Rule of three

When you see a subject only once you barely learn it and may not remember the subject later when you need it. Our experience is that knowledge does not usually stick after one exposure.

What does work? We have found that three types of exposure to a subject works well. Specifically, we give a pre-class interest exposure, an academic class exposure, and a post class experiential exposure.  As an example, in our university BUILD program, the freshman build a stepper-motor based 3D printer. They measure the performance of the printer, measuring runout and noting what happens if you try to run the machine too fast.

We then hold a design review discussing what is causing these limits. Why is there a runout error? Can we redesign to improve runout?  What limits the speed of the machine?   How could we make it print faster?

The students are then shown the machine that the juniors are building. It is more accurate and runs a LOT faster! The open loop stepper system was replaced by a closed loop PID servo-controller. It is shown to them by example that if you only knew differential equations your machine could run a LOT faster. They are shown an introductory analysis and application of differential equations. After seeing this example, one might even anticipate and look forward to taking differential equations. 

A few semesters later they find themselves in their differential equations class. From their freshman design review they know why they’re there. They've thought a little about differential equations for a few months. They see the application of those equations. They are willing to work hard during this second exposure and learn them well. 

When they are juniors, they make a pick and place machine using what they learned in differential equations and controls courses. They are excited to employ those pesky differential equations. This is their third type of learning and they own the information for life.

We strive to hit every subject in the engineering curriculum with this golden rule of three. In fact, this is how the four BUILD classes and their projects were designed. We took every class in the EE curriculum and mapped it twice into the projects – once as pre-class interest exposure and once as a post-class experiential exposure. This enhances every single class in their academic career without changing the classes themselves.

We strive to hit every subject in the engineering curriculum with this golden rule of three. In fact, this is how the four BUILD classes and their projects were designed. We took every major concept in the EE curriculum and mapped it twice into the projects – once as pre-class interest exposure and once as a post-class experiential exposure. The goal was to enhance every single class in the curriculum without changing the classes themselves. Figure 1 shows the mapping for differential equations. As freshman, the students attend design reviews for the sophomore and junior projects, seeing the product of the differential equation tool. Here, depicted by the black arrow, they see how much faster and smoother the junior pick and place machine runs than the sophomore and freshman machines. They see how PID control works and understand that if they just knew differential equations they can do this. As sophomores, as depicted in the brown arrow, they take the differential equations and get a deep, motivated dive into the subject. As juniors, they design, build, test, and perfect their pick and place machines and use differential equations. They’re still learning about them as depicted by the bidirectional red arrow. As Seniors they are using and teaching them as depicted in orange. In this way the four flagship courses enhance every single class in their academic career without changing the classes themselves.

One very good way to become a deep expert in a subject is to teach it and the BUILD program takes this to heart. The fourth of our three stages of learning is a teach-back approach that has proven very effective in our programs. Sophomores teach freshman and juniors teach sophomores. This is done in a variety of places throughout the program but is best exemplified by active attendance in each other’s design reviews.

It has been pointed out to us that our rule of three teaching style nearly mirrors that practiced in the medical field. The traditional method of teaching surgery is known as See One, Do One, Teach One (SODOTO). This is a mature learning realm that we were unaware of and have since adopted aspects from after learning about it. Developed in the 1800’s, SODOTO is still an active, developing field.

Figure 1: The BUILD program maps every class in the EE curriculum twice into the BUILD projects to enhance every single class in the curriculum without changing the classes themselves. As an example, here is how Differential Equations is threaded into the BUILD courses.

Obviously, not all information gets all three within the university program. It is not possible, for example, to give them a preclass exposure for things they learn their first semester and it is not possible to give them a post class experiential exposure for what they are learning their last semester. We do, however, include these in the BUILD Foundation K-12 and post graduate mentor programs.  One of the best ways to teach critical thinking and curiosity is running experiments and testing products.  This should start in kindergarten and never stop being part of the process.  Nothing is better at teaching a person how to learn, how to think critically, and how to appreciate learning than venturing into the unknown and trying to prove or disprove something.

Let’s take a look at the Rule of 3 put into place with Op-amps.

One of the Freshman exercises is to build a line-following car kit. The idea is simple - a little car uses light sensors to measure it’s left-right position on a line. If the car is too far to the left, the left wheel spins and the right does not, turning the car to the right. If the car is too far to the right, only the right wheel spins, turning the car to the left. A comparator is used to determine whether the car is too far left or to far right. This is called bang-bang control and is shown on the left.

They are then shown a modified car where the comparator is replaced with an op-amp and the bang-bang control is replaced with a proportion control. In this case, the amount of steering is proportion to the error - if we’re just a little to the right, we turn a little to the left. If we’re very far right, we turn a harder left.

We then teach a little about op-amps and the students modify their cars to add proportional control to their project. This is shown on the right. Note that the cars are going the same speed but the Freshman car takes 33% longer (12 seconds versus 9 seconds) because it is taking a longer, more sporadic path. Note that about seconds into the sophomore video the car gets off track a little. Adding Integral and Differential control to the Proportional control (PID Control) will fix that the following year.

With this quick lesson, we give the pre-academic interest exposure for op amps and closed loop control theory.

The following year they take a their usual course on op-amps. But for a year they’ve know why op-amps are so useful and know a little about using them. The math they encounter in this class is not abstract, it is understandably applied. Their second exposure, the academic class, is now meaningful and they have built-in interest and incentive because they know where they’re going.

They then use op-amp and full PID controls in their sophomore year when they build their pick and place machines. They truly understand these things as they apply them and own the tools for life after this third, applied exposure.

Summary: What’s in this for you?

Engineering classes are hard and occasionally boring. This is in large part because you don’t know why you’re learning these things and don’t see why you are there part of the time. We have worked hard in the BUILD program to fix this. You are going to be introduced to each subject before you learn it so you know what you can do if you master this academic material. Then you’re going to learn it. Then you’re going to forget it if you don’t use it! What a waste! So you’re going to apply it. And then you’re going to teach it and help others do it. You are going to be excited about the material and you’re going to own it, not just learn it for the test and then forget it. This program is different. It really is.