theorem
A tool for turning beliefs about how learning works into explicit formulas.
These formulas are simplifications, not simulations.
They're thinking tools meant to make what you actually believe visible and debatable.
Foundational theories of learning, each reduced to its essential variables and relationships.
Deci & Ryan, 1985
L = A × Cm × Rl
People learn deeply when they feel autonomous, competent, and connected. Remove any one, and motivation collapses.
Explore this model →Skinner, 1938
L = Σ(S × R × Rf) − P
Learning is behavior change. Reinforce what you want to see more of. Punish what you want to see less of. Everything else is noise.
Explore this model →Ericsson, 1993
L = (E × Fq × T) / Cp
Mastery emerges from sustained, effortful repetition at the edge of one's ability, guided by expert feedback.
Explore this model →Csikszentmihalyi, 1990
L = Im × min(Ch, Sk) / |Ch - Sk|
The deepest learning happens when you're so absorbed that time disappears, when challenge and skill are in perfect balance.
Explore this model →Piaget & Vygotsky, 1978
L = (Pr × Sc) × (Ch - Cu) + D
Understanding is built, not received: constructed through experience and social interaction within the learner's zone of proximal development.
Explore this model →Ebbinghaus, 1885
L = R₀ × e^(-t/S) + ΣRᵢ
Retention is not about how hard you study but when you review. Timing defeats forgetting.
Explore this model →Kolb, 1984
L = (Ex × Rf × Ab) × Ae
Learning is a cycle, not a line. You must experience, reflect, conceptualize, and experiment, then do it again.
Explore this model →Sweller, 1988
L = G / (I + E)
The bottleneck of learning is working memory. Exceed its capacity and no amount of motivation or time will help.
Explore this model →Wenger, 1991
L = (P × E × Id) / Is
Learning is becoming. You don't acquire knowledge; you become a participant, moving from the periphery of a community toward its center.
Explore this model →Kapur, 2008
L = (St × Ga) × Dᵢ − Pr
The best preparation for learning is failing first. Struggle generates the gaps that instruction fills.
Explore this model →Bjork, 1994
L = (D × V × G) / Fl
If it feels easy, you're probably not learning. The conditions that slow you down are the ones that make knowledge last.
Explore this model →Bandura, 1977
L = (At × Rt × Rp) × Se
You don't have to do it yourself to learn it. Observation, attention, and the belief that you can replicate what you saw are enough.
Explore this model →Dweck, 2006
L = (Ef × Ch) × Md / Av
What you believe about your own ability changes how much you actually learn. A growth mindset turns effort into progress. A fixed mindset turns failure into identity.
Explore this model →Paivio, 1971
L = (V + Vi) × C
Two channels are better than one. When you see it and hear it, you remember it. Words and images encode separately and reinforce each other.
Explore this model →Not every learning system has a brain. These models describe how complex systems acquire, retain, and adapt knowledge, and what human educators might learn from them.
Biological System
L = (Ex × Rₛ × Mc) × Gn
The body learns the way the mind should: through exposure, struggle, memory, and the ability to recognize what it hasn't seen before.
Explore this model →Biological System
L = (V × Sp × Rt) / Cf
Generate variety. Let the environment decide. Keep what survives. The system learns without any individual understanding.
Explore this model →None of these quite right?
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