Response to Skemp's Article on Relational and Instrumental Understanding

The article on relational understanding and instrumental understanding brings up a great point in the subject of mathematics. In so many areas of math, so much emphasis is put on rules in figuring out problems. It seems a lot of the people I interact with have an instrumental understanding of math, as formulas and equations, and find the subject difficult because of the number of rules associated with it. So it’s interesting when Kemp states that “instrumental understanding I would until recently not have regarded as understanding at all” (pg. 2). Knowing when the rules work is only part of the understanding and the rest of it is how and why it works, so I would agree with Kemp’s previous regard of instrumental understanding. Although this type of understanding is not as effective it does seem that more students would prefer it this way. “As soon as this is [rules for getting answers] are reached, [the students] latch on to it and ignore the rest” (pg. 4). So trying to teach a different way or trying to expand previous knowledge to your students might not be effective. So it does encourage to try to teach a relational approach immediately if that’s what you intend to do later in the course. It seems the less they can know but still pass the better, “if pupils can get the right answer…, they will not take kindly to suggestions that they should try for something beyond this” (pg. 5). There’s also the fact that relational understanding would require more work and more time and students will probably complain and lose interest in the subject after a certain point. It is also more appealing to students that often with the instrumental method, “the rewards are more immediate and more apparent” (8), giving the students a short-term pleasure, though may cause long-term turmoil. Though the students might want the instrumental way of understanding, as teachers we must realize that long term, it is better for them to know how things work. If there’s something that goes wrong during problem solving, they are able to “produce an infinite number of plans for getting from any starting point to any finishing point.” (14) Kemp’s analogy of traveling from point A to point B also applies to teachers. There are times when you are explaining a subject and different students will not understand it, so knowing a different route helps you get to point B in order for your student to get there as well.