3 Matching Annotations
  1. Jan 2023
    1. Woit does provide problems, but they are all at the back of the book. It would have been better to see them between chapters. That provides a natural break in the material and gives the student a quick check on his understanding.

      Homework problems are pedagogical devices and many (most) authors place them in the text near where they would be profitably be done. They also provide a useful break in the text to prompt more novice students to actually perform them at the end of a section.

      More advanced students, however, should have caught on eventually at the need to work out examples for themselves which are presented in a textbook, but they should also be seeking out additional problems where ever they appear in the text, not to mention seeing out any outside additional problems, making up their own, and exploring any additional questions these pose.

      In mathematics textbooks this working of problems, expanding on them and seeking out new ones is often a large part of what is lurking behind the sometimes nebulous sounding idea of "mathematical sophistication". The rest of that equation typically includes experience with the various methods and means of proofs and some basic background in logic.

    1. One even better plan is to get regular library index cards and, afterthe lecture is fairly well learned, transfer the points underlined to them, onecard to a lecture. These cards can be carried about and studied at oddmoments. One is enabled by their use to get the perspective view of thelecture which brings out the sense of values which one loses when onestudies the notes in their mass of detail only. With the skeleton in mindone has little difficulty in recalling the details .

      Here again he comes close to some of the methods and ideas of having flashcards for spaced repetition, but isn't explicitly aware of the words or techniques. Note that he also doesn't use the word flashcard. When was the word first used?

      Rewriting things as flashcards also tends to be a part of the spaced repetition itself.

      By cutting the notes up he's specifically decontextualizing them so as to make one's memory be better tested in coming up with the solutions/answers as they are more likely to appear on a test, decontextualized from the original lecture.

  2. Nov 2022