3 Mathematics Support Programme. This programme will combine the support currently provided by the FMSP with additional support for teachers and students for Core Maths. The L3MSP will continue to provide tuition for AS and A level Further Mathematics, enrichment for students and professional development for teachers. They will target it at schools and colleges that are most in need. MEI, which has successfully managed the FMSP contract since 2009, and before that the FM Network since 2005, strongly supports the decision to fund a new L3MSP and hopes to play a significant role in its work. It is envisaged that there will be a transfer of support activities from the FMSP to the L3MSP during the summer of 2018. In the meantime the FMSP will continue to provide the best support possible . Any teacher or student participating in CPD or tuition with the FMSP will continue to receive support until the completion of their course in the summer term.

Entries for both A level Mathematics and Further Mathematics were up again this summer which is excellent news. This summer entries for AS Further Mathematics entries increased by 4.6% despite large decreases in many other AS level qualifications. The FMSP is delighted that more schools/colleges are now able to offer Further Mathematics and more state-educated students have access to Further Mathematics.

Kevin Lord, Programme Leader

Continued support for AS / A level Mathematics and Further Mathematics

The funding for the FMSP has been extended by the DfE for another year. This means that we are able to provide support for students and teachers at this important time, as they embark on new AS and A level courses for Mathematics and Further Mathematics in 2017/18. The FMSP has planned an extensive programme of CPD to enable teachers to feel confident in addressing the overarching themes, such as problem-solving, modelling, and proof, in their teaching and enhance their subject knowledge. New online teaching resources are available via MEI’s Integral website, which has been updated for the new specifications. These remain free to schools/colleges registered with the FMSP. In addition the FMSP has produced a series of video lectures covering the content of AS and A level Further Mathematics to enable more students to successfully study the course. These videos are also freely available to all students in registered schools/colleges. Details of CPD, tuition and enrichment are covered in more detail in this newsletter and further information is on the FMSP website. In July Prof. Sir Adrian Smith’s review of post-16 mathematics was published. The FMSP was praised for the positive impact it has had on participation and A level Further Mathematics provision in

schools and colleges. In response,

Nick Gibb MP, Minister for School Standards, announced a new Level

Autumn 2017

Issue 17

Teacher Support

Student Support

Enrichment

Encouraging Further Mathematics

News and Events from the FMSP Regions

Recreational Mathematics and Contact Details

2

5

6

8

9

12

September 2017 sees the start of the new linear A levels and the FMSP Professional Development programmes have been extended and developed to help prepare teachers for the new A level Mathematics and Further Mathematics courses, with some exciting new developments.

Following on from the 53 Preparing for the new 2017 A Levels events, which were attended by over 1200 teachers from 898 schools and colleges, we ran two online courses for those that were unable to attend the days and these attracted 43 teachers. We have now developed a range of one-day courses to support the needs of teachers delivering the new A level Maths such as Teaching mechanics for the first time, Using large data sets and Teaching using technology. Area Coordinators began offering these in the summer term and they have been received with enthusiasm. We anticipate that there will be on-going demand for these and similar courses throughout the year. In addition there will be new courses to support the Further Mathematics A level.

The sustained professional development courses have grown in popularity. This academic year, with DfE support, we are able to offer a fee reimbursement to all teachers in state-funded institutions who successfully complete any of the sustained courses. In 2016/17 a total of around 200 teachers participated in Teaching Further Mathematics (TFM), Teaching Mechanics (TM), and Teaching Statistics (TS). This Autumn we have 200 teachers beginning the new TFM1, TM1 and TS1 courses and all these will be offered again in the new year alongside the TFM2, TM2 and TS2 courses. We anticipate the number of participants this year could be double that of last year.

Teacher Support In addition to the 43 who participated in the online Preparing for new 2017 A levels courses, the Live Online Professional Development (LOPD) programme provided courses for over 100 teachers. The online PD programme is also developing and, having adapted the current LOPD courses for new A level, is running a pilot for asynchronous online courses, called On Demand PD, aimed at giving teachers greater flexibility with their study times. Courses for teachers supporting students with higher level problem-solving, STEP and university entrance exams will continue to be offered throughout 2017/18. There will also be support for GCSE Mathematics teachers through the Extension and Enrichment courses which will be running in 2017/18.

The FMSP has produced a series of twenty-five short videos showing A level teaching in several schools. The videos focus on five areas which are compulsory within the new A level: problem-solving, reasoning and proof, use of technology, mechanics and statistics. The aim of the videos is to give teachers an opportunity to see how a range of resources and approaches can be incorporated into lessons. Each video is accompanied by the resources used in the clip, suggested lesson plans and sheets to encourage teacher reflection and discussion. The videos and accompanying materials can be used in a variety of ways such as:

By departments or groups within a department towatch together and discuss

By individual teachers, particularly those new toteaching A level, who will be able to use theseresources to help develop their classroompractice

The videos and resources will soon be available from the FMSP website, along with suggestions for how they can be used flexibly to support departmental development for A level as well as providing ideas and stimuli for individual teachers.

Sue de Pomerai, Deputy Programme Leader and Teacher Support Leader

P A G E 2

This course is the single most inspiring

thing I have done and it has had a big impact

on my teaching.

FMSP professional development

FMSP lesson videos

The FMSP’s national framework of over 60 active teacher networks has continued to be very active in the last year. In particular, these network meetings have been an important platform for the support that the FMSP has been offering teachers in preparation for the introduction of the new mathematics A levels. Most networks meet half-termly and the balance of the advertised content of these meetings has been heavily tilted towards understanding the changes at A level and offering specific training to meet the resulting needs. Over 80% of network sessions this year have focused on one or more of the following topics relating to the new A levels:

Changes to the content of Mathematics/Further Mathematics

Statistics in the new A level and the use of theLarge Data Set

The new Mechanics content

Uses of Technology including GraphicCalculators

This confirms that the teacher networks are an essential forum for teachers getting to grips with

curriculum change and through which they can access training. Centrally written materials have been made

available to be used by the team of Associates who lead the local networks to ensure all the information shared is correct and up to date. With mathematics teachers experiencing so much change this year, it is expected that the number of networks and the frequency with which they meet will continue to increase. More information about the location and activities of the networks can be found on the FMSP website: furthermaths.org.uk/networks.

Jeff Trim, FMSP Central Coordinator

Teacher Support

In July, UCL Institute of Education presented three papers based on our research and design work, with FMSP, at the IMA conference entitled Mathematics Education beyond 16: Pathways and Transitions. Our first paper describes five key pedagogic messages arising from our iterative design of the Advanced Mathematics Teaching in Early Career (AMTEC) course:

A level planning starts by understandingprogression from GCSE

use precise mathematical language and‘unpick’ notation

prioritise students’ engagement through and inmathematical reasoning

make connections between mathematicaltopics and representations

use tools deliberately so that students canmake predictions

We use these key pedagogic messages in the AMTEC course to make our own thinking about pedagogy explicit and hence available to teachers for reflection. The second paper reports our research comparing the online and face-to-face modes of AMTEC course delivery. Key findings were that the online course provides opportunities for wider access and variation in course structure but presents challenges in formative assessment and modelling pedagogy. The third paper explores teachers’ knowledge about assessing semi-structured problems in advanced mathematics, see furthermaths.org.uk/ucl-ioe for the full report.

Over the summer holidays, UCL IoE presented the AMTEC course to over 90 early career teachers. The course aims to develop teachers’ subject knowledge and pedagogy for teaching A level mathematics. Sessions have a ‘beginning teacher’-friendly focus on planning, sequencing and key ideas, with one session devoted to classroom management at KS5. We are grateful for FMSP funding, which means the course is freely available to NQTs, NQT+1s and teachers in their training year, allowing AMTEC to reach well over 300 teachers in total to date. Our next twilight online course will start on October 10

th

with 10 weekly sessions and we are planning a three-day face-to-face course in Easter 2018. The course materials are also available free of charge to all school-led and HEI-led training providers. If you are a teacher interested in attending AMTEC or a teacher educator interested in using our materials or recommending our course to your early career teachers, please contact n.bretscher@ucl.ac.uk for more details. Nicola Bretscher, UCL IoE

P A G E 3

Teacher Networks AMTEC

The Advanced Maths PD Lead Development and Accreditation programme is run by the FMSP and the NCETM. It aims to increase capacity for high quality professional development leadership in Advanced Mathematics and offered 5 cohorts in 2016/17, recruiting 43 starters of whom 39 have now been accredited as NCETM PD Leads. This brings the total accreditations for the last three academic years to almost 170. Successfully accredited delegates are based across all regions of England.

For 2017/18, NCETM are undertaking a full review and revision and alignment of the PD Lead programme across the Primary, Secondary and Advanced Maths versions to increase consistency and parity across phases. This will involve revision of content (still with a PD Lead focus rather than a subject knowledge or a subject leadership focus), programme management and the re-registration process together with improving the public directory on the NCETM website and sustainable support for the accredited PD Lead community.

The Advanced Maths PD Lead course will run again in 2017/18 with further demand-led regional cohorts nominated by Maths Hubs together with external applicants from organisations such as the FMSP. Applications will be coordinated centrally via the NCETM. Each cohort will follow a three-day model interweaving PD Lead, mathematics pedagogy and reflection and planning sessions around the five key CPD questions. Documentation will also be adapted to include both a planning and evaluation framework and a reflective learning journal.

The resulting cadre of Advanced Maths PD Leads will be well placed to support the implementation of new A levels in Mathematics and Further Mathematics from September 2017 onwards and to lead further professional development through Maths Hubs and other mathematics teacher support organisations in the future.

The Maths Hubs programme is now three years old and has continued DfE funding to 2019 and hence longer-term planning stability into the future. The FMSP continues its partnership role with the Maths Hubs programme primarily as a key member of Level 3 Co-ordination Groups in each Hub and also through continued membership of Hub strategic boards, providing advice and guidance in relation to post-16 mathematics education (especially AS/A Level Mathematics and Further Mathematics) and

Teacher Support leading Maths Hub Work Groups in Advanced Mathematics or other relevant KS5 Mathematics related Work Groups.

Within the Maths Hubs programme there is a post-16 Network Co-ordination Team (NCT), led by Maths Hub Leads and supported by NCETM staff. The NCT focuses on post-16 mathematics priorities and have produced Network Collaborative Project (NCP) plans to support the following four strategically important areas in 17/18:

Supporting post-16 GCSE resit of the newlinear GCSE Mathematics

Working with and supporting institutionalleadership to develop appropriate post-16mathematics pathways

Supporting Core Maths

Supporting teaching of the new linear A levelsusing technology

The NCPs are planned with the potential to go on a developmental journey, if successful and still relevant, to reach increasing numbers of schools over time. Maths Hubs are also running Innovation Work Groups in 2017/18.

Left: Great North Maths Hub Summer Conference

Maths Hubs Level 3 Leads recently attended a successful Forum at Keele University on 30

th June

run in conjunction with the MEI Conference. This allowed Level 3 Leads to attend a range of sessions at the MEI Conference and provided time for joint Maths Hubs post-16 planning work.

During the 2017/18 year, the FMSP will continue to work with the Maths Hubs programme to achieve their shared goals of increased participation (particularly by girls), wider curriculum provision and entitlement pathways in Level 3 Mathematics, improved teaching, learning and outcomes for students, better preparation for HE study and greater leadership capacity in post-16 Advanced Mathematics. For more details of Maths Hubs and what they are doing please visit mathshubs.org.uk.

Andy Tharratt, FMSP Central Coordinator

P A G E 4

Advanced Maths PD Lead course

Working with Maths Hubs

The FMSP continues to support schools in delivering AS and A level qualifications in Further Mathematics in a cost-effective way. However our online support is changing to reflect the introduction of the new A Level specification. From September 2017 we will replace our Live Interactive Lectures (LIL) for Further Mathematics with collections of short pre-recorded videos (see screenshots, right). For more detail on the videos, please see the next column.

These videos will be freely available to all FMSP registered schools and colleges. Teachers will be able to access the videos through the school Integral account and there will also be a new 'student account' for each registered school that they can share with their students. For exemplar videos and more information see furthermaths.org.uk/fm-videos.

The Live Interactive Lectures will still be available for students studying the legacy modular qualification and the courses offered can be viewed at furthermaths.org.uk/lilfm.

Live Online Tuition (LOT) will be offered to students studying both legacy and new qualifications. It can be used by schools and colleges that are not able to offer any tutorial support to their students. It is designed to complement the use of LIL or FM Videos. In addition to the online sessions, students are set additional exercises and receive follow up support from their FMSP tutor.

For the legacy qualification LOT will still be organised by module but for the new A level, students will study the complete course over 28 weeks with one online tutor. For more detail see furthermaths.org.uk/lot.

LOT group sizes are small, usually between one and seven students per tutor. Tutors are all experienced teachers of Further Mathematics. A recording is made of each session so that students can return to and review the material covered at a later date.

In 2016/17 the FMSP provided direct tuition for 156 students from 54 schools.

Schools/colleges can contact their local FMSP Area Coordinator (listed at furthermaths.org.uk/regions) to discuss tuition requirements including LOT.

Paul Chillingworth, FMSP Central Coordinator

Student Support

From September 2017 we are providing FM Videos for the new AS/A level Further Mathematics qualifications. These are collections of short pre-recorded videos of 5-10 minutes in length that introduce students to the mathematics required to study the topics in Further Mathematics. The intention of these videos is that they are sufficient to cover the basic concepts so that students can then start learning the material by working through appropriate examples. Schools can use the videos to complement their existing Further Mathematics provision or as a basis for supporting students who are studying on limited contact time.

Above: Screen shots from the Core Pure sample videos on successive transformations in 2D and transformations in 3D. The videos have been produced for routes through all 4 of the major Further Mathematics qualifications (AQA, Edexcel, MEI and OCR). For more details see: furthermaths.org.uk/fm-videos. Tom Button, Student Support Leader

P A G E 5

FMSP Tuition FMSP Videos

The FMSP is committed to increasing participation in AS and A level Mathematics and Further Mathematics by sharing some of the uses of mathematics with students before they take their GCSE examinations. Last year the FMSP ran a variety of enrichment events across the country that engaged over 15,000 secondary school students. These events ranged from large one-day events held at universities, through the ever-popular Maths Feast competition, to smaller, shorter sessions held at local schools. All focused on the ways that mathematics is be used in the world. Students always feedback about their enjoyment of these events, rating them highly, not just in terms of content and delivery, but also in usefulness in helping them make more informed decisions about their choices at A level and beyond. This year the FMSP will continue to provide these

enrichment opportunities and the Maths Feast

competitions for students across the country.

Over the last few years the FMSP has supported many teachers through our KS4 Extension & Enrichment two-day course. This course has been supported by DfE funding so that it is provided free to teachers in state-funded schools and in addition a contribution is made toward cover costs to enable teachers to attend. In response to demand from teachers, a series of 18 one-day courses ran in the summer term to support teachers with the new content of Higher Tier GCSE Mathematics. While the two-day course will be running again this year, the FMSP will also be piloting a new three-day course, called ‘Reasoning, Extending and Problem- Solving with 11-16 students’ which focuses on deepening the students’ understanding and communication across both Key Stage 3 and Key Stage 4. The course will encourage teachers to look beyond just their own classroom practice to supporting colleagues in developing their professional skills so that even more mathematics departments and their students can benefit.

Cath Moore, FMSP Central Coordinator

Enrichment

The Maths Feast competition, which is for teams of four Year 10 students, proved popular again this year with over 80 events held across the country, attended by over 3000 state-school students. The competition focuses on developing problem-solving and teamwork. The rounds this year were engaging and the problem-solving round particularly was enjoyed as students worked in teams to provide their best four answers to six questions. Different strategies were used, with some teams attempting all six before choosing, while others decided to focus on the four they submitted to ensure that they got full marks on them. The FMSP ran the ‘Summer Snacks’ again, where materials are provided for schools to run an internal Maths Feast in the summer term and there was high demand for these resources yet again.

Above: Ifield Maths Feast 2016 Right: Students tackle the comprehension round

The FMSP has developed many resources to support

teachers within the classroom. These resources have

been organised and are available from the general

enrichment page: furthermaths.org.uk/enrichment,

from where all resources, events and courses are

linked.

Cath Moore, FMSP Central Coordinator

P A G E 6

Maths Feasts

Teacher Support for KS3 and KS4

11-16 Enrichment Events

Enrichment Resources

The FMSP regular problem-solving classes aim to provide experience of applying skills from A level Mathematics and Further Mathematics to challenging problems that help to stretch students’ understanding. Classes run for both Year 12 and Year 13 students; each year group being set problems carefully chosen to develop their skills. For students wishing to sit the STEP/AEA/MAT or TMUA examinations, the classes provide valuable practice in developing the mind-set required for success. In 2016/17, the FMSP provided more regular problem-solving classes than in any previous year with 34 classes taking place across the country. Of these, 12 classes have been aimed at Year 12 students, 18 have been aimed at Year 13 students and 4 have been joint classes where Year 12 and 13 students separate into appropriate groups for the work. The Year 12 classes include work to develop students’ algebra, geometry and calculus skills as well as extending the students’ knowledge in the less familiar area of combinatorics. The Year 13 classes continue to develop the skills from Year 12 with the addition of units looking at trigonometry, logic, vectors and differential equations. The classes have had a good spread across the country this year with at least 3 sets of classes taking place in each region. Sessions typically took place on Saturdays in the spring term and consisted of 10 to 15 classes of 3 hours duration.

Feedback from the classes has been universally very good with the attending students particularly citing the tutoring as being excellent across the board. Here are some of the student comments about what they particularly enjoyed: “Being together with a group of like-minded mathematicians.” “Going through each topic in detail before doing past papers.” “I found it useful when we worked in small groups and then explained our solutions to each other by writing on whiteboards on the walls.”

Enrichment

Above: A typical problem students might tackle in the problem solving classes. “The classes were absolutely incredible. The teachers were fantastic, dedicated and inspiring, I really enjoyed working through the problems. I wish there were more classes like this throughout the year. Very rarely (if ever) do you get classes of such high quality, with such dedicated teaching free of charge and close to home. Thank you so, so much for giving up your time for us, and everything else. It was incredibly beneficial”. The regular problem solving classes will be taking place in the academic year 2017/18. Details can be found on the regional pages furthermaths.org.uk/regions and on the STEP/AEA/MAT/TMUA pages furthermaths.org.uk/step-aea-mat of the FMSP website. Phil Chaffé, FMSP Central Coordinator

In 2017/18 the FMSP will once again be working with the UK Mathematics Trust to run the Senior Team Maths Challenge (STMC), which is sponsored by Rolls-Royce. Dates for Regional Heats can be viewed at furthermaths.org.uk/stmchallenge and schools and colleges have been sent an entry form via email or can download it from the webpage above. This year there will be capacity for nearly 1350 teams across England. Training resources to introduce the Senior Team Maths Challenge to students can be downloaded from furthermaths.org.uk/stmc_training. The National Final for 2017/18 will be held in London on 6

th February 2018. Winners of all the Regional

Heats will be invited together with the best runners-up nationally. The final includes a poster round, information for which is sent out in advance to finalists. Last year’s theme was Cellular Automata of which Conway’s Game of Life is perhaps the most famous example. It was introduced to the public by Martin Gardner in his Scientific American column in October 1970. The winning poster by RGS Newcastle can be seen at: furthermaths.org.uk/docs/STMCPoster2017-draft.pdf. Paul Chillingworth, FMSP Central Coordinator

P A G E 7

Senior Team Maths Challenge

Problem-Solving Classes

The FMSP continues to provide a range of information and guidance to students, parents, schools and universities about the importance of studying AS and A levels in Mathematics and Further Mathematics as effective preparation for a range of degree courses. The recent Smith Review of post 16 mathematics emphasised the importance of clear signalling and recommended “The Department for Education should work with UK learned societies to encourage universities to better signal and recognise the value of level 3 mathematics qualifications for entry to undergraduate courses with a significant quantitative element.”. The FMSP also provide information for universities and in 2016/17 ran two successful Level 3 Mathematics Conferences attended by 70 university representatives. The FMSP plans to visit individual HEIs in 2017/18 to speak to groups of staff about the changes to mathematics qualifications at GCSE and post-16 and the implications for future undergraduate cohorts. If you would be interested in arranging a visit please contact clairebaldwin@furthermaths.org.uk. Claire Baldwin & Chris Saker, FMSP Central Coordinators

I joined the FMSP as a central coordinator at the start of September. I have spent the last sixteen years teaching at Backwell School in North Somerset, where I was also Head of Sixth Form. I am very much looking forward to spending more time focusing on maths. As part of my role I am taking over the lead on increasing girls’ participation in A level Mathematics. Away from maths, my main interest is drama. In addition to regularly attending the theatre I enjoy acting and improvising, and have written many plays. I have yet to write a play with a particularly mathematical focus, but perhaps this new role will give me some inspiration! Toby Rome, FMSP Central Coordinator

Encouraging Further Mathematics

Professor Sir Adrian Smith’s review of post-16 mathematics education was published in July 2017. It supports the FMSP’s view of the importance of increasing participation in post-16 mathematics education and the review’s recommendations recognise the actions that are required to drive further improvements in levels of student participation and achievement. The review also notes the serious risks to Further Mathematics provision arising from funding changes and the decoupling of AS and A levels. Prof. Smith makes a number of key recommendations in relation to Further Mathematics including the need for increasing the financial incentives for both AS and A level Further Mathematics. Since 2014, the FMSP have liaised with universities to encourage the importance of AS and A level Mathematics and Further Mathematics qualifications for a range of degree courses to be made explicit in their entry requirements and the advice and guidance provided to potential applicants. This is echoed in the Smith review which recommends that universities should be encouraged to ‘support 16-18 mathematics education in the context of access for and success of students from disadvantaged backgrounds’.

The Smith review also highlights the ongoing concerns relating to girls’ participation in mathematics, noting that ‘despite good GCSE achievement by girls, in 2015/16 only 50 per cent of girls with GCSE A grades continued to AS/A level compared to 70 per cent of boys’. The FMSP continue to disseminate research findings relating to good practice in terms of encouraging increased girls’ participation in AS and A level Mathematics and Further Mathematics, more information can be found at: furthermaths.org.uk/encouraging-girls-maths. The Government response to the Smith review announces a new £16 million Level 3 Maths Support Programme to ‘build on the momentum created by the Further Mathematics and Core Maths Support Programmes’. Claire Baldwin, FMSP Central Coordinator

Access to Higher Education

P A G E 8

The Smith Review

Some 180,000 of those accepted into university will encounter a significant amount of mathematics on their degree courses.

New member of the FMSP team

As well as arranging Further Mathematics tuition for hundreds of students each year the FMSP Area Coordinators lead and develop many other activities in their regions to foster interest and provide training in mathematics.

A summary of some of these activities is given below.

Mathematics and Further Mathematics A level results are a cause for celebration in Wales this year allowing many more Welsh students to use their Further Mathematics qualifications to pursue their chosen study or career path. The results have built upon last year’s entry:

A level Mathematics numbers are up from 3719 to 3931, a 5.7% increase.

A level Further Mathematics numbers are up from 502 to 588, a 17% increase.

AS Mathematics numbers are down from 5501 to 5409, a 1.7% decrease.

AS Further Mathematics numbers are up from 458 to 498, a 6.7% increase.

Mathematics remains the most popular AS and A level in Wales followed by History and Biology. The proportion of Mathematics students who sat Further Mathematics A level reached 14.95%, which is the highest result ever in Wales. In 2017 Further Mathematics became the fourth fastest growing subject in the UK. The numbers of students more than doubled in Wales since FMSP Wales was launched in 2010. For the full press release see: furthermaths.org.uk/wales-news. As in previous years, FMSP Wales will provide Further Mathematics tuition for students whose school and college are unable to provide it. Tuition for 2017/18 will commence in October, full details can be found by visiting: furthermaths.org.uk/wales-tuition.

News and Events from the FMSP Regions

FMSP Wales held five Year 10 conferences during June and July 2017 at Swansea, Glyndwr and Aberystwyth Universities, Pembrokeshire College and the University of South Wales. Over 400 students attended from 30 schools from across Wales, including two new schools who had not attended FMSP conferences before. Students were split into groups and participated in two workshops and attended a final talk. The conferences aim to show students different ways in which Maths is applied and demonstrate the many different Maths

focused careers. Talks were delivered by academic staff from Mathematics and STEM subjects at each of the Universities as well as innovative and interactive Mathematicians. The feedback was very positive:

“It demonstrated the relevance of Maths outside the classroom”. “I really enjoyed it”. Teacher, Wrexham “It was engaging and delivered very well, I learnt about more complex Maths and was able to understand further due to the content and delivery of it.” Student, Swansea During 2017/18 FMSP Wales will continue to provide a range of professional learning events to support teachers of A level Mathematics and Further Mathematics. These include one-day courses for statistics and mechanics aspects of the new A levels for Mathematics and Further Mathematics. For full details about teacher support available in Wales, see: furthermaths.org.uk/Wales_CPD.

FMSP Wales has produced a new briefing document summarising recent research relating to girls’ participation in Advanced level Mathematics and providing recommendations for schools and colleges for increasing girls’ participation accessible from: furthermaths.org.uk/wales-news.

Sofya Lyakhova, FMSP Wales Area Coordinator

FMSP Wales

P A G E 9

At the University of Hertfordshire on 4th April and Cambourne Village College on 20th April Tom Button led two afternoon courses on GeoGebra and its uses in the new A level. The most expert of experts on GeoGebra within the FMSP central team, Tom demonstrated key techniques for dynamic graphs when teaching pure mathematical topics and statistical techniques when working with the large data sets. The chance to get hands-on experience with GeoGebra was particularly appreciated, supported by clear instructions for teachers to access at their own pace. A final treat was using tinted glasses to view vectors in 3 dimensions. Comments included: “Vectors in 3D was brilliant.” Great afternoon.” “Excellent hands-on introduction to GeoGebra.”

East of England, FMSP Area Coordinators

In March the North East region hosted the annual GCSE Extension and Enrichment conference at the Marriott Hotel in Gateshead. This attracted 75 teachers from around the country. A plenary session from Rob Eastaway rounded off the day where workshops including proof, paperfolding, reasoning, data handling, random events and developing problem-solving skills had been delivered.

Due to demand we repeated

our two one-day GCSE Extension and Enrichment CPD days; one day looking at Functions and Graphs and the second on Reasoning and Proof. The two-day course is being

repeated later this term in Darlington and Gateshead and details will be on our FMSP website. North East, FMSP Area Coordinators

News and Events from the FMSP Regions

During 2016/17 the North West team ran a series of successful free Key Stage 5 Teachers’ Network sessions which will continue in 2017/18, repeating and extending the previous programme to include themes such as:

IncorporatingProblem-Solving into A level classrooms

Embedding technology into mathematicsteaching

The use of data in Statistics

Mechanics for the 2017 A Levels

Another new approach is the development of some new CPD resources. The team recognise that it is sometimes difficult for teachers to get out of school/college for

training or to share ideas. In a new initiative this year the North West team have developed packs of materials to support areas of the new A Level which are designed to be used in department meetings. These packs give about 40 minutes (or more in the case of technology) of material with a PowerPoint, presenter’s notes and activities and are designed to complement the KS5 Teachers’ meetings (although they are available even if a teacher hasn’t attended these). The packs will be promoted in the Autumn term.

Sue Harkness is retiring as Assistant Area Coordinator for the North West, but will continue to work as an FMSP Associate. The North West team are very happy to welcome Mike Baxter (pictured below, with Sue) as our new Assistant Area Coordinator. He gained a degree in Mathematics before completing his PGCE at University of Manchester in 1990. He worked at several sixth form colleges in the North West before completing 15 years at Sir John Deane’s College in Northwich. He has already worked for the FMSP presenting a variety of CPD and student events, as well as delivering several online LIL & LOT courses.

North West, FMSP Area Coordinators

North West East of England

P A G E 1 0

North East

News and Events from the FMSP Regions

In July 2017, the London Area Coordinators hosted free enrichment events attracting Year 10 students from all across London. The events featured a variety of talks, workshops and

quizzes and several Year 10 students commented at the end that their minds had been blown! The images show mathematical enthusiast Katie Steckles exploring logic using dominoes with students at Queen Mary University of London and Adam Townsend sharing the mathematics of his chocolate fountain at Kingston University.

Problem-solving courses for Year 12 students will run again this year, at both Kingston University and Queen Mary University of London. These free sessions give students an excellent opportunity to develop the skills that will be useful for mathematical study — as well as the chance to discuss mathematics with students

from other schools. These courses will start in November and details will be emailed to registered schools. Professional development to support the new A levels in Mathematics and Further Mathematics will continue in 2017/18. Courses address questions such as: What are large data sets? In what order should we teach topics? Can we still teach Further Mathematics alongside Mathematics? What do we do at the end of Year 12? Pictured right, teachers new to teaching Mechanics tackle a Newton’s Laws activity.

London, FMSP Area Coordinators

London

The annual Mathematics Conference for Year 12 students, held at the University of Warwick, was a highlight of the summer term in the West Midlands. It was mainly aimed at those who are considering taking their study of mathematics beyond A level, although all who take a keen interest in the subject were very welcome. This year the conference was held on 5th and 13th July and had students from local schools as well as those who travelled from London, Manchester and Harrogate. The day was comprised of four sessions which are designed to provide a range of content across a variety of learning contexts.

The fun maths roadshow was one of the more active sessions which had an element of competition, with prizes for the top two teams in each group! There was a session which looks more in depth at university admissions examinations including STEP (Sixth Term Examination Paper), AEA (Advanced Extension Award), MAT (Maths Admissions Test) and the relatively new TMUA (Test of Mathematics for University Admission). This session was also a great opportunity to have a go at tackling some of the questions on these papers with support and guidance from an expert. Students practiced their presentation skills in a session called ‘Writing and Presenting Solutions’; a highly interactive time of exploring a range of interesting mathematical problems. Finally, students delved into mathematical proof; an area

which permeates the study of mathematics at university level. This session opened up some key techniques and looks at many different ways of proving results, with students commenting on finding valuable methods and new ways of thinking.

An enjoyable and valuable day was had by all and here are just a few comments from those in attendance:

“I could see other ways of solving a problem that were new”

“The proof session actually begins to introduce what university level maths is like”

West Midlands, FMSP Area Coordinators

West Midlands

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The Spring 2017 FMSP newsletter featured two problems, the first from the Underground Maths resources and the second from the FMSP’s Problem- Solving Masterclasses Proof Workbook.

Problem 1 was Pairs of Circles in which an equilateral triangle is inscribed in a circle and a second circle is then inscribed in the triangle, as shown. The challenge is to use a graphing package such as Demos or GeoGebra to construct the diagram. Also, given the equation of one of the circles, can you find the equation of the other circle? A full solution can be found on the Underground Maths website.

Problem 2 was:

Suppose a, b and c are integers such that

a √2 + b = c √3

By squaring both sides of the equation, show that a = b = c = 0.

[You may assume that √2, √3 and √⅔ are irrational].

This can be solved using proof by contradiction—the full solution can be found in the Proof section of the Problem-Solving Masterclasses on the FMSP’s A level Problem-Solving webpage, along with a wide range of other engaging and challenging activities for the A level classroom.

Recreational Mathematics This issue’s problems:

Problem 1 is taken from the Rich Starting Points (RiSPs) activities.

Can you deduce, from the following four clues, the values of a, b and c in the equation y=ax

2+bx+c?

Clue 1: the y-intercept is (0,6)

Clue 2: the curve goes through (4,5)

Clue 3: the curve has a turning point at (2,3)

Clue 4: the line of symmetry is x=1

It is not possible for all of the clues to be true at the same time—why not?

Which combination of clues enable you to identify exactly what a, b and c must be?

Problem 2

The reciprocal 1/x key on my calculator has broken.

How can I use the trigonometry buttons sin x, cos x, tan x, sin

-1 x, cos

-1 x and tan

-1 x to calculate

reciprocals?

If you have a puzzle that you would like to see featured in the Recreational Maths section of the FMSP’s Spring 2018 national newsletter, please email it to: clairebaldwin@furthermaths.org.uk.

FMSP Central Team

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Left to right: Kevin Lord, Sue de Pomerai, Tom Button, Sharon Tripconey, Phil

Chaffé, Stephen Lee, Avril Steele, Dave Griffiths, Andy Tharratt, Claire

Baldwin, Paul Chillingworth, Cath Moore, Jo Sibley, Jeff Trim, Chris Saker,

Amelia Rose, Toby Rome, Venetia Anstee.