Is Calculating Math? Part 1

I was reading a book one of my students lent me The Geeks' Guide to World Domination (excellent read, I love my students). There are 314 (yes, pi reference) short essays about all sorts of interesting topics about geek culture. One topic which interested me greatly was regarding Artificial Intelligence and what John Searle referred to as the Chinese Room Thought Experiment.

Quoting from Wikipedia (image also from Wikipedia):
Searle imagines himself in a room acting as a computer by manually executing a program that convincingly simulates the behavior of a native Chinese speaker. People outside the room slide Chinese characters under the door and Searle is able to create sensible replies, in Chinese, by following the instructions of the program; that is, by moving papers back and forth under the door.

When I read this, it immediately brought to mind many of our "A" students in our math/physics classes. A lot of students become extremely good at learning how to do a specific task (e.g. factor a quadratic equation or find the third side of a right triangle), yet you ask them to apply or use that information in a new situation and they are stuck. 

This is why the Chinese Room experiment spoke to me, as I wondered how many students leave our classes, giving the appearance of knowing how to do a calculation but one summer break later and they are tabula rasa.

There are two complaints I hear about math class from adults and students alike:
  1. It's not fun
  2. When will we ever have to use this?
Now we could draw the conclusion that they just don't get it, they are lazy, maybe they had poor quality teachers, etc, etc. But I would like to propose another theory, maybe they are right. Maybe math class isn't enjoyable or relevant.

Now before you start to email me about your class, remember that I am talking about the large number of people I have talked to over the years who just can't understand why I enjoy math so much, let alone teaching it. 

If I can be so bold, I think I fell in love with math in spite of my math classes. Don't get me wrong, I had some incredibly interesting math teachers but most of the lessons just involved various ways of moving x's and y's around. Who could honestly enjoy that?

If we look at the curriculum set forth in textbooks and standards, they all involve calculations and remembering which formula to use. Patterns, creativity and problem solving are never addressed. Yet these are the fun and relevant parts our students crave.

But, we have state and federal standards and textbooks filled with lessons that we can barely get through you say. The content in our classrooms is increasing exponentially and teachers are struggling to keep up. With a general pacing of one maybe two days per topic rarely provides any time to devote to depth or application. 

If you have not read Paul Lockhart's thought provoking treatise on the subject of math and creativity I highly recommend it. You can read it for free here and if you would like, you can purchase a paper copy: A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form.

For me and I am sure many of you, the difficulty lies in releasing ourselves from the cycle. Most of us went to a US Public School where our math classrooms were filled with endless rote calculations and 30 or more problems a night. If we examine this practice, the primary goal of this routine is for students to perform the task so many times that they can perform it in their sleep.

The Navy traines it's sailors the same way. Drilling for battle stations and damage control over and over again until we could do it in our sleep. The question is whether or not we want math to be something that is robotic and automatic or requiring imagination and creativity. From the mathematicians I have read and heard from (e.g. Letters to a Young Mathematician), calculation should certainly not be our primary goal. The great mathematical discoveries have begun with wonder and inquiry and only later would calculation be needed to test the theory.

How can we set ourselves and our students free from the antiquated and aggravating structure of American Math Class. Why do we teach what we teach? What is truly important in a math class? For me, it is students being able to leave thinking math is enjoyable. My hope is to inspire and create opportunities for this to happen. When all else fails, geeking out and sharing historical background (which for a lot of math is right out of a mystery thriller), a puzzle, real life application, or an extremely esoteric problem that only those inducted into the deepest of the mathematical mysteries usually get to experience. 

As for the calculation, that comes with time and help but unless we seek to inspire interest and awe in our students first they will not learn. They might remember it for a time but they will not learn.

For part 2, I would like to share more about what inspires me and what I think is a new direction for high school math and science.

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