This course is all about how we introduce, explain and model new ideas to our students. We discuss how to show students that a new idea matters, and how to deal with technical language and key decisions. We talk about the importance and practicalities of live modelling, before taking a deep dive into my worked example process, including example-problem pairs, Silent Teacher and making use of self-explanation prompts. We also discuss what happens after that first worked example in terms of the We Do and Your Turn, and exactly what should our students be copying down? It's a big one, so make sure you are sitting comfortably.
See the bottom of this page for FAQs.
Course overview
Making the most of this course
Tip 1. Five ideas to show students why what we are learning today matters
Tip 2. Use related examples and non-examples to explain technical language
Tip 3. Thirteen ideas to improve the explanation of a concept
Tip 4. Teach decision-making separately
Tip 5. Five ideas to improve our choice of examples
Tip 6. Model techniques live
Tip 7. Use a teacher examples book
Tip 8. Use student example books
Tip 9. Make use of the power of Example-Problem Pairs
Tip 10. Fourteen ideas to improve Silent Teacher
Tip 11. Use self-explanation prompts after a worked example
Tip 12. Six ideas to improve “copy down the worked example”
Tip 13. Vary the means of participation for the "We do"
Tip 14. Three errors to avoid with the "Your Turn" questions
Tip 15. Reflect after a worked example
Tip 16. Beware of seductive details
Going forward
Contents
How to make the most of this course
The issue with FOMO
2 mins
24.5 MB
Two questions to consider
548 KB
Two types of tips to look for
3 mins
64.1 MB
The issue with good intentions
1 min
16.1 MB
Two questions to consider
553 KB
Implementation intentions
4 mins
118 MB
Tip 1 - Five ideas to show students why what we are learning today matters
Where we are at
33.8 KB
What is the problem?
1 min
13.5 MB
Two questions to consider
545 KB
Idea 1 - Show connections
2 mins
62.6 MB
Idea 2 - Connect the Big Ideas
3 mins
98.1 MB
Idea 3 - Share hinterland knowledge
4 mins
91.1 MB
Idea 4 - Introduce a headache
3 mins
65.3 MB
Idea 5 - Show why it matters to you
2 mins
40.3 MB
Reflection on all 5 ideas
1 min
18.5 MB
Image of all 5 ideas
47 KB
Implementation intention
76.2 KB
Tip 2 - Use related examples and non-examples to explain technical language
Where we are at
34 KB
A challenge for you
1 min
6.19 MB
What I used to do
3 mins
60.1 MB
Two questions to consider
555 KB
The three principles
2 mins
62.2 MB
The triangle sequence
4 mins
95.2 MB
Image of the triangle sequence
56.1 KB
The flow
1 min
28.6 MB
Image of the flow
27.1 KB
Check for understanding 1 - Give an example
3 mins
61.2 MB
Check for understanding 2 - Frayer diagram
1 min
21.3 MB
Etymology
2 mins
30.5 MB
Adjacent angles on a straight line
4 mins
99.2 MB
Check for understanding - Adjacent angles
1 min
23.3 MB
Other examples from maths
2 mins
34 MB
An example from English
1 min
13.9 MB
Reflection
1 min
23.8 MB
Implementation intention
76.2 KB
Tip 3 - Fourteen ideas to improve the explanation of a concept
Where we are at
33.9 KB
What is the problem?
1 min
17.6 MB
Two questions to consider
552 KB
Idea 1 - Plan two explanations
2 mins
45.1 MB
Idea 2 - Understand what the explanation of the concept is, and what it is not
2 mins
42.1 MB
Idea 3 - Tell students that this is something they need to remember
2 mins
38.4 MB
Idea 4 - Say less
1 min
15.1 MB
Idea 5 - Plan the explanation in advance
2 mins
26.5 MB
Idea 6 - Connect explanations to things students know
2 mins
47.6 MB
Idea 7 - Go from concrete to abstract
2 mins
28.3 MB
Idea 8 - Use models
2 mins
32.3 MB
Idea 9 - Use demonstrations instead of proof
2 mins
45.2 MB
Idea 10 - Start from a blank canvas
2 mins
47.3 MB
Idea 11 - Consider providing a cue during the explanation
2 mins
47.1 MB
Idea 12 - Question, don’t tell
2 mins
36.9 MB
Idea 13 - Say it again?
2 mins
28.7 MB
Idea 14 - Have students stand during the explanation
2 mins
49 MB
Reflection on all 14 ideas
1 min
25.7 MB
Image of all 14 ideas
30 KB
Implementation intention
74.9 KB
Tip 4 - Teach decision-making separately
Where we are at
34.1 KB
What is the problem?
2 mins
60.1 MB
Two questions to consider
542 KB
What was my mistake?
3 mins
75.5 MB
Step 1 - identify the decisions
2 mins
44.8 MB
Step 2 - teach the decisions
2 mins
41.7 MB
Task - is a the subject?
8 mins
282 MB
The flow
1 min
28.2 MB
Image of the flow
27.1 KB
Check for understanding
2 mins
44.6 MB
Reflection
2 mins
40.5 MB
Introduction to the trapezium example
1 min
18.2 MB
Reflection on the worksheet
3 mins
98.8 MB
Task - sides of a trapezium
4 mins
133 MB
Check for understanding
1 min
27.6 MB
Four types of decisions
3 mins
134 MB
Image of the types of decisions
49.4 KB
Implementation intention
72.6 KB
Tip 5 - Five ideas to improve your choice of worked examples
Where we are at
34 KB
A challenge for you
1 min
13.7 MB
Two questions to consider
541 KB
Idea 1 - Get the pitch right
1 min
20.9 MB
Idea 2 - Try to avoid erroneous generalisations
1 min
14.3 MB
Image of the examples
98.7 KB
Reflection on Idea 2
4 mins
110 MB
Image of the mean example
196 KB
Idea 3 - Avoid repeating elements within a worked example
1 min
22.8 MB
Idea 4 - Have a single intended object of learning per worked example
1 min
26.4 MB
Idea 5 - Use a pair of related worked examples
3 mins
94.6 MB
Reflection on all 5 ideas
2 mins
47.6 MB
Image of all 5 ideas
42.9 KB
Implementation intention
76.2 KB
Tip 6 - Model techniques live
Where we are at
33.9 KB
What is the problem?
3 mins
91.9 MB
Two questions to consider
548 KB
Model techniques live
1 min
31.2 MB
What about technology?
2 mins
46.1 MB
Answers to practice questions?
1 min
54.2 MB
Implementation intention
71 KB
Tip 7 - Use a teacher worked examples book
Where we are at
34.4 KB
What is the problem?
2 mins
29.7 MB
Two questions to consider
539 KB
Teacher examples book
2 mins
34.3 MB
Three reasons a teacher worked examples book is a good idea
2 mins
42.4 MB
Three extra tips
3 mins
64.3 MB
Implementation intention
72.7 KB
Tip 8 - Use student worked example books
Where we are at
34.4 KB
Three questions for you
1 min
16.2 MB
Two questions to consider
550 KB
Three benefits of student worked examples books
3 mins
91.8 MB
Implementation intention
72.8 KB
Tip 9 - Make use of the power of Example-Problem Pairs
Where we are at
34.1 KB
What do you do?
3 mins
59.5 MB
Two questions to consider
554 KB
What I do now
2 mins
56.9 MB
Implementation intention
75.7 KB
Tip 10 - Fourteen ideas to improve Silent Teacher
Where we are at
34.6 KB
Two types of pedagogy I see with worked examples
2 mins
41.3 MB
Two questions to consider
548 KB
A quick word about explicit instruction
2 mins
35.7 MB
Silent Teacher: overview
2 mins
53.2 MB
Silent Teacher: the exeprience
3 mins
56.4 MB
Idea 1 - Tell your students what you are doing and why
1 min
20.6 MB
Idea 2 - Don’t start until you have silence
1 min
9.97 MB
Idea 3 - Model by hand
1 min
13.7 MB
Idea 4 - Gesture
1 min
23.3 MB
Idea 5 - Teach students how to behave when doing Silent Teacher
2 mins
52.8 MB
Idea 6 - Use Reflect, Expect, Check, Explain
2 mins
37.7 MB
Idea 7 - Provide a cue for self-explaining
1 min
25.8 MB
Idea 8 - Allow adequate wait time before and after a step
2 mins
30 MB
Idea 9 - Ask students to stand during Silent Teacher
1 min
23 MB
Idea 10 - Allow students to make notes after Silent Teacher
2 mins
30.6 MB
Idea 11 - Allow paired discussion after Silent Teacher
2 mins
31.2 MB
Idea 12 - Break-up Silent Teacher
1 min
24.3 MB
Idea 13 - Don’t feel you have to do Silent Teacher for everything
2 mins
34.7 MB
Idea 14 - Be ready for some funny looks
1 min
16.7 MB
Reflection on all 14 ideas
1 min
30.3 MB
Image of all 14 ideas
40.4 KB
Silent Teacher challenge
1 min
18.7 MB
Implementation intention
72.9 KB
Tip 11 - Use self-explanation prompts after a worked example
Where we are at
34.6 KB
What do you do?
1 min
15.7 MB
Two questions to consider
555 KB
The research into the Self-Explanation Effect
4 mins
178 MB
What makes a good Self-Explanation Prompt?
2 mins
70.4 MB
My self-explanation prompts
3 mins
57.2 MB
Other examples of principled prompts
1 min
30.7 MB
Self-explanation prompt tips
2 mins
45.2 MB
Self-explanation in practice
3 mins
96.8 MB
Three key things
2 mins
48.8 MB
Start to finish, or break it up?
1 min
26.3 MB
Means of participation
2 mins
62.9 MB
Make sure you explain the answer
1 min
18.7 MB
Self-explanation challenge!
1 min
17.8 MB
Implementation intention
77.5 KB
Tip 12 - Six ideas to improve “copy down the worked example”
Where we are at
39.9 KB
Q1 - When do students copy down worked examples?
1 min
8.2 MB
Q1 - reflection
2 mins
35.2 MB
Q2 - Is copying down worked examples a good use of time?
1 min
4.1 MB
Q2 - reflection
3 mins
83.2 MB
Two questions to consider
552 KB
Idea 1 - Whatever you ask students to write, ask them to do it after you have finished modelling
1 min
12.4 MB
Idea 2 - Print out some of the worked example
2 mins
35.8 MB
Idea 3 - Ask students to answer the self-explanation prompts
2 mins
61.5 MB
Idea 4 - Ask students to write notes for their forgetful future self
2 mins
43.6 MB
Idea 5 - Ask students to look away and write
1 min
22.8 MB
Idea 6 - Don't bother with any notes at all!
2 mins
35.3 MB
Reflection on all 6 ideas
1 min
27 MB
Image of all 6 ideas
41 KB
Implementation intention
76.9 KB
Tip 13 - Vary the means of participation for the "We do"
Where we are at
39.8 KB
What is the problem?
2 mins
60.8 MB
Two questions to consider
542 KB
When to do the We Do
1 min
23.2 MB
Vary the means of participation of the We Do
6 mins
200 MB
Where do you write the We Do?
1 min
34.2 MB
We Do challenge
1 min
16.2 MB
Implementation intention
74.7 KB
Tip 14 - Three errors to avoid with the "Your Turn" questions
Where we are at
39.9 KB
Three Your Turn errors I have made
1 min
25.7 MB
Two questions to consider
553 KB
Resolving issue 1
1 min
19.8 MB
Resolving issue 2
1 min
30.8 MB
Resolving issue 3
1 min
15.6 MB
What does the Your Turn look like?
3 mins
75.3 MB
Answering and assessing the Your Turn
3 mins
86 MB
Your Turn challenge
1 min
11.2 MB
Implementation intention
74.8 KB
Tip 15 - Reflect after a worked example
Where we are at
39.8 KB
What is the problem?
1 min
11.2 MB
Two questions to consider
555 KB
Wood trees wood
2 mins
35.8 MB
Idea 1 - Go through process as a whole, quickly
2 mins
32.8 MB
Idea 2 - Show and alternate methods or representations
2 mins
67.5 MB
Idea 3 - If appropriate, explain the why
1 min
20.4 MB
Idea 4 - Do a final check for understanding
2 mins
34.1 MB
Reflection on all 4 ideas
1 min
22.5 MB
Image of all 4 ideas
28.6 KB
Implementation intention
71.5 KB
Tip 16 - Beware of seductive details
Where we are at
33.7 KB
What is the problem?
1 min
45.2 MB
Two questions to consider
555 KB
Key principle
1 min
17.1 MB
What I do now
5 mins
219 MB
Implementation intention
71.8 KB
Going forward
Reflection on what we have learned
2 mins
52.7 MB
Image of what we have covered
38.1 KB
Goodbye!
1 min
16.2 MB
Links to my other work
My books
246 KB
My podcasts
146 KB
My websites
20.9 KB
FAQs
Is this course suitable for primary school teachers?
I am a secondary school maths teacher by training, and I make no claim whatsoever to have any expertise in the domain of primary teaching. However, I have been lucky enough to run this course lots of times with primary colleagues, and it seems to go down well. The key ideas concerning explanations and modelling should transfer to different phases.
Is this course suitable for non-maths teachers?
I am not so sure. Whilst tips surrounding explanations will be relevant, I think maths is quite unique in the focus on worked examples as a key aspect of the modelling process. If you are a science or languages teacher, then there may be value in this course, but I think teachers of other subjects will find my other courses of more relevance.
Is this course suitable for non-UK teachers?
Yes! I have been lucky enough to work with teachers all around the world, and I ensure wherever possible that my courses are not tied to any specific curriculum or specification. I am confident that aside form my weird accent, teachers from other countries will find most of the ideas relevant and transferable.
How long does it take to do the course
You could whizz through all the videos in a a few hours. But the idea is you watch the video where I present a problem, reflect where you are at, listen to my proposed solution, reflect upon that, and consider what you would need to change to make it work for you.
Therefore, a day to a day and a half is probably suitable to do the course.
Even better if you can do a section of the course, try some ideas in your classroom, reflect on what worked and what didn't, and then move on to the next section of the course.
How long can I access the course content for?
As long as this platform exists! That is one of the key advantages of an online course - you can go back over the content again and again.
If, for whatever reason, the platform shuts down or I need to remove content, I will give you as much notice as possible (I will aim for at least 6 months) so you can complete the courses.
Can I pay with an invoice instead of online?
The easiest way to pay is online. The service accepts all major cards as well as PayPal. Paying this way gives you immediate access to the course.
But if you need to pay via invoice, then no problem! Just send an email to mrbartonmaths@gmail.com with details of:
1. The email addresses of the delegates taking the course
2. Your school name and address
3. Who to email to invoice to
Then I will send you an invoice and register your colleagues on the course.
Can I get a VAT receipt?
Of course!
If you have paid online, just login, click on the drop-down menu next to your picture on the top-right of the screen, select Billing and you can print off your VAT receipt(s) there.
If you pay-offline (by emailing me as described above) then I will email you an invoice which will serve as your VAT receipt.
Can I buy one pass and then share it with my colleagues?
I am afraid not. The price of each course is per person.
Each person who pays for the course has their own log-in details, so the platform can keep track of their individual progress. This allows you to log back on using any device and pick up where you left off.
Are there discounts available?
If you want to purchase a bundle of passes for the courses - perhaps you have a large department or you are part of an Academy chain - send me an email telling me what you have in mind, and hopefully we can reach a deal!
