Chinh (lelouvincx) / Book - How To Solve It

Created Mon, 25 May 2026 00:00:00 +0000 Modified Mon, 25 May 2026 06:02:25 +0000
400 Words
page
  • Author: [[George Polya]]
  • I just bought the book. It’s $10. Not expensive. But the value it brings is huge. Worth it.

  • Key notes

    • Chap 1

      • Problem solving is a muscle. The more we practice solving problems, the better we are.
      • Problem solving is like swimming. We learn by imitating and practicing.
      • The teacher who wishes to develop his students’ ability to do problems must instill some interest into their mind and give them plenty of opportunity for imitation and practice.
      • 4 steps of problem solving:
        • Understand the problem logseq.order-list-type:: number
          • What is the unknown? logseq.order-list-type:: number
        • Devise a plan - connect the data, the condition, the unknown logseq.order-list-type:: number
          • Have you solve a similar problem before? logseq.order-list-type:: number
        • Carry out the plan logseq.order-list-type:: number
          • Can you prove it’s correct? logseq.order-list-type:: number
        • Look back logseq.order-list-type:: number
          • What have you done good and bad? logseq.order-list-type:: number
          • Can you derive the result differently and extend this problem? logseq.order-list-type:: number
      • The teacher should be in his student’s shoe, to help him understand and devise the plan better.
      • Do by example.
      • Could you restate the problem?

  • Quotes

    • “If you cannot solve a problem, there is an easier problem that you cannot solve.”
    • “The main danger is that the student forgets his plan. This may easily happen if the student received this plan from outside, and accepted it on the authority of the teacher, but if he worked for it himself, even with some help, and conceived the final idea with satisfaction, he will not lose this idea easily.”
    • “The teacher may ask: Can you see clearly that the triangle with sides x, y, c is a right triangle? To this question, the student may answer honestly “yes”, but he could be much embarrassed if the teacher be not satisfied with the intuitive conviction, then go on asking: But can you prove that this triangle is a right triangle? Thus, the teacher should suppress this question for now.”
      • Reflect on myself, sometimes I ask questions that dive very deep into one side of the problem, and it goes beyond my initial intention - just want to provide more knowledge to the student. Most cases it’s not good.
      • Because it kills the interest.
      • Don’t dive deep too much, just enough to get the student’s interest. This is more important.
    • “It is better to solve one problem in five ways, rather than solve five problems in one way.”