There aren't many teachers (or indeed people in general) who would argue with the desire for education to lead to students having flexible, transferable knowledge. That is, that kids learn stuff, but are also able to transfer this knowledge into new an unfamiliar situations easily. As an example from my own subject, we want students to be able to spot when to use Pythagoras'  Theorem even when it crops up in a question which has nothing to do with triangles (on the surface), or, even better, when it appears in a different subject (surely the true Holy Grail).  All subjects have ideas like this (perhaps this is what we mean by concepts?) that we want students to be able to recognise outside of the narrow confines of the lesson or topic. It is worthwhile spending a few minutes thinking about some of these in your subject.

But as teachers we also know that this is surprisingly difficult to achieve, and are often astounded that students just can't see it when this concept appears somewhere new, especially when we know they can do it.

Throughout 2019 I worked alongside two teachers in my department on Checking for Understanding, but early on we diverted to thinking more about what we meant by understanding. Without going into too much detail, we settled on 6 stages of understanding, as shown below in a display I now have in my room.

This made me think about the excellent Daniel Willingham article for the AFT titled "Inflexible Knowledge: The First Step to Expertise", and how Willingham distinguishes between rote, inflexible and flexible knowledge. I would say that our stages 1-4 of our model above are a break down of inflexible knowledge (although 1 could be rote in certain contexts), and that only 5 is true flexible knowledge.

But anyway, the point of this blog was not to delve into the details of the differences between these types of knowledge (read the article above if you want that), but rather to get a bit meta on the idea that inflexible knowledge comes before flexible knowledge can fully develop, which stemmed from this tweet:

If we take the idea that we need to pass through inflexible knowledge to get to flexible knowledge (which is not universally accepted), then this has implications on the understanding of that very statement for teachers.

For teachers to be able to think flexibly about the idea that students need to pass through inflexible knowledge to get to flexible knowledge, the teachers must first pass through an inflexible knowledge of this very idea. 

That is, it is completely natural for teachers to know that students need to first develop inflexible knowledge before being able to reach the heights of flexible knowledge, but for those teachers to be unable to apply this to their teaching (which would be showing a flexible knowledge).

If a teacher has passed on to flexible knowledge of the idea that inflexible knowledge is a precursor to flexible knowledge, then they will plan activities to make use of this. Perhaps this would involve using retrieval practice (with higher order questions as suggested here) or something else (this would depend on the individual teachers flexible knowledge of other areas of pedagogy). Once you start to dig a little deeper into this idea, it becomes clear that pretty much everything a teacher does is also subject to this principle. First we learn some new idea, perhaps we play around with it a little, we read more about it, and gradually, as we develop more experience we are able to incorporate it into our teaching practice flexibly.

And that includes our understanding of developing flexible knowledge. This understanding needs to pass through being inflexible before we can flexibly use it.

Thinking about that makes my head hurt, but I think it has implications for teacher professional development. It also make me feel a bit better about knowing I should be doing some things in the classroom, but not being able to do it flexibly.

This time last year I wrote a post on the Successes and Targets I had, and as the new year starts I find myself once again reflecting on last year.

My highlights/successes for 2019 have been:

1. IB HL Lesson Sheets
   After success with booklets in the IGCSE course I have been creating lesson sheets for IB this year. Really they are skill sheets, as each sheet covers a subskill of a unit, rather than a lesson. Like booklets, I now teach the sheet in however much time it takes, rather than trying to teach a skill in a lesson, and this is aided by having resources available on the sheet. The benefit compared to booklets is replacing a lost sheet is easier, and less time os wasted finding the right page etc. I am teaching one of the new IB courses starting March, so will be creating these for that course too.
2. Learning Maps
   I have been making use of Learning Maps to overview a topic at the start, and then review it systematically as we progress through the unit. This also gives students a revision map for use later. I find one of the biggest benefits is actually in planning the unit, as the map gives me a clear picture of the whole unit and so makes creating lesson sheets easier. I would like to collaborate in making these for the courses I am teaching next year.
3. Learning about Instructional Coaching
   In April I went the Instructional Coaching Institute run by Jim Knight, and it opened a whole new world of professional development to me. Learning about the Better Conversations model has changed the way I talk with people. And dabbling in the process of the impact cycle has been fascinating. I am really excited to start coaching properly, with a team of 4 others whom I have trained, in 2020.
4. The Principles of Great Teaching
   The introduction of the Principles of Great Teaching was a little bumpy this year as I didn't anticipate certain reactions to it (namely a belief that I was telling people how to teach), but overall, the document has started to make a difference. Teachers are talking about teaching and learning more and more, and the framework has given a language to enable this. Work in this direction is by no means finished, but it has been such a big part of my life this year, that it has to be listed here. Next year the focus will be on getting departments to work with them in their context. 

What about my targets from last year?

1. Assessing prior knowledge
   I did not use Diagnostic Questions to do this in the end, but I did build in a Get Ready section to my lesson sheets. These were one or two questions based on prior learning that students needed to be able to continue onto the current skill. As this was a higher level class, I am not sure I got the full benefit from these, and I am interested to see how these work next year with a year 7 class.
   
2. More time for independent practice
   This has been hard as we have had the number of lessons reduced by between 20 and 25% for middle school and IB classes. I certainly made headway with this for IGCSE before they went on exam leave, but my IB classes did not get enough independent practice. However, I have made more use of varied questions, and other activities to make students think more deeply in the time we have, such as Venn Diagrams and Open Middle problems.
3. Increasing wait time, and using cold call
   I have gotten better at using cold call, but still need to work on wait time, especially between student responses. I also need to use more questions when going through examples to get a wider sample of responses.
4. Drop in to more classes
   I have managed to average at least one learning walk a week this year, so have spent a lot more time in classrooms. I have also managed to get more members of the management team to join me on learning walks, which has been a good step forward. In terms of more personalised PD opportunities, the coaching should help with this. 

And looking forward to 2020, I have decided to follow the advice I got from the coaching course, which was to work on one target at a time. So these targets are what I shall work on in my teaching ine the respective bimester. I detailed some things I wanted to work on after reading Making Every Maths Lesson Count. 

On top of targets for my teaching, I have some targets for my role as T&L Coordinator.

1. Apply the ideas of Wholesome Leadership, and read more about leadership
2. Keep visiting as many classrooms as possible, and develop a feedback system for learning walks
3. Put the emphasis on departments to support the professional development of their teachers within the constructs of the Principles of Great Teaching

So there it is. Some highlight from 2019, progress against my targets from last year, and some targets for 2020.