# Course design: basics first or teach "as you go"

I am going to offer an elective course which I am free to design. The topic is a bit special, but we can assume I give a robotics course. I will teach a fair amount of probability theory which I need to solve problems in robotics. Therefore I have to teach both and there are, I think, two ways:

1. Teach probability theory first, then robotics.

This is what all my professors did as I was studying. The problem here is, that there is no concrete application to robotics at the time I teach probability theory. Examples are "made up" and so is the homework.

2. Teach robotics and introduce the necessary probability theory when needed.

The students see immediately why it is necessary to learn probability theory. They can directly apply the theory to solve their real problem in robotics. However, it interrupts the robotic topic. The first time I need (parts of) probability theory takes two weeks. Then we would do robotics again and apply the new concepts. Then, after 2/3 of the course comes probability theory again, as we need a further different topics to solve more problems. Maybe once more.

Are there any good resources on howto teach courses like this?

• Do (2) but make the probability notes independent from the other notes such that they can be read in a selfcontained way. Commented Nov 27, 2020 at 15:11
• @user111388 Good idea. Commented Nov 27, 2020 at 17:39

I assume you know your students better than I do, but this would depend to a certain amount on what sorts of things they expect. At base, it seems like they are expecting/wanting a course in robotics. Starting out with something different might disappoint them and turn them against you in a way that could be hard to "make up" later. This implies doing statistics/probability "just in time".

However, students who are used to, and comfortable with, highly theoretical courses might be fine with "basics first."

But another alternative is to give them, early on, a set of readings on probability that you advertise as being essential a bit later in the course, while you focus on the robotics part. The better students might spend some time scanning, at least, those readings, making it easier to do the probability stuff when it becomes essential. You might even be able to find a vehicle for responding to questions on the readings without cutting too much into the time you spend on robotics early on.

And, of course, if their expectation is that robotics is just "applied probability" then theory first would likely be better.

But, think first of the student expectations and work to satisfy that as much as is reasonable.

Context always helps me to learn something. By giving the robotics topic first, you provide context on the probability, which makes it less abstract and easier to understand, which is very useful for the practically minded learners. For the theoretical learners, switching contexts from robotics, to probability and then back to robotics should be easy enough.

The biggest problem I had in my university education was always "why". By showing the context first, you address that for free, and can use examples that your students should understand.

Also, if you give something to get started with on robotics, an excited student can carry on with that in their own time while also learning probability, instead of twiddling their thumbs waiting for the robotics part, resenting that they have to do the theory first.

Motivating the students to learn probability theory is important, so if you can do it well, I think the "just in time" method (option 2) is the better method. There are challenges with teaching a subject like probability theory in a piecemeal way, but you might be able to teach the parts you need effectively using examples in robotics. If you can do this well then the robotics course might even serve to whet the appetites of your students to learn probability theory more systemtically in a full course.

The evidence-based approach is to do both: If you teach something early and teach it again later, students will build long term memory.

• +1 and thanks for the reminder that a spiral approach is usually best. Each return to a topic takes the student deeper. Commented Dec 30, 2020 at 13:40