I have probably missed some really important ideas, or badly explained some of the ones I have chosen to mention. Sorry if your favourite thing isn’t included here – I’ve probably missed something very important. Happy to receive useful feedback on what I have written here – you can get in touch on Twitter (@mrallanmaths) or leave a comment below.

It’s inservice day next week, and I was asked if I could do a session on Cognitive Load Theory – 30 minutes. I’ve presented about CLT a lot in the past and 30 minutes isn’t very long, so I thought I’d talk about a collection of ideas that I think are important for teachers to think about that can maximise pupil learning.

Huge thanks to the teachers who got in touch on Twitter with ideas for this workshop (see replies to this tweet). The trick will be to make the workshop fit into 30 minutes!

The title isn’t overly catchy, but it’s what I set out to achieve with the workshop. Here’s what I have included.

Learning Intentions and Success Criteria

These are important, but not the focus of this workshop. I’ll be talking about some results from cognitive science and research that suggest there are other important things we can focus our attention on that have the potential to maximise pupil learning.

I’ll also be talking about some of the things we probably should do less of or stop doing altogether.

This workshop will have been successful if teachers leave and have a conversation with each other about any element of the workshop.

We often run focus groups and ask pupils how their learning experience can be improved. Here are some of the common suggestions pupils give…

• Fun lessons – we ought not to prioritise fun over learning. Learning doesn’t need to be fun. It’s fine if it is fun, but it is more important that there is something meaningful to be learned.
• Posters/PowerPoints/Presentations/Animations – this often means pupils get better at bubble writing, PowerPoint or using animation software. Memory is the residue of thought, and if you are thinking about how to put together a stop animation as a way to demonstrate your learning about some scientific principle, let’s not kid ourselves that you’re learning about science – the learning outcome ought to be “how to use stop animation software” as this is probably what will be learned during this time.
• Make the learning relevant to pupil interests – their focus becomes about their interests. Including a contextualised question about baseball instead of football can minimise off task discussions about football (pupils in Scotland tend to be far more into football than baseball).
• Project based learning (and Interdisciplinary Learning)– this is fine if they have learned all of the content and are working on project skills. Not fair for novices to try to learn through projects but this is definitely good for experts (expertise reversal effect).
• Discovery based learning (or problem based learning) – what about equity? – those who learned about it at home (or elsewhere) can already do it. Pupils like the idea of figuring things out for themselves. This should be used with care, since misconceptions can grow easily and can be shared by pupils working in groups with minimal guidance.
• Games based learning – there’s perhaps some merit to this, but when the attention is on the games, how much working memory is able to focus on creating deep and durable long term memories? I have seen some good looking lessons where pupils have designed a board game to play that requires them to answer knowledge based questions to progress in the game. I think the playing of the game is good, but I don’t think it makes much sense to spend any length of class time letting pupils design these games, (including drawing the pictures/logos/game boards that are required for the game).
• Choice of task/method/format etc – pupils will always choose the path of least resistance – they will opt for the easy task. Why give them the choice? Just so they can have choice? Do we really trust pupils to make the best choice for their learning? We know the tasks and we know the pupils. We (experts) can look at a set of questions and decide if they are easy or if they are hard, but pupils (novices) cannot.

Which task would pupils pick given the choice? I reckon Task A looks easier to novices, because the numbers are easier looking (smaller numbers). Task B is in fact easier even though the numbers are bigger. You have to think about different things for each of these tasks. Task A involves negative numbers and fractions, but Task B involves whole numbers only. If novices are looking for a challenge, which one would they pick?

More on Minimally Guided Learning:http://www.cogtech.usc.edu/publications/kirschner_Sweller_Clark.pdf

These are some suggestions of things that are better:

• Working just beyond their capabilities – you get better because you are challenged. The best performers in any field set themselves goals that are just beyond what they are comfortable with.
• Feeling successful early in a lesson – success leads to motivation. This doesn’t mean we make the work too easy. We need to get the level of challenge right when it comes to learning the new stuff, otherwise it isn’t worth learning. A good starting point is where pupils have already felt some success. Intrinsic motivation can even come from seeing the success somebody else has had with a task.
• Attending to their work – pupils need to give their attention to the task they are working on – we can bring this about through carefully planned and consistent routines and by minimising cognitive load – more on this later.
• Explicit instruction of new ideas – Pupils cannot figure out novel content on their own – we need to guide them fully in the initial stages of learning.
• Purposeful practice of new material – this does not mean pages and pages of questions – even just 4 or 5 questions have been shown to be effective – see graph below.
• Teacher directed 80% of the time – that’s why schools were built – explicit teaching of new ideas to a large group of novices. This explicit instruction doesn’t need to be chalk and talk the whole time. Expert teachers use a mixture of exposition, explanation, analogies, questioning, guided practice and so on to fully develop a new concept in the minds of their pupils, using their wealth of pedagogical subject knowledge to maximise the chances that pupils will be thinking about the things they need to be thinking about.
• Inquiry learning 20% of the time – We need to build in time for pupils to conjecture, behave mathematically, behave like scientists, reason using known facts, analyse etc. This can only happen with a foundation of knowledge. You can’t think critically if you have nothing to think about. We want our pupils to be able to tackle unfamiliar problems using what they have learned – this might be the ultimate goal of education. We need to provide opportunities for this.

Overlearning versus Distributed Practice

The Effects of Overlearning and Distributed Practise on the Retention of Mathematics Knowledge. DOUG ROHRER and KELLI TAYLOR

In an experiment by Rohrer and Taylor, Hi Massers were given 9 practice questions to complete and then tested on this in Week 1.
Lo Massers were given 3 practice questions to complete and then tested on this in Week 1.
After 4 weeks they were given another test on the same material.
Lo Massers are only very slightly worse off in the assessment in week 4, to the point where I think this is negligible.
The main takeaway from this (for me) is that overlearning isn’t impactful.
The authors go on to show that distributed practice (5 questions one week, 5 questions the next week) is more effective than 10 questions in one week.
Distributed practice is better than overlearning.

Further reading on this: https://pdfs.semanticscholar.org/5720/cbea1d4dc2d3da3b2ee176ee9d3ef377f294.pdf

80%/20% split of direct instruction and inquiry-based learning

This is very often referred to as the “sweet spot”. Further reading on this can be found here: https://tomneedhamteach.wordpress.com/2019/01/29/the-application-of-theory-8-propositions-that-underpin-our-approach/

Problem Solving and Arbitrary/Necessary Knowledge

What makes something a problem?

Teachers can structure the learning so that pupils can use their awareness and what is arbitrary to figure out that which is necessary.

I recently listened to Stuart Welsh (@maths180) talk about this at the La Salle Education PT Maths Conference in January and I really like the way this language makes it clear to teachers how we can get pupils to think, and what we should get them to think about. I think there are applications for this in all subjects.

Knowledge that is arbitrary can’t be worked out by a student unless they are simply told it, for example the name of a particular quadrilateral or the sum of the angles in a full turn. Knowledge that is necessary can be worked out by the student as long as they are thinking, and have access to the arbitrary knowledge. An example of necessary knowledge (again from maths!) could be that once pupils know how to draw the graph of a derived function, deducing the derivatives of the sine and cosine functions can come from their awareness of what is happening with the gradient of the functions.

All of this concerns ensuring that pupils have the necessary knowledge to tackle problems that are unfamiliar. Generic thinking skills are useless in the absence of knowledge – more on this later.

You can read more on arbitrary and necessary knowledge at: https://dspace.lboro.ac.uk/dspace-jspui/bitstream/2134/18847/3/hewitt1.pdf

Exit passes are crap*

*Wrong answers are more useful than right answers.
Exit passes used badly only measure performance. You cannot tell if a pupil has learned something in a lesson. Exit passes can be used well – just don’t expect them to tell you that your class have learned what you just taught them. They were just shown how to do it 5 minutes ago – of course they can still do it now.

Exit passes can be used as distributed practice, where perhaps the exit pass question can be about something that was taught 4 weeks ago.

There is a difference between learning and performance

Learning happens over time – performance is when I see a pupil get a question right today, after just having taught him that thing today.

Pupils get into a false sense of security if they get a page of questions right during a lesson. They think “I’ve learned this” and don’t feel then need to re-visit it. We need to train them about this and encourage distributed practice.

Learning is a change in long term memory

If nothing has been changed in Long Term Memory, nothing has been learned. We cannot measure learning easily. We can only measure performance. The sad reality is that by the time pupils get their exam results in August they will have forgotten lots of the stuff they got right in the exam. Long term memory hasn’t been changed if pupils cram for exams – this explains why many Higher Maths pupils get a strong pass at N5 but consistently make mistakes in higher questions when relying on content from N5.

Above is the Ebbinghaus Forgetting Curve. It is a useful thing to refer to when you are trying to convince pupils (or teachers) that forgetting is part of learning, and that they need to retrieve facts again and again to build durable long term memories. I refer to it often with my classes.

Retrieval Practice

Getting pupils to recall facts and knowledge (and even complete skills) from memory is a way to strengthen long term memories.

You can think of the retriever dog (stolen this from Stuart Welsh as well!). You ask yourself a question and the retriever goes away through your mind looking for the answer. He passes by relevant, related information, becoming more familiar with the path every time. The more times he retrieves the easier it becomes. Eventually he knows exactly where the information is.*

*(The brain doesn’t actually work like this, but it’s a nice wee analogy to use with pupils).

Retrieval practice can come in many forms. A few are:

• interleaving of previous skills within new skills – either by having to use previous knowledge to answer a question on the new topic or just by including a question on a previous topic among questions on a new topic.
• distributed practice – rather than having all of the practice of a new skill within the lesson where it was introduced, split the questions up across a week or more. See the Rohrer and Taylor article (linked above) for more on this.
• low stakes quizzes – Neil Tilston (@MrTilston) spoke about these at the Scottish Maths Conference (and Angus Maths and #MathsConf12 Dunfermline). Low stakes quizzes are extremely effective, when planned carefully, and can offer opportunities for pupils to take advantage of the retrieval effect. Here’s Neil’s presentations slides on low stakes assessments in maths (you can do this in any subject): https://sway.office.com/obhJhSOzOLEBZKBI?ref=Link
• regular homework, that is planned meticulously so that topics re-appear after a few weeks. Keep the skills from dropping away.
• … and many other ways are possible – teachers are always coming up with new methods for everything.

Worth noting that retrieval beats re-exposure, so it is better to have pupils think of something from memory rather than re-read it from a textbook. This is one of the reasons I don’t put formulas or exact value triangles and the like on my classroom walls.

More information on Retrieval Practice here:http://www.learningscientists.org/retrieval-practice/

Success leads to Motivation

This works. If you can build the lesson in such a way that pupils get stuff right early on, they have a better chance of pushing on and working hard on new stuff. This makes sense if you think about how you would feel if you started off a 50 minute lesson by getting the first few questions wrong straight away. This is a balancing act, though. Don’t make it too easy just so that they get it right. You need to know the pupils in the class and what they are capable of.

It’s definitely not the case that pupils need to be motivated first so that they can be successful – you show me a kid who is intrinsically motivated to solve simultaneous equations. I get my N5 class fully on board with this by letting them see that they can do it easily. For more on this (maths specific) see: https://tothereal.wordpress.com/2017/08/12/my-best-planning-part-1/ from Kris Boulton (@Kris_Boulton).

Visual, Auditory and Kinesthetic Learners

We might have a preference for one of these, but try learning the key features of a corrie by having somebody read about it to you (Geography example – you’re welcome). A diagram (visual) will help with this. Or try telling the difference between the sounds a trumpet and French horn make (if you’ve never heard them before) by looking at pictures of them (visual). Unfortunately, I still hear people talking about V/A/K, and have recently seen a study guide telling pupils to complete an online questionnaire to tell them if they are a V/A/K learner, then give advice such as “you are a visual learner so you should turn your notes into diagrams and look at the diagrams” or “as an auditory learner you will find it easier to learn by reading your notes aloud, since hearing your notes will help you learn better”. Unfortunately, there are no studies that have shown any of this to be effective. The idea is clung onto by teachers and pupils because they themselves might have a preference. There is no evidence that shows there are benefits for pupils (of any learning preference) by tailoring lessons to particular styles.

We CAN boost learning if we provide a diagram (visual) and talk about the diagram (auditory) and this works for all learners, regardless of their learning preference. If you want to learn more about this, here’s Greg Ashman talking briefly about dual coding: https://gregashman.wordpress.com/2017/07/16/we-need-to-talk-about-dual-coding/ 

More information on why VAK is wrong here: http://www.danielwillingham.com/learning-styles-faq.html

The Pyramid of Myth

This is nonsense. The numbers are too nice for this to be real, and in fact it’s not based on any scientific method. One guy liked the idea of these numbers and shared it. Then it got turned into a pyramid. Teachers love a pyramid, so it took on quickly. This was shared with me during my PGDE year, but luckily I only remembered 5% of what they said about it

The idea that you learn better when you explain a concept to somebody else seems to make sense, but how did you come to learn what you are teaching someone else? If you learned it by reading about it (10%) you can only pass on 90% of what you learned, so that’s 9%, right?

More on this here: https://theeffortfuleducator.com/2017/11/29/the-pyramid-of-myth/

Thinking Skills rely on Knowledge

You cannot think if you have nothing to think about. If you do not have the required knowledge, any amount of thinking skills will be useless.

Work out the answer to this:

An impossible question to think about if you don’t have the knowledge required. Maybe you’re not thinking hard enough. Obviously I’d expect maths teachers to solve this easily, but they have a bit of an advantage over non-maths teachers.

You have little chance doing this if you don’t know what it means, no matter how hard you think, or what thinking skills you have.

The answer is 3, in case you were wondering or want to check if you are right.

Try this one (from a History past paper):

This is a National 5 History past paper question. As somebody who knows very little about the Maid of Norway, I cannot answer this question. I cannot think critically about it either.  Although some sources are given in the exam paper, there is a requirement for “using recalled knowledge”. I’m thinking really hard, but still I have nothing.

The rest of the workshop will focus on Cognitive Load Theory (if there is time, which there probably won’t be). 

The Worked Example Effect

Presenting novices with fully worked examples (modelled by the teacher: I do, We do, You do). This helps focus novices on the key features of what a correct answer looks like and how to structure their response. These can be enhanced further by considering fading the steps in a sequence of questions so that all steps are given in the first question, all but the last step in the second, all but the last two steps in the third (and so on) until pupils eventually have to complete a full question on their own.

Reading out slides – we really mustn’t do this. I give an example of this in the presentation, but basically, pupils cannot read a slide and listen to you talking about the slide and think about the content all at the same time. It’s too much. Put a picture on the slide and talk to the class – that’s fine. We can process auditory and visual information at the same time, but we cannot read (which uses the auditory part of your working memory) and listen to someone speak (also auditory) at the same time. It’s too much. I will try to model this throughout the workshop.

The Split Attention Effect

This occurs when pupils need to look at two different sources of information to make sense of the whole thing. This can be avoided by integrating the two sources. Example below:

Now re-reading this post before publishing, I realise that I am giving an example of the split attention effect by splitting your attention across two diagrams. The complexity of this (fairly low) and what you are required to do with the diagrams (nothing, really) makes this okay, I hope.

Classroom Design

We can minimise distractions by considering the classroom environment carefully. See examples on the slides or in the blog post linked below.

Here’s a blog post I wrote about Cognitive Load Theory which goes into much more detail: https://mrallanmaths.wordpress.com/2018/05/07/cognitive-load-theory/

What I really hope will happen as a result of reading this post and/or attending the workshop is that teachers reflect on how the things that make their practice routine could be changed to be more impactful.

@maths180 provided this image that speaks volumes