# Mathematising

### How do you get students to build their own mathematical strategies?

RME teachers employ a number of techniques to engage students in ways that produce authentic and meaningful mathematical ideas. This page introduces **key strategies** that RME teachers use to support students’ mathematising, from building on their **informal understanding of context**, to **making connections across different areas of mathematics**. We highlight several examples drawn from our materials that will help you to develop your practice – remember that the teaching guides include a section on ‘about the maths’ for individual slides and activity sheets.

Here are four to begin with – you can read more about these and other techniques on our putting it all together page.

### 1. Go back to the context.

RME aims to build mathematics from contexts which students can visualise as a basis for informal models. As they grapple with difficult ideas—like percentage change as in the ‘Bargains’ video on the RME in action page—returning to the details of the context can help them stay on track and make sense of what is going on.

While staying close to the details of particular contexts, RME teachers also aim to support students in making connections across a range of contexts, representations, and mathematical concepts. Our RME modules always contain multiple contexts from within which students can tackle new mathematical concepts and strategies. This means that if students don’t immediately connect with a certain context, they may make these connections in the following one.

### 2. “Where can you see the… in… ?”

RME encourages students to make connections across various representations of a situation – the Landscape diagrams illustrate how starting contexts on the bottom layer connect with models of those contexts above them.

The question ‘Where can you see …. in ……? ‘ helps students to make explicit connections between one representation and another. In the case of the subway sandwich you could ask ‘Where can you see the sandwich in the bar?’.

Read more about this technique here. You can also find a detailed application in Lessons 7 and 11 of the G1 Teaching Guide.

### 3. “Say what you see.”

An RME teacher aims to facilitate mathematical discussions that draw out quite close and technical observations from students. Asking students to ‘say what you see’ leads to subtly different ways of describing the situation, using a variety of language and interpretations.

This image prompts detailed observation of the objects on both sides of the scales, and the fact of balance. Students begin to match items up and make deductions about the equivalence of what is left.

Look at the Teaching Guide from Knowing the Unknown (A1) for more on the application of “say what you see”. This technique appears in Lesson 6 in particular.

### 4. “What is the same?” / “What is different?”

This question helps to stimulate discussion of slides such as this, which focuses on the equivalence of the two expressions for a fish and chip shop order in Knowing the Unknown (A1).

This slide supports an informal expansion of brackets. While the expressions are *mathematically* equivalent, this is not the same as saying they are identical, and the question “are the two expressions the same” may elicit different responses because of this.