Friday, April 15, 2011
Chapter 5 Discussion Prompt
A key take-away for me in this chapter was reflected in the title: equivalence. The notion that an equals sign isn't just followed by "the answer" really hit home for me. As I've been introducing pre-algebra to my struggling 7th graders, it's been mind-boggling to me to unearth so many of their misconceptions. For example, when asking them to define "sum," many of them said "the answer," without any comment related to the total, the operation of addition, missing addends, etc. And exploring the idea of compensation is difficult for them because of their lack of confidence in mental math. How could we be more intentional about developing an understanding of equivalence and compensation in our students from the primary years into Upper School?
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This is a HUGE prompt question. I love the idea of the composition and decomposition of numbers along with the open number line. The section on page 88 in which Olivia generalized, "It's like a mirror on the number line, like symmetry." Students can use the open number line visual model to "SEE" the symmetry in equivalence. They can also see how numbers/quantities can be taken apart and redistributed, put back together, moved around, etc. more like a puzzle to be played with than a problem to be "solved."
ReplyDeleteI also want to explore the idea of "problem strings." Which have been expressed in several examples. I'd like to see how these help students create mental connections to concepts of similar and different identities.
Going back to Chapter 4 - I won't use the term "FOIL" in my Algebra class, because the "method" offers no connection to the distributive property, nor does it allow for the possibility of multiplication using an array.