A Mathematics Manifesto

This post is for the Virtual Conference on Core Values ( http://larkolicio.us/blog/?page_id=873).

I believe all students people are good at math.

I believe all students people struggle with math.

THERE IS NO CONTRADICTION.

Going back into my ancient history, I don’t think I ever really “did math” until I was in eighth grade. I followed directions. I obeyed the rules. I applied procedures correctly, and often quickly. I was a successful math student.

And…I was bored out of my mind. I hated math.

But the thing is, I didn’t really know what math was. I thought it was memorizing all of the rules and remembering when to use each one, then going through the algorithm and arriving at an answer. Problem solving was nowhere in my definition of “doing math.” Up until eighth grade—when we did factoring—I hadn’t ever had a problem to solve. Not any that I can remember at least. I knew how to do all of the “problems”; hence I didn’t have any problems with doing the “math” that was presented to me.

But factoring, now that was a problem. The way my teacher taught factoring didn’t have a clear cut formula that I could use, or a special algorithm that I could follow to get the right answer. Sometimes there was even more than one right answer. What was the world coming to? No, this whole factoring business was different from all the math I had previously done.

My eighth grade teacher let me grapple with the idea and told me that I would understand factoring eventually. He let me get frustrated, but didn’t let me give up. And he was right. Eventually a light bulb flashed on over my head. I got it! I was able to handle any factoring problem anyone threw my way. I was so happy that I’d figured it out and that it finally made sense to me.

Time and time again I have seen this same moment happen with my own students. I have witnessed the excitement they feel when they figure something out on their own. When something that didn’t make sense yesterday makes sense today. I believe that the most important aspect of my job is protecting my students’ right to experience these moments.

It’s a fine line to walk between letting students struggle too much and not enough. Between giving them too much support or not enough. As their teacher it is a struggle to figure out where that line is for each student and to make sure that they don’t stray too far from it. I don’t want any of my students to become the good—but bored—student that I was; the student who knows how to do everything and therefore learns next to nothing. I also don’t want my students to become so frustrated, so enmeshed in constant struggle, that they feel unsuccessful at math; that they become one of those people who says they “aren’t good at math.” I truly believe that anyone can be is good at math, so long as they are working on problems at the right level of difficulty. Teaching is like walking a tightrope. One that is strung up between two skyscrapers. Falling off of either side is bad news.

It is damn hard though, to let students get frustrated. To let them be confused for a while, to let them struggle with the ideas. Confusion is a sort of conflict, and most teachers don’t really like conflict. But without problems to struggle with, we’re not really doing math. And shouldn’t math be at the center of a good math classroom? Shouldn’t every student get to feel the sense of accomplishment of working hard on something and then succeeding at it? In my classroom, that is always the goal.

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5 thoughts on “A Mathematics Manifesto

  1. I believe that the most important aspect of my job is protecting my students’ right to experience these moments.

    I love this! It’s such a hard thing, to find that perfect balance between support and smothering — but so important to keep looking for it.

  2. Well done! It reminds me of this quote: “Smooth seas do not make skillful sailors.” -African Proverb and the discussion we were having yesterday about the growth mindset in a course for teachers in training. Thanks for sharing your thoughts.

  3. So well put. And I wonder: “As their teacher it is a struggle to figure out where that line is for each student and to make sure that they don’t stray too far from it.” Will figuring out where that line is for each student continue to be a struggle even as I get better at it? In other words, is it not a contradiction to be good at, and struggling with, teaching, just like it is not a contradiction to be good at, and struggle with, math?

    • Great question Dan. I think that teaching–along with all complicated tasks–is something that you are good at and you struggle with, whether you’re in your first year or in your twentieth. Though I haven’t been teaching for that long, so maybe I’m wrong. However, every veteran teacher that I know and respect says that it stays challenging (and therefore engaging) no matter how many years you have behind you. In my own experience, figuring out where “the line” is for my students is easier now than it was five years ago, but it is still definitely a challenge.

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