The Math Practices in Action

It's December.
I think I can safely say I'm starting to see the fruits of our labors each day in class.
Today was the first day that Math Practice 3 showed up without me purposefully instigating it.

It started out rather innocently.
We were reviewing a quiz question..."What would the graph look like for bacteria that doubled every hour."
I thought I knew the answer.
I drew it on the board...the exponential curve that I had been drawing for years for this type of problem.

I talked about the misconception of the most popular quiz answer of the stair steps.

And then my class erupted.
Literally.
Students were trying to make their point known.
It got louder.
Finally a student went up to the board, to illustrate his point.
Soon 6 others joined him.
The noise level reached ginormous proportions as they believed that sound level equated to being able to justify their thinking.
It doesn't.
Communication must be precise for others to follow along.
Not just loud.

A student mentioned that the stair step graph could not work.
It was not a function.
It would not pass the vertical line test.
This swayed several students looking on.

As I stood back and listened to my student's reasoning (math practice 2),
I realized that they all had something in common.
They all agreed on the table of values and how to graph it (math practice 4...models),
It was just how to connect the dots.

When I mentioned this, everyone seemed to agree.
This was where we were stumbling over.
Plus the fact that maybe looking at it from a real life perspective vs. a math perspective might be different.

A student then suggested that maybe the data was discrete
And that the dots were not to be connected at all.
(math practice 6...precision...correct use of vocabulary to be justify thinking...math practice 3)

The students continued this for 45 minutes.
45 minutes on ONE PROBLEM (math practice 1...perseverance!)

We ended with not a definitive answer.
This can be scary...when the teacher doesn't know the answer.
For both the teacher AND the student.
But for some reason, it wasn't.
We were all learning.
We all knew we were learning.
We had crossed the barrier of who's right to what is the right answer.

Baby steps.
But we are getting there.
I can feel it!