Complex Instruction

In her book What's Math Got to Do With It?, Jo Boaler wrote about 'complex instruction' as a vital part of making groupwork function effectively. What I read intrigued me, so I searched for more detailed information online, but I couldn't find much.

This past week I was able to attend a workshop on Complex Instruction put on by the Center for Innovative Teaching, at the Urban School in San Francisco. The workshop was led by Laura Evans, who did a fabulous job of introducing us to these powerful ideas. I'm going to try to explain what I got out of this two-day workshop, but my head is spinning, so I might miss vital pieces or misrepresent parts of the theory. If you were there, and saw different aspects, please speak up. I was the only college teacher there, but there were only a few things I had to translate for my situation.

Here's how it works: Start with a group-worthy task, make sure the students are ready in their groups, and understand the roles they're expected to play, give clear and detailed instructions about how they should work together and what to do when they think they've completed their task. Then, let the math-play (play and work are equivalent in a context like this, right?) begin!


A group-worthy task ...

• is open-ended
• is based on discovery
• is challenging
• requires multiple abilities
• can be represented in more than one way

I'll feel like I really understand this when I can take a task/problem and evaluate it based on these criteria. I'm not there yet. I also need to be able to look at the curriculum we have and decide what sorts of group-worthy tasks would help the students learn each bit.

'Smart in Math'
Before students work in groups, it's important to help them understand that we typically have many misconceptions about what it means to be 'smart'. Typically, people think that someone who is 'smart in math' ...

• answers questions quickly
• always gets the right answer
• doesn't have to work at it

But, really, people who are good at math ...

• are persistent
• wonder about relationships between numbers, shapes, functions, ...
• check their answers for reasonableness
• make connections
• are willing to try things out, experiment, take risks
• are resilient
• want to know why
• contribute to group intelligence by asking good questions
• notice and learn from their mistakes
• try to extend and generalize their results

Students may also need to know how synapses (the connections between neurons that are created each time you learn something new) are strengthened by repeated use. A new connection isn't strong until it's been used:

• multiple times
• in multiple ways
• after a time away

Roles for Group Members
Before the groups dive into a math task, the group members also need to understand the roles they'll take on. Any teacher interested in using these ideas can modify these roles, but the idea is to give students plenty of coaching in how to work productively, and much less coaching on how to do the math.

• The Facilitator asks if everyone understands what's been said, if anyone has a question, ...
• The Team Captain keeps the group on task, reminds people of how they're supposed to proceed, makes sure everyone's ideas are heard.
• The Resource Manager makes sure all conversations happen in the middle of the table, collects materials from the teacher, calls the teacher over when the whole group has a question, returns materials, ...
• The Recorder takes notes on the ideas, questions, hypotheses, prepares the group's presentation paper, makes sure everyone can explain the group's solution.

This list was part of the handout for the problem we were going to work on, which I'll describe next.


The Pile Pattern Problem

We needed to figure out the shapes for piles 5 and 6, and what their areas would be, and then to do the same for the 100th pile. We were also asked to think about the 1st and 0th shape, and if possible the -1th shape. While we worked on our mathematical task, Laura walked around and took notes on what we said to one another. She came up to us at an opportune moment and said things like, "Sue, it was really neat when you said 'I was thinking this, but it sounded like you were thinking about it this other way', you made connections between your thoughts and Rachel's." She had a very specific bit of praise for each of us, related to how we worked within the group, to solve the problem.

We all presented parts of our solutions to the whole group (of about 20). We were able to look at the pattern geometrically, algebraically, numerically, and graphically. We had a recursive formula for the area and an explicit one. We figured out what the 1st shape (#1) would have been, and hypothesized about the #0, #-1, and #-2 shapes. There were definitely some interesting twists to the problem.

Every step along the way, Laura would mention bits about how she'd do this with students. Make sure the group that only got one part gets to go first, have each group after that present one new way of looking at this problem.


Status
Within a group of high school students, each student has high or low social status and high or low academic status. (My question: How is this different among college students?)  If someone is quiet, it's generally because they don't expect their group to be interested in what they have to say, either because of past experience or because of subtle cues from other group members. Laura said, "Students hesitate to share as a way to hide or protect their status. High or low status is a great barrier to risk taking."

The teacher's job is to change that dynamic in a few ways. She has already told the group very explicitly what each person can do to help. She can also look for ways to 'assign competence' to students who have low status. If a low social status student has asked a question, she might mention how that was a great risk to take, and how it helped the group. Laura again, "When we raise their status, we give students excuses to take the risk that they deep down want to take."


I loved this workshop, and I hope to be able to implement some of the ideas. I wish the workshop had been longer. It would have been great to have a chance to practice finding or creating a group-worthy task, writing up instructions for it, seeing how groups work through it, and responding to the 'students' by commenting on how they're working together instead of offering them math tips.

 Edit on 5-30-13: When I wrote this, there were no complex instruction resources online. Now there is this website - it looks good.