Instrumental learning to me was more of a "robotic" type learning. It was like a formula, you plug in an "x" object and out comes a "y" result. I realized that most, if not all, of my High School learning was instrumental. I learned the formulas and then applied it to my homework and it helped me to finish my homework fairly quickly, but not so much on the tests.
Relational learning to me was more of a "curious" kind of learning where one would put question marks after everything until he or she received a background understanding of the concept. I like the ven diagram from class where Instrumental learning was encompassed within relational learning because although they are different, they really are similar and they are complimentary to each other. By this I mean that, sometimes it takes accepting the facts up front and then receive understanding, the "why", later. So in that sense one would receive the formula and apply it and find out later what the formula is used to find and how it applies to more than just the copmutation problems in the homework. So they compliment each other.
Another way I saw a difference between the two as I read the article was that the learning curve for Relational learning seemed to be a linear function where you can achieve a page full of correct answers, as Skemp said it, in a shorter amount of time and be done with the homework. On the other hand, Relational learning was more of an exponential function. By this I mean that it takes longer to learn the background and the concept, but once it is learned you can apply it to more than just the assignment and you can eventually achieve more than by instrumental learning. So it takes more preparation, if I may say, with relational learning which may result in quicker achievement and more understanding, whereas with instrumental learning one may be able to accomplish an assignment with the formulas given, but that would be it. He or she would not be able to apply the formulas to much else, if not anything else.
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You did a very nice job defining what you meant by terms, such as complimentary. I was just asking myself what you meant by that, and then you told me.
ReplyDeleteI believe in the beginning of your second paragraph you meant to say Instrumental instead of Relational learning.
In my classroom, I don't think I would want my students to accept the facts upfront and then receive understanding later. The idea of teaching without giving an example of what should be done immediately seemed crazy to me at first, but math can be taught in a way that students discover new concepts and why they work and then readily accept all the applications and properties. If students are taught this way then it gives them more power, and they can continue to learn and develop their own math skills, rather than waiting for another rule to try to understand.
A great read! Your writing is full of lively details and analogies, and you bring forward several extremly valid points. However, although I love your ideas, I think that for this particular task you need to restrict yourself more to the ideas published by Skemp himself. Perhaps a topic sentence, and mention Skemp and the article before the 3rd paragraph!
ReplyDeleteThis was great. I really liked how you called relational learning "curious" learning. I feel like that's a very good way of describing it. I also liked how you said that instrumental learning helped you on your homework but not on your tests. I feel like that is a huge problem with high school mathematics. I tutor a student who has the same problems. Even though I agree with everything you said, I feel like some bits and pieces were not necessary to complete the assignment. But job well done anyway :)
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