The whole workshop was organized around an outline with the title Everything I Know.

On December 1st, I started with the polyomino perimeter exploration, debriefed, and used the Everything I Know outline to structure the rest of the two hours. I'm told it went well. There was not enough time for the other six handouts: perhaps I'll go over those if I get invited back.

--Henri

Escape! Meeting notes 3 -- habits of mind

This is the third and final installment of my notes from the Bay Area fall meeting  of Escape from the Textbook!

(Part 1) (Part 2)

We ended the meeting with a segment led by Avery Pickford. (See his notes about the meeting.)

He presented this problem:



(He didn't present it exactly like this -- this is how the problem appears in Algebra: Themes, Tools, Concepts. The whole book is available for free here.)

Since I had offered this problem many times to students and teachers, I chose to work with Bree Murray on a generalization. David Louis suggested we go 3-D, which was a great idea. How many unit cubes does a line go through as it connects (0,0,0) to (p,q,r)? (The latter is a lattice point.)

Working on this turned out to be very fun and satisfying, though in retrospect I think we didn't fully solve the problem. Still, we have a partial solution, and we had to bring to bear many habits of mind (as outlined by Avery -- habits of mind was the theme of this segment). Using translucent interlocking cubes helped us get a handle on the problem, but the main issues turned out to be about numbers. I won't say more here.

And speaking of habits of mind: we met in David Louis's classroom at the SF Friends' School. In addition to student work on various problems, the walls feature posters on "thinking like a mathematician", "how to be successful in this classroom", "Solving a problem", "Listen, Understand, Deepen". That is one way to make habits of mind explicit to students. Something I intend to suggest to my colleagues at the Urban School, even though we don't have "our own" classrooms. We might have students create such posters after a teacher-led discussion. Then the posters will be visible to other math classes who meet in the same room.

In Avery's words, habits of mind are part of "math as a verb", but our job also involves teaching "math as a noun", the various skills and understandings of mathematical subject matter that society expects. David's closing comment was about the need to develop "math as a verb" activities that directly link with "math as a noun". Such activities can serve as anchors to our units. Amen! This is precisely what much of my work as a curriculum developer has centered on.

--Henri