Maths talk is more than simply describing the steps when solving a problem (“First, add the ones, then the tens. If you need to regroup, do that.”). Maths discussions are focused on the process of working towards a solution, understanding how others’ think about that process, and developing a plan for similar problems. Students should be pushed to think beyond an explanation of steps to an explanation of process, including making errors and how those were resolved. They should also be encouraged to use different methods and tools when solving a problem, then sharing these ideas with others to build a bank of strategies. How can engaging in maths talk be done successfully?
The objectives of the national curriculum for mathematics include:
- Building fluency in mathematics fundamentals through frequent and wide-ranging practise of progressively complex problems
- Developing conceptual understanding so that new knowledge can be applied to similar problems accurately
- Reasoning mathematically through enquiry, conjecturing on relationships, and developing arguments using mathematical language
- Solving problems by applying mathematics to routine and non-routine problems and persisting in finding solutions
The goal is that as students progress from primary through secondary levels, they become more comfortable using and talking about mathematics concepts and skills including how they are applied outside of math. Because of increasing emphasis on STEM/STEAM learning and 21st century skills, having students talk about their learning is vital. In their conversations, mathematical language is expected for all students. The more that mathematical language is used in direct instruction and modeled in maths discussions, the more students will become confident with using this language in speaking and writing.
Below are suggestions for strengthening maths thinking and incorporating maths discussions. As you review the list, compare with the objectives mentioned above:
- Establish norms for how discussions will take place. This includes active and respectful listening as others share ideas with the expectation that they will provide feedback. In the beginning, teachers will need to model these norms, including “think alouds” of possible feedback (“I’m wondering about why you decided to add instead of multiply”).
- Pose meaningful problems that are relevant to students. As you get to know your students, their prior knowledge, and experiences, develop problems that students can identify with and are applicable to real-life. Problems should also include multiple solution strategies that fosters reasoning on possible entry points.
- Make available a list of discussion prompts to start maths discussions (partner, small group, whole class). As students become more comfortable with giving and receiving feedback, the class can add prompts to the list. Post the list in the classroom so that it is visible to everyone. In the beginning, review the prompts before beginning maths talks.
- Provide opportunities for partner and/or small group talk. Have students engage in ‘turn and talk’ where they can talk with a classmate nearby before relaying to the class. Students can share initial strategies and plans about their attempts at solving a problem. After hearing what peers have to say, students can choose to incorporate the ideas shared. This will help them better understand their own thinking and grow as a “maths thinker.”
- Require visuals in explanations. Visuals can include drawings, models, and slide presentations. Visuals can be shared with a classmate or in small groups, or via a ‘museum walk’ where visuals are displayed, and students can walk and review before commenting. As a whole class, talk about what solutions and strategies stood out for them and why.
- Design assessments that call for creative and critical thinking. Most students have ample experiences with multiple choice and short answer style assessments. Start off simply with a problem that has identifiable errors in the solution process. With the whole class and/or smaller groups, discuss the errors and how they could have been made. Then have students do the same type of activity in small groups. Or, have students write problems targeting a newly learned concept or skill. Review the problems, assign them to others, then have students share solutions.
As students grow comfortable with maths discussions, require more from these sessions like detailed feedback and questions, especially as the complexity of the problems increases. Push students to incorporate alternative strategies without overwhelming them with too many strategy options. Prioritise what and how you will present strategies when you plan and as you observe how students are grasping new skills. The opportunity for strengthening critical thinking and communication skills is great in math discussions. The time invested in thoughtful planning will bring positive learning outcomes.