Scemp's Article: Relational and Instrumental Understanding

This blog entry is to summarize Skemp's ideas about relational and instrumental understanding. What each one is, how their related (if at all) and the pros and cons of each one. According to the article instrumental is to have an equation or concept and how to plug things into it or use it but to not know where the equation or idea came from. Relational understanding is to know not only how to use the equation but to know where the equation or idea came from and how it related to other ideas in Mathematics.

There are overlaps between these two types of understanding. Meaning that these two understandings are not mutually exclusive. Relational understanding of mathematics is a deeper form or Instrumental understanding. With instrumental understanding you can know how to use the equation. Relational understanding takes instrumental understanding a step further. It lets you know where the concept and equation comes from and why plugging in numbers into the equation works.

There are pros and cons to each type of understanding. Some pros for instrumental understanding is that it is quick to learn at first. If the problem does not deviate from the set pattern, answers can be obtained fairly simply. Some of the cons for instrumental understanding is that not knowing why an equation works or the general ideas behind it and where it comes from can create problems when presented with problems out side of the set equation. Another con with instrumental understanding is that you will have to remember every equation because you might not be able to see where each equation comes from and the a general idea can be formed to give you various individual equations.

Some pros for relational understanding are that it allows you to see where the equation comes from and why it works thus allowing a student to do problems that are outside any given equation and students can derive the equations from understanding and not have to memorize each equation for every situation like they would have to do if their understanding was only instrumental. The main con for relational understanding is that it takes more time to learn than instrumental and that some times relational understanding might not be as obvious to understand as the instrumental idea of "here is the equation, it works, use it."