I have purposefully made this a click-bait title as I suspect that is what Kris Boulton also did with his session during #mathsconf23, “Always teach what before why” (emphasis my own). This is the start of a series of blog posts inspired by this session where I respond to the questions that Kris poses and also explore different approaches to maths teaching.
I think the sign of a good CPD session is how deeply it gets you to think about your own practice and with that regard this is one of the best CPD sessions I have been to for a very long time. I’m still sat here chewing over it a many days later and felt compelled to write down my thoughts so that I could properly reflect on it. So first of all, thank you Kris.
When I originally made my session choices I chose this on the assumption that it would challenge my ideas of maths teaching and that I wouldn’t really agree with it. To be more honest I was expecting to really enjoy getting angry during it and that I’d be able to pick loads of holes in it. Who doesn’t enjoy getting out of their echo chamber once in a while to prove to themselves that they’re right? What I found though was a very well argued approach to teaching maths that would resonate with pupils from certain backgrounds and with many maths teachers. The chat box during the session seemed to be split evenly for and against. There did seem to be more anger about the session afterwards on Twitter but from what I can see it was led more by people who weren’t at the session and Twitter also does tend towards outrage anyway.
(I would like to take a timeout here and just state categorically that you will not get anything out of this post if you haven’t seen Kris’ session. I highly recommend that you watch it here but if you’re reading this you probably have/will. I also don’t know how you could form clear or strong opinions on the matter unless you have first-hand knowledge of what was discussed. Making assumptions and getting angry is what Daily Mail readers do. Be better than that.)
To what extent I agree with Kris has changed and evolved during the session and over the days since then. There are two main issues people seem to have problems with:
· Teaching “the what” first turns the focus into just being able to answer questions
· The word always
I believe that your response to Kris’ session is based on what your “maths values” are and the kind of maths teacher that you want to be.
I believe that teachers aim to be the kind of teacher they wish they had at school. When it comes to maths teaching this is based on what you enjoyed most about studying it. For me it was about making connections and being able to “see” the next steps before being explicitly told what they were. I loved the feeling of building up my knowledge and that maths made sense; it’s why I never enjoyed science as I found there to be too much arbitrary knowledge and not enough necessary (thank you Stuart Welsh for the addition to my vocabulary!). That’s the feeling that I try to create in my students, “aha” moments mixed in with a sense of control of their own learning. For others it could be they enjoyed the sense of achievement from being able to clearly demonstrate their knowledge: you know you’ve learned it if you can answer the questions. Often a great source of satisfaction or frustration in maths. Individuals strong reactions to the session stems from what they believe great teaching is.
In September I will be a Head of Maths for the first time and something I’ve been trying to answer for myself is what makes a great maths teacher and is there a “best” way to teach maths. After reading Mark McCourt’s excellent book “Teaching for Mastery” I’ve also been concerned about the difficulty of seeing the difference between a good performance and encouraging deep learning. Clearly if a pupil is only able to answer questions that are written in a specific format with little flexibility to their knowledge then it is just a performance. If the knowledge is chunked up into minuscule sections then you are disengaging the pupils’ attention and they are only thinking at a surface level. Something I don’t think you could argue with is that Kris’s session did not in any way suggest teaching in that manner. He wants his pupils to be able to answer questions in a variety of forms and constantly push the outer limits of their knowledge and its application. What Kris asked us to think about was the timing of the “why” and how does knowing "why" help you to answer questions.
Kris’ arguments could be summed up as: explaining “why” first causes too much cognitive overload, do students practice the “why” and is it ever really addressed again once they know how to get answers? What I would add to these arguments is that the “why” is also the most difficult part of teaching maths! It takes a really high level of subject knowledge and it can take years to get your explanations to a level where pupils are able to understand and infer from it. Bad explanations cause unnecessary issues, leading to misconceptions and creating more barriers as pupils’ confidence is knocked. By having the explanation after the pupils are successful you are allowing them to be able to create links with already secure knowledge which they also might not have been able to see without getting to grips with the content first.
My reaction to this session was similar to how I reacted to silent modelling when it was first introduced to me, absolute horror. However that’s because I want to be more in control of and change how my pupils are thinking (or arguably over emphasise my importance as the expert in the room). I also trust my ability to do that successfully because of my high level of subject knowledge and decade of experience. I’ve since realised through supporting trainee teachers that it’s incredibly powerful for your own development to learn the importance of the words that you use and enables you to be as concise as possible when you start adding a script to your modelling. Similarly I think this would be a very useful way to approach teaching when you start out. Focus first on being able to get pupils answering questions; that is currently the only way that we are assessed as teachers and it is essential to be successful in it. Pupils won’t trust you until you demonstrate that ability and after behaviour management it is the most important skill to master. Then you can focus on improving your explanations in isolation when the entire lesson doesn’t hinge on it.
So should you always teach what before why? It’s not for me to tell you. I personally would feel dirty if I always taught like this. But that doesn’t mean it isn’t a valid way to teach maths or a useful tool to have in your arsenal. I wouldn’t be dismissive of a teacher in my department who taught this way or force them to change. If pupils can demonstrate having flexible knowledge and can articulate why by the end of the learning episode does it really matter what order that happens in?
Teaching the “what” first is a legitimate way to help students gain knowledge and I’ve spent a lot of this post arguing it’s merits, so why wouldn’t I do it?
I’m a teacher because I want to make mathematicians. That is my driving force. I love maths but struggled during University because I wasn’t used to having to think independently or creatively about it. I’m always on the lookout for little Nicks in the classroom to nurture the mathematician within them; I want to share my passion and joy for a gorgeous piece of reasoning and foster that feeling of calm when everything is logical and makes sense.
However, that is only my internal motivation. When you break it down we are employed to ensure that pupils are as successful as they can be in a test they take at the end of Year 11 and every decision we take as educators is based around making that as likely as possible. It would be fair to say that at the start of my career I made that less likely due to poor explanations that caused everything after it to be more challenging than necessary. During the session Kris implied that this style of teaching resonated more with pupils that are lower attaining or have low confidence in maths. These are probably the exact pupils I let down in the beginning of my career with this approach. I now love teaching these pupils and feel successful in improving their confidence. Even children who don’t see themselves as mathematicians deserve that feeling of power when you figure something out on your own. There is no best way to teach in terms of style, there are only styles that resonate more with your values and how good you are at teaching in that style. I would like to think that the style of teaching I have developed over the last decade makes it more likely for my pupils to be successful than always teaching “what” first, but I wouldn’t know unless I tried.
In my next post I discuss how I would have started these two topics instead