After reading Skemps article I can see that both relational mathematics and instrumental mathematics have their pro's and con's. In a perfect world I think most teachers would agree that relational mathematics is more beneficial to students in the long run. It allows for better adaptation skills to new problems, offers alternate way's to solve problems, and is cemented in our memory for longer. Those are just a few to name. However, the problem is that the world is not perfect. I don't think relational mathematics is practical from a teaching perspective. There isn't enough time to describe the why's of every formula, our curriculum is to heavy to do so, and it's substantially harder to test for. Also if we start to give up some in class time to teach relationally, then we must me giving up some time to teach other subject areas. From a practical point of view, I think instrumental teaching is far more realistic. In addition, Skemps states that instrumental mathematics is a quicker and easier way of boosting self confidence in students than relational! I think self confidence plays a huge role in learning for any discipline, not just math. This definitely appeals to me as a teacher candidate. I hope to be wrong though, maybe we do have the time and resources to integrate relational understanding and I am just unaware of it? And I am sure there are other methods of boosting self confidence in students than instrumental understanding.
Another point brought up in Skemps article was the fact that most teachers use instrumental mathematics and in obvious relation, most students have an instrumental understanding. So how can we expect our teachers to be more relational if they themselves haven't been taught in a relational way? Also should we even be thinking in such a binary way(Relational vs instrumental). Maybe it's optimal to have a blend of both. I am sure many teachers already teach in a blended fashion. There are topics that are easily explained relationally and for those that are substantially harder they most likely resort to instrumental to meet curriculum standards in a timely manner. So while I think that relational understanding is the most desired, instrumental understanding seems more practical and is suffice enough for most students. Personally I hope to blend both into my teaching.
One final thought I had was that regardless of the way they students were taught, a lot of them may resort to a instrumental understanding anyways just because it is so much easier and quicker to learn that way. So even if we try to teach relationally, students might learn instrumentally anyways.
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| True instrumental understanding :) |
Love the photo and caption.
ReplyDeleteI agree with you that both instrumental and relational ways of understanding have their place. The question is, how to bring them together, so that students can use the instrumental to gain relational understanding (and vice versa -- so that students can use deep understanding to put together quicker, 'shortcut' ways of doing things when that is appropriate)?
I think it is a shame if you are already saying "the curriculum is too packed" when you haven't even taken a close look at the revised curriculum yet, nor started teaching! That begins to sound like an excuse for not trying something new and unfamiliar... See how it is when you are 'at the chalkface' and working with the kids and curriculum in the schools. I think you'll find there is quite a lot of time available to teachers, if you are willing to use it!
You quote Skemp as writing, " instrumental mathematics is a quicker and easier way of boosting self confidence in students than relational!" Is that really what he says? In what context? This seems so contrary to his point of view in the article generally!