In the curriculum I’m building, I center the use of Habits of Mind and Habits of Interaction. “Listen to Understand” is one. And, yes, naming and teaching it helps a lot.

Maybe not a proof, but it seems to me like these second differences create some intuition?

Yes. But this is what is kinda weird/wonky. In your Desmos file, the transformations are defined according to the mathematical conventions. But, like you can see in my attached image, JavaScript treats it differently. The same commands result in a rectangle that is in a different location.

If I start with a rectangle centered at the origin, and 1) rotate 90 degrees about the origin then 2) translate (100,100) I get a result that is in the second quadrant. The translation is in reference to the rotated coordinate plane.

I’m curious how people think about this…

Here are two different sequences of transformations applied to the picture below:

1. Rotate 90, translate (100,100)
2. Translate (100,00), rotate 90

Do they produce the same result? Why or why not? #iteachmath

In the upcoming unit I'm working on for #MathThatMatters (math-that-matters.com), students will learn transformational, coordinate geometry in order to build their own 'joyful gif.' I'm excited to see what they create. Here is mine... #mtbos #iteachmath #mathstoday

4. There is explicit attention to teaching and nurturing the development of mathematical 'Habits of Mind' and 'Habits of Interaction.' These are named and integrated into the daily activities of the curriculum, not as a 'once-a-week' problem solving activity.