Make time for thinking
Slowing the pace is important in RME lessons.
RME invites students to explore a context and develop ways of talking about it mathematically. But thinking takes time and formulating ideas as speech is difficult. Students need support to organise their ideas and develop strategies. A variety of teaching strategies can make time for thinking, and these often appear in our materials. On this page, we discuss three strategies:
- What else do you know?
- Pass the pen
- Wait time
What else do you know?
This strategy arises naturally when students work with the ratio table or the bar. The slides on “Battery life” in Filling the Whole (PR1) use this question to give students time to use the bar creatively to calculate percentages. Some will mark in 33% and 66% and then divide 33% by 3. They then find multiples of 11%. Others will mark in 33%, 66% and 100%, then find 10%, 20%, 40% and 80%. Later, they use “What else do you know?” to solve a specific question: the price of jeans before the sales.
In Seeing it Differently (N2), students are presented with bare facts: “A 400g block of cheese has a volume of 320cm sq”. Without being offered a specific question about the volume of half a block of cheese, the slide asks students to say: What else do you know? This helps them to work out how to use a ratio table to solve problems about rates/speed and density. Once students are used to this question, they may even ask it themselves as they work alone or with others.
Pass the pen
Pass the pen is a strategy related to “What else do you know?” Here, students can come up to the board to fill in one more item that they know, then pass the pen to another student. An important by-product of this strategy is that it hands over responsibility for learning to the students — giving the teacher a chance to move away from the front of the class.
Teachers are often under pressure to move on in a lesson, and waiting a long time for students to respond can be challenging. In fact, research by Mary Rowe back in 1972 tells us that teachers rarely wait more than a second before they move on. Try timing yourself! Rowe found that extending wait time to betweeen three and five seconds makes a big difference to how students respond. Students’ responses are longer, they are more confident and willing to speculate, they ask more questions and lower attainers say more.
Re-watch the video of the RME lesson and notice how the teacher uses extended wait times in many places. You might be surprised by how supportive the students are of a long wait-time. These periods of wait-time not only give students space to think – they also give a teacher time to think. What is the crux of the difficulty we are having? What should my next move be?
Sometimes students find it hard to respond, even when you wait. In the video, the teacher also asks a student to ask a question which might help them – this is one way of helping them to begin speaking.