Did a lab today on Desmos playing with linear, quadratic, and for kids who got to it, exponential functions. Lots to talk about, but the most interesting moment for me was totally unrelated to functions or the goals of the class.
This was the first time my students had used Desmos in class. One girl, while she was playing with a quadratic function, started zooming out, and just kept going. The look on her face when she got to about here
was priceless. “OH my God it’s in scientific notation!”
I don’t think she’d ever really thought about how big numbers in scientific notation are. I mean, she could regurgitate that they were big numbers (or small numbers as the case may be), but watching the numbers on the axes get bigger and bigger and bigger and all of a sudden feel the intellectual need for scientific notation made something click in her brain.
I introduced scientific notation this year with lots of examples about the measurements of atoms and distances in the solar system and age of the universe. There was definitely some engagement there, and some measure of intellectual need — but the power of what my student watched happen on Desmos today bridged the gap between numbers as we normally work with them and numbers that are better expressed in scientific notation.
Of course, this was one student (with another looking over her shoulder and several more who listened to us talk about it), and the question is how to structure a lesson (unfortunately probably not until next year when I introduce scientific notation again) where all of my students feel that intellectual need.