Who knew Systems in 3 Variables could be fun?

I’ve been tweeting about various highlights of the start of the school year – wonderful Beyond White Dudes signcomments on name tents, successful ‘stand and talks’, the launching of “Mathematicians Beyond White Dudes”, and the “What is Math?” lesson. The last two in this list, I am convinced, has won me some engagement for which I might have otherwise needed to fight, if indeed those students were willing to become involved at all in my math madness. And I owe debts to Rachel Rosales, Sara Vanderwerf, Annie Perkins, and Brian Palacios for sharing their hard work so that I might improve my practice, and the IMG_2376educational experience of my students, hereinafter occasionally referred to as “the kiddies,” with great affection. I have hesitated to blog about all this, because I am standing on a lot of shoulders, and don’t want to claim someone else’s genius as my own (that, and the fact that my body is screaming from the enforced transition from an 8 am wake-up time, to 5:15 am, or, as appropriately dubbed by my daughter, ass o’clock.

But today I had a success that I am pleased to own. This is a lesson that flopped dismally last year which I was able, with reflection, to fix. In our department, we have debated the value of teaching systems of equations in three variables; we don’t do 3D graphing, or cover the equation of a plane, and opportunities for context are thus lacking. But the Math Overlords in Albany (aka the Board of Regents) have included it in the standards, which by the way, have been recently revised and renamed the Next Generation Learning Standards- but I digress and will only inflict THAT rant on close family and friends.

Whether or not I feel content is appropriately placed in the curriculum, I owe it to my students to prepare them for the gatekeeping exam they will take at the end of my course, and it behooves me to find some way to make the topic intriguing without having the time to address graphing in three dimensions, providing adequate context and background. Last year I came up with the idea of having the kiddies make up number puzzles. I opened the lesson with Task Cards; when students entered the room, each table had a different set of requirements of their card. I made sure my instructions were clear and easy to follow (famous last words, right?). Total flop- the kids had no idea what to do, and looked at me like I was speaking a language that none of them knew. I guess I was. After a little flailing about on my part, we abandoned the activity, and I launched into the very dry task of demonstrating how to solve a system in 3 variables.

Fast forward to Fall 2017. One year more experience, one more year of sharing online, participating in the #DITL (Day in the Life) blogging challenge, and attending high quality professional development at Math for America and being a part of that community. Another attendance at wonderful, inspiring Twitter Math Camp – probably most important of all – surrounded by friends, progressive teaching, and a group of educators dedicated to continual growth for both themselves and their students. A booster shot for my teacher soul, which I was terribly afraid was burning out.

Today, the 6th full day of school, I introduced Visibly Random Groupings in this class.  I waited a week because this class is not in my regular classroom with its lovely tables, and we have to put the desks into groups when we enter.  I’m still trying to work out the logistics in my mind of moving in and out of a classroom for one period, moving the desks, giving out cards for seating…I know there’s a smooth solution that I just haven’t envisioned yet (feel free to make suggestions!).

UntitledI began the lesson with a number puzzle above – it involved three numbers, didn’t necessarily require a system with three variables to solve. The kiddies got busy as soon as they entered the room.  Several did write systems with three variables, and quickly substituted into them.  Jonathan, my super-eager, super bright 9th grader in Algebra 2, asked if  he ‘was allowed’ to solve it with just one variable.  Pretty quickly, students arrived at solutions, and wanted to share them.  We put some work on the board, discussed all the different strategies involved – guess and check, elimination, substitution – everything we had used when reviewing systems with 2 variables for the last two days.

Then I put this task on the board.  I read the directions to them, giving them Untitled2examples of what the result of each step might result be.  I learned last year that it was crucial to the success of this task to be explicit – despite my faith in my students’ abilities, they needed some translation of what I was looking for; this leg up and the experience of the warm-up gave them enough support to begin to play without me telling them exactly what to do.  The room was BUZZING.  The kids debated which numbers to choose.  They debated which variables to use.  IMG_2390They wrote the systems and then tested them. Twice.  And then I gave each group a small whiteboard on which to write their system.  The groups swapped boards, and tried to find solutions.  There were heads together, signaling across the room.  Not a phone in sight.  And I heard lots of great talk – students justifying to one another, arguing with each other.  No one needed my help, so I walked around eavesdropping, and grinning.  There was frustration and struggle, but the IMG_2386kiddies were so motivated to figure things out, that they took that frustration and used it to fuel another attempt.  They took pictures of the whiteboards so they could continue working on them later.  And I could see that the class NOW was truly primed for solving the more difficult systems that they will encounter on the state assessment.  As the end of the period drew near, I presented an example of the type of system we would be working on next week, just to get them thinking.  When the bell rang, several students stayed behind, continuing to work/argue/get excited about solving the systems they had traded with one another.

I’ve been working hard to incorporate engagement strategies and keep the kiddies talking about math to each other.  I’ve seen enough positive action thus far to keep moving forward.  I love the feeling of being so intentional and witnessing the results. Okay – I know the school year is only six full days old, but I’m on the right path.

A postscript that I’m trying not to dwell on: As of this fall, there are two tracks for Algebra 2 in my school: one for students who passed the Geometry Regents, and one for those who did not.  (Students who retake the Geometry Regents and pass it in January can move from one track to the other).  There are reasons for this that make sense and others with which I disagree.  But the issue at hand is that many students were erroneously programmed in Algebra 2, and this is allegedly going to be fixed early next week – which means A LOT of students are going to be reprogrammed.  I am currently teaching 2 sections of Regents Algebra 2 and 2 sections of non-Regents Algebra 2, and all this good work I’ve been doing of introducing my classroom culture and connecting with my students – well, we’re all in for some disruption. Wish me luck in weathering it all.

 

 

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2 comments

  1. merryfwilliams

    How wonderful, Wendy! I love that you reflected on last year’s experience and found a way to make it super successful with your kids – and the comments on those cards? “I’m starting to finally understand math” and “challenging and fun.” I mean, it just doesn’t get any better than that. Kudos!!

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