“To explain something to someone is first of all to show him he cannot understand it by himself.”
The previous post in this series looked at developing a love of Mathematics itself, and how an appreciation of the history and impact of Mathematics makes a difference to your team’s practice in the classroom.
This time around, I’ll be talking about how an appreciation of pedagogy, the philosophy of Mathematics education and what engaging students in the subject really means (spoiler: it doesn’t mean ‘fun’ tasks for their own sake). So let’s begin.
I cannot emphasise the importance of sound pedagogical practice in one’s team. The obviousness of this statement perhaps means it won’t be taken seriously in some quarters. However my experience tells me that one would be surprised how often leaders carry on regardless, making up for deficiencies, constantly focused on short term gains rather than long term benefits.
So, what does sound pedagocial practice actually look like?
Like many others in this profession, my beliefs about pedagogy in Mathemtics go back to the long standing but long neglected Mathematics Counts, the 1982 report by Dr W.H. Cockcroft into the state of primary and secondary Mathematics teaching. Cockcroft, right in the middle of the report, stated (rightly), what should be taking place regularly in the classroom:
- exposition by the teacher;
- discussion between teacher and pupils and between pupils themselves;
- appropriate practical work;
- consolidation and practice of fundamental skills and routines;
- problem solving, including the application of mathematics to everyday situations
- investigational work.
In my practice, I boil this down to the SPIDER acronym: Solving Problems; Practical Work; Investigation; Discussion; Exposition; Routines.
The report repeatedly mentions that teaching pedagogy should in itself constantly develop basic factual knowledge, build skills that help students apply this, and ultimately a wider understanding of the whole mathematical field – or KSU, for short. Thus, we can see pedagogical practice in Maths as two-dimensional: one axis of teaching methods, and another of learning outcomes.
How, therefore, do we develop such teaching practice in our department, and get them to enjoy it?
Well, in terms of exposition and routines, I think 90% of teaching that goes on in Mathematics departments is based on these two themes. Whilst the execution of these methods might be left to be desired by some of your team, they’re the bread-and-butter way of teaching Maths. They work, for the most part in imparting knowledge and to a certain extent, allowing students to apply their learning. They’re definitely effective in terms of ensuring progress is measureable and outcomes are being achieved. But in terms of developing a wider understanding of Mathematics, they’re lacking.
So, it’s to solving problems, practical work, investigation and discussion that we must look to in order to create students who are confident mathematically. Now in terms of developing a love of these concepts, well, it’s simple.
Sit down, as a department, every week, and do some problem solving tasks. Collaboratively plan and try out some practical lessons – even better if you do this in partnership with other departments (Technology and Science particularly). Download some investigations and get staff try them out on their own, and then bring the team together and discuss their findings. Encourage your team to set out their classrooms so they foster discussion (the ‘horseshoe’ table layout is perfect for this).
Notice that nothing, not one thing I’ve mentioned so far, is rocket science. The Cockcroft Report is 32 years old, for God’s sake! Yet we’re still having to go back to it, quite simply because it contains a wealth of undeniable truths. We have to constantly, constantly reiterate these truths throughout everything we do, through our teaching, our liasion with our peers, those who manage us and those who we train to be teachers. If not, then fads and pseudo-pedagogy (hello Brain Gym, VAK, Thinking Hats, Emotional Intelligences, etc, etc, etc…) will continue to find their place in the classroom. And I still haven’t mentioned fun, yet…
Stuck for ideas on where to begin? Well, let’s take a look:
Dan Meyer’s Three Act Maths pretty much ticks every single SPIDER/KSU box. Each problem is rooted in proper real-life context, and has a detailed lesson plan to follow. Easy peasy.
Thinking Mathematically is the gospel of problem solving methods. It’s full of problems to solve and advice on how to solve them. The advice is sound and easily transferable to classroom practice. Spare a few quid from the department budget and buy a copy for your team.
The ATM’s Questions and Prompts for Mathematical Thinking gives you rubrics to follow to promote discussion in the classroom, a framework that has the development of understanding at the centre. You can’t argue with it.
Ed Southall’s Solve My Maths website is brilliant as a whole, but his problems are amazing. Most of the problems are set in the geometric area of the curriculum – but in order to solve them students need to have confidence across the board. They’re challenging, but students will enjoy working through them.
NRich. Do I need to say any more?
Lastly for these starting points, one for the practical minded of you out there. Cre8ate Maths was a project started by teams from Sheffield Hallam University in order to promote the teaching of Mathematics through contextual problems. It launched with great fanfare in South Yorkshire but perhaps didn’t have the momentum behind it to take a rightful place in the teaching and learning pantheon. If you do one thing after reading this post, get on the website and download all of their materials – there are a wealth of practical tasks in there, many pre-made and as part of detailed lesson plans. My personal favourite is the Buildings and Structures unit – even if you do it as a end-of-term lesson, it’s absolutely fantastic, students love it, and it’s proper Maths, as we say ‘oop north’.
One final thing before I end this post. Notice how I haven’t mentioned fun. We are teachers, not entertainers or childminders. We are judged ultimately by the powers that be on progress and outcomes, not on how much colouring in or cut-and-stick goes on in our lessons. I will say this time and time again: engagement comes from the personality and style of the teacher – not, in no way shape or form, the activity going on in the classroom. I have never seen a teacher improve as a practioner by getting students to make board games, or use flip cameras to make revision videos, or make posters. I’ve seen great teachers use these methods in their everyday practice, but I haven’t seen these methods make a teacher any better at actual teaching…
Next time, we’ll look at leading by example.