Illustrative preset
You changed the assumptions. The story is a starting point, not evidence for these values.
Learning Equations
Explore a learning episode
Choose a familiar situation, then change the assumptions. See how attention, maintenance, and memory formation combine.
For the reasoning, assumptions, and examples, read the full explanation on Substack (opens in a new tab).
Start with an example
Familiar stories. Invented numbers.
Model probability of initial encoding
For one specified piece of information new to the learner, in this episode.
η = A × M × Q
× ×
=
The probability through each operation
Percentages are rounded to whole numbers. Each bar uses the same scale. These are probabilities, not counts of memories or a literal picture of the brain.
Illustration, not a measured prediction.Precise arithmetic does not make the assumptions precise. Neither these probabilities nor their differences are established estimates for a child.
What do the probabilities mean?
A is the probability of sufficient attention. M is the probability of sufficient maintenance given that attention succeeded. Q is the probability of initial memory formation given that both attention and maintenance succeeded.
Multiplying these conditional probabilities does not assume independence. This is a proposed account of initial encoding, not a measure of durable recall, understanding, or transfer.
Why can one situation change several sliders?
Instruction, prior knowledge, fatigue, and distractions may influence more than one operation. A diagram could reduce what must be held in mind and clarify a relationship at the same time.
Moving one slider holds the others fixed to explore the arithmetic. The example stories stipulate which effects change; real interventions need evidence. Q concerns the intended target information, not every memory the learner might form.