Confession: I obsess over the details of curriculum design. For me, having the opportunity to design and create challenging, perplexing learning situations is one of the best parts of my job as a teacher. I also think that the details of these designs can have a lasting impact on our students. Last time I posted about this
(read this first), the class left off knowing that population growth was not linear (as they had expected) but that, in fact, it was increasing by and increasing amount each period (as they put it). Here is how the sequence of curriculum design has gone since then and I'm wondering....did I get this wrong?
1. The next lesson was designed to get them thinking about multiplicative structures/exponential growth. We experimented with the problem below and then did a bunch of variations/extensions to eventually come up with this generalization (in their words): starting value (multiplier)^"iteration-1"
2. All of the variations from the previous lesson were whole number "multipliers." So, I decided to follow up with this video (thanks Dan). We talked about how big the 100th dollar would be and how big the "nth" dollar would be.
3. Now that they had an idea about percent growth, I decided to push their thinking with this "sequel." I gave them the resulting dollar bill.
As I have mentioned previously, I am really pushing myself with every lesson to put students into a place of cognitive dissonance or disequilibrium. With that in mind, I'm wondering:
1. Did I get this curriculum sequence wrong?
2. What would have made it better in terms of promoting disequilibrium?