Natural Sciences: Prerequisite diagnosis
Find out that your physics problem is a maths problem, which it usually is.
What you'll be able to do: Find out that your physics problem is a maths problem, which it usually is.
The specific pattern in the sciences
A student says they can't do energy problems. They read the chapter again. They do more energy problems. Nothing improves, and they conclude they're bad at physics.
The chain underneath: energy problems → work → the dot product → vector components → trigonometry.
They're bad at trigonometry, and every topic resting on it will fail unpredictably in ways that look like difficulty with the topic on top.
This is the defining prerequisite pattern in the natural sciences, and it has a name worth saying plainly: most science difficulty is mathematical difficulty wearing science clothing. Not all of it, misconceptions account for a great deal (article 01): but enough that this should be the first thing you check when a whole topic won't come.
The chains that actually recur
| Can't do | Usually broken at |
|---|---|
| Energy and work problems | Dot product → vector components → trigonometry |
| Titration calculations | Moles → mass/moles/molar mass → unit manipulation |
| Rate equations | Logarithms → what an inverse function is |
| Equilibrium calculations | Quadratics → algebraic rearrangement |
| Anything with pH | Logs, again, usually the whole difficulty |
| Circuit analysis | Simultaneous equations → algebraic manipulation |
| Genetics probability | Basic probability → fractions |
| Radioactive decay | Exponentials → logs |
| Gas laws | Proportionality → algebraic rearrangement |
| Stellar magnitudes | Logs, a third time |
Notice how much of this is logarithms, units, and rearrangement. Three mathematical skills, taught elsewhere, assumed everywhere in science, and never re-taught because they aren't on the science syllabus.
The other recurring floor is proportional reasoning: "if I double this, what happens to that?", which underlies gas laws, rates, dilutions, inverse square laws and scaling arguments, and which a surprising number of students cannot do reliably.
How to run it
I can't do [SPECIFIC THING, the move, not the topic]. Don't teach it to me.
List what it depends on, three or four levels down, and be explicit about which links are mathematical rather than scientific. Then give me ONE diagnostic question per link, starting from the bottom, and wait for my answers.Asking it to flag the mathematical links is the addition that matters here. It tells you immediately whether you're facing a science problem or a maths problem, and those go to completely different remedies.
A worked diagnosis
"I can't do anything with pH."
Chain: pH calculations → logarithms → inverse functions → indices.
Questions, bottom up: 1. What is 10³?. Fine. 2. What power of 10 gives 1000?. Fine. 3. What does log₁₀(1000) mean, in words?: "Log of a thousand." Recited, not understood. 4. If pH is −log[H⁺] and [H⁺] goes down by a factor of 10, what happens to pH?, Stall.
The gap is at 3, and it isn't pH. It's that log is asking "what power?" Ten minutes there, and every pH question becomes arithmetic, because pH was never the problem.
Scaling
- School: two levels, run with an adult. Most "I'm bad at chemistry" at this age is units and proportional reasoning.
- A-level: run it at the start of each module. Physics modules in particular have a mathematical floor that isn't stated anywhere.
- Undergraduate: the chains cross into mathematics you were assumed to have from a different course, vector calculus, differential equations, statistics. Nobody checks.
- Returning after a break: the mathematical floor decays faster than the science, so check it first.
Pitfalls
- Assuming it's the science. The habit this article exists to break.
- Skipping the easy maths questions. The gap is usually in something you were taught years ago and have been routing around.
- Accepting a recitation. "Log of a thousand" is not an understanding of what log asks.
- Fixing the maths and not returning. Go back to the science problem and confirm it's now tractable.
- The tell: you diagnosed a mathematical gap and went back to doing more physics problems anyway.
Try this today
Name the science topic you consistently can't do.
Ask for its dependency chain with the mathematical links flagged separately, and one diagnostic question per level, bottom-up.
If the lowest failure is mathematical, that's tonight's work, and it isn't physics.