In Praise of Difficulty

In the past academic year several thought provoking articles have been published concerning Mathematics teaching, education and the nature of success. Many of these ideas have been used in the department this year. For example:

The Reform Group Report on “The Value of Mathematics” - June 2008

“Rigour and challenge is the basis of successful Mathematics teaching. The “eureka” moment experienced on the solving of a difficult problem is what motivates and spurs people on”.

The answer to effective learning

In the TES 21/11/2008 was a report on the results of world wide research by Professor Hattic of Auckland University. In a nutshell, the key to raising standards is the quality of pupil-teacher interactions. How?

• Encouraging pupils to question teachers on what they do and do not understand about a subject.
• Setting pupils work which is one level above their current development.
• Teachers’ clarity of explanation.
• Feedback from pupils to teacher and vice versa.
• Allowing pupils the freedom to make mistakes.

The report states, “A teacher’s job is not to make the work easy, it is to make it difficult. If you are not challenged, you do not make mistakes. If you do not make mistakes, feedback is useless”.

“Talent is overrated” - Geoff Calvin (Senior Editor - FORTUNE)

The central theme of the book is that top performers in any field are not determined by their inborn talents. Success comes from practice and perseverance. This “deliberate practice” is outside one’s comfort zone, it is difficult, it is hard and you need a teacher to correct mistakes, give instant feedback and to set you tasks slightly beyond your capabilities.

Throwing down the gauntlet to Years 7, 8 and 9

It has been a difficult year in the Maths department; but we like it that way. We have exposed all pupils to work that is hard, challenging and often outside the syllabus or scheme of work that we are using to guide our teaching. Why do we choose to make life difficult for our students? The answer is simple - because of the “Eureka Moment”.

While we don’t encourage our pupils to do their homework in the bath, we do support the idea of commitment to a problem until a solution presents itself and, as Archimedes discovered, solutions can present themselves at any time and often in situations where you least expect to find them.

Once a week, students in Year 7 and 8 have been taken out of their comfort zone and have completed a selection of different challenges. Many of these challenges have been open-ended investigations into patterns or discovering properties of different numbers or shapes, but all have pushed the pupils to their Mathematical limits, demanding a new way of thinking about Maths and solving difficult problems.

Here are some examples of Year 7 challenge work:

• Combinations and permutations
• Topology (Möbius strip)
• Patterns, number, shape
• Symmetry in paper folding
• UKMT Challenge questions

The thirst for knowledge in Year 8 has been quenched with some of the following investigations:

• The Golden Ratio
• Fibonacci numbers/spiral
• Bridge building
• Maximising volume project (boxes, cylinders)
• Circle theories
• Astronomy, gravity
• Trigonometric graphs
• River project (source to mouth as a factor of Pi)
• The binary system

This development of a new way of thinking about Mathematics has helped pupils to achieve excellent results in this year’s UKMT Mathematics Challenge, open to schools worldwide. Of the 76 pupils entered into the three Challenge categories (Senior, Intermediate and Junior), 38 received Gold, Silver or Bronze certificates. This is surely testament to the benefits of having “a difficult year”.

The Year 9 students have been pushed to the extreme! Throughout the year they have been attempting IGCSE questions and their end of year exam was solely made up of IGCSE past paper questions. To complete the year, they are attempting to make a life-size 2D representation of a Mini Cooper, drawn up from an A3 size plan to test accuracy and team work.

Isabel Mota & James Stubberfield

Year 10

Eight members of the extended group: Douglas, Fern, Alex, Lucy, Philip, Koen, James and William took IGCSE this year and have already started differential calculus. The year group achieved record Checkpoint results in Year 9 and we have no doubt they will achieve success in Year 11.

Year 11 The Thursday afternoon Maths Club

From January to May on average twenty students attended the Thursday Club every week to explore algebraic links between topics of the syllabus. Difficult, unusual problems were made up by Maths staff, designed to stretch the students, however, help was on hand and mistakes were corrected! By May there was a discernible increase in confidence and many students were enjoying their new powers of algebra!

V Artacho/I Mota/M Sutcliffe

The Sixth Form

As usual there was a large uptake at all levels. This year was notable for the Year 12 “Maths Club” - Daniella, Nadia, Zoe and Marion with invited guests and the corresponding Year 13 club - Clara, Lydia, Jordana, Josh and occasionally Tristan and Adham. The level of hard work displayed in and around the Maths rooms has been truly impressive in the last few months and they all deserve their success. The school is losing some huge personalities and the Maths Department will miss the likes of Winston, Xavier, Tristan, Adham, Sven, Zachary, Harold, Mason, Josh, Clara, Jordana and Lydia.

Resumé of results 2008

Congratulations to Mark, Theo, Gideon and Ali for achieving As last year - especially to Winston, Zachary, Harold and Mason for grade As at A level in Year 12.

• Further Maths: two grade As
• A level: eight grade As, five grade Bs and two grade Cs
• AS level: eleven grade As, two grade Bs and one grade C
• IGCSE: six grade A*, six grade As, twelve grade Bs, fourteen grades Cs.
• A* - C 75%

Thanks to Val Artacho, James Stubberfield, Isabel Mota and Roger Lang-Gordon for all their hard work. The Maths Department is committed to a variety of teaching styles, investigations, lateral thinking, exciting and success orientated difficult lessons. Hasta luego,

Dr Mike Sutcliffe

Maths Quest

On the 8th, 9th and 10th of May 2009, after a rigorous selection procedure, Tristan Hidalgo Hopson, Jago Thomas, Zoe Cole and Christopher Steiner embarked on their journey to Amsterdam for the annual Maths Quest accompanied by Mr Stubberfield and Miss Mota.

In Amsterdam, pupils were taken to their host families where they would stay for the weekend. The following day pupils had to complete a Group Maths Trail in Den Haag. This involved a series of challenging Maths questions based on different Dutch landmarks. We were then taken to Scheveningen Beach where we were treated to delicious pancakes (pannekoeken). We soon ran off all the calories on the very windy beach. Well done to Zoe for being the fastest runner in the team!

The afternoon was spent in Madurodam (miniature Dutch town), where pupils managed to spend most of their money on sweets and touristy things!

The following day was the real challenge . . . Pupils worked through several rounds of mathematical questions, both individually and as a group. In between rounds they were provided with snacks and regular breaks in the gorgeous playground, whilst the teachers marked their answers. Christopher was a very good team member in the group rounds with his quiet yet confident contributions. It was an exhausting, yet productive day, which was followed by a disco where Jago was able to show off his dance moves!

On the final day pupils had to complete four rounds of investigations involving tricky algebraic answers that made everyone’s brain ache! The final challenge was to build a barge in mixed groups that could transport as many Cadbury Cream Eggs through a sluice gate of a certain restricted dimension. This was perhaps the best part of the competition to see pupils working together, building and testing their rather strange barges made of card, cling film and anything else they could beg, borrow or steal!

We were all very impressed at the commitment and determination the pupils showed and their willingness to participate in every activity with enthusiasm and confidence. It was a great competition with 19 schools from all over the world, each with 4 pupils. As a team we came in 7th place. Special congratulations to Tristan who came 11th out of 76 competitors.

Well done EIC Maths Team.

James Stubberfield & Isabel Mota