We had the back-to-school edition of our Math Institute this week. Our focus, appropriately enough, is on what is our administration wants to see when they are observing our classes. These are the four goals introduced in our June institute, namely:
Modes of Response
We wanted to work on how we are planning our lessons, with emphasis on making an engaging lesson plan and what students look like during our lessons.
Previously, the majority of us planned our lessons in a teacher-led fashion where the teacher is walking the student through the class. These classes tended to be more algorithmic, focusing on steps to take to solve a problem, and less concept-driven. We concentrated on teaching “this problem” rather than problem solving strategies. Going forward, we’d like to make lessons more engaging by utilizing guided discovery lessons that illuminate larger concepts through student-driven explorations. I interpret this to mean the students will be doing more thinking about what they’re doing and justifying it.
We also wanted to redefine what a “perfect” classroom looks like. In the past we might have said that the ideal student would be looking at the board, paying attention, taking notes, and asking questions. But now we want to put more emphasis on group discussion, so we want to encourage students to support each other (teamwork) and get excited to debate and defend their ideas. I would add that I want to foster an environment where making mistakes is okay, and admitting a mistake is seen as a way to further explore and learn about a topic.
Some of us admitted to being apprehensive about group work because one student always seems to dominate while the other group members just sit back. Possible solutions are to make sure each member knows that they are responsible for the task, and perhaps even asking the perceived “weakest” member to be responsible for explaining the solution. But the bigger issue is to structure lessons where the journey is the issue, rather than putting all the focus on the solution.
In short, we need to be conscious of how we’re leading in the classroom. Modes of Response have to with the actions we’re asking student to take. Which individual are you calling on? Are students to write down their answers or pair-share? Are they supposed to brainstorm on their own or have a group discussion? Teacher Discourse is about what questions we are asking to keep the focus not on the answer, but on the journey – making students become conscious of their thought processes. (Resource for question types: Developing Mathematical Thinking With Effective Questioning )
Strategies for implementation:
- Assign roles for group work: Manager, Liaison, Recorder, Quality Control. Make the Liaison the mouthpiece of the group and only talk to that student. At the end of the lesson have the students grade each other on how well they did each job and why they gave that grade.
- Make a poster to hang in the classroom listing effective questions, or tape a list to the back of a clipboard.
- Don’t ask the questions. Give the students the set up and then let them pick the question (i.e. what do you want to find?)
- Use a Discussion Rubric to let students know how they’re being evaluated and how they are getting points.
- Teach students to explain wrong answers, or even give them the wrong answers and have them explain how that answer might have been reached.
- Let kids know explicitly what we expect a discussion to look like.
- BE PATIENT with yourself and your class. There will be awkward silences, or classes won’t listen, or there may be management issues, but remember that it is a process.
There are concerns that we won’t be able to cover as much as we have in the past as we switch to this kind of discourse. Yes, it may be slower, but as the students start to get more comfortable with these classroom conversations eventually the pace will pick up. Also, remember that the goal is that the students will learn how to think and problem solve, so when they encounter something unfamiliar or more difficult they will have the skills and the confidence to tackle it.
The rest of the time was spent creating and teaching lessons in pairs and getting feedback from the rest of the group on our modes of response and teacher discourse.
Also of interest:
Interactive notebook reference
Styles and Strategies for Teaching High School Mathematics: 21 Techniques for Differentiating Instruction and Assessment by Edward J. Thomas, John R. Brunsting, Pam L. Warrick