A Culture of Problem-Solving

There’s been quite a bit of puzzle sharing going around on Twitter lately and the timing fits well as our department is looking at how me might fully integrate problem-solving into our schemes of work for the new A level spec. Here are a couple of Twitter puzzles from recent weeks that you might like to try:

Also in the past couple of days, Jamie Frost (@DrFrostMaths) published this webpage in which he discusses a departmental shift-change to include more puzzles and problem-solving in their teaching, and the noticeable impact this has had on the pupils’ performance in UKMT maths challenges and olympiads.

With our A level students (particularly focussing on those doing Further Maths in the first instance) we are keen to give them much more exposure to mathematical puzzles and problems to solve. This will hopefully raise our students’ performance in the Senior Maths Challenge and also be of significant benefit to those who may need to take STEP papers for university entrance. Of course, another aspect of this is the building of a very positive culture of mathematics within our student community.

Sources of Puzzles and Problems

Very briefly I’ll mention just a handful of sources of potential puzzles and problems that can be used, before dissecting a few problems much more deeply.

  • Past maths challenge papers are available directly from the UKMT and they’re now also available online. (Jamie Frost is also integrating them into his online homework platform, available soon.)
  • Cambridge have created a series of STEP Support assignments that help to bridge the gap between A level study and the demands of STEP questions.
  • Books: there are innumerable books published with collections of mathematical problems but often it can be tricky to found those pitched at just the right level. One which I cannot recommend highly enough (and from which the problems below have been taken) is “A Moscow Math Circle” published by the American Mathematical Society. The introduction of this book also includes a very clear depiction of how mathematical circles are run in the Russian tradition.
  • Magazines: I have recently, discovered a magazine called Quantum that was published in US in the 90s, based on the Russian publication Kvanta. All the past issues of Quantum are archived online, and many of the problems they contain are pretty demanding! (I’ve included samples at the very end of this post.)

Homework for Part II

I’m breaking my original idea for this blog post into two separate sections. The second will focus on the difficulty with giving hints to students when they are stuck or have arrived at an incorrect answer. You might like to try the following problems (from A Moscow Math Circle) in advance of reading my thoughts on them in the next few days.

Excerpts from Quantum

As mentioned earlier, Quantum magazine includes some quite challenging brain teasers (as they call them) and problems to solve. Here are the ones presented in Volume 7, No. 5 from May/June 1997.

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