Dialogue in Math Class

Today began the real work of the year after three half-days last week.  We’re at the beginning of a 1-to-1 chromebook initiative, which comes with its own pitfalls and moments of bliss.  Last week I had students complete a ‘menu’ for reviewing previous courses.  In the past, I’ve had it on paper, where it looks something like this:


Students were asked to complete at least one problem from each column, and score a minimum of 50 points.  Digitizing this using Khan Academy, I came up with a similar set up:



I really like the principle here–students having some choice as to their review, but still starting out the first three awkward days of the year (37 minute classes) with some actual math.  This year, I definitely did not allow enough time for the material, but I’m not sure if that was a matter of students getting used to chromebooks, technical difficulties, and lack of access (some students still haven’t picked theirs up as of today…), or that I put way too much in there for students to complete in the given time.  I’m a little mixed in terms of my feelings of how the opening activity went, so I’ll take a look over the course of the next week or so at the work students completed, and comment on that a little later.

Today’s work in most of my classes was completing our first math labs of the year.  I created ‘lab documents’ guiding students through activities (some borrowed, some created) built using the teacher.desmos system spread throughout the year in Algebra II and Precalculus.  Today, one Algebra II class explored Linear Marbleslides while my co-teacher and I went around the room chatting and listening to students interactions.  My Precalculus class completed a pair of creating functions activities (Part 1, and Part 2), both created by Megan Schmidt.  I really enjoyed listening to the students arguing about math, and coming up with some interesting discoveries.

Here’s a snippet of one conversation that I particularly enjoyed, where students were trying to figure out if it were possible for an interval to be decreasing, but positive.  These are two students in a lower level precalculus class.

A:  Can I tell you what I said to see if it makes sense?

M:  OK.

A:  His statement is false.  Just because the graph is decreasing doesn’t mean that–the function can decrease even if it is not hitting negative numbers.

I’ll close with that thought today–two students having deep conversations and thoughts about mathematics, caused by their exploration using some cool activities from desmos.