Craig Barton's online courses/3. Making the most of worked examples

  • £25

3. Making the most of worked examples

How can we model new ideas, methods and concepts to our students effectively?

Course overview

How can we model new ideas, methods and concepts to our students effectively?

In this course I look at four significant mistakes I used to make with my worked examples, which I considered to be good practice. Then I go through, in detail, exactly how I now present worked examples, incorporating the principles of Example-Problem Pairs, Silent Teacher, Show Call and more, including examples from teachers and feedback from students who have used this approach. It is a process that I use with every class, from my lower-achieving Year 7s to my Year 13 Further Mathematicians. However, not everyone likes this approach, and we will address the most common concerns head-on! To end, we discuss the merits of an alternative approach to worked examples that I never even considered until I spoke to someone in New York...

Please see the bottom of the page for FAQs about suitability, cost, payment options, and more.

Feedback from the end of course survey

Insightful, research-informed and really engaging. It has given me so much to think about. Also v easy to dip in and out of to fit in around the kids!

This course has really got me thinking about my practice - not easy after 20 years on the classroom. Really seems to make sense.

This course cemented my understanding of the key elements of the approach and made me think about several elements I can refine in my teaching, such as the the specific use of show-call. The best bits were the specifics of you talking through exactly how you model it e.g. where you look during a silent teacher phase.

I love learning about the research that informs your practice! I also really enjoyed going step-by-step through an entire Example-Problem Pair cycle.

I really enjoyed being able to experience what the different elements feel like from a student's perspective. I liked seeing how different people put the ideas into practice too and it helped me think about how I would make it work for my classes.

I have done worked examples before with my students, but I haven’t used a “Thinking” column before. I can see so many possibilities, and I love the idea of students having an annotated column to refer back to.

Contents

Introduction

What is this course all about, and how can you get the most out of it?
1. Introduction to the course
Preview
Image: My model of a Learning Episode
Preview
2. Getting the most out of the course
Preview
3. Where are you at?
Preview

What my worked examples used to look like... and why I changed my mind

What is the research surrounding effective worked examples, and what are the four principles I try to stick to?
1. Research into worked examples
Link: My research collection
Podcast: Greg Ashman interview
Research: Example‐Based Learning: New Theoretical Perspectives and Use‐Inspired Advances to a Contemporary Instructional Approach
2. Four mistakes I used to make
3. Principle 1 - I atomise
3a. What is Atomisation?
3b. Prerequisite knowledge
3c. An example of Atomisation
Image: My process of Atomisation
Link: Diagnostic Questions
Activity: What is a factor?
4. Principle 2 - I try to avoid the Split-Attention Effect
Link: Research papers on Cognitive Load Theory
5. Principle 3 - I am more careful with discussions
6. Principle 4 - I try to ensure my students are actively involved (Self-Explanation Effect)
Link: Research papers on the Self-Explanation Effect
Podcast: Ollie Lovell interviews Alexander Renkl
6a. Time and the double-pause of questioning
Image: The double pause of questioning
6b. Creating the right conditions
6c. Providing support
Image: Student prompt cards - different sizes
Resource: Student prompt cards - editable
Resource: Student prompt cards - editable from George Stone
Resource: Student Prompt cards from Laura Conroy
7. Summary of my four principles

The set-up

Where do worked examples fit into my teaching, and what does my board look like?
1. Where do Example-Problem Pairs fit in?
Image: My model of a Learning Episode
2. What my board looks like

Stage 1 - Silent Teacher

What does Silent Teacher look like, what adaptations have teachers made, and what do teachers and students think about it?
1. Silent Teacher - the set-up
Image: Silent Teacher behaviour
2. Silent Teacher - the experience
3. Silent Teacher extra!
4. What do teachers say?
5. What do students say?

Stage 2 - Narration

What does the Narration stage look like, and what do other schools do?
1. Narration - the experience
Image: Narration behaviour
2. Narration - what other schools do
Examples from Simon Garrett

Stage 3 - Read the maths

Why don't my students copy down worked examples any more, and what do they do instead?
1. Do your students copy down worked examples?
2. Issues with copying down worked examples
3. Read the maths - the experience
Image: Read the maths behaviour
Blog: The beauty of annotating
4. Read the maths - what other schools do

Stage 4 - Your Turn

What does students' first practice question look like, and what do other schools do?
1. Your Turn - the experience
2. The purpose of Your Turn
Image: Your Turn behaviour
Image: Your Turn prompts if finished
Image: Your Turn prompts for paired discussion
3. Your Turn - what other schools do

Stage 5 - Show Call

How do we showcase students' work to the rest of the class to address misconceptions and see excellence?
1. Show Call - the experience
Podcast: Doug Lemov interview
Podcast: Ollie Lovell interview
Image: Show Call behaviour (mistake)
Image: Show Call behaviour (excellence)
2. What other schools do
3. Capturing the images
Using Show-Call when teaching online

Reflection

Now we have seen the 5 stages, how long do they last, and what do you make of the process as a whole?
1. Timings
2. Putting it all together
Image: The 5 stage Example-Problem Pair process
Resource: Example-Problem Pair (blank) by Nathan Day
Resource: Example-Problem Pair (example) by Nathan Day

Feedback

What do teachers and students make of the Example-Problem Pair process?
1. Feedback from teachers
Blog: A first attempt at silent teacher by Miss Olive
Tweet: An example of the 5 stage process for quadratic graphs
2. Feedback from students

What do other schools do?

What tweaks, adaptions and complete transformations have other schools made to the Example-Problem Pair process?
1. Tweaks
2. Fading
Website: Berwick Maths
3. Departmental planning
4. One-to-one support
5. Notes book
6. Written feedback
7. Example-Problem Pairs in other subjects
Resource: Worked examples GCSE / IGCSE Mathematics

FAQs

What questions, concerns and complaints do teachers have about the Example-Problem Pair process, and what are my answers?
1. Telling students what to do feels like cheating
2. This must take ages
3. How does it work for shorter examples?
4. How does it work for longer examples?
5. Does it work for everything?
6. Does it tie me to certain methods?
7. What if I want to show my students more than one method?
8. Where is the why?
9. Do you do this every lesson?
10. Your students are not actively engaged
11. Where is the differentiation????
12. I am doing this already!

Moving forward

What tips have I picked up from schools who have made Example-Problem Pairs work, and how can we plan our own Example-Problem Pairs?
1. Tips from teachers who have made this work
2. Planning our own Example-Problem Pair

An alternate approach!

Twist time - we discuss a different way of presenting worked examples which is based on the same research
1. What Michael Pershan does
Podcast: Michael Pershan on worked examples
Link: Michael Pershan's post on worked examples
2. The resources
Link: Algebra by Example
Link: Math by Example
3. Where does this approach fit in?

Useful links - from others

Links from other people that are relevant to the content of this course
Video: Creating Effective Lessons the Easy way with Dr. Fred Jones
Clare Sealy's blog on using worked examples in a primary context
Emma McCrea's presentation about worked examples
Ollie Lovell interview with John Sweller about worked examples
Greg Ashman's blog post on Example-Problem Pairs
Research: Example‐Based Learning: New Theoretical Perspectives and Use‐Inspired Advances to a Contemporary Instructional Approach

Conclusion

What are the best ways to embed these ideas into your practice, and then it is time to say goodbye!
1. Where to next?
2. Wrap up
Feedback form
Course certificate
My online courses
Preview

Useful links - from me

Links to some of my work that you might find useful
My research paper collection
Book: How I wish I'd taught maths
Book: Reflect, Expect, Check, Explain
Mr Barton Maths website
Mr Barton Maths Podcast
Diagnostic Questions
Variation Theory
SSDD Problems
Maths Venns

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 on primary teaching. However, I have been lucky enough to run this Worked Examples course over 20 times with primary colleagues, and it seems to go down well. The key example I base the course around it writing a number as its product of prime factors, which should make the course content itself accessible and relevant to teachers of Years 4, 5 and 6 (that is 9 year olds and above for teachers from somewhere other than England). For teachers of younger students, I believe the ideas are transferable, but I make no promises! 

Is this course suitable for non-maths teachers?

I am not so sure. My background is in mathematics, and that is all I really know about. Since my first book, How I wish I'd taught maths, was released, many teachers of other subjects have contacted me to say they have found ways to transfer my ideas with regard to worked examples to their subject domain, but I can make no promises. If pushed, my instinct is that this approach may work well in subjects with set methods and procedures that students need to learn - so the sciences, languages, and certain technical aspects of English, for example.

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 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. 

In addition, from time to time I will update the course content with new videos, resources and ideas. I will email you when this happens and you will have access to this as well for no extra cost.

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.

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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!

My email is mrbartonmaths@gmail.com

Can I show the videos as part of a meeting or training event?

I am afraid not. The prices of the course are per person.

If you wish to discuss using the materials as part of a meeting or training event, please email me at mrbartonmaths@gmail.com.

About Craig Barton

​Craig Barton has been involved in teaching maths for 15 years. He was the the TES Maths Adviser for 10 years and is now the Head of Education at Eedi.  Craig is the author of the best-selling books “How I wish I’d taught maths” and "Reflect, Expect, Check, Explain", the host of the Mr Barton Maths Podcast, the creator of mrbartonmaths.com, diagnosticquestions.com, variationtheory.com, ssddproblems.com and mathsvenns.com, and Visiting Fellow at the Mathematics Education Centre at the University of Loughborough.