Previously, I have been happy to understand the reasoning behind an algorithm. Now I am looking for new ways to solve problems.
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6 comments:
I think these alternative methods of performing subtraction actually require a deeper understanding. I think it may be a good exercise for most students in advanced elementary school grades to be given a word bank, and list explicit steps to an alternaitve method and explain why it works.
Although I like the idea of mulitple strategies to, for example, subtract, I think that we do need to be cautious as to how we use them. I agree that some may require deeper understanding and/or can be very confusing to students and result in creating confusion with the concept, in general. I like the idea of examining, as best we can, how a student approaches a subtraction equation and then trying to capitalize on that approach. For some this may be the Kye method. For others it may be something else. I work with students with learning difficulties and again, attempting to teach mulitple strategies can serve to confuse rather than to gain deeper understanding. Perhaps this suggests that the underlying concept is not solid??
This is a rich thread. Your comments are thoughtful. I am adding to it only because I do want to clarify that the principle benefit of alternate algorithms is to have kids (of all ages) realize AND believe that the marks we make on that page simply reflect the thinking path we were on. They are an instrument of communication, not the math itself, any more than a map of a territory is the territory itself. An alternate algorithm such Kye's method of subtraction doesn't add much to a learner's tool belt if it is just another procedure to learn in sequence without real understanding. An alternate algorithm should, in fact, be a reflection of deep understanding. I think you all have more or less said this, but perhaps this comment will serve to reinforce it. Good job, everyone! You can be proud of yourselves.
An alternative algorithim is pointless unless the student has the number sense and understanding to use the process. It is most important to get kids to talk about and record their thinking about how they got there. This is one of the harder parts to teaching math since math came easy to me and I made it through by memorizing facts and rules. It wasn't until later in my math years did I find understanding as to why and how.
During todays morning break some of us were talking about the idea of journaling for Math. The idea that the journal would be one strategy a student could use to help him think his way through problems. It would be the students representation of how they think and the steps it took to get there. Many representations could be included. (pictures, vocabulary etc..) anything to teach them how to think.
Hey Rita,
You are going to love the new Investigations program. It is all about finding various ways and methods to 'do the math'.
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