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Mostly a linkfest for now. Note that, as in any scientific work, the hypotheses can be based on flawed experimentation or apply only in specific conditions or domains, which I may not have necessarily tried to reproduce in my one-liners. Please add and discuss! I'll try to compile on a wiki or something eventually.
# Observations
Spaced repetition is effective for memorization (Piotr Wozniak)
* http://www.supermemo.com/
* http://www.wired.com/medtech/health/magazine/16-05/ff_wozniak
* http://www.optimallearning.org/people/pavlikvitae.htm
Analogy, vivid imagery, mnemonics are effective for memory
* http://amzn.com/159420229X
* http://www.scotthyoung.com/blog/
* http://en.wikipedia.org/wiki/Tony_Buzan
* http://amzn.com/0979777747
Numerical problem solving results can mask misunderstanding of fundamental concepts (Eric Mazur)
* http://www.youtube.com/watch?v=WwslBPj8GgI
Mastery is a process of extensive "deliberate practice" -- more people can succeed by following that process (K. Anders Ericsson, Shinichi Suzuki)
* http://amzn.com/0848817672
* http://amzn.com/0521600812
* http://amzn.com/0802777074
* http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math/
* http://amzn.com/055380684X
* http://thetalentcode.com/
* http://amzn.com/1591842948
* http://thedanplan.com/
Worked examples and faded examples are effective for learning
* http://en.wikipedia.org/wiki/Cognitive_load
* http://en.wikipedia.org/wiki/Worked-example_effect
* http://portal.acm.org/citation.cfm?id=1503301
Constructivism and problem solving skills are not effective for math education (John Sweller)
* http://www.cogtech.usc.edu/publications/clark_etal_2010_math.pdf
* http://www.cogtech.usc.edu/publications/kirschner_Sweller_Clark.pdf
Presenting misconceptions along with correct explanations is more effective (Derek Muller)
* http://www.veritasium.com/2011/03/khan-academy-and-effectiveness-of.html
Collaboratively observing tutoring is effective (Michelene Chi)
* http://www.public.asu.edu/~mtchi/papers/Craig_Chi_Vanlehn2009.pdf
* http://chilab.asu.edu/papers/Chi_Observer_Final_8.07.pdf
Teaching/practicing subtle knowledge components can improve and accelerate learning (Koedinger)
* http://www.learnlab.org/research/wiki/index.php/Knowledge_components
* https://pslcdatashop.web.cmu.edu/about/pubs/16_Koedinger_45.pdf
* http://www.learnlab.org/uploads/mypslc/publications/learning_factor_analysis_5.2.pdf
* http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math (again!)
Children ought to be educated humanely, being first exposed to the beauty and usefulness of the subject rather than starting with testing standards and drills (Papert, Lockhart)
* http://www.maa.org/devlin/LockhartsLament.pdf
* http://amzn.com/B003F3PN3S
We apply mental models (gained from our culture) to understand and learn new ideas (Piaget, Papert, Munger)
* http://ycombinator.com/munger.html
* http://amzn.com/B003F3PN3S
Understanding how learning works can help improve learning (Medina)
* [Brain Rules](http://www.amazon.com/Brain-Rules-Principles-Surviving-Thriving/dp/0979777747/)
Working memory can be improved
* [Improving fluid intelligence with training on working memory](http://www.pnas.org/content/early/2008/04/25/0801268105.abstract)
* [Brain Workshop](http://brainworkshop.sourceforge.net/)
# Unsorted ideas
* Teaching others is effective (Koedinger - teaching SimStudent, Cal Newport)
* "All Japanese children speak Japanese" (Suzuki, Khatzumoto) - the implication is that some set of conditions make learning "automatic"
* Learning something new requires making it extremely simplified and repeating it many times (Deb Roy TED talk, Suzuki)
* Importance of timing and rate of change (Suzuki) - overlaps with [Productivitiy]()
* Idea of the 80/20 principle and minimum effective dose to make learning more efficient - overlaps with [Productivity]()
* "Delayed feedback", such as you would get in many videogames, is not effective (Aleven)
* Why does categorizing things help us understand them?
* How do we actually create new knowledge -- Meno's paradox, Sweller paper:
> employ a ver- sion of means-ends analysis in which differences between a current problem-state and goal-state are identified and problem-solving operators are found to reduce those differences
* Worked example instruction http://www.sciencedirect.com/science/article/pii/S0959475206000181
* The importance of pattern recognition; how do we handle big, abstract patterns?
* Cognitive load, focusing on one possibility at a time -- can anything useful along these lines be taught?
* Developing intuition: how does it happen? how long does it take? (Can't be 10000 hours for *everything*)
* Learning styles don't exist http://www.youtube.com/watch?v=sIv9rz2NTUk
* Introduction to learning theories http://www.youtube.com/watch?v=hsX5Tq3WTBw
* From http://tech.mit.edu/V130/N49/normandin.html
> This was one of the failures of lecture-based freshman physics. For most students, they’d never had to utilize “expert” techniques during high school. The formulas were all they needed. As a result, lectures that professors delivered which seemed clear and carefully thought out were perceived in an entirely different light by their students, who had yet to develop the problem-solving skills and advanced reasoning that the lecturer took for granted. Research supports this; Wieman points out that it has been shown that even when looking at a simulation on a computer screen, students “literally see different things happening… than do the experts. As a result, the student can interpret what is shown very differently from what was intended, and learn incorrect ideas.”
* [A very good strategy for mastering topics like programming and math...](http://www.perlmonks.org/?node_id=70113) - go back and learn what you don't understand; other tips for getting the most out of lecture
* [How to develop insight in technical courses](http://calnewport.com/blog/2008/11/14/how-to-ace-calculus-the-art-of-doing-well-in-technical-courses/)
# Further references
* http://www.learnlab.org/research/wiki/index.php/Main_Page
* http://learnlab.org/opportunities/summer/readings/
* http://chilab.asu.edu/publish.html
* http://www.leactivemath.org/publications1.html