How to Orchestrate Productive Mathematics Discussions in the Classroom

As we rapidly move to the conclusion of the Primary Maths Specialist program, we took the opportunity to map out ways we can sustain and continue to innovate our approach to maths teaching and learning. We have made great improvements in so many areas but what Pete and I are most proud of is the dispositions our students display when learning maths. Peter Burrows from EdPartnerships Intl. refers to Costa and Kallick’s (2009) sixteen ‘habits of mind’ which includes questioning and posing problems as a ‘habit’ that could play a key role in learning maths. Our work has focussed on using Jo Boaler’s maths mindsets to build positive attitudes towards learning maths and developing productive dispositions that students can apply to all areas of learning. Our signpost statement clearly identifies our vision for maths teaching and learning – ‘Everyone can do maths; it’s creative, exciting and useful.’ We strive to show students the beauty of maths, how it is a creative are of learning where student reasoning and multiple perspectives are valued.

We have embedded a ‘challenge first’ teaching and learning model (see previous post) over the last two years and our plan this year was to add more rigour to the ‘explore’ phase by developing teacher knowledge around effective questioning. We want questions to be open, to encourage multiple methods/ ways of seeing and thinking and to clarify/extend student thinking. Creating a classroom culture that is built on positive mathematical mindsets encourages productive dispositions and is the foundation upon which students feel comfortable to share their thinking, knowing that their work is valued by their teacher and their peers.

The ‘challenge first’ approach presents challenges for teachers in knowing what to look for in a lesson and how to create the conditions to allow for explicit teaching. We believe that we can create the conditions for explicit teaching through designing good challenging tasks – with enablers and extenders – and using ‘5 Practices for Orchestrating Productive Mathematics Discussions’ by Margaret S. Smith and Mary Kay Stein. By using both effectively, we have created a pedagogical approach that is built on student thinking. The challenge on knowing what to look for and how to guide students to mathematical understandings is addressed by the five practices of Anticipate, Monitor, Select, Sequence and Connect. The aim of using the five practices is to create a classroom environment where student agency is at the core and adding ‘structural support’ to make it more manageable for the teacher. The five practices lessen the need of the teacher to respond to student learning ‘in-the-moment’ by anticipating what responses the students may have prior to the lesson and how they can prepare questions/comments to delve deeper into student thinking or further their learning.

The Five Practices are:

1. Anticipating likely responses and questions to ask during the lesson.

2. Monitoring students’ actual responses to the task.

3. Selecting students to present their strategy and explain their thinking during whole class discussions.

4. Sequencing student responses to be presented in a specific order and,

5. Connecting different students’ responses and making connections to the maths focus of the lesson/key mathematical ideas.

It has been challenging for some teachers to adapt to doing the anticipation stage but they are starting to see the benefit of seeing other ways of thinking and working collaboratively to think of questions to create the conditions for explicit teaching.

After teachers have solved the problem in numerous ways and created some questions to use in the classroom, we try to put the strategies into a learning sequence. We use the National Numeracy Learning Progressions to help guide this process.

The strategy board can be used as a formative assessment tracker and helps to sequence the student samples the teacher chooses to share with the class based on the strategy/strategies that the class is using. For example, if the majority of the class are using repeat addition/subtraction to solve a multiplication problem, a teacher may choose to highlight this strategy with the class and use targeted questions to encourage the class to they could use more efficient multiplication strategies to solve the problem.

Matt Sexton’s Talk moves have been an inspiration and necessary resource to help guide teachers in what types of questions to ask and the many variations in the way they can be asked in the classroom.

As we continue to refine and adapt our approach how we plan for maths lessons and what the teacher and learner is doing within the lessons. We would love to hear from others about the way you plan maths lessons, please contact us on twitter @SamandPeteEdu