Subjects · Engineering & Technology
Engineering & Technology: Prerequisite diagnosis
Find out whether your engineering problem is a mechanics problem, a maths problem, or a units problem, because it's usually one of those three and they need different fixes.
What you'll be able to do: Find out whether your engineering problem is a mechanics problem, a maths problem, or a units problem, because it's usually one of those three and they need different fixes.
The three floors
Engineering sits on three foundations, and a gap in any of them produces failures at the top that look like difficulty with the engineering topic.
Mathematics. Calculus for anything varying, differential equations for anything dynamic, linear algebra for systems, statistics for tolerance and reliability.
Mechanics and physics. Equilibrium, energy, momentum. Most mechanical and civil difficulty is a statics gap.
Units and dimensional reasoning. The floor beneath both, and the one most often missing. A student who cannot fluently convert, cancel and check dimensions will produce errors in every quantitative topic, and each will look like a different problem.
The diagnostic value here is high because the remedies are so different. A mathematics gap needs mathematics. A units gap needs an afternoon and then disappears forever.
The chains that recur
| Can't do | Usually broken at |
|---|---|
| Beam deflection | Integration → boundary conditions → what the constants mean |
| Dynamics problems | Newton's laws → free-body diagrams → vector components |
| Circuit analysis | Simultaneous equations → algebraic manipulation |
| Control systems | Laplace transforms → complex numbers → differential equations |
| Fluid mechanics | Dimensional analysis → units → algebraic rearrangement |
| Thermodynamics | What a system boundary is → conservation → algebra |
| Stress analysis | Statics → equilibrium → vector resolution |
| Any reliability topic | Probability → what a distribution is |
| Heat transfer | Differential equations → calculus |
| Anything with logs or decibels | Logarithms → indices |
Statics, units and calculus account for most of it. All three are taught early, assumed permanently, and never revisited, the same pattern as in the sciences, and for the same reason.
How to run it
I can't do [SPECIFIC THING, the move, not the module]. Don't teach it. List what it depends on three or four levels down, and flag which links are mathematical, which are mechanics, and which are units and dimensional reasoning. Then give me ONE diagnostic question per link, bottom-up, and wait.The three-way flag is the addition that matters here, because it routes you correctly. Students who can't do thermodynamics do not need more thermodynamics; they usually need to be able to define a system boundary, which is a five-minute conversation.
A worked diagnosis
"I can't do control systems."
Chain: control → Laplace transforms → complex numbers → differential equations → calculus.
Bottom-up: 1. Differentiate e^(kt).. Fine. 2. What does a solution to a differential equation represent?: "The answer." Recited. 3. What does a complex exponential describe physically?. Stall. 4. Why does a pole in the right half-plane mean instability?. No idea.
The gap is at 3: complex exponentials as rotation and growth, not as an algebraic device. Without it, poles and stability are arbitrary rules. With it, they're obvious. And it isn't control systems, it's a complex-numbers gap wearing a control-systems uniform.
The units case, which deserves its own treatment
If the diagnosis lands on units, the fix is faster and more complete than anywhere else in the curriculum:
Test me on dimensional reasoning: give me ten expressions and ask whether the dimensions are consistent. Then ten conversions across systems. Then three problems where a units error produces a plausible-looking wrong answer.An afternoon of this eliminates a category of error permanently, and students routinely spend a term working around it instead.
Pitfalls
- Assuming it's the engineering. Usually it's one of the three floors.
- Skipping the easy questions. "What's a system boundary" feels beneath you and is frequently the gap.
- Accepting a recitation. "The solution to the equation" is not a model.
- Doing more problems of the top-level type. Cannot help if the floor is broken.
- The tell: you understand the lectures and can't do the problem sheets, That gap is almost always a floor problem, not a comprehension problem.
Try this today
Name the engineering topic that consistently defeats you.
Ask for its chain with mathematics, mechanics and units flagged separately, and one diagnostic question per level, bottom-up.
If the lowest failure is units, that's an afternoon, not a term.