How do we help our students get better at solving problems?
For many years I have failed to help my students become the problem solvers I want them to be. Finally, I think I am getting somewhere. In this course we will look at which types of problems students struggle with, and then I will make some controversial statements about problem solving to try to explain why they struggle. I then present my present my Four Ingredients of Problem Solving. I believe that these four ingredients help our students develop the capabilities to be knowledgeable, creative problem-solving mathematicians, allowing them to tackle those tricky exam questions, as well develop more of a love for our subject. In this course we look at the research behind these ideas, what they look like in the classroom, and then see how different schools around the world have taken them and made them work for their students and their context.
Please see the bottom of the page for FAQs about suitability, cost, payment options, and more.
Feedback from the end of course survey
The use of specific examples was particularly helpful in making the ideas concrete in my mind, plus it is always good to do a bit of maths!
What are the main types of problems students struggle with that will be at the centre of this course?
1. The contextual problem
2. The subtle contextual problem
3. The multi-topic problem
4. What about other types of problems?
Some controversial statements about problem solving
What did I used to believe about problem solving, why did I change my mind, and what do I believe now?
1. Problem solving and learning
Research: Consequences of history-cued and means-end strategies in problem solving
Blog: The Difference Between Solving a Problem and Learning Some Math From It
2. When to do problem solving
Podcast: Andrew Blair interview from 2017
Podcast: Andrew Blair interview from 2014
Link: Inquiry maths website
Link: Kapur's section on Productive Failure
Research: Element interactivity as a factor influencing the effectiveness of worked example–problem solving and problem solving–worked example sequences
Blog: John Sweller on Productive Failure
3. The two year rule
Article: The fundamental problem with teaching problem solving
4. Problem solving strategies
Podcast: Michael Pershan on problem solving strategies
Routines
Why are routines so important to my teaching, in particular when it comes to problem solving?
The importance of routines.mp4
Podcast: Bruno Reddy on routines
Ingredient 1 - SSDD Problems
What are SSDD Problems and how can they be used effectively in the classroom?
1. What is the problem?
Research: The Benefit of Interleaved Mathematics Practice is not limited to Superficially Similar kinds of Problems
2. What is the solution?
Link: SSDD Problems website
3. Why might SSDD Problems be a good idea?
4. Some of my favourite SSDD Problems
5. Narrow the domain (method select)
6. The SSDD Problems website.mp4
7. SSDD Problems with different age groups
8. SSDD Problems in different subjects
9. SSDD Problems in the classroom
10. What do students say?
11. Idea: Mixed-topic starters
Research: Using Spacing to Enhance Diverse Forms of Learning
12. Idea: Command words
A teacher's guide to command words
13. Idea: Problem solving for all
14. Idea: Group work
15. Idea: High-value skills
16. Idea: DSID
Link: Miss Konstantine on Twitter
17. Idea: Planning for error
18. Idea: Providing a purpose
19. Idea: Reacting to exam questions
20. Idea: (Blind) modeling
21. Idea: What is the question?
22. Final reflection
Resource: SSDD Problems (blank) by Nathan Day
Resource: SSDD Problems (example) by Nathan Day
Ingredient 2 - Goal-Free Problems
What are Goal-Free Problems, and how can they be used effectively in the classroom?
1. What is the problem?
Research: Cognitive Load Theory, Learning Difficulty and Instructional Design
Blog: The goal-free approach: My talk from CogSciSci 2019
2. What is the solution?
Blog: Sweller on the difference between Goal-Free Problems and minimally guided instruction
3. Goal-Free Problems with different age groups
4. The Goal-Free Problems website
Link: The Goal-Free Problems website
5. But they won't look like this in the exam
6. Goal-Free Problems in the classroom
7. Idea: In lessons
Link: White Rose Maths problems of the day
8. Idea: Exam preparation
9. Idea: Exam technique
Blog: John Sweller on exam technqiue
10. Idea: Goal-Free mock exams
11. Idea: Problem of the week
12. Idea: When to use Goal-Free Problems
13. Reflection
Ingredient 3 - Purposeful practice
What is purposeful practice, and what are some of my favourite sources and activities?
1. What is the problem?
Book: The hidden lives of learners
2. What is the solution?
Activity: Simplifying ratio Venn Diagram 1
Activity: Simplifying ratio Venn Diagram 2
3. Principles of Purposeful Practice
Research: Developing mathematical fluency: comparing exercises and rich tasks
4. The power of Purposeful Practice
5. Purposeful Practive versus Intelligent Practice
6. Venn Diagrams - laying the foundations
Link: CIMT MEP materials
Link: Maths Venns website
7. Venn Diagrams - prompts for thinking deeper
Prompts for thinking deeper
8. Venn Diagrams - in the classroom
Activity: Types of number Venn Diagram
9. Venn Diagram - averages and range
Activity: Averages and range Venn Diagram
10. Venn Diagrams - straight line graphs
Activity: Straight line graphs Venn Diagram
Venn Diagrams on the playground
11. Venn Diagrams - time to move on
12. Colin Foster - linear equations
Link: Mathematical etudes website
Activity: Expression polygons
13. Colin Foster - enlargement
Activity: Staying on the page
Resource: Geogebra file for enlargements
14. Don Steward - written subtraction
Link: Median maths blog
Activity: Two-digit subtraction
15. Don Steward - factors
Activity: Four factors
Activity: Factor facts
16. Open Middle - FPD conversions
Link: Open Middle website
Activity: Converting between fractions and decimals
17. Open Middle - area of quadrilaterals
Activity: Area of a quadrilateral
18. NRICH - adding fractions
Link: NRICH website
Activity: Almost one
19. NRICH - expanding and simplifying
Activity: The simple life
20. Reflection
Ingredient 4 - UKMT questions
What are UKMT questions, where can you get them from, and how can they be used effectively?
1. Introduction
Link: UKMT website
2. UKMT Problems in the classroom
3. Source - Diagnostic Questions
Link: UKMT questions on Diagnostic Questions
Resource: UKMT (example) by Nathan Day
Resource: UKMT questions (blank) by Nathan Day
4. Source - Dr Frost Maths
Link: Dr Frost Maths
5. Source - NRICH short problems
Link: NRICH short problems
6. Reflection
Useful links - from others
A selection of links from other people relevant to this problem solving course
10 part blog series: How do kids think about solving equations?
Research: Developing students’ strategies for problem solving in mathematics
Video: Lessons for Mathematical Problem Solving
Video: Alan Schoenfeld on Poyla's problem solving approach
Blog: Problem solving or explicit instruction: Which should go first when element interactivity is high? by Greg Ashman
Conclusion
Time to reflect what we have learned during this course
A selection of some of my work 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 Problem Solving course many times with primary colleagues, and it seems to go down well. I believe that the key principles are transferable, and I try my best to use a wide variety of examples that are suitable for all age groups. The challenge - as it is with everyone who takes the course - will be to think hard about what they would need to do to make the ideas work for them and their students.
Is this course suitable for non-maths teachers?
I don't think so. There may be key principles that science teachers find transferable, but every example is from the domain of mathematics. This course is certainly more domain-specific than my Retrieval course.
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.
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!
