Mrs. Arratia-Walters Dreams of Math

Monday, September 12, 2016

Why am I studying math...again?

In pursuit of my classroom teacher license, taking a course on elementary math instruction was essential.  But that's not why.  From a bird's eye view, my professional goals are quite simple: to make learning equitable and exciting for every child I teach.  So digging deep into my memories of math vocabulary and the perseverance needed to succeed with this realm of learning was the place I started.  

The first couple of weeks of studying critical thinking with a deep foundation in algebraic forms and their application to new problems was challenging.  It brought to the surface the reasons I haven't studied math, engaged myself to learn more, in more than 15 years (which isn't to say I haven't used it on a daily basis, but I'll return to that later).  Initially, there's is anxiety in approaching a problem I might not understand the first, second, third...x (as an unknown variable) times.  The current ethos of our country is data-driven and doesn't typically necessitate applying formulas to abstract situations.  The issue of time, or lack there of it for a teacher-by-day, student-by night, was also worrisome.  How much time spent attempting to fully understand a problem was TOO much time?  Could I let myself-gasp!- give up on any problem, to maintain a calm work/study-life balance?  

In actuality, those first battles with my inner perfectionistic qualities and stopwatch of my waking hours created in me the perseverance I want to teach my students to embrace from the start.  There shouldn't be a similar amount of time, wrong answers, confusion, and erasing that makes a task "hard" applied to math as is to other situations.  If it were to take me 30 minutes to read and understand a paragraph of literature or informational text, that material is probably too challenging for me to read for learning or pleasure.  Children must be explicitly taught that math requires mistakes: the more we make, the closer we get to the answer!  And every time we try to solve any future problem, we reflect on what we learned from those small mistakes, and, suddenly we've got stamina!  We're mathematicians who approach this work as marathoners, not sprinters and feel comfortable doing so.  That's the biggest "hurdle" for me and most people in approaching math.  Which is why it's my goal to start math as a fun albeit different model for thinking, solving problems that are authentic and value every culture and language present, and promoting collaboration.  I can't wait to see what their growing minds can do, and I can't wait to see the "I get it" sparkle in their eyes.

Here's an example of authentic and exciting math that I did last weekend with my "little brother" (I'm a Big Sister).  We were walking near the Mississippi River on Labor day when he posed a simple question: "Can you swim in the river?"  

I turned the question around to hear his perspective.  I asked, "What do you think?"  He said he thought it was dirty (and I agreed), but the water was moving pretty slowly where we were.  Maybe there was another factor there.  I asked him if there's anything else we would need to consider before we dove in. He pondered for a minute and replied, "How deep it is?"  "Interesting," I remarked, "but how could we find out how deep it is?"

We didn't have any measurement tools,  so this simple discussion led to us dragging a 20ft. branch off of the river bank, putting it into the river until the top touched the river floor, then measuring it with the only item we had which we knew the length of (my iPhone).  We discovered it was 49 inches deep in that spot.  Then we wondered how tall that was in feet since it's hard to picture depth in inches.  He knew a ruler was 12 inches.  He chose to say multiples of 12 in ascending order until we got close to 49 inches, and concluded that the river at that spot was 4ft. 1 inch deep.  Then we talked about our own heights (he's much taller than I) and what swimming would be like at this spot for both of us.

"So do you want to go swimming now?" I joked.  Neither of us did.  I pushed a little further, though.  Since we knew the depth, what wisdom could we share with people who do want to swim there right now.  He contemplated that for two minutes, then responded, "Don't dive!" and seemed very proud that he could very simply apply what we learned to keeping others safe.  My dream of math came true.