Yesterday, as part of the SocMedHE20 conference, we ran a competition to guess where Hamish the Cow was. Hamish was originally knitted by me back in the old world of social contact, before we realised we’d have to run this year’s event online. I remembered him this week, so we devised a plan to photoedit him into a series of images of Glasgow and tweet them out during the day using the hashtags #WheresHamishNoo and #WinHamishTheCoo We had a lot of fun. Maybe you will too.
As a Scottish (Maths) Teacher, I have access to Glow Scotland. Within Glow, teachers have access to Microsoft tools such as Teams, OneNote, Forms and Sway. In this blog post, I will introduce you to each of these, link to examples of each and get you started on using these tools in your own practice.
I have presented a workshop on this at the Scottish Mathematical Council’s Conference (9th March 2019), and will be talking about it at the first Tay Collab Maths Conference on 23rd March 2019. If you’re attending this, you will get a decent head start by reading this blog, as the blog summarises my talk.
Let’s get started with OneNote.
OneNote is excellent.
If you’re not using it yet, you really should be.
OneNote allows you to store and share absolutely any type of digital content.
Notebook – This is the full OneNote – it contains all of the sections and pages.
Section – A section is the first level down within a Notebook. This particular Notebook you are looking at has two sections. The one you are in just now is called “Microsoft Tools on Glow”. The other one is called “Other Section”, and contains only one page, which has not yet been used.
Page – The level you are at right now, where I am typing this text and where you are reading this text is called a Page. Pages can be extended in all directions, indefinitely.
Every Notebook can have as many Sections as you like and every section can have as many Pages as you like. There’s no limit other than, I guess, the amount of storage you have in OneDrive, which is where the Notebook is saved.
Creating a new OneNote Notebook
Sign into Glow, open OneDrive and Click on New – this lets you create a new OneNote Notebook in the folder you are currently in on your OneDrive.
This will create a brand new OneNote Notebook, ready to be populated with whatever you want to populate it with.
Sharing your OneNote Notebook
To share this Notebook with you, I clicked on the three dots next to the Notebook’s name and clicked Share:
This box appeared:
And I clicked on the wee arrow next to “Only the people you specify who have this link can edit”
And clicked on “Anyone with this link”
Then, when you hit apply you can copy the link to the OneNote
That’s not easy to jot down, or remember, so I used bit.ly to create a shortened link.
The shortened link is bit.ly/MAllanSMC2019
If you want to create a OneNote Notebook and share it with a whole class, it’s probably going to be easier to use Teams…
Microsoft Teams will change the way you work.
If you’re familiar with Edmodo, Schoology, Show My Homework etc, you’ll find Teams easy to use. Even if you’re not, you’ll find Teams easy to use, because it’s really easy to use!
Watch this short video for an intro to Teams: https://support.office.com/en-us/article/video-welcome-to-microsoft-teams-b98d533f-118e-4bae-bf44-3df2470c2b12
To create a Team (and this can be staff only or Teacher and pupils) your best option is to Download Teams (it’s free). https://products.office.com/en-us/microsoft-teams/group-chat-software
If you work in a Scottish School, chances are Teams is already on your work computer.
Once you open up Teams, sign in using your Glow username and password.
This is what it looks like when I sign in:
You can see I am a member of 3 Teams (GHS Maths, Team MIEExpert Scotland and Bertha Park High – PT Team)
To create a new Team, you click on the button near the bottom left that says “Join or Create a Team” You’ll then see this:
If you want to create a Team, then it’s obvious which button to click. If you have been invited to Join a Team (and have been given a code) then that’s obvious too.
When you choose “Create Team” you’ll see this:
Choose whichever option you need. I’m going to create a Class. Give your class a Name and description (if you like).
You can then add students and other teachers to your Team:
Once the Team has been made, you can do a few things with it. Best to play around with these options and see what happens when you press the different buttons. Most of it is pretty obvious.
Clicking on “Manage Team” and then hitting “Settings” shows this page:
You can then create a Team Code by clicking “Generate Code”
Feel free to join my class (you know how to do that if you read the bit above)
At the top of the Team, when you are in “General” you can set up the Class Notebook. This is the OneNote Notebook for your Team.
When you click on “Set up a OneNote Class Notebook” you will be walked through the process. You can customise the Notebook so that it has all the sections you want it to have.
There’s a video here that will show you (pretty slowly) how this works: Teachers – Get Started with OneNote Class Notebook Creator
My OneNote Class Notebook has been created, ready for using with the class.
I have one pupil in the class (Isaac Newton) but if I had more, they would be listed below. I find it a lot easier to work with the OneNote Notebook in the full desktop version of OneNote, so I click on “Open in OneNote” at the top of the screen.
The types of content you might put into the OneNote is entirely up to you. I have an Example OneNote Notebook that you can take a look at here: bit.ly/MathsOneNoteTeachers
Using OneNote as a Planner
I have blogged about using OneNote as a planner. I no longer use a physical planner, instead choosing to use OneNote. You can find out how to set up your own Planner OneNote here: https://mrallanmaths.wordpress.com/2018/12/03/using-onenote-as-a-planner-a-few-years-on/
Immersive Reader (also known as Microsoft Learning Tools) allows pupils with additional support needs to access text in a fully supported way. The support is customisable, and the best way to learn about it is to give it a go.
You click on “View” in the toolbar then select “Immersive Reader”
This is available in OneNote, Word, PowerPoint and so on.
Sway lets you create interactive newsletters, and much more.
Here’s how to get started.
Log into Glow and open up OneDrive. You then want to click on the 9 dots at the top left of the screen:
And select Sway:
You can then choose to start a New Blank Sway:
To begin with, the Sway looks pretty boring, but you need to put some content in and choose a design:
I’ve given it a title and written a little bit of text and added a picture:
Now I’m going to choose a Design.
Click on Design in the top left corner then Styles in the top right corner:
Pick a design you like:
Then click “Play” in the top right:
You can view the Sway here: Sway
Here are some more examples of Sways that you can take a look at:
Glenrothes High School Pupil Equity Fund Update: https://sway.office.com/t4Xy1SIHNRV94wmn?ref=Link
Bertha Park High School Winter Update: https://sway.office.com/dOuvWTYJz8KIOsED?ref=Link&loc=play
N5/Higher Maths Revision: bit.ly/MathsRevisionN5H (This one is worth sharing with pupils)
Ever used Survey Monkey? Well there’s a better version of that available from Microsoft and it’s called Forms.
You can use Forms to get feedback from pupils/parents/staff for any number of things.
You can also use it to build Quizzes that can serve as assessments.
To access Forms, you click on the 9 dots at the top left in OneDrive:
“New Form” lets you make a survey. “New Quiz” works in pretty much the same way, but you also can assign points to each question and select correct answers.
The best thing to do if you want to learn more about using Forms it to use this link here: https://education.microsoft.com/courses-and-resources/courses/forms
Sharing with people outside Glow or Pupils/Staff who don’t know Usernames/Passwords
Ideally, the solution to this is to get staff and pupils to just remember their passwords. However, I have found it useful to be able to share links that work without signing in.
I use bit.ly to create shortened web links. If you sign up for a free account your can customise the links. Paying for a subscription allows you to edit and delete links once you’ve made them – I haven’t bothered to do this.
Learning More / Getting Help
You will find lots of free courses available here: https://education.microsoft.com/
Log in using your Glow username and password and you can build up a profile and collect points and badges once you have completed the courses. It’s the best way to learn about the Microsoft tools available on Glow apart from this Blog post!
OneNote intro: https://education.microsoft.com/Getting-Started-with-OneNote
I hope you found this useful.
If you have any questions that you think I might be able to answer, do get in touch on Twitter or in the comments below.
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.
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
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.
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:
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):
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:
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.
A week and a bit on from #mathsconf16, here are some thoughts that have been buzzing around in my head. I’ve tried to keep my thoughts separated into the different sessions, but there is a bit of overlap – particularly between Session 1 and Session 2.
Keynote – Craig Barton – Reflect/Expect/Check
The main thing I took away from this was to be sure to include the awkward question types from as early as possible. The first time pupils see an equation with one of the sides equal to zero shouldn’t be at National 5. They should be solving x+3=0 and 0=5-x from as early on as possible. That way these types of questions don’t seem like tricky questions. Because, really, they aren’t.
Making pupils slow down their thinking and reflect on what the answer might be to the next question in a carefully chosen sequence of questions and then check what the answer is can create a cognitive shock. Sets of well written questions can be found at Craig’s website variationtheory.com and one of the examples Craig used was Solving Linear Equations: https://variationtheory.com/2018/03/26/equations-one-step-adding-and-subtracting/ I’ve been using the resources from variationtheory.com to plan some of my lessons for next term, and they are of excellent quality. Looking forward to seeing how it goes with my classes.
Session 1 – Gary Lamb – Maths, Maths and More Maths
Gary’s provocative statement was along the lines of “Every child should be able to get a pass at N5 maths by the end of S6”. I fully agree, but the reality in my school is that this does not happen. Perhaps because we haven’t got S1-S3 right yet. We have lots of work to do on our journey towards a mastery curriculum, and this is one of the areas I am focussing on this year. Progress with this has been slow, possibly because there is so much to do and because we are trying to adapt what we already do to fit a mastery approach. I think we need to do more learning about the principles of curriculum design for a mastery model and start a new BGE course from scratch rather than trying to make what we already have fit. What I think is missing is the rigorous formative assessment cycle that Chris McGrane talked about in Session 2. See below.
Another thing Gary said was that “low ability pupils should be able to answer 5 questions quickly as long as they are the right 5 questions”. This struck a chord with me, and has made me think about whether I have the ability level right for my S2 and S3 classes. Perhaps behaviour comes into it too. Also, the idea that 5 questions answered correctly is plenty – additional questions are redundant. I really like this idea, and it has made me realise that this is one way I can get time in my lessons for retrieval practice and behaving mathematically. I also liked the way Gary talked about starter questions. Maybe we don’t need them. Maybe we should use homework for testing pre-requisites and collect this in on a Monday, review it on the Monday night and teach Tuesday’s lessons knowing what we know from this valuable piece of diagnostic assessment. I really like this idea, but can see the increased demand on teacher workload. Perhaps just a short 4 questions diagnostic assessment would suffice – similar to Neil Tilston’s Low Stakes Assessments (see https://sway.office.com/obhJhSOzOLEBZKBI)
Session 2 – Chris McGrane – Smashing The Bell Curve
The 6 most dangerous words in education – “They seemed to get it OK”. How do you know when you have taught something? How do you know that learning has taken place? We need to be as rigorous as possible. Mastery is a rigorous formative assessment cycle. I really liked Chris’ passion for getting rid of the fluff from the BGE in S1-S3. They don’t need to be doing line symmetry and rotational symmetry. “Fair enough, it’s nice to do and the beauty of mathematics and all that but the reality is that they are failing N5 maths in S5. We just don’t have time for this stuff.” This is a brave statement to make, but it makes a lot of sense to me. We need to be filling our boots with equations, substitution, expressions, integers, fractions, co-ordinates and basic area (this list was taken from Chris’ 2017 slides) as these topics are relied heavily on in N5 maths in order to give them the best chance of making new learning at N5 stick. These third level topics are the foundation of future learning. We often try to build on shaky foundations – you can build a house on sand, but it’s not going to last very long.
A task is not a rich task unless it is used richly. Brilliant, and, for those who think about the types of tasks we get pupils to do, this is probably quite an obvious point.
Both Gary and Chris talked about “teaching between the desks”, and I liked how Chris mentioned that this can be a way to give correctives bespoke to each pupil. The feedback we give pupils during a lesson has the potential to be extremely powerful because we are able to induce cognitive conflict by providing the right feedback at the right time.
A final thought from this session was when Chris said that we can reduce the need for perseverance by improving the quality of instruction. This ties together nicely with what Gary said about low ability pupils being able to answer 5 questions quickly. If they have the right questions to do after appropriately chosen examples and instruction then the need for perseverance will reduce. There is obviously a very thin line between making it too easy and making it too difficult, and I guess we learn to make better decisions about the work we set by using formative and summative assessment information. Again, “mastery is a rigorous formative assessment cycle.”
Session 3 – Kris Boulton – How To Solve Linear Equations 100% Guaranteed
I wasn’t sold on this, and was a little disappointed. Maybe I need to re-visit it when Kris blogs about it. Maybe I built it up too much because of the Simultaneous Equations lessons that Kris blogged about previously and talked about on the Mr Barton Maths Podcast. I have used Kris’ method for teaching Simultaneous Equations and found it to be extremely effective. I can see what Kris was trying to do with this session, and liked the idea of overtisation and then covertisation.
I’m not sure if I agree with the need for this level of detail when introducing solving equations, especially when pupils want to just tell you the solution when the equations are simple. A huge focus of the session seemed to be about language, and I’m all for that. I think pupils can pick up the language when the balancing method is taught explicitly the way I normally would. Perhaps the atomisation of the topic doesn’t need to happen when pupils start algebra in S1. Maybe they should be taught about identities, equations, conditional equations and so on whilst learning to work with numbers and algebra from an earlier stage, and perhaps this was what Kris intended. I did like the idea of showing how to “break” an equation and how to “repair” an equation.
I’m also not sure how easy it will be to get all of maths education using the identity symbol rather than the equality symbol when working with an identity. It would be nice, though.
Session 4 – Michael Allan – Cognitive Load Theory
I’ve seen this guy before. It was excellent.
There is enough time in secondary school for pupils to begin S1 with a very low ability in mathematics and then end S6 passing N5. I believe this to be true. I think one of the ways to achieve this is to improve the quality of teaching in all lessons. Sounds simple enough.
My current job title is Principal Teacher – Equity in Numeracy and there’s part of my current approach to delivering equity in numeracy that I don’t think is very effective. Something we did last year and something we would like to do again this year is to focus on targeted groups of pupils and put interventions in place such as targeted study sessions. What I think will make a more important difference is improving the quality of teaching in all lessons.
The La Salle Education Maths Conferences are excellent. Definitely up there with the best subject specific CPD I’ve been to in my teaching career to date. I’d like to get to one of the conferences down south, since they seem a lot bigger and busier. The buzz in the room at the beginning of #mathsconf is very exciting – perhaps it is up to Scottish Maths Teachers to make the next Scottish mathsconf even bigger. I’m looking forward to it.
In 2017, Dylan Wiliam tweeted: “I’ve come to the conclusion Sweller’s Cognitive Load Theory is the single most important thing for teachers to know http://bit.ly/2kouLOq “ (see here for original tweet).
In very simple terms, Cognitive Load Theory is about considering the limitations of pupils’ working memory at the point of initial instruction.
I decided to offer to run a workshop about Cognitive Load Theory at the Scottish Mathematical Council’s conference in Stirling in March, 2018, and this blog post will be a summary of my presentation. Note: the SMC conference was postponed due to adverse weather, and has been rescheduled for Saturday 19th May.
As well as Dylan William, Greg Ashman, Craig Barton and John Sweller, I have also read some of the work of Daisy Christodoulou and the paper by Kirschner, Sweller and Clark titled “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential and Inquiry-Based Teaching”. Another great summary of Cognitive Load Theory can be found at this link.
Take a moment to answer this question before you read on:
What are some of the things that you know?
You know a lot of stuff. Some of it is important – like date of birth, phone numbers, passwords, pin codes. Some of it is not important – like the lyrics to Aga Do. Some of it is long lasting and easy to retrieve. Some of it is to do with what is happening right now – the brightness and temperature in the room you are sitting in. Some of it is to do with what happened tens of years ago and you probably can’t remember it right now. But it’s in there… What was the name of the teacher you had in Primary 1?
You know how to write but is that the same as knowing how to speak?
You know how to multiply numbers but is that the same as knowing how to count?
Is knowing that things fall towards the ground when they are dropped the same as knowing the formulae for potential energy and kinetic energy?
David Geary (2007) talks about two different types of knowledge: Biologically Primary and Biologically Secondary. Biologically Primary Knowledge includes things like being able to speak your native language, being able to read people’s body language and being able to make sense of how things interact in our physical environment. Biologically Secondary Knowledge concerns everything that has to be learned through effort. Learning a new language, knowing your times tables and being able to tie shoelaces are examples of biologically secondary knowledge. In fact, pretty much everything we teach in our classes in school can be described as biologically secondary.
To understand cognitive load, we must define what we mean by novices and experts and consider how they differ when learning new material. Novices are people who have a very limited experience in a particular domain. Experts are extremely knowledgeable in a particular domain. Novices and Experts think and learn differently. The differences are discussed further in this post by David Didau.
When we learn new material, our working memories are stretched significantly. Everything we think about contributes to working memory. It is thought that our working memories is limited to (7±2) items. There isn’t really an agreed consensus on the number of items that can be held in working memory at any one time, and it depends on many factors such as how complicated the items are and what we are required to do with them once they are in our working memories.
The main points here are:
- our working memories are limited
- everything we must think about uses up space in working memory
- learning is defined as a change in long term memory (Kirschner, Sweller and Clark)
- learning requires effort in working memory
There is no known limit to our long term memories. In the long term memory, information is organised in schemas.
You have schemas for everything. And you can have unlimited schemas (as far as we know). They can be vast or they can be simple. My schema for solving a Rubik’s cube is, like most of yours I am sure, vast and complex. But my schema for crochet patterns is very small – there are, I am assured, lots of different abbreviations used for different stitches, and these vary depending on the country where the pattern originated from etc.
A person with a highly developed schema for, say, solving simple problems involving differentiation (i.e. just finding the derivative of lots of functions) will have a more success learning how to find the stationary points of a function or the equation of a tangent to a function than a person who does not have that schema as well developed. A really good way to develop schemas is through practice of the component parts.
How can we tell if a student is a novice or an expert? We need to use formative assessment and perhaps diagnostic assessment before the first lesson in a particular topic. Note that a student who is an expert in one domain may not be an expert in another.
There are three main types of cognitive load:
Extraneous Load: caused by inappropriate instructional designs that ignore working memory limits and fail to focus working resources on schema construction or automation. This type of load is mostly environmental and always unhelpful for learning. This may include noise, unhelpful or unnecessary pictures/graphics/animations and poorly structured learning activities.
Intrinsic Load: caused by the natural complexity and structure of the material that must be processed. Necessary for learning – it is what makes it worth learning. Some things are harder to learn than others, based on their complexity and the prior knowledge of the learner. 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 Capital means) 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 in that specific domain.
Germane Load: caused by effortful learning, resulting in schema construction and automation. This is the effort required to actually learn material (if our definition of learning is “a change in long term memory”).
As teachers (or “instructional designers”) we need to ensure we do the following:
- Minimise extraneous load – consider the environment and anything you make students think about that isn’t to do with the new learning.
- Minimise intrinsic load – break down the problem for novices. Present small parts at a time before approaching a whole problem that requires several new steps.
- Maximise germane load – by reducing extraneous load and making the intrinsic load more manageable for learners, schema construction is much easier.
The Phonological Loop
The part of the working memory that processes written and spoken material is called the Phonological Loop. When you read something, you generate a sound in your head. When you listen to someone speak this is also processed as a sound. If you are trying to read something while someone is speaking, you get cognitively overloaded straight away. As teachers, we should avoid things like reading out slides or, even worse, talking about slides that have text on them while the students are reading the slides. For novices who are not familiar with the content, this will cause them excessive cognitive load. More on this when we get to the modality effect.
Cognitive Load Effects
I will mention 6 cognitive load effects briefly, and give some examples of each one.
- Worked Example
- Expertise Reversal
- Split Attention
- Goal Free
The Worked Example Effect
At the point of initial instruction, novices benefit from seeing worked examples. An effective strategy is to present a worked example to the class (you can use questioning about the parts that they can already do – this isn’t necessarily chalk and talk) followed by the class completing a very similar problem for themselves. When I do this, my classes don’t copy the worked example, but they do write their solutions to the problems they will try into their notes. When we discuss the problem as a class and go over the correct solution (or a correct solution) they then have the chance to change their answers. The worked example should allow all pupils who are paying attention the chance to get the problem correct without too much of a demand on their working memories. This allows them to see the ways that the parts of the example interact and allows easier formation of schemas. Some examples of worked examples are given below:
Questioning and discussion of steps is what makes this effective. Cannot just be pupils following the same steps without using their brains.
The Expertise Reversal Effect
It has been shown that worked examples are more useful for novices than they are for experts. As expertise grows through experience, worked examples are no longer needed, and in fact can cause unnecessary cognitive load (extrinsic) for experts. Instead of presenting experts in a particular domain with worked examples, it is more beneficial to have them solving problems. Learning through problems is only possible when a strong foundation of knowledge has been built up by the student.
The Redundancy Effect
Any information that is additional to the problem is redundant information. For example, when students are solving geometry problems, an annotated diagram alongside text that tells you the lengths of the sides and the sizes of the angles (which are already marked on the diagram). In this case one of these sources of information is redundant, since the problem could be fully understood with just one of them.
Here is an example:
We can cope with this as experts, because we look at this question and instantly think “Pythagoras!” but remember that novices do not work in the same way. A novice needs to process everything in the problem.
Other sources of redundant information include teachers reading out slides and drawings/images on slides and worksheets that have little to do with the problem. At the point of initial instruction, these additional things are not helpful for learning, and so they should be avoided.
Some teachers tell me that the reason they read out slides is that they do not trust their pupils to read the slides for themselves. A simple fix in this case is to simply put a picture on the slide that represents the idea being discussed and to simply say the things that would have been text on the slide.
The Split Attention Effect
This occurs when two or more sources of information must be integrated in order to make sense of the whole problem or idea. This can easily be eliminated by integrating the two sources. This differs from the redundancy effect in that both pieces of information must be thought of together to make sense of the whole.
Here is an example from a Higher Maths past paper:
A simple fix:
The equations could easily be added to the diagram, thus removing the need to interpret two sources of information to make sense of the whole.
The Modality Effect
This concerns the way that new information is presented, whether it be auditory, written (which is also auditory by the time it is processed) or visual. 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. 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.
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 – you get the split attention effect if they have to read about the diagram while looking at the diagram.
The Goal Free Effect
This effect concerns the idea of “problem solving search”. When novices are presented with a problem such as the one on the left in the diagram below, they tend to think of the whole problem in one go and suffer cognitive overload as a result.
Taking the specific goal out of the problem and re-framing it as is shown on the right eliminates problem solving search so that the novice learner may use any angle facts they know to fill in as many angles as they can. When the problem is framed this way, novices are able to make sense of the individual steps they take, and this allows them to assimilate long term memories of angle facts.
The idea that novices can learn new knowledge through discovery learning is flawed due to what we know from Cognitive Load Theory. Kirschner, Sweller and Clark (2006) state that “The goal of instruction…is to give learners specific guidance about how to cognitively manipulate information in ways that are consistent with a learning goal, and store the result in long-term memory”. Discovery Learning does not easily facilitate this. I used to attempt to teach Pythagoras’ Theorem through a discovery task. The class would investigate the relationship by matching around 15 squares to the correct 5 triangles by finding the sides that matched. No relationship yet discovered. They then had to measure the lengths of the sides of each square and work out the areas of each square.
Only a small number of pupils in the class managed to calculate the correct areas, and nobody noticed that the two small squares had a combined area that was equal to that of the large square. So I reluctantly told them that this relationship would exist. “It doesn’t work on mine! 3.1 squared plus 3.9 squared doesn’t make 5.2 squared”. If only they could measure accurately. This type of discovery investigation task looks lovely – I was observed by a depute head teacher doing it with a second year class. His comments were “You could just feel the learning in the room – they are so engaged”. No you couldn’t and their engagement was with glue sticks and scissors. They only learned Pythagoras’ Theorem in the last few minutes when I explained it quickly before the bell. They still were not convinced that it works because for their squares and triangles it didn’t work. It was a discovery learning failure. I now start the Pythagoras’ Theorem topic by telling them that the two small squares have the same total area as the large square and I demonstrate it with a few Pythagorean Triples (3, 4, 5), (5, 12, 13). We sketch a diagram of a right-angled triangle with three squares every time we answer a question. The success rate is much higher and they feel like they are doing pretty advanced maths. The paper by Kirschner, Sweller and Clark in the references list is well worth a read for more on this, as is listening to Greg Ashman and Daisy Christodoulou on the @mrbartonmaths podcast.
This is a great way for pupils to apply what they have already learned in different and unfamiliar contexts. The trouble is, often interdisciplinary learning attempts to teach new content through interdisciplinary learning projects. It is not fair on novices to expect them to synthesise new material at the point of initial instruction. I’m not saying that Interdisciplinary Learning is a bad idea. What I am saying is that, when designing learning experiences, we need to be mindful of the fact that we are experts and that our pupils are novices.
Classroom displays often contribute to the extraneous load we impose on our learners, particularly when the displays are engaging. With this in mind, I have removed as much clutter as I could from the walls in my classroom. All of my displays are now on the back wall (my pupils sit in rows, facing the front). The only things worth looking at on the wall at the front of my classroom are the two whiteboards. Examples of pupils’ work are shown using the visualiser and do not become wallpaper on my walls. The walls at the side are plain, with the exception of the fire evacuation instructions. Perhaps you’re not ready to give up your classroom displays, but please consider what they add to the learning in your classroom. If it’s formulas for pupils to use, are you happy that they don’t need to commit these to their long term memories, and instead just rely on them being on the wall?
If you only remember three things from this blog post:
- Novices and experts learn differently
- Working memory is limited
- Effects: Worked Examples, Redundancy, Split-Attention, Modality, Goal-Free
Barton, C. (2017) ‘Greg Ashman – Cognitive Load Theory and Direct Instruction vs Inquiry Based Learning‘, Mr Barton Maths Podcast.
Barton, C. (2017) ‘Daisy Christodoulou – Assessment, Multiple Choice Questions, 7 Myths about Education‘, Mr Barton Maths Podcast.
Barton, C. (2018). How I Wish I’d Taught Maths. John Catt Educational Ltd. Woodbridge.
Christodoulou, D. (2014) Seven Myths About Education. Routledge. Oxon.
Didau, D. (2018). When do novices become experts?. [Blog] The Learning Spy. Available at: http://www.learningspy.co.uk/psychology/novices-become-experts/ [Accessed 7 May 2018].
Geary, D.,(2007). Educating the Evolved Mind: Conceptual Foundations for an Evolutionary Educational Psychology. In: Carlson, J. S. & Levin, J. R. eds. Educating the Evolved Mind. North Carolina: Information Age Publishing, Inc, pp1-100. Available online at: http://evolution.binghamton.edu/evos/wp-content/uploads/2008/11/Geary01.pdf
Kirschner, P. A., Sweller, J, & Clark, R. E., (2006). Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential and Inquiry-Based Teaching. Educational Psychologist, 41(2), 75–86 Available online at: http://www.cogtech.usc.edu/publications/kirschner_Sweller_Clark.pdf
NSW Department of Education (2017). Cognitive load theory: Research that teachers really need to understand. Sydney: Centre for Education Statistics and Evaluation.
Sweller, J. Story of a Research Program. Education Review. Available online at: http://edrev.asu.edu/edrev/index.php/ER/article/viewFile/2025/545
Willingham, D. T. (2009) Why Don’t Students Like School? Jossey-Bass. San Francisco.
On Friday 26th June I attended the Entrust Primary Languages Conference in Stafford, organised and led by Lorna Harvey. Entitled ‘We’re on our way’, the day began with an excellent keynote from Clare Seccombe aka @valleseco and genius behind LightBulbLanguages.
Sharing a title with the conference, Clare shared her ideas on the journeys involved in primary language learning – for the child, the teacher and as a nation. I love how Clare can express her ideas so well in images. I’ve tried to capture some of them in my sketch note below.
You can read Clare’s presentation for yourself here – We’re on our way!
There were a number of workshops during the day – I attended one on a cluster of schools who use a ‘language investigators’ approach to language learning in Y1-2 and 3-4 before focussing on one language in Y6. My sketch note is below along with a few images.
|Plan for Y1-2||I loved the pizza/paella Italian/Spanish numbers!|
The day was very much a celebration of a project between Stafford and Burgundy, and I’d been asked to speak after lunch about a similar partnership in which I’d been involved, between Birmingham and Barcelona. It was wonderful to prepare my presentation as it sparked so many amazing memories and caused me to reflect on where we’ve gone since the (official) end of the partnership. Below you can see my presentation (although without the video clips I’m afraid) and Clare kindly sketch noted it for me.
— Clare Seccombe (@valleseco) June 26, 2015
We had a brilliant presentation from pupils about their experiences as well as a culinary lesson based on tasting and making mustard. Great fun and with clear language goals too!
I finished the day by presenting about using technology to enhance language learning. You can see my presentation below and access the notes, tutorials etc here.
A great day – not much tweeting as I was too busy sketching or making mustard as was Clare, but here’s the Storify of the tweets anyway.
A great day – thanks Lorna!
PS Clare’s workshop – Be a crafty language teacher is explained here too!
On June 16th I travelled to London for a day long conference organised by UnderstandingModernGov on the subject of Primary Languages – “Successfully implement the new Primary Modern Foreign Languages curriculum”. It was great to see Janet, Sylvie, Nadine and Julie, and to meet all the delegates to spend a day exploring how we can effectively plan, manage and deliver languages to primary aged pupils.
I sketch noted all the sessions as you can see below.
Additionally, you can see what Janet said on her blog.
And here’s the Storify of tweets from the day!