Maths GCSE resit and Functional Skills learners

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Maths GCSE resit and Functional Skills learners

Maths teachers from across the GMC group worked over several weeks to develop a series of lessons targeted at developing student facility in proportional reasoning.

First the group talked about why these learners need different approaches to learning maths:

Issues related to re-sitting Maths GCSE or studying for Functional skills within nine months:

  • Memory of formal mathematical procedures is poor
  • Students resort to ‘doing something with the numbers’ and rarely attempt to make sense of a problem
  • Repeating the whole course in 9 months is not possible to do in real depth
  • Student confidence is often low, due to years of experiencing ‘failure’ in tests

Then we focussed on developing solutions:

  1. Focus in depth on a few related topics using the same solution strategies in Term One

It is helpful if we choose to focus on a few curriculum areas but spend time studying these in depth, so that students can develop confidence and experience some success. Re-visiting formal methods which students have not been able to master in the previous ten years of schooling is not likely to produce different results. It is important to use different approaches which build on learners informal, common-sense strategies. It is important to do this in Term 1, so that learners can bring their new approaches and their increased confidence to past paper practice later in the course.

  1. Use the ratio table to solve many problems which require proportional reasoning

Proportional Reasoning underpins such a lot of the Foundation maths curriculum. As a group we identified over 15 topics which rely on students being able to reason about two quantities which are related in proportion. The topics include: recipes; long multiplication and division; speed, distance time and other compound measures; percentage including reverse percentage; converting measures; best buy and other comparisons; ratio; equivalent fractions; enlargement and similar triangles, trigonometry, pie charts … and more.

If students and their teachers start to see all these topics as the same, so that questions can be answered using the same strategy, then this considerably reduces the load on memory.

During the online sessions we worked on developing our expertise with Realistic Maths Education approaches. (See ) In particular, we considered how digging into the context of recipes can be used to reveal a ratio table.

In the images above we see the salmon pasta recipe written as a recipe become a table of possible values. This table is called a ratio table, it enables students to adjust the quantities of ingredients required to make the recipe for different amounts of people. The power of the ratio table is that it encourages learners to follow their own routes to adjusting the recipe; it empowers them to take ownership.

Through representing many situations by drawing their own ratio table, learners begin to recognise that although the question topic may be different, once the information is represented in a ratio table the strategies for working with the ratio table are the same. A challenge for the teachers and their students is to see how many questions on a GCSE paper they can answer by drawing a ratio table.

  1. Develop our own suite of lessons using context and the ratio table

On 6th May the GMC group of maths teachers met in person and began preparing their lessons. Much deliberation went into choosing contexts where two quantities are in proportion and so can be represented in a ratio table. The lessons will be finalised over the summer with first lesson trials going ahead in the Autumn term.


Lesson Drafts to follow in September

Project Lead: Sue Hough

At the heart of Sue’s work is her belief that with appropriate support all learners can develop mathematical thinking from their own informal approaches. Sue started as a Secondary teacher and now works with trainee teachers at Manchester Metropolitan University. Through projects funded by Nuffield and EEF, Sue has worked with many teachers on how to use context and related models such as the bar model and the ratio table, so that learners can start to see the curriculum as ‘joined up’ rather than trying to remember a variety of different procedures. The origins of these approaches lie in Realistic Maths Education, where Sue has authored books and websites. (See

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