FMSP CPD for Mathematics Problem-Solving at KS5
Throughout 2013-14 the Further Mathematics Support Programme (FMSP) provided CPD events for teachers looking to help sixth formers develop deeper problem-solving skills. Over three hundred teachers attended the events and they were very well-received.
Part of the focus of these events has been supporting students to prepare for the Sixth Term Examination Paper (STEP) and Advanced Extension Award (AEA) mathematics examinations. Some university courses require students to take these examinations to qualify for entry and other university courses encourage their applicants to take them. Supporting students to prepare for STEP and AEA can be challenging, especially when only limited time is available and so making maximum use of resources that are already available is very important. These CPD events provide an opportunity to discuss mathematical topics in a deeper way, as is often demanded in STEP and AEA questions. This can also be of great benefit to teachers for their regular A level classes. STEP and AEA past papers are an excellent resource of mathematical enrichment problems which could be used more generally in maths classes.
If you haven’t attempted a STEP or AEA question before, have a go. Past papers for STEP are available on the Admissions Testing Service website, and for AEA on the Edexcel website.
In 2014-15, FMSP events will also cover the Mathematics Admissions Test (MAT) which is run by the University of Oxford as part of the entrance requirement for some of its courses.
Past papers for the MAT are available on the University of Oxford Mathematical Institute website.
Although these problems can sometimes be very challenging, the feeling of satisfaction from thinking about and solving these questions is great! By encouraging more participation in deeper problem-solving and STEP, AEA and MAT we hope that more teachers and students will catch the ‘problem-solving bug’.
If your institution is registered with the FMSP it has access to a set of teaching and learning resources for STEP and AEA as well as full solutions to past papers.
During 2013-14 the FMSP also provided CPD events focusing on introducing all AS level Mathematics students to more problem-solving during year 12, together with a number of problem-solving conferences for sixth form students. The aim of the conferences was to provide students with experience of a range of skills and techniques associated with mathematical problem-solving. These include group work, individual work, working on less-familiar mathematical areas, and writing and communicating solutions to problems.
Here is a problem that students were asked to present solutions to at a conference:
In the diagram below what is the sum of the four shaded angles?
Here is an example of a problem that students looked at during an extension session on number (the solution is given below!):
Prove that n5 – n is divisible by 5 for all natural numbers n.
The student conferences have proved to be very popular this year and more will take place during 2014-15. Visit the regional pages of the FMSP website for more information.
These events are just part of FMSP work to promote and encourage greater engagement with mathematical problem-solving. FMSP Maths Feast events starting in 2014/15 will provide a great opportunity for KS4 students to have fun with problem-solving. The Senior Team Mathematics Challenge which the FMSP runs jointly with the United Kingdom Mathematics Trust is a national team maths competition aimed at year 11 and sixth form students. All the materials used in FMSP competitions are available via the FMSP website. Teachers are encouraged to use these with as many students as possible, not just those that go on to represent their schools/college at the events.
During 2014-15, the FMSP will continue to provide CPD support for teachers with problem-solving. Events for teachers for problem-solving aimed at KS4 level, AS Mathematics level, the Mathematics Admissions Test (MAT) and at Sixth Term Examination Paper (STEP), Advanced Extension Award (AEA) level mathematics will all take place. Again, please visit the regional pages of the FMSP website for more details.
Solution to problem: Let n be a natural number. Observe that n5 – n = n(n-1)(n+1)(n2+1). If the last digit of n is 0,1,4,5,6 or 9 then one of n, n-1 or n+1 is divisible by 5. If the last digit of n is 2,3,7 or 8 then n2 ends in a 4 or a 9 and n2 +1 is divisible by 5. In all cases n5 – n is a multiple of 5.