Scott Macleod says, "We now live within multidirectional conversation spaces in which 12-year-olds can reach audiences at scales that previously were reserved for major media companies, large corporations, and governments. We all now can have a voice. We all now can be publishers. We all now can find each other’s thoughts and ideas and can share, cooperate, collaborate, and take collective action."
So how should addition, and by extension subtraction, be taught?The standard algorithm or by piecewise addition?
Weigh in on the "Letter to Jack".
How would you teach these two problems?
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My preference is to give them a collection of robust models for the operation and then give them a lot of interesting opportunities and contexts to practice. Here's a post where our family listed all of our models for addition: Bigger Collection. Please add to our list!
ReplyDeleteTake this conceptual basis, combine with knowledge of place value, then show them several different algorithms. Our kids have comfortably grabbed at least 4 approaches, with regrouping and the standard algorithm as their two favorites. Notice I used a fuzzy verb "grabbed" as I can't tell how much these were taught vs discovered.
Now, my own frustration about the "Jack" problem (and the other two in your post) is that I don't care about the calculations or the answers. That is, I don't have any context for why we are doing this calculation and can't choose a natural algorithm for getting my answer. For example, if that's 427 ml of water in my pyrex measuring cup, I knew that I had 316 ml and want to know how much my son added, then 100 ml is probably correct within the precision of the measurement tool.
I know that is picky, not every calculation can be put in an interesting context, and there is a place for practicing pure computations. Just that I've seen this problem so many times and I feel that good problems should be our showpieces.