Study guide

• When a student is exasperatingly slow, the trouble is almost always the same
  • he has no desire at all to solve the problem,
  • even no desire to understand it properly
    • a lack of concentration, wait clumsily for some idea to come and connot do anythign that would accelerate it's coming
    • rush into calculations or constructions without any plan or general idea
  • so stir up his curiosity, give him some desire to solve the problem
  • allow some time to the student to make his mind, to settle down to his task

• Teaching to solve problems is education of the will

  • Solving problems which are not too easy for him, the student learns to
    • persevere through unsuccess,
    • to appreciate small advances,
    • to wait for the essential idea
    • to concentrate with all his might when it appears
    • familiarize with the varying emotions of the struggle for the solution

• anchor points are an extremely strong tool, to anchor your thoughts and thought directions

  • They can be questions, key properties, objectives
  • Without anchor points, your mind can wander and you can feel naseous

• Problem solving is a loop process

  • Define problem (impact what do we need to know, what are the key elements of problem? what are the issues?
  • Where should we spend our time? Analysis what are we trying to prove/disprove?
  • So what, what implications does our findings have?
  • potential solution: what should we do?
  • next iteration

• 4 phases of solution

  • understanding of problem
    • incomplete understanding, lack of concentration
  • devise a plan
    • rush into calclation and construction without any plan or general idea
    • wait clumsily for some idea to come and cannot do anythign that would accelerate its coming
  • Carrying out the plan
    • carelessness, lack of patience checking each steap
  • Check the result
    • failure to check result
• Create questions whose answer will allow you to retrace the development of the ideas
• Ask questions as you go and answer them

• Active Learning Mapping Exercise

  • Identify each component in the definition
    • See what the extremes of this component along various dimensions (length, other characteristic)
    • Can/How other properties component affect/interact with the definition? (It almost certainly will)
  • Ask questions about new description
  • What essential informations is being captured from the definition? Why this definition?

• short list of recurring, important, fundamental ideas

• less is more
• Time, time to grow

Exercises

• discourse with author
  • where you can gain new insights

Goal

• be able to reason and solve questions in the field effectively
  • even though they may take some time, ultimately be able to draw conclusions
• it is not: a list of problems and theorems you have originally found or proven

Mood

• Be happy and thankful
• Give glory to God
• Cautious optimism
• If uncomfortable/head hurts, reorganize and consider better way
• Rest, sleep, health, relaxed-alert
• Be careful of your sources of motivation; internal/external
• Before, I used to feel proud of myself of my little accomplishments to help me feel better and safer
  • But now... I can't. I know how little these things mean
  • And with more I learn, the more I realize how little I know
  • I will not boast of works
  • I will just be happy for the sake of being happy

Heuristic

• Anchor points
• Consider the most basic facts and lay them out
• When really stuck, investigate the objects & their properties that are involved
• Consider the opposite, other-direction
• Focus on the big picture

• Mapping

  • what is the mindset that will naturally give these mappings?
    • In what way can, A interact with B? A&B interact with C? ... for all A,B,C in knowledge

  • When learning set of new objects X

    • XRX->B
    • +:XxX -> X
    • special objects in X with respect to *
    • f(X) ~ g(X)
    • = <
    • How does it relate to old definitions/relations?
    • Consider the variations in the defintion?
    • intra and inter relationship of definition

  • When learning set of new objects X Y

    • XRY -> YRX
    • XRY -> X~Y

Notes

• sectioned, modular pairings of (details, outline)
  • details: notes, proofs, insights
  • outline: concise organization of ideas
    • similar to cs program
• Want them to be useful, refreshing myself on the topic, dont want to forget

Learning by managing stress and repetition

• short-term stress enhances the connections your brain makes, require fewer repetitions
  • coffee, cold water, exercise
• repetition types
  • writing notes
  • explaining from scratch
  • orating, teaching