# Fostering discussion

### RME is about promoting and sustaining *mathematical* discussions

When they work with RME, students generate their own representations of context and problems, but they need to **articulate their reasoning** and **listen** to others’ strategies and explanations. One key aspect of RME practice is supporting your students to engage as mathematicians, and to help them listen to one another and collaboratively refine their thinking. Poorly formulated ideas are finessed, not rejected. And, even when they might conventionally be considered “wrong”, a students’ idea should be heard and explored. These conversations help the classroom explore a misconception, and see why it isn’t right.

This page introduces key strategies for promoting mathematical discussion. We draw on examples from our materials to help you develop your practice – remember that the teaching guides include a section on ‘what the teacher might do’ for individual slides. They also have a section on ‘what the student might do’ – this section provides details on the **variety** of strategies or solutions (not necessarily ‘correct’) that students might come up with; working with this variety is central to classroom discussion.

Read more about these and other strategies on our putting it all together page.

Here are four strategies to begin with:

### 1. “Can you say what he/she said?”

RME classrooms rely on a culture of working together, and listening to what other students say. Students also need to explain their own ideas clearly—one reason for “convince us” strategy described below. Careful listening enables students to engage in discussion with each other and get to the bottom of the problem they are dealing with. Maybe without the teacher’s help….

Students who know that they may be asked to repeat what another just said will listen carefully. Formulating another persons idea in their own words helps everyone to make sense of a novel insight or strategy. As students become used to working in with RME, they are unlikely to need reminding.

The importance of listening and thinking about other points of view is embedded in our RME materials. In this Activity Sheet from **Seeing it Differently (N2)**, students are invited to think about what Emma would say, and be able to describe her approach. This creates the foundation for the next question—why?

### 2. Make time for thinking

Teachers are often under pressure to move on in a lesson, and waiting a long time for students to respond can be challenging. Our materials are designed to support students to develop their own strategies and explanations which they can share in the classroom. Thinking takes time and formulating ideas as speech is difficult. Research tells us that teachers rarely wait more than a second before they move on. Try timing yourself!

Re-watch the video on the RME in action page and notice how supportive the students are of a long wait-time. Long wait-time gives a teacher time to think too about what the difficulty might be, and to plan their next move. This could include asking the student to ask a question which might help them.

### 3. Remain neutral

RME teaching relies on students feeling free to offer strategies and solutions, without fear of being ‘wrong’. Multiple ways of looking at the same problem can be discussed and explored, leading students toward a more connected view of mathematics. Remaining neutral encourages more contributions to a problem—students who are used to RME classrooms don’t expect to stop thinking once someone has come up with ‘the right answer’.

These slides from Sorting It Out (D1) invite students to develop a variety of strategies which will eventually lead them to a deep understanding of what we mean by ‘average’.

The first slide elicits a variety of strategies:

- Guessing a value and checking by totalling the values and dividing by how many there are
- Recognising that the total needs to be 25+25 (for 2 throws) or (25 +25+25) for three throws and working back from there
- Comparing how far scores are from 25 and balancing the gaps below with the gaps above

The second encourages a honing down of strategies, and students develop the argument that Kelly does not qualify, with various strategies:

**Re-distributing:**9 from the 35 goes to the 16 to make 25. 3 from the 28 goes to the 20 plus from 1 the 35 goes to the 20. This gives scores of 25 24 25 25 25.**Balancing:**Comparing with 25 gives -9 -5 0 +3 +10 = -1 below 25**Totalling and dividing:**124 divided by 5 is 24 r 4

Remaining neutral and encouraging students to explain to the rest of the class enables new connections. Which brings us to the importance of explaining clearly….

### 4. “Convince us.”

Remaining neutral sets the scene for “convince us”. Without the teacher as the final arbiter of right and wrong, students must be the explainers in the classroom. “Convince *us*” emphasises that everyone, not just the teacher, needs to be persuaded. The requirement to explain and convince is present in all the modules. See more about students as explainers here.