Teach Integration from Day One

Posted 3 weeks, 1 day ago | Originally written on 28 Jun 2024

One day I will teach.

That has been my dream for most of my life ever since I was asked by my maths teacher to give the class an introduction to calculus in high school. I was lucky because I grew up in a house that revered books. Books were everywhere and one day, I chanced upon a book that broke down the two fundamental concepts of calculus before I even knew how to express them mathematically.

And so I was thrust before my class in the empty hours before we finished high school. The maths teacher knew well enough that there was way that calculus would feature in the final exam so he could risk having this enthusiastic neophyte lead the class astray.

In my later years, having worked with Python from over a decade, I felt confident enough to put together my knowledge into a course. My first attempt was pitiful, though the remains are still at large for the world to see. In retrospect, they were nothing more than the ordinary YouTube 'course': the author, brimming over with excessive confidence, graciously shows off how easy it all comes to him. I wasn't really teaching; I was doing a tour of my knowledge. And for that I am ashamed.

My second attempt was more measured but just as unsuccessful. I substantially toned down the volume and complexity and opted for something more approachable. I do feel that I put more of an emphasis of the subject that on the author but this is where I new revelation has subsequently dawned on me. And I blame it on systems thinking.

One of the key insights of systems thinking is the notion of emergence. The outcome of assembling a viable system is often an effect which does not exist in any of its components––subtle but profound. I cannot put it better than the Systems Bible by John Gall:

"An Airplane has been defined as a collection of parts having an inherent tendency to fall to earth, and requiring constant effort and supervision to stave off that outcome. The System called “airplane” may have been designed to fly, but the parts don’t share that tendency. In fact, they share the opposite tendency. And the System will fly—if at all—only as a System."

If there is any reason why anyone should practice systems thinking, this is, by far, the best. In most scenarios, we are primarily interested in some effect arising from a complex interplay of factors or components. Therefore, considering anything other than the complete system amounts to complete failure. And it is for this reason that I decided to revise my approach to teaching.

Integration from Day One

When I find time to teach again, here is my strategy: give the students a complete real-world example from day one. I know it will be overwhelming at first but you would be surprised how fast we tend to get over the initial shock and cozy ourselves to our knew surroundings. Students should only and always every work with complete systems. This means that, even if they don't know how to create that example, they should be aware of its existence. In any case, your role as a teacher is to be present to provide answers in keeping with the extent of their knowledge.

What would this look like in practice? Well, suppose the goal of the course was to get the students to confidently set up some data analysis workflow. I would ensure that they start off with a complete workflow that does something. It should not produce any errors––that is confounding. It should do what they expect of it and illustrate it with best practice. Thereafter, it can be used for illustrations and the students can then be gradually guided on how to make adjustments to achieve variations in the goal.

Only after completing this exercise does it then make sense to 'analyse' the components. Unfortunately, this is where we often begin. Once students have a hint of how the functional pipeline works does it make sense to now explore what a list is and study its properties and behaviours. In fact, this provides a excellent launch pad from which to develop exercises and challenges.

This approach––first demonstrate a complete solution and only after perform an analytical tour––means that we start with an integrated view from the outset. This is what I should have done and this is what 99% of all YouTube educators fail to do.