Problem-solving is not only a prominent Maths activity, as shown in the Maths ability pyramid. It is also a discipline of its own, with its specific know-how. In other words, the specific skills of problem-solving can be learnt too. By doing so, students will not only learn to solve problems more efficiently, they will also make the best of problem-solving’s high educational value.
For Maths teachers, it means that it is possible to choose problems for students not only according to a particular Maths topic (fractions, algebra, trigonometry, etc.) but also with a view to practise one or several problem-solving skills.
In order to do this, it is necessary to identify and name these skills. This post covers 10 problem-solving skills, which you can see in action in UKMT JMC 2015 (cf. my JMC 2015 teacher’s notes).
Read More »
This is the first post presenting my teacher’s notes of past UKMT papers, starting with JMC 2015.
The objective of these teacher’s notes is not to provide solutions — UKMT already provides an excellent Pdf of solutions and further investigations, which you can download here — but to provide insights to teachers as to how UKMT questions can be used in the classroom.
In other words, these teacher’s notes are about making the best of the educational value of UKMT questions. Which, by the way, extends the scope of UKMT questions beyond their target age group. For example, some JMC questions, although intended for Year 7-8 students, can be used for educational purposes up to GCSE, sometimes even with A level students with the addition of relevant extensions and investigations.
Read More »
After weeks of writing and talking to teachers about behaviour management, I am back (with relief) to posting on my favourite topic: Maths teaching. That is no doubt the effect of meeting two highly inspirational people (one Maths teacher and one Headmaster) within a few days.
I would like to start this post with a seemingly remote comment which was kindly sent to me by a reader concerning the Maths ability pyramid, pointing out that the pyramid does explain ‘what we do in Maths and why we do it’, but not HOW we do it.
Which is absolutely true: the HOW question is extremely important and it will require several posts to develop this (inexhaustible) point. One could even say that, for Maths students, it’s the ‘HOW we do Maths’ that makes a huge difference.Read More »
This post provides a few practical tips on how to develop fundamental abilities (i.e. the first level of the Maths ability pyramid), thus helping students to become more confident by increasing their awareness and fluency with the mental manipulation of objects and processes such as order, numbers, causes and consequences.
There is a double benefit in working on this development: not only does it help teenagers to focus and develop mental resources, but it does so by involving them in a series of lively exercises that look very much like collective games with relatively little Maths involved. In other words, developing fundamental abilities is both low-cost and high-benefit.Read More »
Yes, you’ve heard it before… ‘Students can’t do sums anymore’.
You had heard it before, hadn’t you ? Well, just in case you hadn’t, that’s exactly what someone was telling me last night at the pub: ’Oh, you’re a Maths teacher, eh ? Well, I’ll tell you one thing, mate: kids can’t do sums anymore !’
That was just in case you hadn’t heard it before.
True or not true ? Important or not ?Read More »
The Maths ability pyramid is a communication tool I have created in order to explain more easily to students and parents what we do in Maths and why we do it.
The initial idea behind the Maths ability pyramid is not only to access a better understanding of what learning Maths is, but also to get rid of this highly misleading fiction: the one monolithic so-called ‘Maths ability’ (you know, when parents or students tell you: ‘Sir/Miss, I’m not good at Maths anyway’…).Read More »