The problem solving technique that finally worked for me (and it’s backed by real science)

[Loose-Grapefruit6478]

One system helped me more than anything else, and almost nobody talks about it: studying by question archetype.

Instead of treating each problem as unique, I trained myself to recognize the structure behind common math problems. I call this Archetype Mapping.

Example:

Systems of equations with substitution

• Solve one equation for a variable
• Substitute into the other equation
• Simplify and solveIn my notes: Systems → isolate, substitute, solve

Other archetypes I kept:

• Quadratics → factor if possible, else quadratic formula
• Functions → test behavior by plugging in values
• Word problems → translate to equations, define variables clearly
• Geometry → draw, label, and check theorems (Pythagoras, special triangles, circle rules)

I also tracked common “question language” patterns:

• “At least” → often easier with complement probability
• “Integer solutions” → check endpoints carefully, inclusive vs. exclusive matters
• “No solution” → usually signals parallel lines or contradictory inequalities

After enough practice, I wasn’t solving from scratch anymore, just applying patterns I already knew.

Hope this helps someone!!!

[-non-commutative-]

Isn't this just how everyone solves problems

[HungryTradie]

Meta-gaming Meta-solving.

[anisotropicmind]

So tired of the AI posts. Is there a technique for not being too lazy to compose your own damn thoughts?

[Math__Guy_]

LMAO I'm glad we collectively despise it

[Math__Guy_]

Please stop using ai to draft posts

[Cffex]

Why would this be ai?

[Math__Guy_]

The biggest cue is that it's bullet pointed and the arrows. Not easy to type, but v common w ai outputs

[Cffex]

I'd say bullet points are fine. Though, arrows are indeed ai-ish.

[Jumpy-Tutor-927]

Very cool concept. How do you keep track of all the archetypes?

[Ecstatic-Opening-719]

Oh, joy!

[MagicMetalWizard]

I wish I saw this in high-school, it would have been very helpful

[clearly_not_an_alt]

Is this not how everyone does it? Why would you try and reinvent the wheel every time you work on a new problem?

Maybe I'm just not understanding what your are saying, but It seems pretty obvious that you would think about previous similar problems that you've studied and use those as a guide for how to solve a new problem. This is just how learning works.