15. ORGANIZE YOUR SOLUTION FOR THE NEXT PROBLEMS WHICH HAVE NEAR SITUATION OF YOU HAVE STUDIED JUST NOW.

The main purpose of daily solving problems is learning a lesson. This lesson will work when you meet the near situation in the exam. In other words, you should write down lessons on your notebook, for solving next “similar problems”.
For example, “Prove that square root 2 is irrational.” This problem shows a common solution for “proving that a number is irrational”. You may take “reductio ad absurdum (in Japanese, HAIRIHOU)”. This is common one. If you really understand this, you can also solve “Prove that square root 3 is irrational.”

Next, I will advise you how to make your notes. I name this “CMD system”.
If you can get a correct answer, you should leave “a learning from this problems” with red ink. And write down in small size “C” (means CLEAR) and date near the top of the sentence of problem.
Or if you take a suitable solution but make mistakes, write down “M” (means MISTAKE) and date.
Or if you can do nothing, or if you take a bad solution, write down “D” (means DIFFICULT) and date.
When you leave “M” or “D”, you must copy the suggested answer in your text by hand with understanding it. It may be hard and take much time. But never move your hand with only moving. Please write, think, write, think, …. And make sure about the type of the problem in front of you. That is, “Hmm, I will do like this in next chance. It will be OK!”. With saying like this, proceed next problem on your workbook.

I think this action is a core of studying Math in high school. It’s very important.

See you next.

Nasuno Kumao