If you are given a standard math problem such as: David, who is the camp leader has a bag full of tokens how many tokens does he have? Then you, the student, are given a bag full of blocks and asked to count how many you have? How would you count it?
Well, in my class everyone came up with different ways of counting them; some started counting the big blocks (100) and then counted the row blocks (10) then the individual blocks (1). Others counted by combining the same colours and counting them that way---by the way everyone had a total of 272 blocks. Now, we where asked to demonstrate using paper how we many blocks two groups had combined. And again, we began to group our blocks in accordance with big blocks, row blocks and then the individual block--coming up with the number of 544. Now, we were asked to calculate the sum in a different way. So, majority of the groups came up with this equation:
Look familiar? This is the traditional method that we were taught, but do you understand how we actually get to this number? I mean if you think about it we have 200 big blocks, 70 row blocks and 2 individual blocks. So, why are those numbers not represented in the equation? When you actual add up for example 7 and 7 you get 14 blocks, but when we were actually counting the blocks that would not be correct. When we were counting the blocks we counted 70 row blocks by 70 row blocks which make 140 blocks--this makes sense visually! How come it doesn't make sense mathematically? Simple! Traditional math has taught us in a way where efficiency and speed mattered the most, where conceptual understanding of the problem didn't matter. Here is another way to approach this problem on paper:
Now most of you seeing this will think: "WHAT?"; "I DON'T GET IT"; "IT'S TOO LONG."
The point of this is not compare the two methods, to say that one is better than the other. The point of this is to understand another way of thinking about the problem or approaching a problem. Some students (myself included) cannot understand the first approach. We do not understand how we can relate it to the real world. So, the second approach, though difficult for some to understand, can be really easy to relate to the real world. What I learned today was that anyone is able to be "mathematically smart," there is no secret to being good in Math--it is simply finding another approach. And this is where the role of teacher comes in, that is it is the role of the teacher to help facilitate a classroom environment where coming up with other approaches to a problem is OKAY, and allowing for students to try out a different approach and have a discussion about why they used that particular method. In the end, that helps the student become more confident in math and allows them to actually learn.
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