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MIND THE LOAD:�SMARTER MATHS TEACHING WITH COGNITIVE SCIENCE

Michael Allan

Morgan Academy, Dundee

mrallanmaths@gmail.com mallan590@dundeeschools.scot

@mrallanmaths on X (Twitter)

Please use the Notes for each slide to find out what each slide means. (View, Notes)

Please feel free to send any feedback to me. I am particularly interested in knowing if and how any of this impacts on your classroom practice.

My name is Michael Allan and I am a maths teacher at Morgan Academy in Dundee. I have taught there since June 2024, and previously taught at Glenrothes High School in Fife and briefly spent time as PT Maths at Bertha Park High School in Perth and Kinross.

This session is an introduction to Cognitive Load Theory for Maths Teachers and will delve into other areas of cognitive science.

The effects discussed are transferable to any subject and are important for primary and secondary teachers. Most of my examples will be from a maths background. I do not claim to be an expert in cognitive load theory or any of the ideas shared. I have not conducted any research or written any papers on these ideas. I’m interested in it, and anything that can improve teaching. If you’ve been listening to the @mrbartonmaths podcasts and reading Craig Barton’s book and following a lot of the recent discussion on Twitter then a lot of what you hear today may sound familiar. Zach Groshell, Blake Harvard, Adam Boxer, Greg Ashman, Richard Mayer… all of these people and more have helped me to develop my understanding of the ideas I share today. Please do ask questions if you like, but wait until appropriate times. I don’t want to talk at you for the full 50 minutes but I do have a lot to say. The slides will be made available and if you want to tweet (X) me or email me with any questions you may have, if you think I can answer them, please do.

AIMS of the workshop…

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LEARNING INTENTIONS

Cognitive Load Theory – Overview/Reminder
Attention and the environment
Generative Learning Strategies
Conceptual Learning
Pre-Teaching
Retrieval and Spaced Practice
Explicit Instruction

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THE MAIN IDEA

Pupils are novices; we need to make the path to learning as clear as possible for them.

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PODCASTS

Mr Barton Maths��
Progressively Incorrect (Zach Groshell)��
Education Research Reading Room (Oli Lovell)��
They Behave For Me (Adam Boxer)

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BOOKS

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PUBLICATIONS

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BLOG POSTS (MY OWN)

https://mrallanmaths.wordpress.com/category/cognitive-load-theory/

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WHY ARE YOU HERE?

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SET A GOAL TODAY

“I want to explain things more clearly.”

“I want to help my pupils remember the things I taught them last month/term.”

“I want to help my pupils develop better study habits.”

“I want to…

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NOVICES AND EXPERTS

As experts, we know much more than our pupils know.

When teaching, we must remember that our pupils are not experts.

Novices and experts categorise problems differently.

Pupils are novices. Even when they have learned something, they are still really novices.

In a paper titled "Categorization and Representation of Physics Problems by Experts and Novices.”, Michelene Chi, Paul Feltovich, and Robert Glaser from in 1981 gave physics undergraduate and physics PHD students a selection of problems to categorise. No instruction as to how they were to categorise the problems. The undergraduates categorised the problems based on the surface features. The PHD students categorised the problems based on the physics principles required to solve the problem i.e. deeper structure.

Think about when your students first ask to do Past Papers – Do we say “Do the questions you’ve learned how to do and skip the ones we haven’t covered yet.” How do they know which ones they can’t do? A trig equation might look OK but it may require the double angle formulae or wave function, which you have not covered yet.

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Want to feel like an expert?...

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Working Memory

Limited to 5-9 things at a time.

Takeaway Order (Zach Groshell).

Connected ideas.

Long term memory advantage.

It is thought that you can hold on to somewhere between 5 and 9 items of knowledge in your head at one time before it gets too difficult.

Telephone numbers are the length they are for this reason. Most have an area code, which for locals is stored as one piece of information. Then the number has 5 or 6 digits. Easy enough to hold in your memory (at least for as long as it takes you to find a pen and write the number down).

Imagine placing an order for a takeaway over the phone. If it is just you and one or two others you are ordering for, you can manage this easily. If you have a house full of people and are taking the orders for 6 or 7 people, you probably write the order down before you phone. Going to the shops for 2 or 3 things? No problem. Doing the big shop? Better write a list.

When ideas are connected, it is easier to remember them.

If you hold something in your long term memory (such as the area code for a Dundee telephone number (01382)) then you have an advantage. If you already know the procedure for using Pythagoras’ Theorem in 2D, applying it in 3D is a doddle because you are able to lean heavily on your long term memory.

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Cognitive Load Theory

Learning new material is difficult for novices.

All the things we attend to when learning new material contribute to cognitive load.

Working memory is limited (a small number of items) and is easily overloaded by poor instructional design.

A novice is someone who is not already trained in the domain in question. So, that’s the vast majority of pupils in our classes.

Novices do not have well developed schemas to connect new learning to. Novices and experts learn in different ways.

If a pupil is trying to calculate the area of a triangle with base 6 and height 7 units, they need to work out 6 times 7 and know to divide that by 2. If 6x7 is a struggle for them then the whole process becomes very difficult. They get to the answer of 42 but do not know what to do now (or even what this means in the context of the problem) because their working memory is overloaded.

Experts have better developed schemas (due to experience of solving similar and related problems – this is called episodic knowledge).

Working memory is limited, and when we are asked to make the items we are holding in our working memory interact in some way we put further burden on the working memory unless our long term memory can help out.

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Extraneous Load
Intrinsic Load
Germane Load

Environmental – unhelpful for learning.

Some things are harder to learn than others

Effort required to actually learn something.

These three different types of cognitive load work together when we are learning something new.

Extraneous Load: noise, unhelpful or unnecessary pictures/graphics/animations, the environment e.g. the classroom or the room we are studying in at home.

Intrinsic Load: caused by how some things are harder to learn than others, based on their complexity. Learning capital cities is pretty easy – I tell you that Paris is the capital of France, you understand what I mean (as long as you know that France is a country and you have an idea of what a Capital city is) but if I tell you that the area under the curve sinx from 0 to pi/2 is 1 square unit you need to know quite a few things in order to understand it. The intrinsic load depends on two main factors – the complexity of the material and how knowledgeable you already are. Asking pupils to answer questions that synthesise key skills too early in the acquisition of knowledge required to access the problem is a bad idea.

Germane load is good – we want that – it’s the part of the trio that is responsible for helping us organise our experiences into long term memories and facilitates schema construction.

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Eradicate Extraneous Load

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Optimise Intrinsic Load

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Maximise Germane Load

Good load – we want to make it as easy as possible for learners to get to the point during instruction where things make sense and schema construction can happen without distraction or without too much effort.

Germane Load is “caused by a supportive instructional design and is helpful for effective learning”

Problem solving search hinders germane load – presenting novices with problems they can’t do too early during instruction causes them to spend time trying to find a solution, and this is difficult for novices who do not have a wealth of experience to fall back on, so they focus on solving the problem (and might manage to solve it successfully) but may not actually be able to learn anything from it.

Greg Ashman talks about pupils who conduct experiments in science – they don’t learn anything because their minds are occupied with questions such as where are the clamps, how do I set up the tripod, where do I record the results…

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Reading Out Slides

Many people who present information via PowerPoint (including many teachers) make this mistake: they read out their slides. There are two reasons why this is a bad idea. One is the redundancy effect and one is the phonological loop.

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This is even worse

It’s worse if the words you are hearing are different compared to the words that are on the slide. If you are asked to read the slide while the presenter talks about something else it’s not only infuriating but leads to overload straight away.

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Design slides with these in mind:

Use plain colours and sensible fonts
No moving graphics at the same time as you want them to think about something else
Use images carefully
Limit your use of text if you can speak instead

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Design slides with these in mind:

Use plain colours and clear fonts
No moving graphics at the same time as you want them to think about something else
Use images carefully

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WHAT TO DO

Reduce text on slides
Give time for audience to read
Use images and narrate – Dual Coding
Use animations to bring into view/focus
Don’t read out your slides
Generate diagrams in real time, by hand

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FLMOP

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Some Cognitive Load Theory Effects

Worked Example
Redundancy
Split Attention
Modality
Goal Free

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CLT Effect: Worked Example

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CLT Effect: Worked Example

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CLT Effect: Worked Example

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WHAT TO DO

Split your board in half
Present the example and problem together
Complete the example fully and interactively
Give time for pupils to do the problem
Repeat, gradually increasing the difficulty

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FADED EXAMPLES – RICHARD GLENNIE

Calculate the area of each triangle.

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The Redundancy Effect

Text and a diagram, where both say the same thing.

*Listen for this one.*

Redundancy can be a major cause for instructional failure.

The text is redundant. Or the diagram is redundant. I don’t know – do you want the pupils to have to generate the diagram from the text – in which case miss out the diagram. Does the text add any value to the diagram anyway? Does the diagram say everything we need it to say? Perhaps miss out the text. (If there is mathematical notation in the diagram (equal sides, parallel sides, right angle etc) then the pupils must be familiar with these if the text is omitted.)

Many exam questions have this – examples to follow.

Reading out the slides is redundant also – and very difficult to not do as a presenter. The point that says *listen for this one* is where I am telling you about the effect of not needing to read out slides. You’re listening to me speaking and you understand what I mean so there is no need for everything I am going to say to be on the slide all the time. (I use the slides for structure and for cues for me more than anything). It’s very hard to give a presentation without putting loads of information on the slides. Also, the information I am presenting isn’t confusing to you (I hope) – you understand it.

Providing unnecessary information may seem at worst harmless. Redundancy can be a major cause of instructional failure – this is because we make students pay attention to things they don’t need to pay attention to at the cost of them losing out on space in their working memory that could be take up by building schemas (germane load).

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CLT Effect: Redundancy

This is an example of the redundancy effect. It is not necessary to state the distances in text alongside the diagram when pupils can clearly get the meaning from the diagram alone.

As experts, we’re not bothered by this. But we are not novices. Novices need to process everything so that they can decide what is important and what is not. We have episodic knowledge – we know how to approach a variety of problems and are experienced enough. Do you ever answer an exam question or textbook question that is “in context”, finish the solution then need to check what you have actually solved? (I once showed this image and the SQA question writer who made the question was IN THE AUDIENCE!! – this is an example of anecdotal extraneous load – telling you this doesn’t add anything (other than giving me the opportunity to talk about how bad it is to add nice anecdotes to your teaching).

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CLT Effect: Redundancy

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The Split Attention Effect

Two or more sources of information which need to be thought of at the same time

Too much for the working memory

Integrating sources of information can eliminate this.

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CLT Effect: Split Attention

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CLT Effect: Split Attention

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Listen + Look 🡨 This is fine

Listen + Listen 🡨 You can’t do it

Look + Look 🡨 You can’t do it

CLT Effect: Modality

We can cope with listening to speech and seeing something in a diagram at the same time without impacting on cognitive load. This is better than integrating text and a diagram. Use of interactive online resources such as Desoms or Geogebra is a good example. I might show transformation of functions on Desmos. My pupils can look at things happening and listen to me describing it. That’s OK.

Have you ever been on a museum tour with a headphone set? This is effective because it is easier than reading text then looking at things. Yes, it’s saving us from having to read – effort - but also it cuts down on reading (with eyes) and seeing the exhibits (with eyes).

What we can’t do is listen to something while listening to something else. We can’t read something (which uses visual channel and auditory channel) and listen to someone speaking or listen to music (some people say they can – adults, I wouldn’t argue with you. For children, they absolutely should not).

A diagram for a question (or to demonstrate a relationship) that would normally have text alongside it can be replaced with just the diagram and the teacher narrating over the top. If you have pupils who need the written form too (not all of them will) then you can give them a written copy, but it will be better for everyone else if they hear the question and see the diagram rather than having the text, which you will probably redundantly read out and the diagram too – split attention when you’re not reading.

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