This topic flummoxes me every year. I want the Ss to understand WHY a shift 3 to the right is achieved by replacing every x with x-3 (not x+3), rather than just memorize, "It's the opposite."
I'm convinced that we need to start talking about this with relations, not functions.
I'm convinced that we need to start talking about this with relations, not functions.
https://twitter.com/bowenkerins/status/1427992995924697088
Something like this.
"Here is a relation R. Complicated, huh? Fortunately, I have a computer program that will tell me whether or not a given point is an element of R. I give it an (x,y), and it tells me yes or no. I don't know how it figures it out... but I don't need to!"
"Here is a relation R. Complicated, huh? Fortunately, I have a computer program that will tell me whether or not a given point is an element of R. I give it an (x,y), and it tells me yes or no. I don't know how it figures it out... but I don't need to!"
"Here is a second relation, S. Unfortunately, I do NOT have a point-testing program for this relation... But I DO still have one for R! Can I use the R program to test whether points are elements of S? If so, how?"
Then give them bunch of other relations to try to use the R-tester on. Like so.
(This is just a germ of an idea; very little thought has gone into the selection and ordering of the examples.)
(This is just a germ of an idea; very little thought has gone into the selection and ordering of the examples.)
It still feels like it would be confusing, but within a #thinkingclassroom framework that may be ameliorated.
I will always gamble on aiming for understanding over memorization.
I will always gamble on aiming for understanding over memorization.
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