It’s called pedagogical scaffolding for a reason.

Structure versus unstructured — it’s the age-old debate in education. It’s popped up recently in my department, my lab, and my family. While thinking about this in passing I had a major shift in how I view the problem. Hopefully, it will change how you consider the problem too.

The problem is best exemplified for engineers by the traditional mathematics curriculum. Anybody that’s had a calculus class knows that the textbook is packed with equations that you, through repetition, are supposed to derive the solution for. Nobody has any clue where the starting equations come from, what they are connected to, or why they matter. The instructor assigns a few exercises that they find interesting, the solutions are kept by the instructor in a solutions manual, you do the exercises, submit your work, and get judged on accuracy. It’s been that way for over a century.

Times have changed.

When I was a student the tradition was that as soon as a textbook came out, the solution manual would be posted to some back-channel website and everyone would have the solution. This started as I was graduating college and grew to a terrible state where nobody had any idea how to do any work because they’d just record the solution from the manual. It’s just natural to take the path of least resistance.

Since I started at WSU I’ve worked hard to break this cycle by using software to come up with my own original homework assignments with motivation and inspiration coming directly from the research in my laboratory — which I happen to find fun. Only solution is in my head. However, this semester’s class surprised me. I would make up a homework assignment (literally about one of my old cars) and within 30 minutes of it being assigned someone from the class would post it to The irony is that even I had not made up a solution to the problem yet!

Thinking back on my math days as a student — I really didn’t understand differential equations until my graduate-level heat transfer course from my advisor Greg Nellis at Wisconsin. In the class, he’d give us a situation — a temperature or heat transfer boundary condition and ask for some kind of solution based on a typical problem that would come up in the field. We had to derive the sets of equations that governed the problem from scratch! The challenge was to use your judgment to include only the physics that the problem was sensitive to. Once you had the governing equations derived, we’d just plug it into software like Wolfram Alpha or Maple which would do the math to spit out the solution from those already known to humanity. The machines are good at this. Graph the solution to solve initial customer requirements. Voila! Sadly though, this heuristic approach to setting up problems is not typically emphasized by engineering curricula; with notable exceptions like Olin College.

What I’ve noticed recently is the difficulty that students have transitioning from the structured traditional algorithmic problem-solution based paradigm to the less-structured heuristic problem formulation based paradigm. I’ve had several students who are absolutely brilliant with traditional algorithmic problems, only to become unhinged or unmoored when freed from the algorithmic structure. Change the situation and your students totally forget to apply the basic rules and processes you’ve taught them. Lord of the flies…

It reminds me of a problem from my childhood.

A dog “choker” chain — it looks menacing for a reason.

From age 6 through probably 13 I was involved with a 4-H dog obedience club. Through repetitive use of treats and a “choker” chain (carrots and sticks), you can teach a dog to walk alongside you, sit when you stop, stay when commanded, and many other exercises in “obedience”. I’d be able to train a dog well, win awards, etc. It’s really not that hard it just takes time. I learned to exercise restraint with authority after choking my dog once in front of an audience — one of a handful of griefs I have in life. What I noticed though was that, despite being very obedient, when my dogs got out of the yard, or the leash came off, they’d lose their minds. Really, they’d take off, not listen to anything, pee all over everything, run out into traffic, etc.

Watch a dog trained in the woods without a leash and the situation is very different. They know to stick within earshot because they could get attacked by an animal, left, lost, etc. They can govern and bound the problems for themselves and improvise solutions when needed. That said, they probably don’t know when to sit when they should, may have problems staying on command, and probably wouldn’t do well in a city with a leash law.

What you can see from this comparison is that neither approach to education — algorithms or heuristics, structure versus unstructured, problem-solution versus problem formulation — is optimal for all situations. The challenge is a healthy contrast that teaches people when and how to ‘shift gears’ between these paradigms based on the environment and situation.

If we rebalanced curricula to promote the foundational algorithmic solutions in morning classes as predicated by real industry-sponsored design problems in afternoon classes, a process known as pedagogical scaffolding, we may get to where we want to be. Websites like and others would become completely silly in the eyes of the students relative to professional faculty backed by industry. They’d be well on the path to proficiency. See this post from 3 years ago for more info: 

And, unlike the old adage, I know first hand it’s totally possible to teach an old dog new tricks. You just have to begin.