Why teach Algebra

I've been thinking about a response to the article published in the New York Times, "Is Algebra Necessary?"  for over a year.  I've started maybe 10 different draft posts and scrapped them.  I've been following the follow-up debates in blogs (see Wiggins' post on algebra 1 as a poorly designed course and Honner's response to Wiggins) and thinking about related articles like "Wrong Answer: The Case Against Algebra II" and "The Mathematician's Lament".

I've been so torn about how to respond because as a math teacher, of course I believe teaching math is vital.  I became a teacher because I wanted to save the world and martyr myself with 80 hour work weeks and panicked sweats every Sunday night.  And reading these articles seems to trivialize what I have poured sweat, tears and many many gallons of coffee into.  Yet I see their side of things.  I hate the idea of algebra 1 being the barrier between a talented artist and a career in art.  I am now teaching students in algebra 1 who have failed it two or three times before and it broke my heart yesterday when I handed back a  homework assignment I had given a 7/10 to a student and her face lit up as she said that she'd never gotten a passing score on a math assignment.

Also, I've never used math in "the real world".  I'm not an engineer, an economist, a physicist or a banker.  I don't know how math gets used out there so who am I to tell students year after year that they're going to need these skills when I don't know that they will.  The argument that math sharpens general cognitive skills and teaches students problem solving strategies that will be useful later in life, especially as it's backed up by research, holds water but that doesn't help us algebra teachers argue for teaching algebra.  Why not teach statistics?  Or a formal logic class?  Should we defend the traditional math sequence, or should we branch out and give students who are failing at algebra alternative math options?

But the other day I was talking with my husband and I realized why I love math, not why I teach it or how I use it, but why I love it.  And I think the reason for my love is also the reason it needs to be taught.  I am decidedly introverted, perhaps the queen of introverts.  I can't handle phones- it's very very difficult for me to talk on the phone with those I love and even harder with those I don't know.  I need to see eyes, to gauge reactions, to be able to comment on surroundings or engage my conversation partner in a task that removes the focus of conversation off of me.  I've found the adult world intimidating and overwhelming and need frequent breaks from it.  I like playing board games to escape because they have defined protocols.  I know exactly what the object of the game is and how to get there.  I can enjoy socializing while playing because of the game's comforting structure.

The world is overwhelming for anyone- even those not so introverted as I am.  There are complex political systems to understand, the natural world can be scary and confusing, bad things happen to good people inexplicably, we are born with deficiencies and insecurities that make socializing difficult or awkward.  School is for this- to help our young students learn that knowledge will conquer their confusions and difficulties.   When they understand how something works, they aren't as afraid of it and they know how to navigate it.   Or when they understand how something works, they won't make a mess of it because of overconfidence or arrogance.  Understanding our history and political systems is vital but impossible.  We give our students the best analysis tools we can and hope that time and a love of learning will help guide them in making wise decisions for themselves.  Learning science is fascinating and practical, but requires lots of field trips, labs, props and math to even begin understanding the basics of how our world works.  Math is the only field where understanding can be created by the student with nothing more than a pencil, a paper and a system of logical rules- just like a board game.  Yet unlike a board game, math helps us untangle the mysteries of how the world around us works.  It gives us a sense of order and control over our own minds and our own environments.  Isn't our job as educators to help students make sense of the world around them and to help them feel in control of their own lives?  Math is instrumental in accomplishing these two goals but especially for helping students realize what their minds are capable of and that they don't have to go outside to conquer a small piece of their universe.

So this is why we need algebra and not just statistics or logic.  Algebra is about finding the unknowns.  It's about looking at how the complex variables in our lives that affect each other and us. It has the further advantage of being the bedrock of higher level math so that if a student chose to pursue advanced math, she could.  It's got an easily understood framework of logic so that when the basic properties of algebra are mastered, all the other results are easily provable by a 14 year old with a pencil.  But most importantly, mastering algebra - especially because it can be such a difficult transition for many students- makes a student feel powerful and in control of her mind and world.  Isn't this how we want students to feel when they go out to help shape our society?

Baby steps

There was a good discussion recently on Twitter about complex tasks and why many teachers and students shy away from engaging with them or give up in frustration and return to low-level tasks.

Thoughts/critiques of this framework? pic.twitter.com/vsTdBKbOhC
— Geoff Krall (@emergentmath) November 20, 2013

I think that we can all come up with reasons why it's difficult for many teachers (including myself) to move out of their comfort zones and implement rich tasks in their classrooms. I am also interested in figuring out why students would resist complex tasks. @MathEdnet blogged about the various reasons that complex tasks can empower students by giving them more control and a voice as mathematicians and doers. The idea is that working with rich problems allows students to see their knowledge as valuable and themselves as active users of such knowledge. In implementing such tasks in the classroom, however, I have often seen student frustration and discomfort with the change in expectations from previous classes or from how the class had been functioning. This is sometimes especially true for students who care about their progress the most and who have certain ways of doing mathematics that have worked for them in the past that no longer work in a framework of complex problem solving. For these students, complex tasks appear confusing, unfamiliar, and an obstacle to their goal of doing well in the class. It can feel very frustrating to the teacher, especially if she hopes that implementing a complex task will increase student buy-in and engagement. Everybody is unhappy.

There are many ways of working on this issue, I think, and each is unique to the particular confluence of school, teacher, and group of students. Some teachers have big enough personalities that they can persuade students to trust them and step out of their comfort zones through sheer awesomeness.

Not a teacher, but would probably be an awesome one.

Teachers like me who have a hard time not being liked by our students and are not inspiring enough to get everyone to drink the Kool Aid come up with more gentle approaches. Baby steps, if you will. I have been working on a mix of traditional and complex instruction that takes students from the type of work that they're used to doing in math classes and gradually, inserts some open problems, starting with smaller tasks that are worked on in class and give students plenty of supports to hopefully build on more and more rich problems as students' comfort level increases.

I am, by no means, amazing at this. I definitely give tasks that are too open for students to handle and they freak out. Or alternatively, too many low-level tasks, which undo some of the work I've put into pushing them past that point. But this is the type of thing that is really, really hard to learn to do. Or, at least, it is for me. It's not something that is part of a graduate course or can be picked up by watching a lesson or two taught by a master teacher. And I have certainly never seen a pre-made curriculum that does this type of nuanced dance between what this particular group of students is comfortable doing and something that's just a bit outside of their comfort and ability zone so that they feel challenged and interested, but not overwhelmed and frustrated or bored and disengaged. So. My point. I did have one. I feel like lots of us on Twitter are stabbing away at this teaching thing, but with different tools, personalities, and kids. And it's easy to feel frustrated that I'm not doing amazing open tasks every day with my students or month-long cross-curricular projects that empower and engage them to the utmost.

Wait, this isn't what your classroom looks like every day?

But, I'm working just outside of my comfort zone and pushing my students to do the same. Baby steps. But progress, nonetheless. And I'm confident that y'all are doing the same, in your own way.

So coming back to the original question - perhaps what I'm hoping for is more recognition of baby steps and meeting people where they are, both teachers and students, to help them make small, but noticeable progress, as a way out of the cycle that @emergentmath described.

Congruent Triangles Review Game

I played a review game with my geometry class a few weeks ago that they loved so I thought I'd share it.  I think I stole this idea from a blog, but I can't for the life of me remember which blog, so if it's yours let me know.

I stole the problems from the Pearson Geometry Common Core Edition. 

I printed the document below double sided but didn't staple it.  Then I shuffled the pages and made 8 or so copies of all of them for the 8 groups in my class.  The groups needed to start with the page that has "RP" at the top and do the proof.  Then they hunt for the answer in the sheaf of papers.  When they find the answer, they grade their proof against the answer key, turn the answer key over and work the problem on the back of the answer key.  Then they hunt out the answer key to the new problem.

If they keep track of the order in which they did the problems, they can write down all the letters from the upper right hand corners of the problems, unscramble them and a message appears.

I had students for the first time actually paying close attention to every step of the proof, asking great questions about why different steps appeared, if they were necessary, and if/how order in the proof matters.  They also really loved working out the code.

I know it's just drill and kill two-column proofing, but it did a nice job of getting my students to compare different proving methods and getting them to analyze their own work.

Here it is:

Triangle Congruence Proofs Review Game

Awesome Article

Here's an AWESOME article on that oft heard phase that crushes teachers' souls, "I'm not a math person."  It's titled "Miles Kimball and Noah Smith  on the fallacy of inborn math ability."