Math and physics tutoring by Dr. Dave
Your brain needs rest after practice, just like muscles.

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Deliberate Practice

Deliberate practice means working on math problems in a calm, organized and sensible manner. Focusing on easy questions can lead to an illusion of competence, meaning you think you know your stuff, but are really just going through the motions over and over. This is not a very effective way to study. To really boost the learning process when practicing, keep in mind two important things:

  1. Don't do too much repitition of similar problems in one session. Move on to sometihng else if it starts to get boring or you're thinking "I'm getting good at this."
  2. Attempt more and more difficult problems. The ideal zone is right in between the work being easy and boring, and it being too difficult to complete. You have to be challenged a little bit most of the time.

Interleaving is another very effective way to practice. This means frequently switching the type of problem you are working on - mix it up! That can sometimes be difficult in math or physics because homework and textbook sections typically emphasize one or two topics or strategies. Find different problems in previous or upcoming sections, and in chapter review and test sections. Another strategy is to do the (a) and (b) parts of assigned questions on one day, and the (c) and (d) parts the next.

Practice and repitition helps build chunks (established neural patterns that represent ways of solving different problems) whereas interleaving builds flexibility and creativity, and helps us move beyond the world of practice and into independent thinking.