Thinking and learning processes occur in two main different ways known as relational and instrumental understanding. Where one is easier to learn and to teach than the other, the other proves to be the most important thing that needs to be the focus of every teacher, especially in mathematics.
Instrumental thinking, in short, is knowing how to get from point A to point B. It gives a step by step process that can be followed. This is the easier one to teach because it doesn't explain why, just how. Students also typically prefer this method because it's easier for them to remember and it's not as difficult to understand but this is what limits them because they don't learn how to see how things are connected and how they can be transposed into different situations.
Relational thinking is knowing how to do something and why it is done. It's knowing how to take different routes to find answers and connecting not only A and B but also the rest of the alphabet. This is harder to learn simply because it's not just an easy answer. It requires reasoning and it also requires more time.
Instrumental understanding is not related to relational understanding, but relational is related to instrumental because instrumental doesn't include any relational understanding. It's just knowing a process. Relational understanding, on the other hand, includes instrumental understanding plus more.
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I feel ths author wrote a good summary on the article like the asignment said to do. I like her definition of relational understanding and instumental understanding.
ReplyDeleteI however do think that the relationship between the 2 types of understanding summed up what Kemp was saying about the two types of understanding. I however might be wrong. My interpretation about what Kemp said about the two types of understanding was that instrumental understanding is a element of relational undertanding. Relational understanding is the set. so by the fact that relational understanding has instrumental understanding as an element, I believe Kemp is saing that Instumental understanding is related to relational because relation is related to intrumental. If A is true, B is true, if B then A. So to say Kemp said intrumental unserstanding is not related to relational I believe may be a mis interpritation of Kemp's views.
I liked your analogy connecting the letters of the alphabet.
ReplyDeleteI don't think Skemp thought instrumental learning was easier to remember and understand. In relational understanding, you know why something works and why the equations work, so it's much easier to remember because it has meaning.