Creating Mathematical Inquiry Communities

I've been doing a lot of thinking about how to accelerate the achievement of the students in my class in mathematics.  A few years ago I listened to Zain Thompson speak about creating mathematical inquiry communites as a way to do this.   This year I have a class that ranges from curriculum level 1 to 4 and I believe that this would be the perfect model for accelerating most of these students.

What is typical in an inquiry-based mathematics classroom?  Students who actively drive their learning, communicate mathematically, think critically, question, collaborate and support each other.

This teaching approach is culturally responsive and supports students to work together to solve mathematical problems, accelerating achievement for the students involved.

These are the inital steps I will be taking and developing from there.

Starting with one problem (may move to more than one problem at later stage).
The class is split into two groups that are mixed ability - the teacher spends half the time with each group.
No learning intentions are shared but can be discussed at the end of the lesson.

1.  Students solve the problem individually - they are given thinking time and may represent their thinking in any way.  If they are finished early they can come up with a different strategy.  The teacher anticipates the students solutions.

2.  Students then share their strategies with group members.  As a group they decide on one solution to become the group strategy.  They must explain, question and justify until each member of the group can understand and explain the strategy.  The teacher spends this time monitoring the group with limited input.

3.  Students rehearse their explanantion and check that everyone in the group can explain the solution.  The teacher then selects particular students to present their solution strategies (simplest strategy to begin and sequence until the most difficult).

4.  One student from each group share their group strategy with the bigger group.  It is not just a show and tell, they must actively question, explain and justify their thinking. 

5.  Have a whole group discussion after the strategies have been shared.  Can they make connections, see any patterns, reflect on learning and identify next steps.

My first step before attempting this is to spend time developing groups and how they work.  I may use the waka analogy - if one person stops paddling, you go round in circles and go off course so everyone in the group has to be on board with the strategy.
 
Here is the BES Exemplar with the mathematics communication and participation framework phases that I will be working through with my class and ground rules for talk examples.  It is good reading and a must if you are interested in using this approach in your class.

Other readings that relate to this:
Learning to "friendly argue" in a mathematical inquiry
Video resource from NZmaths
Effective pedagogy in mathematics