03_Believing_You_Can — what does a belief have to do with the evidence?¶
Level: 101 · for anyone who stopped trying something because it failed before
Two lessons about beliefs, checked the way the first chapter checks knowledge. The first is about believing in yourself: a belief low enough to stop you trying cuts off the only evidence that could raise it, so honest counting alone can make a learner helpless and keep them so after the world changes. The second is about believing you are right: a confident yes-or-no usually sits on a smooth quantity with a cutoff nobody named, and naming it is where perspective taking starts. Both follow Todd Zakrajsek's The New Science of Learning.
| # | Lesson | The question it answers |
|---|---|---|
| 1 | Learned helplessness | Why does honest counting leave a learner who failed ten times never trying again, and what gets them started? |
| 2 | Day or night: perspective taking | Why do two people who agree about every fact still say "day" and "night" about the same sky, and what ends the argument? |
The through-line¶
Both lessons find the same structure: a belief that looks like a fact about the world is a rule for handling evidence, and the rule can be changed. In lesson 1 the rule is "try when the chance is worth it", and the fix is not to believe harder but to make trying cheap, with a small step or a similar person's success, so the record starts growing again. In lesson 2 the rule is a cutoff on a continuous quantity, and the fix is to say which cutoff you are using. The softer claims around these, mindset, self-efficacy, imposter syndrome, stress, are on the evidence-graded page mindset and motivation.
Po polsku, w skrócie¶
Dwie lekcje o przekonaniach, sprawdzanych tak samo jak wiedza w pierwszym rozdziale. Wyuczona bezradność: kto po wielu porażkach przestaje próbować, rozumuje poprawnie ze swoich danych, ale tylko próba daje nowe dane, więc przekonanie nigdy się nie zmieni; wyjściem są małe kroki i cudze sukcesy. Dzień czy noc: pewne „tak albo nie” zwykle kryje próg na wielkości ciągłej, a spór kończy się, gdy każdy powie, jakiego progu używa.
A note on the code¶
Lesson 1's learner is a model with Laplace's rule of succession and a threshold; its arithmetic is exact and its numbers are not measurements. Lesson 2 computes the sun's height from NOAA's formulas, good to about a minute.