What Mathematicians Do...

I think the universe is trying to tell me something.  

School started this week and, as part of that, I had my geometry students working through the Packing A Truck problem from the Mathematics Assessment Project.  The activity required two class days.  On day one, I gave the students time to work on the problem individually, followed by group work time.  Each group was then instructed to put their best solution (no groups had the "right" answer), as well as an explanation of their solution, on a half sheet of poster board.  The groups rotated about the room making notice & wonder statements about each of the other group's solutions.  On day two, I gave the students the correct answer and asked them to try to produce it - only one group succeeded.  After working through the solution as a class, I asked them why they thought I would give them a problem that I didn't expect them to complete correctly.  Some answers I received:

• "You wanted to see if we would stick with it."  
• "You wanted to see how well we could explain our thinking."  
• "You wanted to see how well we work in groups."  

YES!!!  

I tried to make them understand that mathematics is not about always knowing how to solve a problem on the first try; that mathematicians may attack a problem from several directions and may never reach the answer they sought.  Mathematics is about the struggle and the persistence to continue.

My online graduate level course for the semester (technically) begins on the 21st, but he professor opened it a few days early.  The topic of the class is about problem solving.  In his opening remarks, the professor made these statements:

• "Problem solving, to me, really captures the essence of mathematical practice - the idea of exploration, and conjecture, and even collaboration, together with rigorous argument - that, to me is what a mathematician does."
• "Mathematics is a creative, and intellectually engaging activity.  It is not a collection of dusty old algorithms. And yet, a lot of the time, we lead our students to believe that it is." 
• "The value of challenge problems is that we'll be struggling. Sometimes we will be failing to solve them, and that's fine." 
• "Mathematicians don't work by themselves; they work with collaborators."
• "You're going to feel frustrated more than you're going to feel successful, but that frustration is valuable."
• "We shouldn't hide our struggles.  We want to normalize our struggles. Struggles are important;  hiding it creates a fear of failure. So, let's celebrate our failure." 

Scrolling through Twitter early this morning (before any sane teacher would have been awake after the first week of school) I ran across this image in a tweet from Anna Vance (@TypeAMathLand) that echoed the professor's statements. 

It's as if the universe is trying to tell me something.  My #1TMCthing is to include more rich tasks and activities into my courses.  I want my students to act like mathematicians.  I want them to face problems that are at the edge of their comfort level.  I want them to productively struggle with solutions.  I want them to verbalize their thinking more.  I want to transition away from two column proofs to the more mathematician appropriate written response.  Seeing and hearing all of these cues in this first week of classes is making me think that I am doing something right.

Ok, universe. I'm listening!