Rediscovering the Beauty of a Triangle in a Square

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By way of being diplomatic, one of my teachers would ask students a simple question when they expressed an opinion that was controversial. The question went something like this: "What in your past experience has led you to make this statement?" Surprisingly, I often use this question as a way to explain my own perspectives, justifying the conclusion I come to with an experience. Here's one example:

"Every day, I'd go to school and work my way through a mound of math problems. I often didn't know why I was doing things, only following the formula that would result. When I arrived at home, my Mom would demand of me, 'Miguel, you have to understand WHY you do this problem in this way.' Trying to balance the two worlds--do whatever you need to so as to get the assignment finished with a passing grade and the understand the beauty of the math puzzle--left me thoroughly disgusted with mathematics.

In the end, I suppose I made a choice--survive, thrive in the classroom. It's not a choice unlike what many schoolchildren make every day. Was it the right choice? Definitely not, but can you blame a child?"

I've always known I missed the point of mathematics, failed to see the beauty, like some art-insensitive, blind buffoon. I'm grateful to read that not all math teachers had the same point of view as my many teachers. Lockhart's Lament--as explained here--makes this point:

So how do we teach our students to do mathematics? By choosing engaging and natural problems suitable to their tastes, personalities, and level of experience. By giving them time to make discoveries and formulate conjectures. By helping them to refine their arguments and creating an atmosphere of healthy and vibrant mathematical criticism. By being flexible and open to sudden changes in direction to which their curiosity may lead. In short, by having an honest intellectual relationship with our students and our subject.

Of course what I’m suggesting is impossible for a number of reasons. Even putting aside the fact that statewide curricula and standardized tests virtually eliminate teacher autonomy, I doubt that most teachers even want to have such an intense relationship with their students. It requires too much vulnerability and too much responsibility— in short, it’s too much work!

It is far easier to be a passive conduit of some publisher’s “materials” and to follow the shampoo-bottle instruction “lecture, test, repeat” than to think deeply and thoughtfully about the meaning of one’s subject and how best to convey that meaning directly and honestly to one’s students. We are encouraged to forego the difficult task of making decisions based on our individual wisdom and conscience, and to “get with the program.”

It's not surprising that teachers buffetted by incessant complaints about their performance lose the desire to connect with students, to have "honest intellectual relationships" with their students. When I read Paul Lockhart's points about a subject he is passionate about, I can't help but think, "Wow, aren't these the same points educational technologists make about learning with technology? And writing teachers about writing?"

I do encourage you to read the whole of Lockhart's Lament and ask yourself what this would like in YOUR field of interest.

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Everything posted on Miguel Guhlin's blogs/wikis are his personal opinion and do not necessarily represent the views of his employer(s) or its clients. Read Full Disclosure


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