Clip 1/5: Pre-Lesson Graphs Equation Tables
Jake Disston and Jesse Ragent discuss their plans for the day's lesson with a group of colleagues, having students classify and organize different representations of mathematical functions. They wonder, "What salient features will they attend to? What will they use to sort them?"
JESSE RAGENT: The main thrust of this lesson is to see how students are able to navigate among multiple representations of functions and to communicate about the connections that they see. The use of card sorts provides an opportunity for each student to "play around" with connecting an equation to a graph and to a T-chart in a safer fashion, since moving cards around on a desk is not immutable -- if an initial idea of how things fit together proves to be untrue or unworkable, then the cards can easily be moved into a different grouping. A second big idea is to see how language and vocabulary might drive student thinking and learning. Will the academic language generated in a whole class discussion trickle down to individual students as they describe their thinking? Will students move from "kid-friendly" language to academic language as the lesson proceeds?
Viewing this clip now reminds me of the value of letting the students themselves negotiate meaning. Too often I default to "telling them how it is." Of course I try to do this in as clear and as interesting a way as possible, but still I am the wise one imparting knowledge to the unenlightened. And of course what invariably happens is that some kids "get it," some are quite lost, and a big chunk of kids in the middle have some murky understanding. The structure of this lesson forces students to grapple with the mathematical concepts while at the same time providing me with a window into their thinking.
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