I have to say that this is the first time I've had a student bust out the old f(x) in class since my days of teaching advanced biology at another district many moons ago. This math outbreak occurred in one of my environmental science classes today. We were NGSS-ing it up, working on a piece of what's known in Next Gen Science lingo as HS-LS2-4. This performance expectation, in case you don't have them memorized already, involves students generating models to represent nutrient cycling and energy flow in ecosystems. We were working on the flow of energy piece of that standard, having students first make an original student-thunk-up energy-flow analogy/model. Later on, after studying the biogeochemical cycles, they will then build upon their energy analogies and work these analogies into models of the biogeochemical cycles, using proportional mathematical reasoning as well as revealing connections between energy flow and fun stuff like the carbon, nitrogen, phosphorus, and water cycles. Below you can see some of my student's efforts at mastering this performance expectation through the generation and sharing (on the whiteboards) of their analogies (which will later become a part of a larger model):
Were all of the models perfect? Nope. Were my students not used to thinking this way, coming up with an original model using math to represent a concept? Yep. Yesterday, when I introduced the activity, most groups tried to Google the answer to no avail. They then asked for examples, which I did not provide until today - I firmly believe in not giving examples up front for these types of activities, or you squash any creativity that may burst forth from their brains by putting in a preconceived notion of what is "right." Then you inevitably get 30 or so of the same example you showed students, only slightly modified. That depresses me, and my students don't do anything but waste time copying an example. So I don't do it. I give examples AFTER students have come up with their own idea - any idea - as long as it's theirs. And then I show an example (which they are not allowed to copy), and students can modify their existing idea to their heart's content.
But the ideas must come from the students first, not the teacher. They have to do the learning after all. And this is what I like about the NGSS - they allow for this type of thinking on the part of students, rather then giving me a vague laundry list of science stuff students have to "know" and "understand."
And they allow for random math to burst forth onto a whiteboard. That's pretty cool.
