Learning Efficiency
Learning Efficiency
Learning efficiency is usable knowledge kept per hour spent, hidden by tracking pages covered. Two learners can log the same hours and leave with different usable knowledge. A plateau after honest hours is usually a method ceiling, not a time shortage.
The ratio you can actually run
The house formula is total mastery and retention divided by total time spent learning. It is a self-check, not a published metric. The older model underneath is the same shape: degree of learning is time spent over time needed, and time needed moves with method.
Knowledge Mastery: From Recognition to Usable Knowledge owns the levels the numerator averages. This page does not redefine them. For each required level, partial mastery is current retention at that level divided by the retention the assessment will demand. Total mastery is the average of those partials. The average is a first cut, not a law. If the assessment is mostly higher-order, a strong score on recognition does not rescue a weak score on comparison. Weight the levels the way the test weights them.
The percentages have to come from somewhere or the arithmetic is theatre. After one spacing interval, perform each required use from memory. Mark got, half, or gone. That is enough. A full calculation per subject per week is a measurement burden this page does not ask for. Spaced Interleaved Retrieval is the retrieval system that produces those retention numbers — retrieval spread over time and mixed across topics and forms.
A worked pass: 75, 67, 71, and 50 percent of required retention at four levels averages to 66. The same 66 over 30 hours and the same 66 over 80 hours are different problems. The first needs better methods. The second needs more time. Tracking only hours hides that difference entirely. The hours are pictures, not a census.
The hammer
A house can be started with only a hammer. Wiring, plumbing, and the load calculations cannot be finished with a hammer, no matter how long it swings. When the method has a ceiling, adding hours produces diminishing returns. Early on, more time still helps. Coverage increases. Familiarity grows. At the ceiling, further hours produce smaller and smaller gains. Doubling a limited method from 30 hours to 60 is a house illustration of about ten extra points, not a measured curve.
Some methods hit a ceiling regardless of time invested. Others compound with each hour. Some mastery levels require methods built to reach them. Bear Hunter System is the encoding system designed for those higher levels: a rough frame, the questions the material must answer, a working map of connections, and a cut-down structure that survives without the source.
Four profiles, two next moves
The four cells below are this system’s teaching scenarios, not observations. Method quality sets the slope. Deep Processing — encoding that works the meaning and the relationships, not just the surface form — sets how high the slope can go. That dimension most directly determines the method ceiling.
| Method × processing | Scenario | What hours do |
|---|---|---|
| Inefficient, low deep processing | 50% over 100 hours | Hours barely move mastery. Only lower levels stay accessible. Relearning cost stays high |
| Inefficient, high deep processing | 70% over 50 hours | Improvement is slow. The slope is shallow |
| Efficient, low deep processing | 70% over 50 hours | Mastery rises with time. The slope is proportional and has not been given enough hours |
| Efficient, high deep processing | 90% over 30 hours | Each hour produces a proportional gain. Retention stays high. Time cost stays low |
The two middle cells can print the same 70 percent over 50 hours. One is a shallow slope. One is a proportional slope that has not been given enough time. Same observed ratio, different next move.
The useful diagnostic is whether a plateau is a time problem or a method problem. A retention gap after a couple of weeks of honest hours — thirty hours is the picture, not a threshold — usually points to method. Switch techniques rather than add hours. Lower requirements are easier to meet with limited methods. Higher mastery levels require methods that force comparison, evaluation, and relationship-building, not just recognition and recall. Higher-Order Learning is what those higher uses look like in practice.
Time needed also moves with prior knowledge and with the quality of instruction, not only with the technique’s name. Switching method while keeping a bad explanation of the same material will still plateau. Marginal Gains is how to find which part of the system is creating the current ceiling. Metacognition: The Control Layer is the control layer that actually runs the time-versus-method diagnosis.
The equation’s equal-weight average lies when the assessment is not equal-weight. Invented percentages that harden into findings make this page worse than silent. The quit signal is running the arithmetic and then adding hours anyway. The check: after one spacing interval, the higher required uses are either still producible from memory or they are not.
After honest hours
After honest hours the next move is switch method or add time. Higher uses need comparison, evaluation, and relationship-building — not more recognition.
Related
- Knowledge Mastery: From Recognition to Usable Knowledge — owns the mastery levels the equation averages; this page consumes those levels and does not redefine them
- Spaced Interleaved Retrieval — the retrieval system that produces the retention numbers in the numerator
- Bear Hunter System — encoding system designed to reach the higher levels, the methods that raise the ceiling
- Marginal Gains — framework for finding which part of the system is creating the current efficiency ceiling
- Deep Processing — the dimension that most directly determines the method ceiling
- Higher-Order Learning — what higher mastery levels means in practice: comparison, evaluation, relationship-building
- Metacognition: The Control Layer — the control layer that runs the time-versus-method diagnosis
- Retrieval — parent hub for the retention half of the numerator
- Self-Regulation — parent hub for the diagnostic use
Sources
- Carroll, J. B. (1963). A model of school learning. Teachers College Record, 64, 723–733. Degree of learning as time spent over time needed; aptitude as time needed under optimal instruction.
- Bloom, B. S. (1968). Learning for mastery. Evaluation Comment, 1(2). Under variable time, most students reach the criterion.
- Rohrer, D., & Taylor, K. (2006). The effects of overlearning and distributed practise on the retention of mathematics knowledge. Applied Cognitive Psychology / related massed-practice work in Psychonomic Bulletin & Review. Coverage can look better immediately and worse later.
- Craik, F. I. M., & Lockhart, R. S. (1972). Levels of processing. Journal of Verbal Learning and Verbal Behavior, 11, 671–684.
- Anderson, L. W., & Krathwohl, D. R. (Eds.). (2001). A Taxonomy for Learning, Teaching, and Assessing. Analyze, evaluate, and create are not produced by recognition practice.
- Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4–58. Technique utility varies by outcome type.
- Morris, C. D., Bransford, J. D., & Franks, J. J. (1977). Levels of processing versus transfer appropriate processing. Journal of Verbal Learning and Verbal Behavior. A method has to match the use it is asked to produce.