Tag Archives: A level

The Cambridge Mathematics Education Project: The power of CMEP resources

Here is an account by one MA member on using Cambridge Mathematics Education Project resources in the classroom.

Having returned to teaching year 12 core mathematics for the first time in several years I was keen to try out some of the many resources currently being created by the Cambridge Mathematics Education Project (CMEP).

Having initially thought many of the resources would be beneficial for extension and revision but not quite sure how much time I would have to fit things in I was inspired to try something different having heard other teachers discuss how they have used the resources in their classrooms at a recent workshop.

I chose to dive straight in to linear coordinate geometry with a CMEP problem I liked: In-betweens. This problem encouraged students to find the missing value of y for a point on a line segment. Having shown students the initial picture I was impressed at the resilience and collaborate working they displayed as they set about using what they knew about linear equations and supported each other with gaps in their knowledge from GCSE.

What became apparent is that students remember and can apply a lot more than I normally give them credit for. Students argued over methods and quickly became engaged in the recurring decimals they were coming up against accuracy required. A quick discussion about the value of fractions and they were off, having accepted more quickly why exact values are more useful then I have ever experienced before. The problem extends to a similar set of problems (e.g. now finding the y value) that are all subtly different and lead them more generally to the utility of sketches but also the futility of plots which are time consuming and don’t really help anyway. It was a great problem for exploring other geometric methods such as similarity and in one lesson we recapped and covered: gradients, finding the equation of a straight line from two points, midpoints, ratio, substitution, rearranging, Pythagoras and similarity. This is not to say I stopped there and never looked at these topics again but it gave me a great pre-assessment of where students currently were in their knowledge as well as a chance to introduce a more typical A level solving problem than they were used to and get them talking mathematically.

I am impressed at the thought that goes into these resources and the potential they have to help students connect topics and apply knowledge which I have previously found lacking in my students. I am glad I took the risk and decided to try something new.

The Cambridge Mathematics Education Project is a Department for Education funded project in the UK. For further information and access to the pilot site please email cmep@maths.cam.ac.uk. The resources are also being featured in the upper secondary student section on NRICH.

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London Mathematical Society Grants for Teachers

1) Small Grants for Education (from £600 to £800): http://www.lms.ac.uk/grants/small-grants-education
This grant is to stimulate interest and enable involvement in mathematics from Key Stage 1 to 5 (and beyond) by enhancing and enriching mathematical study beyond the curriculum, engaging the public with mathematics and encouraging unusual ways of communicating mathematics.

2) Teacher CPD Grants (up to £400): http://www.lms.ac.uk/grants/teacher-cpd-grants
This grant is here to provide opportunities for mathematics teachers to attend training which is specially mathematical. It is intended to facilitate mathematical professional development to allow teachers in UK schools to develop their subject knowledge, engage in a deeper understanding of how to develop mathematical thinking, appreciate the interconnectivity of mathematical topics, update themselves on mathematical curriculum reform and the use of technology where appropriate.

RISPs

 http://www.risps.co.uk

Brief Outline:

A free website which provides tasks which are laid out in a form which can easily be projected or printed and given straight to students. Each task comes with detailed teachers notes which give some background as to why the task might be useful, suggested ways to lead students through the task and any necessary answers or examples of possible answers. Many of the tasks can be adapted to other topics. The tasks are arranged by topic for AS and A level Core.

How to Use them:

As suggested by the name, the tasks are designed to be interesting starting points for topics. I, however, tend to find students get more out of them if they already have some knowledge of a topic. I find the tasks are great for consolidation and for connecting together ideas. They often encourage students to think things through and generate questions. Many of the tasks can be taken to varying degrees of complexity and hence provide differentiation by outcome.

Some of my favourites:

Risp 10- More Venn Diagrams

A great way for students to consolidate knowledge of straight lines or quadratics. Can be used as a starter with some discussion about what properties are needed to fit each section, or as a plenary to check knowledge of properties.

Risp 24- 3 Fact Triangles

I use this as an introduction to C2 Trigonometry. It allows students to recap knowledge of SOHCAHTOA and non-right angled triangles. I tend to find students need to recap their knowledge of non-right angled triangles. I often adapt this slightly…first I give students time to find as many triangles as they can. We draw these together as a class with discussion about how students approached the problem (strategy) as well as what makes the triangles mathematically different. I then tend to pick a selection of the triangles (including right-angled and non right-angled) and ask students in pairs to work out as much information as they can about those triangles.

Risp 29- Odd One Out

This can be adapted for use with many different topics. Students can argue why they think on of three things is the odd one out and there are often different answers depending on your explanation and reasons. I like using this when discussion properties of functions in Core 3.

STEP

Why STEP?

Well, apart from the need to support candidates whose offers require STEP grades, STEP papers provide rich problem solving questions to extend the high achievers. It is a respected qualification, and I find that not only potential mathematicians want to have a go, but so do physicists, engineers and computer scientists.

When STEP?

Traditionally, students take STEP alongside their A2 exams, and in order to meet UCAS requirements from Cambridge, Warwick, Bath, Bristol and an increasing (it seems to me) number of other universities. But by tackling it early, it could be used to enhance a UCAS application, and in any case, alongside MAT and PAT preparation, looking at STEP questions during the AS year can challenge students independently of any demands made by universities.

How STEP?

The best place to start is obviously the admissions website, the admissions website where you will find comprehensive guidance on the whys and wherefores of STEP, including a link to the STEP specification on the Cambridge Assessment website, where all the key dates, fees, test centres and other administrative details can be found.

There are also links from this site to the very useful Advanced Problems in Mathematics book can be downloaded – a collection of STEP problems with hints and worked solutions, written by Stephen Siklos. This can be used by students individually, or used as a class resource. The two-tier support – hint and then solution – provides excellent scaffolding (for the teacher, as well as student in some cases!) There is a similar booklet of problems – Advanced Problems in Core Mathematics – by the same author. Both contain a lot of Good Advice to students, many of whom will be facing problems outside their normal comfort zone.

Other useful sites include a new area on the Nrich website, the Nrich STEP site which gives students support with specific topics, as well as advice on preparation for interviews, and general problem solving support. It seems very much geared to individuals, and is comprehensive in its scope.

In addition to this, the Cambridge Mathematics Education Project‘s (CMEP) pilot site has a large selection of STEP, MAT and old O and A level questions sorted by topic, with full solutions. The site also contains resources that can be used at all levels of Post 16 mathematics. To gain access to the site your school will need to email and ask to become an affiliate school.

Meikleriggs website has long been providing worked solutions (handwritten at that) to STEP problems, giving us all a good model for how our answers should look. Integral, the FSMP website from MEI also has worked solution for STEP problems in its STEP area.

Which exam board do you use?

After a discussion of the exam boards our schools choose to use at recent meeting we thought it would be useful to share our thoughts.

We are aware many schools are not making decisions at this point in time regarding the new A level qualifications but for now, this is who we currently use and why.  We are aware this is a small sample so please do comment with your school’s experiences of all available exam boards including some reasons for why.

Independent school

“We are currently using Edexcel for historic reasons and have found its consistency over 14 years beneficial in our students success.  Our students all sit Edexcel International GCSE and the transition between the two is well supported.  We’ve found it very accessible for EAL students and the board support invaluable (Maths Emporium and ResultsPlus).  We love Further Pure, however we do think that the Statistics strand content could show better progression.”

6th Form College

“We use AQA, again really for historic reasons.  We like the fact that there are four further pure modules so it gives us more choice.  We like the structure of the exam questions.  We don’t like the variation in the grade boundaries year on year as the papers have become less consistent.  We also like that AQA offer an stand alone A Level in Statistics and have used this as a more suitable alternative to A Level Mathematics for some students.”

Secondary Comprehensive

“We use Edexcel because we like the consistency it gives our students who sit Edexcel GCSE Mathematics.  We have also found the support from Maths Emporium and ResultsPlus beneficial as a department.  We have found the language used in the questions more accessible to our students but don’t feel the scaffolded style of questions best prepares our strongest candidates for further study in Mathematics.”

International 6th Form

“We use CIE partly because it’s recognised and respected by our overseas students and their families but also because the CIE Mathematics A Level syllabus is deeper than some others.  However, we are concerned that the Further Mathematics syllabus does not include a sufficiently broad range of topics.  Another reason for choosing this exam board is that there still exists a November sitting and we have a second cohort that start each January.”