Students must learn how to check their work. I asked one student how to check a problem. He said he would do it again. I explained to him that this merely means that he did the problem twice, not that he checked the work. By carefully isolating each step, the work can be checked properly.

 

Checking involves asking if the result is reasonable.

 

Checking means looking at each aspect separately.

 

When one does something correct and good, one feels good. At mathematics seminars, one frequently hears mathematicians saying that they feel good or do not feel good about their work. Students can do the same. If they do not feel good after working on a problem, they should recheck it. Emotions can serve as an important tool in learning, and students need to be aware of this.

 

In another class, one girl said she did not feel like doing the assignment. I asked her why she felt this way, explaining to her that bad feelings are usually caused by not properly understanding the material at hand. I explained the work to her, and she said that she felt better.

 

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