In my last (and only) blog, I wrote about two changes to my teaching to help improve retention of knowledge. This was inspired from the excellent book ‘Making every lesson count’, and the Mr Barton podcasts. I have continued with low stake quizzing, but switched to fortnightly rather than weekly, due to time constraints. Interleaving is now a large part of the school curriculum and developing well within the maths department. In this blog, I am going to reflect on a different book, ‘Why don’t students like school?’ (WDSLS) – Dan T Willingham, alongside reflections from the Mr Barton podcasts.
Before I talk about recent changes I have made to my teaching practice, I think it would be useful to share two thoughts I have had recently about my own practice.
- When I entered teaching, I had the somewhat arrogant view that my subject knowledge (having a maths degree) would somehow put me above others when teaching maths. Although it does give me a certain advantage in some respects, I never respected how I should or could use this subject knowledge. In the first few years of my practice, I really struggled to empathise why students didn’t ‘get it’ after I had explained a topic. Not enough thought was given over to my explanations, or the cognitive load it had put on learners. My strong subject knowledge almost seemed a hindrance.
- I am told I am a “good teacher” by colleagues, parents and learners*, yet I don’t feel I am (yet). The outcomes I get for my learners are considered good, and if you are to look at the average score my classes gain on assessments, you might consider me to be a “good teacher”. However, the thing which irritates me is the range of scores in my classes. In the most recent GCSE results, I had a learner who achieved 238 marks out of 240, whilst in the same class, a learner with the same attendance, and same KS2 level got 96 out of 240. My goal is to reduce the range, whilst not bringing down the higher end.
Since October, I have changed 3 things in my practice
- Planning for learning over a longer period by breaking down large problems
- Introduction of “Silent teacher”
- Variation of questions
WDSLS really made me reflect on some of the things I do in my classroom, and also what I except learners to be able to do. Willingham opened my eyes to the necessity of background knowledge, in order to clear up space in working memory. The examples he uses in his book are around a number of different subjects covered at school. Whole paragraphs are given and can be read easily, but difficult to comprehend without the essential background knowledge that is withheld. The use of key terminology in these paragraphs opens a whole new world of learning.
Whilst reading this, I kept thinking back to the podcasts discussing cognitive load theory, it also led me to think about my first reflection, why didn’t students ‘get it’? The first time I taught solving simultaneous equations with one quadratic and one linear, I thought I had nailed it. The whiteboard was full of workings, it looked easy to follow, surely the class would understand. In all honesty – it was terrible, I think 3 learners followed and the other 28 nodded along politely, copying down the large example. At that time in the year, I was putting far too much strain on their cognitive load, I simply saw the algorithm of substituting and solving, my subject knowledge got in the way of my empathy for their own subject knowledge. I was asking learners to rearrange formula, substitute an equation into another equation, expand a squared bracket, solve a quadratic equation, then substitute two values into the same equation separately, and come out with two answers, of which I then tried to relate to two coordinates on an abstract graph. It is exhausting just writing about it, I never thought about the students in my class, who were still making the obvious mistakes on expanding a squared bracket. For myself, experience is the best teacher, and I am glad I have gone through and still go through (though with less frequency) these sort of experiences.
Willingham has made me think about the deliberate practice my learners needed to do first and ‘master’. The substitution of an equation into another equation should have been an isolated lesson, filled with lots of practice, which varied slightly to get students thinking about it. Starting off with linear equation into linear equation, then rearranging a liner equation to put in another linear equation, then a linear equation into a quadratic equation, and a rearrangement of linear into a quadratic.
Recently I have taught straight line graphs to Y10, a topic I usually grimace at – but for the first time, I loved it! My planning started at the end, what was the most difficult question I wanted them to answer at the end of the 8 hours allocated? For this group, I wanted everyone to be able to work out the equation of a perpendicular bisector of two coordinates on a graph (tangents to a circle are further on in the scheme of work). I then broke this question down to the background knowledge they would need.
- What does perpendicular mean?
- How do you calculate a perpendicular gradient?
- What is a reciprocal?
- What does bisector mean?
- How do you find the midpoint of two coordinates?
- What is the equation of a line?
- How do you calculate the y-intercept?
- How do you calculate the gradient of a line?
- How will I know if a gradient is positive or negative?
I then began planning my series of lessons; it is the first time I have taught straight line graphs where I spent time on each individual part (this may seen strange to those who do it already). Time was spent with my class on working out the gradient between two coordinates, describing what this meant, showing it on squared paper (not necessary an axis).
The second change in my practice was how I introduced the worked examples, previously, I would go through several examples, explaining each step and asking learners to copy them down for reference. I would then put them on with some work to do and go to the learners with their hands up, unsure of how to start (slightly perplexed as they had copied down 3 examples).
This is where WDSLS helped realise the errors I was making – students were not having to think, as well as being overloaded with new information. Listening to the Mr Barton podcast, particularly the one with Dani Quinn, I began trialling silent teacher, with worked pair example. I would split my board in two, going through an example in silence on the left-hand side. The instructions I gave the learners were clear, watch and do not make any notes. I then had a question on the right-hand side of the board for them to attempt, very similar to the one I had just done. They now had to think, rather than just copy down an example. When learners were asked to then work through a task, I noticed a massive reduction in learners asking for help.
Listening to Doug Lemov on the podcast, I heard him talk about the teaching technique of ‘show call’. I have incorporated this into my silent teacher, whilst learners are working through their example, I will go around and take photos of excellent work, but also were misconceptions have been made. We will then project these on the board and critique the work, this has helped improve the presentation and working out from the boys in my groups.
My iPad gallery since implementing ‘show call’
Isolating the skill of finding the gradient
An improvement in showing working out (Y10 boys book)
The final part of my practice I have focussed more on is the variation and order that I am asking questions. With the gradients, I thought carefully about the points I chose. The first two questions were positive gradients in the first quadrant with an integer gradient, the next two questions were positive gradients in the first quadrant with a fractional gradient, the next two were negative gradients in the first quadrant, I then introduced using a point in the first quadrant, and a point in the second quadrant, working out the gradient between these. Willingham talks about focussing what students think about carefully in the classroom, as memory is the residue of thought. For this task, I wanted them to clearly think what a gradient was, and how to calculate it. The rest of the series of lessons followed a similar pattern.
Slight variation in questions – I would ask when going through answers for similarities and differences.
I have reached a point now where these 3 things are common in my classroom and are very much a habit. Early in my career, I was too quick to try new things for a week, not see an impact then try something else. Experience again has taught me to think a little more and persevere. My concerns around the first point I am doing, is I almost feel like I am ‘spoon-feeding’ the learners, which is why variation is so critical. Willingham talks about all new knowledge should be built upon old knowledge to help understanding and remembering, currently, I do not think I am explicit in explaining this. I had read about knowledge organisers, but I am cautious of introducing too much too soon.
Implementing these 3 changes, I hope to bring the range of outcomes down in my classroom, without decreasing the quality. My aim is to teach to the top but structure my lessons, so everyone has the potential to get there, with no one not feeling challenged. A difficult balancing act which will only be achieved over time and not over night.
After reading posts from Jem Sherwood and Harry Fletcher-Wood, I am going to be introducing exit tickets as the next habit in my practice, to really refine my practice and ensure that I am catching and addressing errors early.
*I can also find some colleagues, parents and learners who would have the opposite view
Mr Barton for his excellent podcasts
Dani Quinn – for introducing me to Silent teacher
Doug Lemov – show call
D.T. Willingham – Why don’t students like school
Harry Fletcher-Wood – Exit Tickets
Jem Sherwood – Exit Tickets