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The Power of Practice

Maths “ability” is just practice. For all the rhetoric we hear about ability in maths, any innate component is of relatively little consequence. What appears to be ability is just practice masquerading as talent. But despite this we have a Western obsession with innate ability. Culturally we treat Maths as something you are either born good at, or born bad at, and those in the latter camp should brashly accept it. After all, if your genes make you bad at something why should you be shy about it?

But innate ability is a distraction from the real cause of good performance – practice. Practice is the single most important component of success in Maths.

Practice matters because knowledge growth is compound. And it’s compound because:

A. Connections strengthen memories. As we learn more, and so have more associations to make with each new piece of content, we remember more. These new connections in turn strengthen our old knowledge, and contribute to the wider structure of knowledge that forms our view of the world. This often looks like innate ability. A student who knows about fractions will learn more from a lesson on percentages than a student who doesn’t know about fractions. We might hypothesise that this is because they are “better at Maths”. In fact it’s because they can build connections with their fractions knowledge, and so understand percentages better (and are more able to remember this new knowledge).

B. Mastery frees up working memory. Our working memories have a limited capacity. Once they’re full they’re full, and we cannot process any more information. One model of working memory conceptualises it as having a fixed number of slots. Each slot can hold one piece of information, like a step in a method or a number being remembered. Trying to carry out a complex process can easily overload working memory as all the slots get filled and thinking grinds to a halt – meaning the thinker is unable to learn. However fluency bypasses the constraints of working memory. Once you have mastered a procedure you carry it out without thinking – it does not occupy multiple slots in your working memory but frees it up to learn instead. This means that the student who has practised to the point of fluency will learn faster, and have an appearance of greater ability.

C. Fluency solves problems. Because fluency frees up working memory, it gives students the space to think about challenging problems and come up with creative solutions. The most well-practised students will therefore come up with ideas that challenge their thinking, and so learn more at the boundaries of their knowledge.

Getting better at practice must be a national priority. We have a national fear of practice. When being trained as a Maths teacher I was told to “Beware the three Xs. Examples, exercises, and more exercises.” The intention – that incredibly dull lessons should be avoided – was a good one. But there is no need to make practice taboo. It is the hallmark of elite performance, a necessary prerequisite to any worthwhile achievement. It is not an end in itself, but the ends we seek cannot be accomplished without significant practice.

There are two components of this challenge to practice better. We need to:

1. Increase the quantity of practice.
Every time a new international study shows that our relative performance is worse than the Far East there is an outcry from people who argue that the outcomes are just not comparable. It is not fair, they argue, to compare UK results to the results of Singapore, Shanghai or South Korea, because in those countries children do hours of homework, have private tutors, and spend far longer practising. This is not an excuse. If the quantity of practice is the cause for this gap in performance then we need to get that same quantity of practice for our children.

2. Increase the quality of practice.
Good practice means learning the right thing, the right way, and with the right feedback. For this we need:

  • Better resources – well thought out sets of practice questions that develop understanding and challenge thinking. No current UK textbooks (that I have found!) are up to scratch, and downloads from TES certainly aren’t. Schools and groups of schools need to put real effort into designing the best resources so that teachers can stop reinventing the wheel and focus on how to teach to the specific group of students in front of them.
  • Better teaching – teachers need deep subject expertise to make sure students receive good quality explanations and are guided through the practice properly. Subject specialism is important here, but so is ongoing professional development. No specialist is too good to carry on learning, so without a better culture of effective CPD we will continually miss out on the potential of the workforce.
  • Better feedback – good feedback is both precise and timely. It must be precise enough to guide you to action (no vague targets please), and timely enough for you to correct any misconceptions before they settle. Without precise and timely feedback your practice could make you learn mistakes rather than the actual concept itself.

The hallmark of elite performance is a relentless dedication to practice. Sportspeople drill basic techniques over and over again, making them instinctive so that in the heat of a game they can be deployed effortlessly. Musicians practise pieces for days and weeks so that they can begin to play them with feeling and creativity. So too must students practise basic techniques until they are fluent, before they can enjoy the dizzying heights of elite performance. Only with fluency can they begin to tackle truly rewarding problems.

Tim Oates describes how, in the drafting stages of the new National Curriculum, he went through battles to have the word “practice” included in the Mathematics section. It was simply too unpalatable. We need to debunk the two pernicious myths: that maths ability is innate, or that fluency is not a prerequisite for good performance. Practice has the power to make everyone good at Maths, and we need to start to unleash it.

This post is based on a presentation I gave to schools at the first Maths Hub Forum in Manchester last month.


The 1 Big Secret to Good Behaviour

Good behaviour is all about self-control. It’s about the self-control to delay the gratification of having a chat/staring out of the window/arguing with Mr Smith/stabbing Jamie with a compass, in favour of the much less immediately appealing orderly learning environment. Students with self-control can resist these temptations to follow rules and learn.But self-control isn’t that simple.

It’s not a fixed trait that you either possess or don’t. Self-control is more like the power in a rechargeable battery: it empties with usage, before replenishing when plugged in. One ingenious experiment showed this by getting university students to attempt some impossible geometry puzzles. However before the puzzles they sat in a waiting room, and on the table was a bowl of radishes, as well as a bowl of freshly-baked chocolate cookies. Some students were allowed the cookies. Others were instructed to resist the cookies and eat the radishes instead.

The cookie-eaters attempted the puzzles for an average of 20 minutes before giving up. The cookie-resisters only held out for 8 minutes. Resisting the cookies used up their self-control.

Stress depletes self-control.

This means that a salesman who was stuck in a traffic jam will be less able to deal with a tricky customer, or a parent with a wailing baby will be less able to deal calmly with an overly playful child. It also means that often we will face students whose self-control is already significantly depleted by the time we see them. This might be because it’s the end of the day, and Period 4 French used up the last bit; or it might be because home is a chaotic hothouse of stress at the moment, and there’s no space to recharge. Either way, their ability to make good decisions has been depleted.

Depleted self-control means poor behaviour.

The tragedy is that the students who most need to value each minute of their education are often those whose self-control has depleted the most. Yet they will be the least able to resist temptations and behave well. It’s not that they don’t have self-control – they’ve just used it all up.

Students need to bypass the self-control system.

There’s no way of fixing their depleted reserves of self-control. They need to bypass the decision-making system, the one that sets up two options and asks them to choose. This system demands self-control, and there’s none of that left.

Habit is the cheat that unlocks good behaviour.

When you act out of habit you don’t need to stop and think, or to weigh up options and make a decision. You just act. Habits are driven by a different part of the brain (they’re tucked away in the basal ganglia, just above the top of the brain stem), and by a different neurological system. If students behave out of habit, then depleting self-control stops being a problem.

Habits are formed of cues, routines, and rewards.

Charles Duhigg’s book, the Power of Habit, teaches us about the habit loop. He says that every habit starts with a cue from the environment, is followed by a routine of behaviour, and culminates in a reward for completion.

For example, a habit of entering the classroom might begin with a cue of being greeted at the door by your teacher, followed by a routine of fetching your folder and immediately beginning the Do Now, and then finished with a reward of being verbally recognised and of completing the first task successfully. A student could choose to do this by using up self-control, or they could launch into autopilot as soon as they are greeted at the door – when habit kicks in and takes over.

The 1 Big Secret to good behaviour is to build habits.

In all schools, but particularly the most challenging, students will come to you with their self-control depleted. They will choose a course of bad behaviour, unless they have a habit of good behaviour that takes over. But there is no one habit called good behaviour – it’s a set of lots of small habits that deal with different cues.

One type of habit is the classroom routine.

Unless you work in an exceptionally well-organised school, you build this yourself. Decide the routine you want the class to have, then decide on a simple and clear cue as well as an appropriate reward. Once established, this habit will make sure your students perform standard tasks just as you wish, regardless of their self-control situation at that time.

Another is the ‘coping strategy’.

Because school isn’t all about predictable situations, students need habits that give them routines for the unexpected. A classic example is ‘counting to ten’ (cue = anger, routine = stop and count to ten, reward = increased calm/reduced risk of regretting a rash action). These are harder to design and teach, particularly for the lone teacher. However if done well they are the most transferable habits, and most useful for students’ futures.

Self-control depletes, habit rescues.

The more stressful situations a student has been through, or difficult decisions they’ve had to make, the lower their self-control will be. This makes it harder for them to behave well if relying on them to make good choices. It is this phenomenon that lies behind much bad behaviour. Habit can rescue students from this problem. It takes over their behaviour, avoiding the need for delayed gratification or tough decisions. If the right habits are in place, depleted self-control is no longer a problem.

How to build habits of good behaviour – coming soon…

Next week’s blog will be on building habits for classroom routines. Then in the coming weeks I’ll cover some different behaviour habits for more general situations, to help students around school and outside of it.

For more reading:

How Best to Track Assessment?

Particularly with the imminent demise of the National Curriculum level, I’m becoming increasingly concerned with how best to manage the assessment of pupils. For me there are two key questions:

  1. When has a concept been ‘mastered’?
  2. What is the best way to represent progress so far, to pupils, teachers and parents?
What does mastery look like?
I’m comfortable assessing how well a pupil understands something at a point in time, and can gain a fairly accurate snapshot of their understanding. The problem is that I’m not content with recognising mastery when a concept is completely fresh in a pupil’s head, and that’s all they’ve been working on for the last week. Of course they’ll do well in that assessment.
There has to be an element of retention and remembering. Does that mean pupils should be tested a few weeks after they’ve studied a concept? Or maybe we should assess after completion and a few weeks later. The relationship between remembering and understand, as Kris Boulton pointed out, is one that needs a lot of thought. A proper assessment system needs to consider both – masters don’t forget their craft.
What is the best way to represent progress?

This year my primary tool has been the “I Can” sheet. Each term pupils get their new “I Can” sheet on coloured card, put it in their folder, and read through what they’re learning for the next couple of months. As the term progresses they rank their understanding and watch the sheet fill up. 
“I Can!”: Pupils and teachers rate understanding of different key outcomes.
It’s definitely proved effective as pupils use the sheet as their guide through Maths, and stop to reflect on how they’re doing. They know what they have to learn to improve, and how their progress relates to what they could potentially have learned.
The problem is that there are too many outcomes, and it’s not set up for a mastery approach. There are so many outcomes after an entire year that it’s hard to see where a pupil’s strengths and weaknesses lie, meaning it ceases to be the useful guide I’d planed. So what could the alternative be?
I’m intrigued by (and experimenting with) the way Bruno Reddy rewards mastery using badges. The binary awarded/not-awarded status fits well with a focus on mastery, and the checklist provides pupils with a very clear guide of what they need to do to demonstrate their understanding. But this version of mastery doesn’t appear to assess whether pupils remember a concept a few weeks down the line, and, like my I Can sheets, there’s too much information to be easily digested. lets you award pixels to achieving pupils
Dan Meyer’s (redesigned) concept checklist takes the visual representation challenge head on. It is clear where pupils have done well and where they need to improve, which makes it much more useful for pupils, parents and teachers. It also does well to require pupils to score highly twice, so prioritising the need to remember. However it is entirely test-based, and doesn’t seem easily adapted for a wider breadth of assessment methods. I can see this working well with exam classes higher up the school, but it seems a bit dry for younger pupils.
Towards A Solution?

There’s a reason kids everywhere love sticker albums. They’re incredibly straightforward, visually appealing, and it’s easy to see where there’s a gap. The sense of satisfaction from filling up a page is immense, and there’s just a joy in lining that sticker up and letting the glue do its work.
Everyone loves sticker albums!
Could we do the same thing for Maths? I’m imagining giving every pupil a sticker album on their first day, that they’ll fill up over the year. In each blank space could be the checklist of what needs to be done to earn that sticker, and, once completed, the pupil can cover it up with a sticker to mark their achievement. That checklist could include a criterion for remembering, as well as whatever range of other assessment was best for each concept.
Please share any thoughts you have – I might get designing this summer!

Meaningful Marking

Marking is something I’ve struggled to master. I know what I want it to achieve, but have gone through many iterations trying to get the process right. My approach has often given too much irrelevant feedback, or gone over the heads of students.

Target tracker marking sheet
The old approach: Plenty of targets, not enough solutions.

In the last few months I’ve given it a lot of thought – trying to make sure I focus on giving the feedback only a teacher can give – and make students as active as possible in the process.

This post by Tom Sherrington was just the inspiration I needed. My marking wasn’t having much effect because students didn’t know what to do with it. They had time to read, to respond, to mark off progress on a checklist, and give off every impression of my time being well spent, but they didn’t really act on it.

This week was different. During Thursday’s lesson I planned to spend three minutes with each student to work out precisely how well they were doing. Using Wednesday’s exit cards as a starting point, I posed them each a question just slightly harder than the last one they got correct the day before. As I watched their thinking process I filled out a WWW and EBI grid, and posed other questions until I got a comfortable feel for their understanding. Then I set them each three questions to take them one step further than they could already go, and told them that they’d have the chance to move up a level at the start of our next lesson if they could solve their new, personalised questions.

The new approach: Built around making visible progress

The student response was excellent. Two of them, without prompting, told me they were really glad I was showing them how to act on feedback as they often wanted to but were confused. It’s also meant that, for the first time, I’ve seen everyone respond meaningfully to marking. Every student pushed themselves to achieve the goals I set, and every one of them learned something new. Setting targets with the explicit steps needed to achieve them – that’s meaningful marking.