I found the article "When Good Teaching Leads to Bad Results: The Disasters of 'Well Taught' Mathematics Courses" by Alan Schoenfeld very interesting and he has definitely outlined a critical issue in mathematics. I always find myself sitting on the fence when it comes to issues similar to this one. On the one hand, I believe children learn best when they explore and there are activities and they find math fun. On the other hand, I believe there is a place for old school mathematics with your proof and your algorithms.
Schoenfeld (1988) describes of an instant where a math problem would have only taken the students five minutes to do, but because they had to outline their process and follow the correct format, it took them 15 minutes. I would like to compare this instant with that of writing an essay. Any child can throw a few ideas on a piece of paper and call it an essay. However, in the higher grades, it would not be accepted as a proper essay unless it had proper paragraphs, an introduction, a conclusion and so on. Why should math be any different?
Jumping back on the other side of the fence, I agree that children have trouble connecting the bits of pieces of math that they learn together. They choose to memorize instead of understand. I like how Shoenfeld does not blame this on teachers, he blames it on the curriculum. I long for the day when children are grouped based on ability, not age, and everything they learn they will find relevance in the world around them. Until a curriculum is designed for us that allows this and standardized testing is not used to criticize us, we will do the best we can with what we have.
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