What are SSDD Problems?
SSDD stands for Same Surface, Different Deep. I introduced SSDD problems in my first book, “How I wish I’d taught maths: Lessons learned from research, conversations with experts, and 12 years of mistakes“, and since then teachers from around the world have shared their efforts at creating them.
SSDD problems are a special type of problem based on the observation from Roher, Dedrick and Burgess (2014) that the correct solution to most mathematical problems involves two steps: identify the strategy needed to solve the problem, and then successfully carry out that strategy.
What I used to do
By always presenting students with a series of problems that are set in different contexts (i.e. have a different surface structure), but which are all from the same topic (i.e. have the same deep structure), we are robbing students of the opportunity to develop the ability to identify the problem’s deep structure and hence identify the strategy needed to solve the problem.
Take the example of Pythagoras.
In the past I would have taught my students the basics of how to find the lengths of hypotenuses and non-hypotenuses. Then would come the application questions, where I would present my students with problems like this:
They would race through them on auto-pilot, happily using and applying Pythagoras and his lovely theorem left, right and centre. I would usually follow this up with a Pythagoras themed homework, and even a Pythagoras assessment, which most of my students would do well in. I would then sleep happy at night, safe in the knowledge that I had taught my students not only how to do Pythagoras’ Theorem, but also how to apply it in different contexts.
Imagine my surprise when it came to an exam a few months later and students were suddenly completely and utterly unable to spot when they should be using Pythagoras. But I should not have been surprised, because through application lessons, and topic-specific homeworks and assessments, I was not developing my students’ abilities to identify the strategy needed to solve the problem – it was flipping obvious that every question required them to use Pythagoras!
SSDD Problems
What I needed instead were a new set of problems – ones where the surfaces were similar, but the deep structures were very different. By exposing students to problems like that, I would ensure that they learned to recognise not just the similarity between problems, but also the differences between them. A collection of problems such as these, for example.
As well as having to really think hard about the underlying deep structure (and hence come off auto-pilot), students also benefit from the effects of spacing and interleaving by revisiting concepts from the past. Hence, SSDD problems were born.
I use SSDD problems in three ways:
- At the end of a topic in the place of a traditional “applications lesson”
- As an end of topic homework – I have really moved away from topic specific homeworks and assessments of late
- As a means of revision, particularly with Year 11 students in the build up to GCSEs. Presenting them with a set of SSDD problems is an excellent revision exercise, covering 4 topics for the price of 1, and compelling students to think hard about the differences between problems in order to identify the correct deep structure.
To learn more about SSDD problems, I recommend you read the Roher, Dedrick and Burgess (2014) paper and listen to my podcast interview with Professors Robert and Elizabeth Bjork, where I first considered the idea. I also write about it extensively in my book, How I wish I’d taught maths, published by John Catt Educational.
How can you get involved?
This site can only continue to grow through you and your contributions. So, if you have a set of SSDD problems to share, or can write some answers to the questions, then please get in touch.
What are teachers saying about SSDD Problems?
Just used it with my yr11s their thinking was electric!
— betty king (@bbking212) March 16, 2018
Amazing resource. Just used ‘Isosceles Triangles 1’ today and it went down a treat leading to some great discussions. Thanks for all your hard work.
— Ms Dolan (@ASHMD16) March 12, 2018
Just used a set with my year 11s… one told me it all made far more sense than the usual set of ‘boring’ questions they do. Thank you!
— Rhona Miller (@teachersltdep) March 19, 2018
I am loving it and have shared with my dept! Really good for starters/plenaries and my y11 said at revision today they really like it because they have to work out what the topic is and what to do!
— Sami Piggott (@Mrs_Piggott1) March 15, 2018
I’m loving it too! I am embedding SSDD tasks in my lessons as Paired Problem Solving time so students can discuss and work together
— Mr Bayew (@MrBayew) March 15, 2018
Fantastic resources! Tried one with my year 3 (15 years old, in The Netherlands) yesterday, they loved it. Thanks so much for sharing, everyone!
— Martine Bode (@MartineB1963) March 15, 2018
Hoping to introduce my colleagues asap, think this will get us enthused and focused on the maths instead of all of the nonsense that is going on around us currently.
— Beckneedsadonut (@1982beckyboo) March 13, 2018
Loving it. Shared with department today and building into Y11 strategy
— M Hussey (@MattyHussey) March 14, 2018
My online courses
My series of online courses are available here: craigbarton.podia.com
My books
How I wish I’d taught maths, which discusses the use of SSDD problems alongside purposeful practice, cognitive load theory, variation theory and much more is available directly from my publisher, John Catt Educational Ltd, from Amazon, and from most good (and evil) bookshops.
My second book – Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom – is now available to buy from Amazon, John Catt, and many other retailers.
As well as exploring how to get the most out of the sequences of questions and examples on my variationtheory.com website, you will find an epic 45,000 word chapter that reflects on what I have learned in the last two years about the core ideas from How I wish I’d taught maths, including SSDD Problems, Low-Stakes Quizzes, and Silent Teacher.