Can AI create a set of SSDD Problems?

If it can, then I am one step closer to retirement

Craig explores whether AI can generate effective Same Surface, Different Deep (SSDD) Problems—a powerful technique for developing problem-solving skills. At Eedi, our Stretch & Challenge quizzes already help students tackle these types of questions, encouraging deeper mathematical thinking— try them out by clicking here and creating your free Eedi account.

Last week, we examined AI's ability to create an Explain the Mistakes GCSE revision resource. This week, we set AI the challenge of doing something else to help save teachers’ time and hopefully do our jobs better - creating a set of SSDD Problems.

What are SSDD Problems?

I wrote about SSDD Problems in my first book, How I wish I’d taught maths. They are a special set of problems with a common surface feature but different deep structures (SSDD stands for Same Surface, Different Depth). In other words, they look similar at first glance, but a more careful inspection reveals they are from different areas of mathematics.

Here are three examples from my SSDD Problems website:

I love these sets of problems because they help students develop a key problem-solving skill: recognising what topic a question is from. Students need to sift through the constant surface features to figure out what the question is asking them to do, instead of just launching into the same procedure every time they see a trapezium or a fraction.

For my fellow geeks, SSDD Problems tap into three of the explanatory mechanisms of interelaving:

1. Retrieval practice – instead of retrieving one idea, students need to retrieve four ideas. Each act of retrieval strengthens that memory.

2. Attention attenuation – students have to pay more attention when topics constantly switch than they would have to if the practice focused on just one idea.

3. Discriminative constant – this is the big one. Research suggests that well-designed interleaved practice assists learners in discriminating between topic areas. Because each set of SSDD Problems has a surface feature in common (an image, a number, or a context), students must think hard about identifying the relevant deep structure to figure out what strategy to use to solve the problem.

SSDD Problems are great to use after you have finished teaching a topic. As long as one of the questions in the set of four relates to that topic and the other questions relate to concepts students have encountered, you have a supercharged, interleaved resource.

SSDD Problems are also fantastic to use in the build-up to exams. After all, a GCSE paper is essentially a high-stakes version of interleaving.

The prompt

As we know from our previous AI explorations, the quality of the output lives or dies on the quality of the prompt. Here was my initial attempt:

Are you aware of Craig Barton’s SSDD Problems? He discusses them in his book, How I wish I’d taught maths. In short, SSDD Problems are sets of 4 questions that each share a common surface feature (this could be an image, a context, a number, an expression), but have different deep structures (in other words, they are from different areas of mathematics).

I would like you to help me write some sets of SSDD Problems. I will give you one topic that I would like to include. I would like you to choose a common surface feature and then write 4 questions using that surface feature. One of the questions is from the topic I stated, and the others are from different areas of mathematics. Make the four questions of similar difficulty.

For the output, please give:

a) the 4 questions

b) the topics they are from

c) the full solutions to each question

Do you understand?

ChatGPT never refuses a challenge:

The outputs

Example 1

The topic I gave it: Division of fractions

The output:

1. You have 3/4 liter of orange juice. If each glass requires 1/2 liter, how many glasses can you fill with the available juice?

2. Solve for x in the equation:

   

3. A circular sector covers 3/4 of a circle’s circumference. What is the measure of the central angle of this sector in degrees?

4. A machine produces 3/4 of its daily quota in 2 hours. Assuming the machine works at a constant rate, how many hours does it take to produce the entire quota?

ChatGPT also displays the topics and solutions as requested:

My verdict:

A pretty good effort! I expected it to just come up with procedural questions with the operation changed (3/4 + 1/2, 3/4 x 1/2, etc), but the fact it has wrapped these questions up in a context increases the challenge. Question 3 is significantly more straightforward than the other 3, but that is not a bad thing. If we change the order around and put Question 3 first, we have a nice way in for the students that might give them the momentum to try the other questions when things get tough.

Example 2

The topic I gave it: Volume of a cuboid

The output:

1. Find the volume of a cuboid with a length of 24 cm, a width of 5 cm, and a height of 3 cm.

2. Solve for x in the equation:

3. Find the sum of all positive divisors of 24.

4. A regular polygon has 24 sides. What is the measure of each interior angle?

My verdict:

This set is not as strong as the last one. The surface feature of 24 alone is not that useful for getting students to think hard about the volume of a cuboid.

Two other things I have noticed:

1. Question 1 is always based on the topic you specify. So, we will need to either edit the order or edit the prompt to ensure students do not pick up on this unintentional cue

2. ChatGPT loves asking a “solve this equation” question for Question 2

So, before giving ChatGPT the next topic, I offered the following feedback:

For future topics please:

a) Do not always put the topic I specific as Question 1

b) Do not always use solving equations questions

c) Whilst the numbers should always be kept constant or similar, please also try to make the questions themselves look as similar as possible (for example in words, objects, context) to increase the challenge in trying to determine what topic the queston is from

Let’s see if this improves this set of SSDD Problems:

1. At the Evergreen Middle School Science Fair, Taylor’s project is one of 15 featured exhibits. One project is chosen at random for a special spotlight. What is the probability that Taylor’s project is selected?

2. The 15 projects are divided into two display types: cuboid displays and triangular displays. The ratio of projects with cuboid displays to those with triangular displays is 2:3. How many projects have cuboid displays?

3. Taylor’s project is showcased in a rectangular container. The container has a length of 12 cm, a width of 8 cm, and a height of 6 cm. What is the volume of the container in cubic centimeters?

4. Taylor’s project was evaluated by 5 judges, receiving scores of 7, 8, 9, 8, and 8. What is the mean score?

This is better, although I think using dimensions 15, 2, and 3 in Question 3 would have improved the challenge of discriminative contrast with Question 2. Likewise, those three numbers could have been included in Question 4.

But making those changes will take me 30 seconds. Writing a set of SSDD Problems from scratch would take much longer.

Example 3

The topic I gave it: Negative number operations

The output:

1. Evaluate the expression: -10 - 6

2. A bag contains 10 marbles, one of which is red and the remaining 9 are blue. If one marble is selected at random, what is the probability of drawing the red marble?

3. Evaluate the product: -10 x 6

4. Solve for x in the equation: 3x - 13 = -10

My verdict:

Again, this is not too bad. ChatGPT loves a probability of a single event question, but I could prevent this by asking it to come up with a question from a different area of maths for Question 2. I like Questions 1, 3 and 4.

The verdict

ChatGPT is good at creating the seeds of a set of SSDD Problems. Whilst no set is perfect, it is undoubtedly good at generating ideas for topics to include, and questions to assess those topics. Hence, it achieves the two things I am primarily interested in when using AI: Can it help teachers do their jobs quicker?… Yes. Can it help teachers do their jobs better?… Yes.

If someone with no experience writing SSDD Problems relied solely on the output of my prompts, the results would not be great. AIs, in their current form, are best used to generate ideas and suggest improvements—they cannot substitute for teacher experience or expertise.

I also find the process of writing and refining prompts fascinating. It helps me improve the clarity of my thinking and communication. Looking back at my original prompt, I can see why ChatGPT produced the second set of questions—my unstated assumptions were to blame. If these models do not produce the output we have in mind, the fault is likely to rest on us. While that is undoubtedly frustrating, writing and refining prompts can help us become better communicators.

Want to know more?

1. You can find 100s of sets of SSDD Problems at SSDDproblems.com

2. I write about how I use SSDD Problems alongside two other activity structures to help students become better problem-solvers here.

3. Subscribe to Neil Almond’s excellent Teacher Prompts newsletter for more weekly AI goodness

Is this a useful use of AI?

What do you agree with, and what have I missed?

Let me know in the comments below!

🏃🏻‍♂️ Before you go, have you…🏃🏻‍♂️

1. … checked out our incredible, brand-new, free resources from Eedi?

2. … read my latest Tips for Teachers newsletter about Inside the Black Box?

3. … listened to my most recent podcast about the Do Now?

4. … read my write-ups of everything I have learned from watching 1000s of lessons?

5. … considered purchasing one of my new 90-minute online CPD courses?

Thanks so much for reading and have a great week!

Craig