Author Archives: mrallanmaths

Microsoft Tools on Glow⤴


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.

1 New OneNote

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:

2 Share

This box appeared:

3 Link

And I clicked on the wee arrow next to “Only the people you specify who have this link can edit”

4 Anyone With

And clicked on “Anyone with this link”

5 Anyone With

Then, when you hit apply you can copy the link to the OneNote

The link looks like this:

That’s not easy to jot down, or remember, so I used to create a shortened link.

The shortened link is

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:

To create a Team (and this can be staff only or Teacher and pupils) your best option is to Download Teams (it’s free).

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:1 Landing

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:

2 Join or Create

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:

3 Team Options

Choose whichever option you need. I’m going to create a Class. Give your class a Name and description (if you like).

4 name Team

You can then add students and other teachers to your Team:

5 Add People

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.

6 Manage Settings

Clicking on “Manage Team” and then hitting “Settings” shows this page:

7 Settings

You can then create a Team Code by clicking “Generate Code”

8 Join 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.

9 Set up Onenote

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.

91 Open In OneNote

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:

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:

Immersive Reader

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:

1 Waffle

And select Sway:

2 Sway

You can then choose to start a New Blank Sway:

3 New Blank

To begin with, the Sway looks pretty boring, but you need to put some content in and choose a design:

4 Title

I’ve given it a title and written a little bit of text and added a picture:

5 Some text

Now I’m going to choose a Design.

Click on Design in the top left corner then Styles in the top right corner:

6 Design

Pick a design you like:

7 New Design

Then click “Play” in the top right:

8 Play

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:

Bertha Park High School Winter Update:

N5/Higher Maths Revision:  (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:

2 New Form or Quiz.png

“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:

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 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:

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:

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.


What can teachers do to maximise pupil learning?⤴


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.
1. Task A Task B

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:

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

2. Hi Masters and Lo Masters

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:

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:

3. Impact of Direct v Inquiry

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:

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.

4. Ebbinghaus

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):
  • 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:

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: from Kris Boulton (@Kris_Boulton).

Visual, Auditory and Kinesthetic Learners

10 VAK

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: 

More information on why VAK is wrong here:

The Pyramid of Myth

5. 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:

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:

6. Integral

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):

7. History Q

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:

8. Split Attention

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:

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.

9. Routines and New Things

@maths180 provided this image that speaks volumes





Using OneNote as a Planner – A few years on…⤴


I have been using OneNote as my planner since October 2015. This has made me more organised and has made it easier for me to plan lessons. In this post, I will give some examples of my planning process through using OneNote and walk you through the steps to follow so that you can get started using OneNote for your planning too.

1. Header

First of all, you need to set up a OneNote Notebook.

Log into Glow and go to OneDrive. Click “New” and select “OneNote Notebook”. Give it a sensible name such as “2018-19 Mr Allan Planner” or even just “2018-19 Mr Allan”. Eventually you will end up with several planner OneNotes over time.

2. On Glow

Once the Notebook is created you need to add some sections to the OneNote Notebook.

Your Notebook will load with one section called “New Section” and will be ready for you to get creative. Here are some of the Sections that my 2018-19 Planner OneNote contains, and some examples of how I use each one:

  • Planner (obviously) – more on this section later.
  • Starters – this section allows me to save my Powerpoints for starter questions for each class.
  • Homework – this section is used for saving homework tasks and a record of homework completion
  • Class Names – I have 6 Sections (one for each class) which contains information about the pupils in each class – ASN info, attainment info, Reports, Course plan to be followed for each class, seating plans, etc. You can probably think of lots of uses for these sections
  • CLPL + Stuff – this section contains my CPD record for the year, including links to blogs/articles/websites that I would like to get round to reading(!) and can also include reflections. I also save any resources or notes taken during CPD courses. This bank of information on my CPD for the year (and over years if I look back through my other planners) makes it very easy to complete my PRD and to complete my Learning Log. I also use this section to keep note of passwords (in a coded way, obviously) and usernames for all of the different online platforms that we need to use.
  • Equity In Numeracy – This section is used for saving my resources and evidence of progress in relation to my role as Principal Teacher Equity in Numeracy. It’s really helpful keeping everything in one place.
  • EMIF 2018 – This section contains all the resources for Enterprising Mathematics in Fife 2018.
  • Reading Group – I run a Professional Reading and Reflection Group in my school. This section allows me to keep track of the different chapters that I think should be included in future weeks, reflections on the reading and notes about our discussion. I also keep a note of the names of staff who reply to my monthly email saying they want to attend.

You might come up with other uses for OneNote – that’s what it’s all about.

Now that you have the sections you think you will need (and you can always add more as the year goes on) you need to build up the planner pages.

I copied an ordinary teacher’s planner to build the template of my planner pages. The basic page looks like this:

3. Basic Planner

The squares next to the period numbers are tick boxes. Once I have planned that lesson I click on the box and that means I don’t need to worry about that lesson until I come to teach it.

I have a different template for the other days of the week, and include the class names. I keep the heading as “Mon ” or “Tues ” etc. Then, once I have a whole week with the class names in the right places, I copy the template for the whole week (5 pages) and paste it below the templates.

4. Week

Then, I manually (it doesn’t take long!) type in the dates. So “Mon ” becomes “Mon 4th June” and so on. Spending a bit of time repeating these steps until the whole year has been built up doesn’t take too long. So far, I have not found a way to make this automatically happen. If anybody can, please share. Note that it is important to put the class names in first, before copying the pages (as this saves you having to type the class names in every day).

Having the whole year in the planner section at the beginning of the year means that if somebody suggests a meeting at the end of the day on the 29th of January, I can quickly check my planner and add it to the page. I guess I should be using the Outlook calendar better – something I will address in the future.

The Lesson Planned column is used for a quick description of the lesson. I have seen myself just type a few words (e.g. “Area of Triangle”) but have also used this cell to include examples of questions I want to ask, screenshots of resources I might use, web links to resources online, ideas for starter questions, reminders to follow up with pupils about behaviour or homework and so on. I also use this column to remind myself of the things I need to do during my non-contact periods, such as keeping myself organised for meetings or reminding myself that I really should make a start to my reports.

The Resource column is possibly the most useful one. OneNote is able to store any type of file in a drag and drop way. You can save a Powerpoint (or ANY file type) like this:

5. Powerpoint

Using OneNote on a PC, if I open the Powerpoint from OneNote and make some changes to the file, then click save, it automatically saves the new version to the OneNote. This means I can plan at home and switch on my PC at work and my lesson is waiting there for me. This works for any type of file – if you have it saved to OneNote and open it then edit it then click on save it will update automatically. And it will be available on all of your devices. Really clever. (Note that this automatic saving feature doesn’t work in OneNote on a Mac. My way around this is to have a folder on my Desktop called “Move to OneNote” where I save the Powerpoint from OneNote, edit it, save it back to the Desktop then copy it back to OneNote. I really should use my Microsoft Surface more!

If you go to you will find, among other things, a template for a week that can easily be edited.

Happy to try to answer questions, or to support people getting started using OneNote. Feel free to get in touch, or to share how you are using OneNote to help you keep yourself organised. Get in touch on Twitter or in the comments.



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 and one of the examples Craig used was Solving Linear Equations: I’ve been using the resources from 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

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.

Final Thoughts

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.



Clear and consistent routines are a significant part of the whole story when it comes to classroom management and behaviour management. Obviously positive relationships and correct support structures are also important, but this post is about routines.

Pupils in my S1-3 classes have lessons that start as follows. Our lessons are all 50 minutes long.

Before they arrive (or just as they are arriving): I put their Numeracy Ninja books and yellow starter question jotters on their desks. They sit in rows of 5, so often this just involves placing two bundles at the end of each row. This takes me around 1 minute. Below I have taken the time to place them on the correct desks. I do this if I don’t have a class the period before.

First 2 minutes: Pupils arriving and getting “organised”. This is very specific. You are not organised until you have a pen/pencil and your maths jotter out of your bag and on your desk. You also need your outside jacket/jumper/hoodie off and your tie on. If you don’t have a jotter you need to ask for a piece of paper and if you don’t have something to write with you need to borrow a pencil straight away. I record a list of names of pupils on an A3 whiteboard on my desk just to remind me to get the pencil back. Sometimes this all takes longer than 2 minutes and sometimes less time depending on how far pupils have to travel. If you come in and waste time, and I catch you doing so, you are given a warning.

Next 5 minutes: Pupils are working on Numeracy Ninjas (see: in silence. The teachers in our department believe that this daily practice of basic numeracy skills is raising the standards of numeracy skills across all classes, so this is the second year we have run it with all BGE classes with the exception of the top sets in S3. I use the time they are completing these questions to go round and double check that everyone has their red maths jotter out, is in correct uniform and is coping with the questions, offering quick help if needed and focussing attention if pupils’ eyes wander and they begin to think about striking up a conversation. If you are stuck, move on to another question. Exactly when there are two minutes remaining on the PowerPoint timer I freeze the screen and start a 2 minute countdown on my Ikea kitchen timer. This allows me to quickly complete the electronic register and check if any urgent emails have been sent (this is probably not necessary, but only costs me seconds). I then spend the remaining time circulating the class. I now have the choice of surreptitiously switching off my Ikea timer (which I carry with me) if I need to extend the time because I might be talking with a pupil about a question or having a quiet word about their negative behaviour at the very beginning of the lesson. This works really well.

Next 2-3 minutes: I read out the answers to the Numeracy Ninjas questions. This used to take much longer, but we are beginning to get faster. The third set of 10 questions (Key Skills) usually take the longest, because I discuss the answers/solutions to most of the questions quickly. Any more involved questions might be gone over in full at the board if I have noticed that several pupils are stuck. If one of the Key Skills is relevant for today’s lesson, I will definitely go over it quickly. I don’t allow this to take very long at all and, like I say, this has taken time to get fast. Not all of the pupils will have attempted the Key Skills questions, so they used to think this meant it was okay for them to close their Numeracy Ninjas booklets and doodle on the cover while they wait. This has taken weeks to get right, but now, because I insist on it, all pupils wait and listen to the explanation/questioning of how these questions are answered and are expected to copy the methods for questions we discuss that they struggled with so that they can attempt the same question type when it next appears (probably next day).

Once we have finished going through the answers: Pupils record their score and belt colour then turn their booklet over and fill in the table that tracks their progress over the term. The Numeracy Ninja booklets are then passed to the end of the row for me to collect and we are then onto our yellow starter question jotters. I already have the starter questions (usually 3 or 4 short questions) prepared on the smart board on a separate PowerPoint, ready to go. These consist of questions that will serve two purposes: revise previously taught topics and prepare pupils for our upcoming lesson. For example, yesterday my S3 class (Third/Fourth Level) had to write out the first 8 multiples of 125. In the lesson, we were learning how to change a decimal number to a fraction. Changing 0.625 to a fraction was a doddle because they already had the multiples of 125 to hand, allowing them to focus on the new learning rather than on “what does 625 divide by that 1000 also divides by?”.

Next 5 minutes: Starter Questions. Pupils answer the starter questions quietly. The advantage to having starter question jotters is that the starters all stay together in one place so that if yesterday’s question 1 was “Change 0.34 to a fraction” and today’s is “Change 0.52 to a fraction” they should have written down how to do yesterday’s question when we went over it. This will help them today. I have only been using the yellow starter jotters since the start of this term, but am already finding pupils using them effectively in this way. While they are working on these questions I am circulating, looking at the work they are doing and checking for misconceptions to point out when we go over the questions. I’m learning who is stuck, how confident the class are as a whole and how much more input they need on the basics before we can start today’s lesson. While I am circulating I will also collect the Numeracy Ninja books. Why not get a pupil to collect them in? Well, I don’t want a pupil out of their seat and if they are collecting the books for me this means they won’t be answering the starter questions. They just don’t have time to collect the books, and I know I’m going to be circulating anyway. Some teachers will probably believe that it is the pupils’ job to distribute and collect resources. I disagree.

Next 3 minutes: I quickly go over the starter questions. I don’t need to get pupils to share their answers because I have already circulated and know what they can and can’t do. I go over the questions and pupils mark their own, making sure to write down a full solution if they have not answered the question yet. Once we have finished going over these, the yellow jotters are passed to the end of the row and put in a neat pile for me to collect when I next walk past.

All of this has taken 18-20 minutes out of our 50 minute lesson (on a good day). I then need to make a decision about how the rest of the lesson will pan out. I will begin the period with a plan such as “Today we are going to learn how to multiply fractions where one of the fractions is a mixed number”. Depending on how well they have coped with the starter question that asked them to change three and two fifths to a mixed number, I might get them to do a few more of these first. In a “normal” lesson, I will introduce the new learning by writing the title on the board. This is copied into their red maths jotter (these came out of their bags right at the beginning of the lesson). I’m a huge proponent of explicit instruction, so I will typically complete some example problems for pupils to think about (My Turn). I will question pupils on the bits they should already know about. They don’t copy these down because they are about to complete some quick problems in their jotter that are similar in format to my examples (Your Turn). While they are working on those (for usually around 3-4 minutes) I will circulate and keep pupils on task and also help those who are stuck. We go over these problems with much more questioning from me than in the starter questions. Pupils generally do fairly well because they have had help and because the questions are very similar to the examples. This success builds confidence and is usually followed by some independent work. When I know that some pupils need more challenging questions to complete, I will write some on the board. If other pupils are stuck I will bring those pupils together at the board and discuss a few more examples with them. This seems to be working very well. The main chunk of the lesson is usually different depending on the tasks I have set for the class.

End of the lesson: I have the time of the bell down to the second so I know when we need to stop and when we need to pack up. We don’t start packing up until there are between 1 and 2 minutes left. That’s way plenty of time. Those who have borrowed pencils need to return them to me. Everyone packs their jotter away and stands at their desks. I might take a moment to speak with the pupils who seemed less confident to begin with and see how they felt about their work. As a class, we might use 1-5 (show 1-5 fingers) to share how confident we are feeling about our lesson. 1 means “I don’t have a clue what we just did” and 5 means “If Mr Allan was off tomorrow I could probably teach the class”. They are beginning to realise that this is valuable feedback for me that helps me to decide how we progress as a class. I have made it a safe place for pupils to say they are stuck or are not confident. I find that almost all of my pupils take this seriously, and don’t just blag their way to a 5. They also know that I already have a pretty good idea how they are getting on. I might also use this time to put the next class’ Numeracy Ninja booklets and yellow starter jotters out, ready to start the whole routine again.

Routines have helped me to get behaviour back on track for two of my junior classes. It now feels like they are learning way more and I feel like I am teaching way more. We are managing to cover far more work and a wider range of problem types. Basic numeracy skills seem to be getting better. I mentioned the importance of relationships at the beginning of this post. Perhaps that should be the focus of another post…

Thanks for reading. “Please return your pencil if you borrowed one and wait at your desk until I ask you to leave.”

Cognitive Load Theory⤴


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 “  (see here for original tweet).

I became interested in Cognitive Load Theory through listening to Greg Ashman talking on the mrbartonmaths podcast.

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.

Cognitive Load

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.

There is an additive relationship among the three types of Cognitive Load. If we get too much in the total, pupils become cognitively overloaded.

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
  • Redundancy
  • Split Attention
  • Modality
  • 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:


This is taken from Nathan Quirk’s board (our probationer). Each example is completed alongside a problem for pupils to complete.

Questioning and discussion of steps is what makes this effective. Cannot just be pupils following the same steps without using their brains.


These worked examples and problems were supplied by Chris McGrane.

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:


The text to the left of the diagram is redundant information. The diagram could be fully understood without it.

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.

Discovery Learning

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.

Interdisciplinary Learning

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

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:

  1. Novices and experts learn differently
  2. Working memory is limited
  3. 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: [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:

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:

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:

Willingham, D. T. (2009) Why Don’t Students Like School? Jossey-Bass. San Francisco.


Order of Operations⤴


BODMAS, BIDMAS, PEMDAS… It doesn’t matter what you call it. As long as they know what order we carry out calculations in.

I decided to begin the topic by showing my S3 class how they could write any expression involving subtraction as a sum. So, for example, we changed everything in the form a – b to a + (-b). We discussed the fact that, because of the commutative law with addition and multiplication, it didn’t matter now which order we carried out the calculation in (since (-b)+a yields the same result). 

We then changed every quotient into a product. So c/d became c x 1/d. We spent a lot of time manipulating expressions this way. I took the opportunity to also introcuce the distributive law, so that I could properly explain what the point of brackets was.

I didn’t mention BODMAS, nor did I teach them an equivalent acronym. Instead, I simply said that they should evaluate products before sums. Anything with powers is just a product, so clearly the powers have to be done first. In fact, they can be done at the same time as the products. It’s important to know the difference between 3a^2 and (3a)^2, and there’s a nice Standards Unit task for that.

We spent some time working on these new skills. Mainly using multiple choice questions and “insert the brackets” questions (see Don Steward). 

In order to assess how well the class had grasped the order of operations work, I presented them with the Four 4s problem. If you’re unfamiliar with this problem, see this

A textbook exercise suggested by our course plan looks like this: 

That’s a fine exercise for some routine practise of integers and powers but a far better task was: “Come up with some tricky looking expressions that evaluate to 17).” Here are some responses:

Using an open question such as this allowed me to see how much they had learned. I also particularly liked this because they are not all correct. This meant that the rest of the class had to evaluate each expression and figure out how to change it so that it did evaluate to 17. Timing the Four 4s problem in the middle of this topic allowed them to really experiment with the capabilities of using fractions, negatives and powers, including roots. Also, they seem to have learned that multiplying by zero results in zero.



Annually, teachers in my school are expected to be observed by a member of the school’s senior management team once. Just once. Departments also have their own internal observation policy, and this usually involves PTCs observing teaching staff in their department one time during every 12 months.

Teachers decide on a focus and pick which class they are observed with. A form is filled in during the observation and time is built in afterwards for feedback. This is all good, because it gives teaching staff an opportunity to get some valuable feedback on their teaching. The problem is…it’s fake.

It’s the same thing that happens with inspections. You get notice. And between getting notice and the time of the observation you stress and stress and stress. So you work jolly hard at making sure everything goes perfectly well in the lesson. Maybe you warn the pupils the day before to “behave” because Mrs So-And-So is coming to see them learn. The observation comes round and you show off the fact that you can write Learning Intentions and Success Criteria and differentiate the material so that the fast finishers are kept busy and the less motivated learners are supported. You even squeeze in a plenary full of AifL.

Is that learning and teaching in action? Ticking boxes in an observation? I want an observation policy that means the senior leaders and my PTC know that I strive to make sure that every lesson ticks all the boxes. I want them to know that sometimes it goes wrong. Sometimes the learners misbehave and sometimes I don’t use clear Success Criteria. Occasionally I forget to make my instructions clear enough. Sometimes I miss out having a tough problem for the high fliers to sink their teeth into when the intended learning has been achieved. Sometimes the bell rings before I expect it to.

What surprised and disappointed me most recently was something that I heard at a union meeting while discussing the Working Time Agreement: “You will be observed once by the senior leadership team. You will agree on a date, time and class and the observation will go into the diary. If, for any reason, the observation is missed (e.g. the senior leader is out of school or has to attend a meeting) you are not required to reschedule your observation. They get one shot.” Who is this for? Is it to comfort teachers that don’t want to be observed? I piped up “But you’d miss out on valuable feedback!?”. The reply was “well if you want to reschedule the observation, you can, but you don’t have to – they can’t make you”.

I think, as teaching staff, we’re missing the point. And our school leaders have got it wrong. It shouldn’t be that easy for teachers to get away without being observed. A colleague of mine recently commented that they hadn’t been observed for 7 years. How does that happen? In my opinion, observations serve a few purposes:

  1. They let teaching staff gain valuable feedback on their teaching – this is the most important purpose.
  2. They allow subject PTCs to gather evidence of how the department is performing – this helps with the writing of department scoping papers and so on.
  3. The allow school leaders to monitor the standards of learning and teaching across the whole school, highlighting areas of strength and areas of weakness so that interventions can be put in place when needed.

Basically, we need to calm down about observations. The stakes are too high and they really don’t need to be. If the school is supportive and the staff are supportive and everyone is reflective then observations should be the norm. They should be able to happen whenever the observer likes. You shouldn’t be putting on a show for an observer then settling for “fine” lessons the rest of the time. Treat every lesson as if it’s an observation. You’ll quickly see that that would be unsustainable. So instead treat every lesson like you want the best possible learning and teaching to happen for the learners in your class. At the end of the day, that’s what really matters.

Higher Maths OneNote⤴


Back in 2016 I was introduced to OneNote. I have since used it to transform the way I work. I may blog about other uses for OneNote in a separate blog post but this one is all about how I have used OneNote to create a digital notebook for Higher Maths.


BONUS: This OneNote also includes information about my Cognitive Load Theory Presentation, that has most recently been presented to Scottish Borders Maths Teachers during their in service in November 2018.


OneNote is accessed through Glow as part of Office 365, though the software can also be downloaded for free from

Glow users in all Local Authorities in Scotland can download the full version of Microsoft Office on up to 5 personal devices for free – speak to your school’s Glow person for more information.

Higher Maths OneNote

Screen Shot 2016-07-04 at 12.06.21

This link will take you to the OneNote where you can view the full thing: Higher OneNote (Glow sign in NOT required). If you would like to be added to the list of users who have permission to edit and add resources please get in touch. Send me a tweet at @mrallanmaths or email me: mrallanmaths at gmail dot com.

What I have done when creating the OneNote is I have made extensive use of the HSN materials (available at I have also uploaded some resources from my department’s course folder, though these are quite outdated. My aim in sharing this has been to encourage teachers across Scotland to pull together and create a digital bank of resources for Higher Maths all in one place.

The OneNote includes instructions to guide teachers through creating a separate OneNote Notebook for their class, which they can share with their pupils in order to allow them to access the content at home or in class.

OneNote can be used as a digital planner. There is an example of this in the shared OneNote.

Pythagoras’ Theorem Pile Up⤴


Towards the end of the Pythagoras’ Theorem topic with my CfE 4th Level S2 class last session, I stood in my classroom 20 minutes before the start of the lesson and wondered: what would be a good starter question that would challenge this class? The majority of the pupils had a firm understanding of Pythagoras’ Theorem, and I wanted them to demonstrate this. I quickly drew this question on my board:

Quickly thrown together on my board, by hand, 20 minutes before the class started.

Quickly thrown together on my board, by hand, 20 minutes before the class started.

This question was inspired, of course, by the “Trigonometry Pile Up!” by Great Maths Teaching Ideas.

Once I had finished drawing the question, I realised that it would take longer than a normal starter question but I still went with it, but instead called it a “Challenge Question”.

What I like about this question is that the pupils can see what they have to do straight away. There are no surprises. I genuinely just wanted them to get some further practice applying Pythagoras’ Theorem, while also stretching their resilience.

I shared a picture of this problem on Twitter and @missradders quickly spotted it and asked if she could make an electronic version. Of course I said yes and this was the result:

The colourful and easier to read version of the Pythagoras' Pile Up, thanks to @missradders

The colourful and easier to read version of the Pythagoras’ Pile Up, thanks to @missradders

When this was then shared on Twitter it quickly became my most favourited and most retweeted tweet of all time. It still gets retweets to this day.

To download the file, click this link.