Collaboration Dynamics

When you think of a math classroom, you probably think of a teacher explaining how to do a problem in the front of the room. You may also think of students doing about 20 of the same problems. Rarely do you think of students discussing problem solving strategies in small groups or wrestling with a concept as an entire class.

However, students talking is the heart of doing PBL in a math classroom. It is a research based practice proven to increase mathematical competence. National Council of Teachers Mathematics explained the necessary elements for mathematical learning in their Principals to Action publication. One of the necessary elements for effective teaching is discourse. "Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments."

It is easy to say students need to have discourse but it is sometimes hard to make it happen. Here are some strategies I have found indispensable to facilitate discourse.

Think-Pair-Share
This is a commonly used strategy and great way to get students started on working collaboratively. I typically start with students thinking about the answer to a success starter (a question at the beginning of class that gets them started with the day rather than review). They then talk it out with a partner even if it is just details about where they got stuck and how they may need help. I don't let them say I don't know. The share is them sharing what the other person said.

Rally Coach
A love a lot of Kagan strategies but this one is a favorite. Here are the steps for the cooperative learning strategy:

1. Pair Shoulder Partners. Determine who is A and who is B.
2. Present a problem for which there is only one correct answer.
3. Partner A solves the problem while Partner B coaches, checks the accuracy of the answer and praises.
4. If the answer is incorrect, Partner B coaches Partner A to the correct answer.
5. Present a new one-answer-only problem. 
6. Partner B solves the problem while Partner B coaches, checks the accuracy of the answer and praises. 
7. Repeat from step 1. 

Some of the twists I make to the process is students are given the problems that have a similar format like the one on this worksheet. I like using it because the answer is the same for the same number problem. I have the students use a colored pencil for accountability purposes. They must write a synopsis of what they said to coach the student using the colored pencil.

Question Formulation Technique (QFT)
This is a great strategy for having students develop their inquiry muscles. Students work individually and small groups to generate questions for them to explore within a unit. Students generate the questions from viewing a prompt (an image or words) that requires following four simple rules. The rules are ask as many questions as you can, do not judge or discuss questions, change any statements into questions and write down every question exactly as stated. Students go through a refining process and use the questions to make sense of the unit. You can find out more details on the technique at rightquestion.org.

Paideia Seminar
Many people are familiar with the socratic seminar. Paideia is similar in that students do have a discussion however it includes more than just a discussion. It is a complete process for reading, writing, speaking and listening. It is one of my students favorite activity in my class. They are always asking me when are we going to do a seminar. I use Paideia seminars to help my students discuss deeply as a class and to deepen their conceptual understanding. Students have a pre-reading which is typically a difficult math problem, a portion of a reading or an examination of a student's math work. Students then move into the discussion which includes them setting goals for the seminar and evaluating themselves at the end of the discussion. The discussion is guided by my questions. Students complete the circle of the seminar with a response to a writing prompt. Get more information about Paideia seminar from their website.

I would love to hear about some of your strategies for having students collaborate. Respond by commenting below.