Suzanne at the Math Forum

We were walking across the street entering “Kristian’s Park” (a name we had made up because that’s where we had met Kristian) and Lee suddenly asked us:

When did the world turn color?

I remember being surprised by the question but I also remember that my husband and I took our 5 year old’s question seriously. Since we didn’t quite know what prompted his question, we asked him some questions to get an idea of what his frame of reference was. I don’t really remember what we asked him but I do know that he provided this additional information:

The photos in our albums are black-and-white but the photos now are in color. When did the world change?

Wow! Now we had something to work with!

Lee, my husband, and I were reminiscing the other day and this story came up. We all remembered that we had a good conversation and Lee, in particular, remembers that we valued his questions and responded accordingly. Lee and I compared the “picture” we each took of that moment in time! As we each described what we remembered of the moment and where we were, it was uncanny how much they matched. We agreed that we are very visual and it seemed quite appropriate that Lee would have thought of that interesting question.

I told him that it reminded me of one of the practices at the Math Forum. We encourage teachers and ourselves to value what a student is thinking. If we’re not sure where the statement or question is coming from, we don’t discount it but instead we ask some questions. Valuing each individual is key.

Take a look at this sample of our Problem Solving and Communication Activity Series!

In early April I posted thoughts about thinking of students as lumps of clay versus sprouting seeds.   This morning I started thinking of clay vs. seeds again but this time in conjunction with the CCSS Standards for Mathematical Practice. The first practice is “Make sense of problems and persevere in solving them.”

When I approach this as a teacher who is nurturing students and creating a healthy environment for each of them to grow, I am hopeful. I’m not in a hurry. I allow the students some space. I encourage them to take accountability. I encourage them to talk with each other to share ideas. There is no rush to be over and done but instead our goal is to think, reflect, discuss, and revise. We might work on a problem a little bit at a time over a month. We might let a problem fade into the background and re-engage with the ideas a week or two later. There is no rush because we want to make sense of things and we want to persevere.

Can a teacher who believes that students are lumps of clay that need molding have a different reaction to “Make sense of problems and persevere in solving them.”? I think they probably can. My guess is that they might approach that phrase to mean that the students listen quietly as the teacher explains how the problem makes sense. And, the students need to persevere and finish by the end of the class period! Yikes, that vision is quite the opposite of what I would want my students to experience.

As I read the paragraph of explanation under that first stated practice, the tone points toward the student having control of their own learning. I just can’t ignore statements that include:
… students start by explaining …
… make conjectures …
… consider …
… try …
… monitor and evaluate …
… change course if necessary …
… help conceptualize …
… continually ask themselves, “Does this make sense?”

For many classrooms this requires quite a shift in the environment. If we even follow this first practice knowing that there are seven others to consider, how does that change things? I’d love to think that we’ll move away from lumps of inanimate clay and more to living, breathing, and individual beings who are trying to make sense of their worlds.

Lee Alejandre making sense of the chairs on Swarthmore’s campus. The photos I took of him on that day inspired the Problem of the Week that we named Lee’s Lawn Chair!

Last week as I was drafting the Teacher Packet for “I Get a Kick Out of Soccer” I was looking through all of the student submissions that we received in 1999 and I suddenly started seeing solution threads from my former students at Frisbie Middle School: Mark, Jessica, Shambria, Ciara, Alicia, Erica, Sharlene, Marvin, Leah, Octavius, Reina, Chanelle, Conseulo, Akira, Regnica, Norma, Bryant, Kathy, Robert, Keturah, Laura, Luis, Faviola, Rickisha, Xuyen, and Shirley. There were 26 of the 31 students I remember having in that math class, the last year I was at Frisbie. Their ages at that time were 12 or 13 and so I realized that now they are 23 or 24 years old. Wow!

The two students on the left are Jessica and Mark. That’s me in the middle photo and on the right Norma and Regnica are sitting together at one of the computers. In the photo below Consuelo is looking toward me. My classroom at Frisbie was a computer lab. We had twenty LC575s each connected to the Internet via ethernet. With 31 students some of them worked in pairs when we used the computers. It was always a challenge to find space for groups to work but moving keyboards out of the way or finding a spot on the carpeted floor became normal for my math students!

Another thing that happened last week was a conversation where we were talking about the order that you have students work on problem solving. We identified the possibilities of having students:

* work individually
* turn and talk
* turn and work

I really like the distinction between “turn and talk” and “turn and work.” And I can see that with some tasks, students would benefit from doing these three in a different order.

What are some tasks you have students work on when they “talk” before they “work” or vice versa? When do you have students work individually before working in pairs or in a group? Do you have students work individually after starting to work in pairs or in a group? Are there other possibilities to add to the list of three I’ve noted here?

Although I’m not preparing to start up my own classroom tomorrow, my thoughts still wander to what I “would do” and that brought me to reminiscing about The Quiet Game. Since being introduced to it in the early 90′s I’ve seen it in various settings and this morning when I googled “cooperative learning squares” I found other names for this game and the most common appears to be broken squares.

At the end of the game the completed puzzle pieces look like this:

If this interests you my full instructions are here:

http://mathforum.org/alejandre/quiet.game.html

And this URL results in the download of a MS Word document with these game pieces but also others — it’s great!

http://suse-step.stanford.edu/sites/default/files/bcstext.doc

With the game/activity or any like it I think it’s important to have the culminating conversation. I asked my students to consider “offer and receive” vs “grab and take” — how are they alike? how are they different?

It takes time and effort to introduce and establish a classroom environment with these characteristics:

* during large group discussions students
- take turns
- explain their own thinking
- listen to other’s thinking
- paraphrase others
- respecting differences of opinion
- justify their own reasoning
- revise their original conjectures

* during transitions from one activity to another students
- watch for signals from the teacher
- listen to directions
- pay attention to the amount of time and pace themselves
- follow classroom routines including know the designated place for handing in their work
- move about the room as directed and then as expected
- accept consequences when disciplined

I tried not to assume that students would know how to behave in my classroom. Playing the Quiet Game was one way to introduce some of these expectations. Each time students reacted differently but it gave me an idea of where they were and what I might need to provide to help them develop a sense of community in my class. Most important for me was the culminating discussion. What was the “real” point of the exercise?

What do you do to build a community atmosphere in your classroom?