What is the right distribution of depth in one’s studies? What kinds of knowledge and skills are actually retained?
I believe there are three kinds of depth achieved, what I call the “toolbox”, “toolshed”, and “catalog”. The toolbox is the collection of skills that one has “ready at hand”: one needs no re-study or practice, and can immediately give guidance on their employment. The engineer can recall from a variety of past examples to judge the suitability of such techniques to any given problem. Their strengths and limitations are situated in the broader disciplinary context so that one can explain, for example, where classical computer vision is the right choice as compared to convolutional neural networks or transformer models, or, the relative merits of nails, screws, and wood glue.
The “toolshed” is the body of knowledge that requires what we could call ‘retrieval and repair effort’: although you may have learned certain concepts in class, you need to refresh your memory and work up with practice problems before tackling the main problem in front of you. You have some sense of when these tools should be used, but you have relatively little practical experience with them. You are aware of the mathematical formulation of these techniques and can trace their prerequisite concepts. You learned about the Fast Fourier Transform in class and did some exercises, but haven’t gotten to use it on the job.
The “catalog” consists of the techniques and domains of which you are aware and have seen others use. You know the right keywords to begin to learn about them and the right kinds of people to learn from. You may have never done Printed Circuit Board prototyping yourself, but you know that it can be done and who to call to get started.
Each of these levels of depth has their place in one’s knowledge. The toolbox skills are the most useful, but also the most expensive to acquire. Design-Build projects add skills to your toolbox. However, the true integration into the disciplinary context is founded upon the theoretical knowledge that typically comes from formal study. The toolshed skills usually come from classes which you haven’t had a chance to use directly. It is usually less time-intensive to put things in your toolshed and still useful for your own general understanding of the discipline. As needed, you can go deeper with these toolshed skills. The catalog comes from survey courses, popular science publications, YouTube videos of people building things, etc. Your catalog is how you know what is even possible.
Most traditional courses consist of readings, lectures, problem sets, and tests. These put skills in your toolshed and not your toolbox. If your toolbox is relatively empty at graduation, and you haven’t had the repeated experience of adding to it, then you will need to develop a new mindset at the beginning of your career: building the bridge between the theoretical knowledge of a domain and its practical application. For this reason, it is critical to have toolbox-depth early in one’s studies. On the other hand, if you only try to gain toolbox skills, then you may have not had the time to develop a broader disciplinary awareness. You might not see how the different theoretical parts of the subject fit together. This tension between depth of skills and breadth of theoretical knowledge necessarily exists in the curriculum because of time constraints.
For these reasons, I think it is profitable to envision the ideal depth distribution as “V-shaped”. The progression from awareness, to knowledge, to confident application as a ‘V’ deepens is itself a mindset to be cultivated. I contrast this with the common vision of the “T-shaped” professional: one who has depth in one specific domain and then breadth in many. It might seem like a quibble, but I think this “T-shape” does a disservice to the project of life-long learning. The “V” is like a wedge that continuously deepens over time across a variety of techniques and disciplines. Progressing in one naturally aids in others. Contrarily, the “T” may get wider in width and deeper in depth but seemingly without a relation between them. Mathematics, learning mindsets, and technical communication skills all overlap between fields and mutually reinforce each other. The curriculum ought to be ordered to creating “V-shaped” engineers.
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