C.3 Self-Explanation Compared with Other Comments

You must also be aware that the self-explanation strategy is not the same as monitoring or paraphrasing. These two methods will not help your learning to the same extent as self-explanation.

Paraphrasing. ‘‘$a,b$ and $c$ have to be positive or negative, even whole numbers.’’

There is no self-explanation in this statement. No additional information is added or linked. The reader merely uses different words to describe what is already represented in the text by the words ‘‘even integers’’. You should avoid using such paraphrasing during your own proof comprehension. Paraphrasing will not improve your understanding of the text as much as self-explanation will.

Monitoring. ‘‘OK, I understand that $2(k+l+p)$ is an even integer.’’

This statement simply shows the reader’s thought process. It is not the same as self-explanation, because the student does note relate the sentence to additional information in the text or to prior knowledge. Please concentrate on self-explanation rather than monitoring.

A possible self-explanation of the same sentence would be:

‘‘OK, $2(k+l+p)$ is an even integer because the sum of $3$ integers is an integer and $2$ times an integer is an even integer.’’

In this example the reader identifies and elaborates the main ideas in the text. They use information that has already been presented to understand the logic of the proof.

This is the approach you should take after reading every line of a proof in order to improve your understanding of the material.