Where things can go wrong…

This student solution will look familiar to many teachers:

The solution features a student ‘doing something with the numbers’. The student applies a number procedure without thinking about how it relates to the question. For many students, this is the only way of doing maths that they know.

How RME can help

RME aims to tackle this problem through a different approach to learning. It encourages students to develop informal strategies for solving problems, and to build on these for a more thoughtful engagement with novel problems. The major benefit of RME is that students are able to use flexible models to make sense of problems, rather than relying on (mis-)remembered rules.

In our trials, we have seen control group students produce solutions like the one above. Intervention students, on the other hand, approach this problem differently. These examples of students’ work illustrate what they gain from RME:

In both examples, we see students reallotting parts of the trapezium to arrive at a meaningful solution. Our geometry module, Fitting It In (G1), helps them develop strategies that give meaning to what area actually measures—a collection of uniform two dimensional units.

Here are some examples of Year 8 work on a more difficult problem—finding the area of a tilted triangle, whose ‘base’ and ‘height’ measurements are not straightforward. Students use variations on a realloting strategy to arrive at a solution:

What do we know about the impact of RME?

RME was first developed in the Netherlands, where it has now been adopted in the majority of schools. A comparative study, carried out by Anghileri, Beishuizen & van Putten (2002), looked closely at Year 5 Dutch and English students’ approaches to division. The researchers found that Dutch students—taught using RME—were not only more accurate when solving division problems, they were also more confident about their methods. The English students made more errors and reporting being less certain about what they were doing.

The researchers concluded that these differences stemmed from the way in which RME pedadogy helped the Dutch students to build increasingly efficient methods from their initial informal approaches to division. The English students’ strategies were less robust because they had been taught the traditional division algorithm from the beginning. This meant that they didn’t recognise the number relationships they were dealing with, and instead used a mechanical procedure cued by the ‘division’ sign. Not surprisingly, perhaps, students in the Netherlands continue to significantly outperform their UK peers in the international PISA mathematics tests.

What else do we know?

In the US, RME appeared in the Mathematics in Context (MiC) textbooks series. Researchers at the University of Wisconsin reported that 8th grade students taught using the MiC materials, along with the associated RME teaching style, performed significantly better than other students in the trial (Romberg and Shafer, 2005). We have learned a lot about the importance of teaching in our own work, and you can read more about teaching RME on our Getting Started pages.

As the Dutch and US data show, RME enables students to develop a deep understanding of mathematics. At Manchester Metropolitan University (MMU) we have been developing and trialling RME materials for more than fifteen years, at Key Stage 3, Key Stage 4, and post-16 GCSE resit.

Key Stage 3: In 2004-7 we trialled the Mathematics in Context materials in Years 7 and 8 in 12 schools, and found that students benefited from its emphasis on developing informal strategies.  Students were more likely to solve a problem correctly, and they could explain their strategy.

Key Stage 4: The materials team wrote ‘Making Sense of Maths’, published by Hodder, and trialled the materials for Key Stage 4 Foundation level pupils. Teachers reported that working with RME had positive effects on students’ engagement and understanding.

Post-16 GCSE resit: This is one of the most challenging groups to work work with.  Interventions using materials based on ‘Making Sense of Maths’ have shown that students taught with RME make significant gains in tests and enjoy maths more.  Download the final report on this project here.