So, as teachers, we are no doubt well aware of the contradictory statements/ideologies below:
Naturally this creates a dilemma, we should not be teaching to the test, and yet will most likely be judged largely on the results of tests. Surely therefore, as our biological instinct for self-preservation kicks in, we should focus on the tests and results? Most teachers are torn here, as we are well aware of the many exciting things we can teach in our subjects that would not be tested, but can we find time to cram them in and cover content as well?
Up to this point, it has probably been assumed that the “tests” I was referring to are GCSEs and A-levels, what with these being used to measure progress, and make judgments. However, there are other tests in Maths which we could consider for measuring progress, which I think most Mathematicians would actually consider to be much more valuable. I am referring mainly to the UK Maths Challenges, run by the UK Maths Trust. For simplicity I will refer to these as tests as well, but I know they are so much more than that.
Have a think about it for a moment – these “tests” are created and provided once a year for all age groups in secondary schools. They can be completed in school and sent off to be marked centrally, with the results usually being completed within 2 weeks (also by the way, each entry only costs about £1!) They have no specific scheme of work, so in that sense they will test students understanding and problem solving skills, rather that the memorization of facts and processes that dominate the first half of a GCSE paper. The vast majority of questions can be solved with higher level applications of lower level knowledge, such as basic angle facts, fraction calculations etc. The questions also promote a variety of approaches, combine topics together, and I have found they often generate excellent classroom discussion between students.
So, what would a curriculum based around the UKMT look like? The focus would largely be around problem solving, the topics themselves being a part of that (rather than the other way round). I guess we would also have activities that cause students to have to think logically, be systematic and use diagrams to help answer questions. There would also be an emphasis on creative ways to use knowledge, rather than just piling more knowledge in. Fortunately, there is already a wealth of resources available to teach this way – the UKMT’s own resources! At my school we have built in UKMT papers into our schemes of learning, so throughout year 7, students have a go at 4-5 papers. There is no preparation required for the lesson, students are free to solve the problems in any way they like and can work wherever in the classroom they want to (they don’t do them as “tests”). It is important to make it clear that students should not worry if they find the questions difficult – if they are thinking, then they are learning.
I often use an analogy of someone going to the gym. Imagine someone is going to the gym and intends to run 10km on the treadmill at a given speed. So they go to the gym, get on the treadmill, and start running. Sadly though, at 8km they just cannot go on any longer and have to stop. Does this mean that they have not improved their fitness? Because they didn’t quite get to the “finish”? Of course not, they have still benefited from the experience. The same with Maths questions. Even if a student doesn’t quite get to the answer, if they have been thinking and working on it then their brains will be stronger as a result. As Miley Cyrus would say, “It’s the climb”.
Not only are the UKMT’s papers usable for this, but they also provide mentoring sheets every month with more problems here, and these are sent to you automatically if you sign up. Of course there is also the excellent site nRich which is a treasure trove of exploratory activities and superb questions. In our year 7 and year 8 schemes of learning, which can be found in the Maths Free Resource Library, we have also tried to include a couple of topic-based questions where appropriate. So in sections on angles for example, we include some UKMT-style questions alongside others. Make no mistake, we still need to teach some topics – I don’t believe that everything is best learnt though exploratory methods. Students need to have a range of inputs if we are to get the best out of them!
So in addition to my previous blog post, our schemes of work are also designed to allow students to cover the material that is needed, but also to help them to develop general problem solving skills. Not only has this improved our results on the Maths challenges, but it has also increased the number of students taking part in such events (all of Year 7 take part so they know what it is like, but from that point on students can decide whether to do it each year or not. This year around 2/3 of year 8 want to do it). I’d be very interested to hear if any other schools are using these kinds of approaches and how effective they have been - please feel free to contact via the email address on the site!