When I was a kid, we learned all about fractions in 6th grade. We learned to simplify them. We learned to add them. We learned to subtract, multiply, and divide them; when we were in sixth grade. Back in the very early 80's, that was normal. Mind you, we learnt how to do all of these things, but we had little to no idea about why we were doing them or why they worked.
Then in the year 2001 I became a teacher and I was thrilled to see that those memorized procedures had all been eliminated in favour of conceptual mathematics. I worked hard with my students and we come to understand conceptually what fractions were, how to add them, and how to subtract them because it made perfect sense. We stuck to friendlier fractions because the kids used models and drawings to find the solutions. This demonstrated to us that, not only could they calculate the correct answer, but that they understood why it worked. They were merely representing their answer in numerical form.
Fast forward to 2010 and a new set of mathematics standards. I now teach 5th graders and the new standards want my 5th graders to simplify fractions by way of greatest common factor and to add or subtract them by way of lowest common multiple.
These things cannot be easily modeled since they are algebraic manipulations; instead they must be memorized procedures; a series of "steps" that one does to magically derive an answer. And that final answer is really all that matters. I cannot wait for my students to "discover" how it all works because there is so much else they have to learn (read "learn" as "be taught).
I feel very much that math class has become something I am doing to students rather than something that we are discovering together. In this context, math is nothing interesting and is not inherently fascinating. It moves from a labor of love to a chore for grades. And I just don't like teaching meaningless procedures.
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