People are already using models to learn anything - and depend on models to answer their questions completely and truthfully.

But that is almost orthogonal to great tutoring. Great tutoring is not about users but about students: playing with them, challenging them, rewarding and consoling them. It is also about repeatedly engaging them and getting them to feel a sense of progress that keeps them coming back excited.

Below are some (rough) sketches of simple things language models can do to improve learning.

Alright, so as we delve into set theory, here's an interesting and easy-to-understand fact about sets. A set is simply a collection of distinct objects, considered as an object in its own right. For example, if you have an apple, a banana, and a cherry, when you group them together, you have a set of fruits. Keep in mind that each item in the set is unique; there can't be duplicates.

I think I get it.

I'm not sure I understand.

Above: A user interface prototype. The gray dot indicates user input

Questions can be answered by a model, but the model can also...

Alright, so as we delve into set theory, here's an interesting and easy-to-understand fact about sets. A set is simply a collection of distinct objects, considered as an object in its own right. For example, if you have an apple, a banana, and a cherry, when you group them together, you have a set of fruits. Keep in mind that each item in the set is unique; there can't be duplicates.

I think I get it.

Now, let me hide my explanation. Can you repeat the definition of a set for me?

Sure. A set is a collection of distinct objects, and it's considered an object on its own. And there can't be any duplicates in a set.

Perfect! Well done. It's essential to grasp these basic concepts as we move deeper into set theory. Keep up the great work!

... hide the previous answers (here, they are covered with a black box) and ask the student to test their recall.

Let's continue with an interesting fact: Every set is a subset of itself. Now, here's an opinion from Carl.

Confident Carl

If every set is a subset of itself, then that means if we have a set ( C = {6, 7, 8} ), there is another set ( D ) that is a subset of ( C ) and is not equal to ( C ) itself!

Is "Confident Carl" correct in his statement? Why or why not? Think and debate.

Correct because

Incorrect because

What if the app wasn't always right? Here, a hypothesis is presented by a hypothethical peer, and the student is challenged to investigate if it's true. More importantly - the student can be probed to provide their reasoning until they fully understand why something is true or false.

Alright! Moving on to another interesting fact about sets. Let me give you a hint: It's something that happens when a set doesn't contain any elements. Can you guess what we're going to discuss?

umm... empty thingy?

Close enough! That's called an "empty set" or "null set." It's a set that has no elements in it. For instance, the set of all unicorns on Earth is an empty set since there are no real unicorns on Earth. The symbol we use for the empty set is ∅. It’s a cool concept, isn't it?

oh! got it. so it's like an empty basket.

Exactly! Just like an empty basket with nothing inside. The concept of the empty set is foundational in set theory. Well done for catching on so quickly! 🌟

Even before knowing the answer, asking the student to apply effort and **guess** the answer improves retention.

Welcome! Today, we're diving into set theory. Before we start, how familiar are you with sets?

kinda know. like groups of stuff?

Exactly! Sets are collections of distinct objects. Let's try an example. Think of a set of your favorite fruits. Can you type them out?

apple, banana, cherry

Great choices! That set can be represented as {apple, banana, cherry}. Now, for our challenge worksheet. Ready?

yup!

BONUS QUESTIONS

Earn up to 10 XP per question

1

If Set A = {apple, banana, cherry} and Set B = {banana, cherry, date}, which fruit is in both sets?

2

If Set C = {grape, apple, banana} and Set D = {apple, kiwi}, which fruits are ONLY in Set C?

When a section is completed, one kind of finishing ceremony could be a worksheet - a short list of questions graded and reviewed. This resembles in-person exams, but is more tailored and more fun via the short feedback times.

Welcome to the Set Theory Module! Today, we have a special challenge for you. We've been discussing various aspects of sets and their properties. As you continue on this learning journey, you'll get to face off with Dr. Miguel. He's a renowned mathematician and a champion of set theory. To make things exciting, you can earn XP for every correct answer. Remember, Dr. Miguel is known for his challenging questions, but he's also fair. Impress him with your understanding, and you'll be well on your way to becoming a set theory master. Ready to take on the challenge?

Challenge

Dr. Miguel

Dr. Miguel

Good day, young learner! Set theory is fascinating, isn't it? Let's start with something simple. Can you tell me, what is the definition of a set?

a set is a collection of distinct objects, considered as a whole.

Dr. Miguel

Well done! You're off to a great start. +10 XP! Now, imagine two sets: A = {1, 2, 3} and B = {3, 4, 5}. Can you tell me what A ∩ B is?

i'm not sure

can you give me a hint?

Another kind of finishing ceremony could be a final boss like challenge, where the student can earn XP for correctly answering questions from a slightly snarky ‘expert’.

Alright! Before we proceed, did you know that in set theory, if you have two sets with exactly the same members, they are considered equal? This means that the set {p, q, r} is the same as the set {q, p, r}. Interesting, right?

yeah, that's cool!

Fantastic! Also, here's some exciting news: You're on a learning streak! If you continue at this pace and attend all sessions this week, you'll earn a special badge. Plus, maintaining a streak will allow you to earn additional experience points (XP) and level up faster! Keep up the momentum!

While most reward mechanisms are similar for the entire student population, new learning apps can gauge sentiment and reward students differently.

The rewards that students earn can be modulated case-by-case. You can motivate students doing poorly by giving them a bonus, and motivate students doing well by tuning the level of challenge.

These brief sketches are just a few examples of how a new learning app can be designed to be more engaging and effective than a traditional chatbot style Q&A app.

Ideally, a content-rich company like Brilliant would build this out internally. But maybe if courses can be built by connecting a model with these behaviours trained, as well as a course outline involving learning objectives serving as journey waypoints, then you might not need a team of course writers at all.

If you see something that I can use that works anything like this, let me know at gytdau@gmail.com.