The Problem with Maths!Posted on: 22/01/2018
Students who attended this Sixth Form Student and Teacher Problem-Solving Conference met students from many other schools. They were encouraged to attempt carefully selected problems, both in small groups and on their own. This allowed them to look at a variety of enriching resources including the Senior Team Mathematics Challenge, the Liverpool Fun Maths Roadshow, STEP, AEA and MAT examinations, Underground Mathematics and NRICH. Following a typical maths lecture, the academics involved attempted to get students thinking about writing and presenting their solutions to problems. It also gave students a chance to explore an area of maths not in the standard curriculum. Meanwhile teachers were given information about the university entrance exams based on advanced problem solving and resources for supporting problem-solving.
On arrival at the Centre for Mathematical Sciences in Cambridge, we prepared for a long day of problem- solving by drinking copious amounts of tea. The day was split up into five sections: an initial introduction (a lecture), followed by four separate problem- solving workshops. The lecture was focused on the most important topic of the day: problem-solving! They first clarified that a real problem is not quite the same as a question from an "exercise", one that you'd find in most textbooks. We'd have to develop a separate set of skills for these.
Workshop 2: "Fun Maths Roadshow" (The Best Workshop)
We paired off and were given three to four difficult mathematical questions that each required a unique method of thinking to get the answer - to be done against the clock in 9 minutes. One question was about the summation of summations, another about ordering a list of powers, say 2^3^4 and 2^4^3 and 3^5^2 into a list from smallest to greatest. After each 9-minute interval, both group members would split off like chain-reacting uranium-235 and we would work with a new person. It was a fun exercise in teamwork and creative thinking, as the questions were quite good.
Workshop 4: "STEP and AEA Questions"
Finally, it was time to move onto the big guns. We were given a list of 20 questions from past STEP and AEA papers—used by university admissions to test a candidate's mathematical creativity and knowledge. The questions were very challenging, but making any progress at all through a STEP question gave a feeling of unparalleled accomplishment.
We rounded off the day with a final presentation on how problems can be solved either graphically or numerically, flaunting the flexibility of maths. After failing to claim a carton of apple juice, it was time to leave, a good deal more knowledgeable and tired than when we came.