Richard Skemp on Relational and Instrumental Mathematics

(p. 2-3)

The examples of instrumental explanations used in mathematics made me pause and re-read them to try to grasp what instrumental explanations were and find how they were being used in the examples because this concept seemed so new to me at this point in the article.

(p. 4)

"All they want is some kind of rule for getting the answer. As soon as this is reached, they latch on to it and ignore the rest." This sentence was an epiphany for me because I finally grasped what Skemp was implying by "instrumental explanations." It also made me recall my experience tutoring students and when they simply wanted to know the formula to plug in values without understanding how those formulas came about and why they work.

(p. 13)

"between where I was staying and the office of the colleague with whom I was working." I read this twice and thought I missed a line and double backed to check only to realize it was indeed repeated twice. (a typo? or was this purposeful?)

My thoughts on the issue Skemp raises:

As the one teaching, I've gained an appreciation of "why" these instrumental methods work, and I agree with Skemp that relational understanding is more beneficial in the long-term. That's not to say instrumental math isn't good, but it should be used in moderation and not overly reliant (similarly with calculators!!!). I've witnessed the issue of using instrumental explanations a lot when tutoring. For example, a student sees an example of a right angle triangle and knows the area is 1/2×b×h, but when given an isosceles triangle, they would become confused because to them it's a different shape. So although instrumental math is easier to grasp, I believe it limits students' abilities to think outside the box, make connections and extend their knowledge further.

However, I realize there are some difficulties with achieving relational mathematics. Finding ways to not make this approach boring, frustrating or time-consuming will be difficult for some topics. Furthermore, many students learn these instrumental methods at an early age, so it will be very difficult to change their way of thinking, especially making them relearn something they believe they already understand but in actuality only memorized a formula. Perhaps the teacher shouldn't give out any formulas so quickly and let students try to brainstorm it themselves. 

I also wonder if other subject areas also have this issue of instrumental vs relational instruction?