Time to revisit...Teaching for Mastery

In two weeks time on October 13th I will be delivering a session that shares the title of this blog. The blog is meant to act as a preview to the session.

“Mastery”. Some people see it as the latest buzz-word to be shunned until we wait for the next “big thing”. For others it is central to teaching. For some it is a confusing term with no clear idea of what it actually means. And I can sympathise with all of these views…

The idea of “mastery” has been around for a long time. People much more knowledgeable have written about its provenance, its history and its progress to the modern day. Neither this blog nor my mathsconf session will be trying to reinforce or reinterpret any of this. I will not be attempting to explain the structure of a mastery curriculum (which is not exclusive to a mathematics curriculum). Better men than me have already done this, not the least of which is the LaSalle CEO Mark McCourt (if you haven’t read his blogs on mastery then you must). Saying that, it is important to understand certain aspects of its structure to understand where I hope my session fits in.

One of the central aspects of a mastery curriculum is teaching in a way that all pupils can access from their starting point, and then carefully assessing their understanding throughout the teaching process. A second is the use of correctives where the initial teaching isn’t successful – having different ways of approaching concepts when the first way falls short. The biggest aim of my session is to try and showcase some of the ways that teachers can approach this. Starting with what I see as important ideas to consider when thinking about structuring learning, I then aim to share practical examples of approaches that could be used either as part of the initial teaching or as a corrective approach. For those that know me, it won’t be surprising to hear that much (but not all) of this focuses on the use of representations to reveal the underlying structure of an idea (given that my book “Visible Maths” is entirely concerned with the use of representations and manipulatives to reveal underlying structure).

As an example, but not one I am using in the session, consider the “rule” that one negative number divided by another negative number results in a positive answer. Consider -15 ÷ -3:

One way of representing this is to use double sided counters; these usually appear with a yellow side (positive) and a red side (negative). Two different coloured counters can also work, and in fact to model this calculation we only need to consider negatives so a single colour of counter will suffice. The image above shows -15, and now we have to think about how we divide that by -3. One way of thinking about division is to think about creating groups, so a possible way of looking at this calculation is, “Start with -15 and create groups of -3.” These groups can be seen below:

When we think about division like this, the result of the division is “How many groups can we create?”. We can see that this process creates 5 groups, which means that -15 ÷ -3 = 5.

  

Often this “rule” is taught as an arbitrary rule, without any attempt to show where it comes from. In many classrooms, one could be forgiven if kids believed that the only reason this is a “rule” of maths is because teachers says so. But this rule is a necessary rule – if division works in the way we know it does then the answer to -15 ÷ -3 cannot be anything but 5. I finish my session with a discussion around other “rules” of maths, how appropriate representations can show where these rules actually come from, and also discuss how we can manage the transition from using representations/manipulatives to the abstract calculations. Hopefully I have whetted your appetite to hear more about teaching approaches that can support mastery in mathematics, and I look forward to seeing you (whether in my session or not) in Birmingham. Don’t forget to join us for the pre-drinks and networking the night before as well!

Relationships in teaching

The topic of relationships is one that undergoes perpetual discussion between people in education. Just the other day my line manager and I were talking about it. I am sure I saw a recent article appear on twitter about personality screening for teachers (although I now can't find it and the only ones appearing in my search are from 2012). Some teachers even profess to believe in a "teacher gene". Many talk about the "magic" of teachers (including this recent TES article).

Now I absolutely believe that relationships are an important, possibly the most important, part of working with young people in the classroom. But this belief raises some interesting questions:

1) How do you train people to build relationships?
2) To what extent do the systems in schools contribute to or detract from teachers' ability to form relationships? And if teachers struggle to form relationships how much of the responsibility lies with the teacher and how much with the school?
3) Can anyone learn to teach?
4) If there are certain people that are more predisposed to teach, because of some gene or some innate personality traits, then does it make economic sense to train people that don't have the predisposition as they are less likely to become "great" teachers?

I have trained a fair few teachers in the last 10 years (teaching for more than that but have been involved in training for about that long) and one of the things I learned early on is that you shouldn't train people to teach like you. However good you may be, your job as a teacher trainer is to help that teacher teach as them, not teach like you. This has obvious challenges, particularly when you are have what might be termed a "robust" personality (as mine has been described) and you are working with someone who is a lot more unassuming in their personality. These people, being more introverted, can struggle to form relationships with pupils as they are more unsure of themselves in those myriad of interactions with all the different types of pupils they come across. But does that mean they can't be effective teachers? From my own experience I would say absolutely not, but it can be hard work to give them the confidence to let them be themselves in the classroom, particularly when the "effective" teachers they are often told to go and observe are those more extroverted individuals that seem to hold a classroom through the power of their presence alone.

I have heard many teachers and leaders say that "if you can't build relationships then no behaviour system can help you". Worse, I have heard many say "the best teachers don't need the behaviour system". I always wince when I hear this, because I always think "what are the behaviour systems for if not to support teachers in building and maintaining relationships?" I know from personal experience that when behaviour systems have been robust, and applied with a measure of consistency across the school, then relationship forming is easier. If kids know that it isn't personal, that when rewards and sanctions are applied they are done so within a clearly defined policy, then it makes it easier to work with them. For this to happen of course, all teachers need to be using them. If the best teachers are not using them, then anyone who does is automatically relegated to a lower status. This tends to be less experienced staff and staff newer to the school who haven't had chance to build those relationships yet, and so this can be a double whammy for those teachers. But is this the teacher's fault for not being "personable" enough to create those relationships, or the school's fault for not setting up their systems to support this in the best way possible?

The last two of my questions are perhaps the most contentious. As a teacher, I am committed to the idea that any of my pupils can learn what I want them to learn given enough time and good teaching. So my ideals should then naturally stretch to training teachers - any one who wants to teach should be able to learn to teach well given enough time and proper support. Of course the reality is slightly different from the ideal; every year that a teacher is not teaching well then kids suffer and the support given is often by other busy practitioners that have a whole lot more on their plate. But does this mean these teachers can't learn to teach, or that we simply don't have the time and tools to teach them? If there is such a thing as a "teacher gene" then does this mean that some could never be good teachers, or just that they will have to work harder to get there. But if that is the case, I wonder how demoralising that could be for those that are committed to teaching but are told time and time again that they don't quite have "it"?

This idea of the teacher gene, or better teachers having certainly personality traits, for me has to raise the question about training. Training and maintaining a teacher costs a huge amount of money, particularly in some subjects that attract large bursaries and golden hellos on top of the large pension contributions, CPD costs etc. And this is in a time when teachers are arguably not paid enough (the English starting salary is below the OECD average, as is the top salary attainable and the average hours are the seventh highest). This has to raise questions about value for money in terms of training people to teach that are unlikely to stay in the profession, or who will take a long time to reach a good level of practice if they do. As mentioned the idea of "personality screening" prior to training a teacher has been mooted before; it was actually part of a department for education white paper in 2010 (the same one that limited the number of attempts at the QTS literacy and numeracy tests) and was due to be introduced in September 2012 according to this Telegraph article, although I don't think it ever made it into practice. The idea was referenced again in this 2016 Guardian article - with a prediction that scenario-based questions could be used to ascertain details of prospective candidates character and thus screen for those that don't have the necessary "character". I must admit to being sceptical of this - I think that most people who would want to teach would be intelligent enough to identify suitable answers to these sorts of scenarios even if it they don't actually believe it. And of course saying you would act in a certain way when faced with a scenario is completely different to being able to actually pull this off in practice.

Overall I think it is clear that relationship building is important in education, and an important thing for teachers to be able to do. The big questions arise for the implications of this in terms of teacher training and school systems. And I think we should probably have a decent go at answering them before we say things like "Good teachers always have classes hanging on their every word", "You need a teacher 'presence'" (whatever that is) or "No system can help you if you can't form relationships".