Instrumental vs. Relational Understanding

There are a few things really interest me when I was reading Richard R. Skemp's article  Relational Understanding and Instrumental Understanding. The word faux ami took me a while to understand. The comparison between those French words and their English translation. My first thought was that those words should have similar meanings as what they "look like". But the fact is that they can be quite different. Another thing was that unit about an area. If the teacher applies too much of instrumental understanding, the students would just memorize the word they see and hear all the time and use that as the unit of all kinds of problems. In that case, students might not even have a clear concept of a unit. Later in the article, it talked about the advantages of instrumental understanding and mentioned that it could be easier to remember. That could be quite essential to some content of mathematical education since the students might not be able to fully understand every part of the equation. Memorizing those content can give the students an opportunity to be able to figure out in the future.

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