Fun milestone a couple weeks ago:
Sounds crazy right? Lots of people would have you believe the future of computers in the classroom is those dystopian pictures of kids in cubicles with headphones on. Turns out you have other choices. So what were we doing during this magical week?
We were wrapping up area between curves and various volume expressions. I figured it was a great opportunity to let them play with integral notation on Desmos. Super duper handy for expressions of volume/area with respect to the y-axis. TI-84s can't touch this.
Later in the week I gave them a pre-loaded set of regions with a request for a particular integral expression (area between curve, solid built with square cross-sections, etc) and had them enter their results into an activity builder.
Student's ability to play with function notation here is awesome. Being able to collect math input through Desmos was a neat experiment.
What haven't we done on computers in Pre-Cal this year?
To start, we finished a study of three-dimensional vectors with an opportunity to make some 3D objects in Tinkercad.
With our study of vectors and polar coordinates, I offered students a glimpse at what spreadsheets can do faster than people. Namely, kick out a bunch of polar points and convert them to x-coordinates and y-coordinates.
Some students needed helpers:
Then, super quickly, and with several "ooooooooohh"s, we dropped the x/y table into Desmos for an initial look at the graphs of polar equations.
We refined the ideas present here through the use of an exploration activity made with Activity Builder.
In each situation the computers came out because they can perform the task better and faster than pencil and paper. In the case of Pre-Cal, they extended math to a place they didn't know it could exist before through spreadsheet formulas. Calculus got a chance to speed through volume because of the ability to see a region, talk through the logic of how to define an integral around it, and then see that integral computed in the same window. That took us a million button presses and a stack of copies previously, with no option for functions defined in terms of y.
A+++ would teach again.