Suzanne at the Math Forum

In July, Craig and I presented to the PCMI SSTP (Park City Mathematics Institute Secondary School Teachers Program) during one of the afternoon sessions. I brought him a Math Forum t-shirt (limited edition!) so that we could wear matching outfits.

Craig recently wrote me:

I wore the “What do you notice? What do you wonder?” t-shirt you gave me to school today.  Several students in the hallway were intrigued by the fractal dragon (I told them to ask their Geometry teacher about it).  The students in my Calculus class noticed the noticing/wondering wording on the shirt and asked me “if I had the shirt specially made.”  They thought I came up with the noticing/wondering strategy!  I answered them that no, neither did I have the shirt custom-made, nor was I the author of the noticing/wondering… that both shirt and idea came from the Math Forum.  I took it as a very high compliment that they would attribute noticing and wondering to me!

Craig’s comment reminded me that we have an activity that we give to teachers who want to show students how to generate the fractal dragon part of our logo.

If you try this activity with your students, let us know how it went! I’m also curious to know if any of them have heard of the book Jurassic Park — it’s fun to look at how they used the fractal on the chapter pages. I just found it on Amazon.com and if you use the “Look Inside” feature, view the First Pages, and scroll some you’ll see what I mean.

If you’re wondering about Michael Crichton’s naming convention, you might find Cynthia Lanius’s page interesting: Is It Really The First Iteration? Check out the links in the left sidebar on her page, too. There’s a fun Java applet to try.

While I was in Park City this summer at PCMI (Park City Mathematics Institute) we were about to leave for dinner when one of the teachers asked Gail Burrill (one of the organizers of the Secondary School Teachers Program) an interesting question. Next thing we know this teacher (I’m not using a name because I promised to keep the photo anonymous!) was taking notes on his hand:

At the time it seemed fun because I thought about how his students might react to taking notes this way. He said he often “freaks them out” by writing on desks. It made me think about how he values taking notes and writing — so much so that he’ll break some “rules” to make sure he writes.

That started me thinking about the note-taking idea itself. He’s going to wash his hand, right? What happens to the notes then? Does he “copy” them to a piece of paper or his computer or somewhere else a bit more permanent? Does he need to do that or does that act of taking notes as Gail was talking help him process the points of that conversation and he can wash his hand without worrying about saving the notes?

Maybe before washing his hand (or the desk) he re-reads the notes, reflects, and writes a new set of notes somewhere?

What would you do? … or … what “do” you do with your notes?

Recently I was reminded of an activity that I used with students that I called The Traffic Jam Activity. View the URLs below if you’re interested in more of the details. There were several ideas that I was working on, but this morning I’m thinking again about concrete (in this case, the little plastic people) manipulatives vs. the virtual (in this case, the Java applet by Mike Morton) manipulatives.

I’m convinced after working for several years with students in a lab environment that using both is better than using one over another. I remember that when I first tried it using both helped me extend the students’ problem solving  experience. My students didn’t complain that we were “still” working on a problem or that we were doing a problem “again” if the second time they were trying it with virtual manipulatives. I’m not sure if they considered it to be a different problem or if they liked working on the computer so much they didn’t want to complain or maybe a little of both?

I often observed that for many of my students we had to really work for them to connect the concrete and the virtual experiences. And, in fact, it reminded me of how much we had to work to go from a manipulative environment to a more symbolic environment.

Do you use both kinds of manipulatives when you’re working on a problem? Do you have students have concrete Activity Pattern Blocks (for example) as your students have that applet in front of them? or Tangrams? or Algebra Tiles? or Dice?

I wonder if the conversations that you might have with students as they make connections between the concrete and the virtual might be a starting point for the conversations that you might have with them about going from the concrete to the abstract?

What are your thoughts?

Some “Traffic Jam” links in case you are interested:

• ON-Math Fall 2002, Volume 1, Number 1: Developing Algebraic Thinking [PDF version]
• Post-lesson Interview with questions posed to me by Ihor Charischak
• Suzanne’s Lessons: Traffic Jam Activity
• Technology Problems of the Week (tPoWs): Traffic Jam

One of the benefits I reap from working with the Park City Mathematics Institute (PCMI) is that I find out about blogs (and other resources!) that the participants have. This morning a 2011 Secondary School Teachers Program (SSTP) participant alerted me to her new blog. She’s named her blog Pi Crust | An accomplished novice wonders about the challenges of depth over breadth. Cool name but also an intriguing short description. I was enticed to read! Her entry about Mr. Benson reminded me of an idea I used in my middle school classroom a little more than a decade ago.

Before I describe that idea…here’s a little background.

Memory 1: Between 1995 and 2000 I attended several Math Forum Summer Institutes where I was introduced to the idea of starting each Institute day with Connections. “Connections is a time when individuals in a group gather to focus, collect, and even share thoughts.” During one of those scheduled reflection times I remember thinking about the importance of celebration in the classroom.  I wondered to myself what could I start in my classroom to celebrate learning. Could I create a celebration that was long enough to create the feeling that I wanted to achieve but not so long that I would be hesitant to use it?

Memory 2: Going in to my first Math Forum Summer Institute, tessellations were a passion of mine. At that point in my classroom teaching career I was teaching computers (and Newspaper) and had developed a tessellation lesson for the students to learn more about HyperCard but I couldn’t resist having them experience some math while they did that!

So…back to my celebration idea. What I thought of doing was use my love of tessellations, the circular physical arrangement from Connections, and woven through it the valuing of both the individual and the group. I bought two sets of Escher Foam Lizards puzzles — each piece is about 3 inches in length. I still have the puzzles — here’s a photo of some of the pieces that I arranged on my desk just now:

In my mind the students (there were 31 in that class!) would stand in a circle each holding one lizard puzzle piece. In the middle of the circle there would be a table and the students would quietly place their pieces one-by-one on the table and together the puzzle would be completed. Ten students have placed their pieces:

If you are a middle school teacher reading this (and, in particular, work in a Title 1 school with a challenging population, as I did) you may be thinking — did she really DO that! Did it take a day to pull it off? Good grief!

I’ll be honest. No, I never managed to do it. One challenge was that my classroom was a computer lab and while I had managed to arrange things so that the tables/computers were in clusters, there still just wasn’t enough floor space to have anything close to a circle. I think if I had started in September with a small activity to work up to this culminating celebration, by February or March it might have started working…but…I didn’t do that. And, the next year I had left the classroom.

But, I still LOVE the idea and reading Allison’s blog this morning brought all of the memories back of why I think celebration, valuing, and creating both individual strength and group strength in a classroom has such value.