I'm worried about my career in math education. I'm worried because I'm starting to wonder if it is a fool's errand to attempt to teach math in a way that goes against the mainstream. It's tiring...and I haven't even been doing it long. Our society has a clear, and in my opinion misguided, perception about the nature of mathematics and particularly about the way that mathematics should be taught in schools. I gave a year-end survey last week and, while there were many things to celebrate, students clearly echo the thoughts/opinions of the masses. Generally, I read a lot of things like:
       
        - We didn't cover enough math topics
        - We should have prepared for the STAR Test
        - We didn't do Algebra II (or whatever math we were supposed to be doing)
        - I didn't like when there wasn't a clear/right answer

As you might guess, I try to create a class in which students are doing math. We have worked on some interesting problems this year (How many combinations are there at Chipotle, What is the area of the Koch Snowflake, How can we predict global population, What is the best strategy for the game of Pig, etc) and students have done some really interesting mathematics as a result. Unfortunately, our society views mathematics as a thing and not an act of creating. Our national content standards, for many, serve as a definition of what mathematics is (and, by comparison, what it is not). In schools, society dictates, math should be compartmentalized and taught by transmission; if you perform well on the STAR/SAT/Whatever then you are good at math and if you don't then you're not.

I have tried really hard to open up this narrow definition of mathematics and to provide all students the opportunity to be mathematical every day, yet some of my students don't even recognize what we do in class as mathematics. It's difficult to be a part of a system while simultaneously doing things that run against it. You can't, and I don't, blame students for their outlook on things. I'm not sure my writing here captures the drama of all this, but I find it really alarming that this is what our educational system is teaching students about mathematics and about themselves. As I reminded my students today, the root of "educate" is "educe," or "to draw out." My job with them has been to teach by offering them an opportunity to express what was already a part of them, the ability to create mathematics, to create powerful ideas.
 


Comments

05/21/2012 11:01am

Bryan,
You are not alone. Twenty years ago, I got the same comment ("We didn't cover enough math topics") from my middle school students because we were doing semester-long projects. Keep swimming against the current - it's how we get stronger.

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blaw0013
05/24/2012 9:13pm

YES. -brian lawler

P.S. My students, having said the same sorts of things, didn't hate me. And run the world today... http://huff.to/Lx1vhR & http://on.fb.me/KSWJc7

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05/21/2012 11:46am

I really connect with your statement:
"Our national content standards, for many, serve as a definition of what mathematics is (and, by comparison, what it is not)."

Especially that final thought. I agree that the standards we've been given seem to dictate what mathematics is not. No matter how often these standards are described as a "guideline," everyone uses them as the curriculum. It's unfortunate, but now that many states are beginning to base teacher evaluations on students' performance on end of year assessments, I find it increasingly unlikely that this trend will change anytime soon.

With that unfortunate comment out of the way, that's why it's even more important that people like you continue to push against this. As each kid who goes through your classes ages and becomes a part of the voting public, hopefully these crazy policies can change and adapt. If you give in (or quit) and just follow the standards and teach them only those required topics and worksheet the crap out of them, then when those kids are adults and parents they won't know mathematics should be anything other than working simple problems from a worksheet over and over.

It's a process, and it'll take a generation at least, but I think that there are enough people like you that we can make some serious progress.

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05/21/2012 11:48am

Bryan, it's brutal at times, but the work you're doing is cutting edge, and the way of the future. It's always hardest for the trailblazers such as yourself. Know that the work you're doing is inspiring to me in Colorado. The nice thing about this Internets thing is you've got a world-wide system of support and thought partners. Keep up the amazing work!

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05/21/2012 12:07pm

I've experienced the same frustration. I covered a colleague's class for a day, and we worked on mathematical puzzles for the class. When asked what the students did the class before, one student responded, "It was great! We didn't even do any math."

Sigh.

I'm going to keep chugging away at this fool's errand, in the hope that I will convince at least one other math teacher to change their practice. If I can do that, I can hope that they will convince one other person, and so on, and we can begin to chip away at the problem.

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05/21/2012 12:37pm

I'm a bit torn. I love math. Really. And loved it in school best of everything. I was taught algebra and calculus with no connection to anything tangible (unlike geometric and trig which we did a lot of applied work, then using the algebra in a practical way) I loved the logic and the reason and straight solving or proofs (though the more complex the better). Later I came to love it for it's applications - when I did physics (specifically astrophysics) as a mature student. I had to adapt quickly and only then realised that my education had been in pure mathematics as opposed to applied mathematics - and I still find the former a more enjoyable challenge. Can do the applied no problem, but no other subject in school matched the type of thinking and challenge of pure maths had.

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05/21/2012 2:45pm

I think you're on point with the importance of thinking and creating mathematically. So much of the current state standards in NY are just a laundry list of skills that asks for little more than procedural understanding. It's exciting, and a bit scary, that we'll soon be expecting students to tackle problems requiring a fusion of skills in novel contexts. It sounds like that's already happening in your classroom.

On the other hand, perception is reality. If students feel like they're not "doing math" or that they're still not good at it, then that's reality for them. In your classes, how do students demonstrate to themselves and you that they are growing as mathematicians? I often think of a musical analogy: a talented pianist doesn't just improvise and compose new songs all day. He or she also spends time practicing scales and working on the basics. Are students given the opportunity to both drill skills and apply their understanding to rich, interesting problems? Often I think the math community is polarized into a false dichotomy...

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05/22/2012 5:34am

Very good point Adam. I agree with you and definitely see that polarization. It's true that we need to make sure those skills are taught and practice, because that's what they're expected to have in their next courses. The problem is that we also want to help show students that mathematics is more than that. I like your musician analogy. I think that it will be helpful for me to keep that in mind while planning my curriculum in the future.

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blaw0013
05/24/2012 9:18pm

I too agree, but with different emphases. It is simply captured as ensuring both mathematical competence (as defined by the culture--including the students) and confidence. My take is not so much to emphasize efficient and accurate procedural fluency, but rather to teach children to deconstruct mathematics as a social construct--a game to be played, as well a playful game, a ticket to power, as well as a powerful ticket...

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05/31/2012 11:21am

I've heard the music analogy before, and there are three critical differences that are important to note.

1. Most children choose whether or not they play music.
2. It is much more obvious that the music drills will make children better at playing music.
3. Children get to play music, whether or not they have completed their drills.

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05/21/2012 3:46pm

That's for sharing.

I support your problem solving efforts, and admire that your students (I assume) leave at the semester with a higher level of perseverance in finding a solution to their problem.

On the other hand, I echo some of what Adam said. Do you ever give in to the students what their learning goals are - what your trying to "educe?" perhaps they don't feel like they're learning because they don't know what they've done. Also, there is a responsibility to your students to cover Algebra II in their Algebra II course because as you are aware, those that continue to another math course will be going to a class unlike your own, with a curriculum presuming your students are now proficient at "Algebra II".

It frustrates me to go to conferences and see middle school and elementary teachers showing off their students' PBL results using essentially basic rates of change, arithmetic, and patterns. Yes, students can get solutions to population problems by really only using multiplication, and hopefully they'll go from their and understand HW growth factors work in exponential equations, but allowing them to stop at using only those multiplication tools is selling them short. It also handcuffs your colleagues next year when they are then filling in the pure mathematics gaps that students were short on.

I really wish to have a purely discovery, problem based Algebra 2 course - I've just only found resources to middle school.

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05/21/2012 5:22pm

I get similar reactions from my students. "please just give me a step by step example" is what I get from the majority of them who have been accustomed to math-by-numbers for too long to change.

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blaw0013
05/21/2012 9:56pm

Might you scan and post some of your student's work to add to the context? I am very curious to see the mathematical activity of students who are concerned about what math they did during the semester...

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05/22/2012 3:43pm

I am often frustrated by what my colleagues, students and community members here perceive it means to be "good" at math. I have many students here who do well in math...which means they study hard (sometimes), follow the rules, and do well on the tests we give them. But when I try to engage students with more complex tasks, examine interesting ideas and theorems, or encourage participation in math programs (like Moody's Math Challenge), my audience shrinks considerably. I think the math community is in some serious need of PR.

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blaw0013
05/24/2012 9:20pm

Oh my goodness YES!!!

"I think the math community is in some serious need of PR."

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05/22/2012 5:07pm

Thank you all for both the kind words of support and the statements of challenge.

I have a lot to say in response to many of the comments here, but I'm going to try to keep it short and summarize my responses to all. There are many things that I would disagree with in the current system of math ed. In many ways, it is a history curriculum more than it is a math curriculum. There is no opportunity for doing mathematics there now. To predict, or insist, that students come to know and understand their world in the same way is to take from them the opportunity for mathematical creation in response to their experience. As it is, the curriculum exists before the student. That, in itself, is problematic but to then hold them accountable for our compartmentalized notion of what it means to come to know mathematics is unethical and, in the long run, meaningless.

Of importance to me is the fact that students and society define mathematics, to a large extent, by their experience with it in school. Until our schools reflect what it means to "do math," we will always be met with opposition in our efforts to teach it that way.

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Greg McClelland
05/25/2012 9:50am

Hey Bryan,

Send me an email let me know how to get in touch with you. I have not found a teaching position and am back in the lab and want to find teaching postion........

Cheers,
Greg

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Jay Nihal
05/25/2012 5:04pm

What is now proved was once only imagined.

-William Blake

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whatevahworks
06/30/2012 2:49pm

Hi Bryan,

I am currently student teaching and my lead teacher has the copy machine work harder than the students with photocopying worksheets. I recently took over the classroom and I brought in some manipulatives and we worked on probability the students were amazed and got so excited. I value your commitment to push students critically and get them excited about math.

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