The last article I wrote for this newsletter elicited a lot of responses. It is the most read and commented upon article in the series thus far. That tells me that many of us have a deep interest in the education and training of engineers. It also revealed something else – many seemed to assume that if you do well on the exam, then you understand the respective theory.
I am going to explore that assumption more in this article: Do good exam marks really mean good understanding?
It’s all on the surface.
When I was an academic and involved in education research, I was introduced to a phenomenon called surface learning. It is where students study to pass the exam as opposed to studying for understanding. We all probably have some experience doing this, where we drilled questions (maybe even used Schaum’s) or we remembered things. Or we know a fellow student who would get good marks, but never seemed to actually understand anything. That’s all surface learning.
You can get away with this when the exam is set such to allow for this.
And many exams are like that.
They don’t assess understanding, just your ability to drill problems to pick up on the procedure and repeat it at speed.
As an example of how pervasive this is, take the time to watch the video below. It features Eric Mazur, a physics lecturer, talking about his students and how shocked he was when he assessed conceptual (read “actual”) understanding after the first year of physics.

Some key points from the video:

• He never asked himself how he would teach.
• He still got high satisfaction ratings.
• He thought the students did well.
• He thought he was a great teacher.
• Exams went well – based on marks.
• He used typical textbook problems.
• When he found that many students at other universities did not learn well, he was convinced his Harvard students were learning.
• He was wrong – it is impressive that he chose to be so scientific about this.
• There was a difference between how students think in daily life and how they think for exams.
• The students used what he called “recipes” (read “surface learning”).
• Once he came up with a better teaching method, one where students actually learned, he does not say anything about how his satisfaction ratings went.

You can infer from this, that his students were engaged in surface learning until he corrected both his teaching style and assessment method.
Surface learning isn’t just about the student it is encouraged by most exams in engineering courses around the world.
As I mentioned in the previous article: many exam questions will list only the variables needed to find the answer. In such a scenario, students only need to recognise the pattern (or the recipe).
This is why grades don’t always (and often don’t) reflect understanding. The exam format can encourage procedural fluency at the cost not conceptual understanding.
But what to do about it now?
If you would like to improve your conceptual understanding of first principles, and you should, then one of the best sites you can go to is Arbor Scientific. They offer numerous teaching resources that you can sign up for, but they also have a great conceptual questions page - https://www.arborsci.com/pages/next-time-questions. Go check them out and get the resources once you are done. I liked the double boiler question and the bikes and bee question.  See which ones get you thinking or reveal your lack of understanding so you can improve it.
Before I finish though, I’d like to ask: what conceptual understanding tools do you know of? I am always keen for more and others here can benefit from them too.

If you have read my book, then you will know that first principles are at the core of good engineering practice. They provide you with excellent constraints when making decisions. This in turn means you can focus your energies on other well less defined decisions.
 
An illustrative example that given by Gordon Murray when he was explaining his thinking process, involved the specification of a steering shaft in F1.
 
It was quite common for engineers to simply specify a nominal diameter – 25mm (around 1”) for example. That was because that was what everyone had done, it seemed to work, and it was thus easier to do that on all other cars.
 
However, that meant you could either be carrying excess weight. Or, it might even mean that you were close to failure and steering could be lost part way through a race. Neither option is ideal. So by taking a relatively small amount of time to calculate the diameter that would be able to transmit forces required, one could, in such an instance, know that they have an optimised and safe design.
 
That’s the power of being a mathematician as an engineer. You optimise.
 
But, there is also something more; something nearly magical. You gain great insights when you use first principles. Insights that can almost make you look like a magician.
 
Back to steering columns.
 
When Gordon Murray started to analyse the steering column, he realised that there were two types of loads: bending and torsion. Bending was mostly from the driver leaning on the steering wheel. Torsion was from the column’s main purpose: steering.
 
From this insight, which was provided by the use of theory and mathematics, it was possible to re-frame the problem. There was to be a structure designed to support radial loads, and the shaft was to be optimised for transmitting torque. This allowed for further optimisation of the overall design.
 
And it all started with the decision to use first principles and mathematics.
 
So by being a mathematician as an engineer, you can also be a bit of magician.
 
But it can also stop you from being a fool.
 
I also mentioned in my book when I was designing a dynamometer for model solar boats. They were small vehicles designed by students. So, it seemed to me, it should not be too much of a challenge to have a design where the water flowed under a stationary boat. That would allow for the boats to stay tethered in one place under a lamp (emulating the sun). Then, students could experiment with different configurations for different solar conditions. It all seemed like an easy way to offer great outcomes.
 
But then I decided to apply some first principles.
 
This was to choose the right pump. And, as it turned out, I needed a pump that could move 1 tonne of water every second!
 
I felt embarrassed.
 
But the senior technician, who was to organise the implementation of the dynamometer I designed, was grateful that I at least did the calculations – later, but before we actually started any construction. It seems many other engineers he had dealt with were neither mathematicians nor magicians.
 
And you now know what that leaves!
 
So, make the choice now to use first principles to guide your engineering decision making. Do some mathematics. And then make the most of those extra magical insights you will gain.