A Tale of Two Subjects
Or why we hated Math class
My last post reminded me of a beautiful short book “A Mathematician’s Lament” by Paul Lockhart. It compares the state of Math education with art and music and at the heart of the issue is that art and music are taught like a layered cake and math is not. So feeding off his example I wanted to compare the experiences with the respective subjects through our education and share thoughts on how we could break this pattern.
Beginning Learning
Our artist career started with an empty pieces of paper and some colored pencils or crayons. Maybe it was even water colors. You probably did not make something meaningful but but still enjoyed creating the cacaphony of color. We even had our artwork displayed in art galleries (refrigerators) and commented on my respected critics (parents).
Before we can do any mathematics it is a commonly understood fact that we have to gain mastery over arithmetics. In order to prepare for that we need to learn numbers. Of course before we can talk about numbers as a concept for quantity we need to memorize them. Oh there are an infinite numbers, well let’s at least get to ten. We can use a mnemonic. How about this nursery rhyme, “One, two, pick up the shoe …” (Fun fact: I have a fairly decent memory but I can’t memorize a rhyme for the life of me and so kindergarten was very very hard). Of course after we go up till ten we can now learn how to count to 100. Although I distinctly remember my book had 1000 after 100. I thought it was odd but I accepted it. Never having seen a 1000 of something made it a lot easier to accept it.
We would of course at some point learn that these numbers represent quantities. The idea of place and hopefully if we’re lucky they were kind enough to say ones place instead of units place. I was not lucky.
Primary School
Our art teacher did want our art to become better, more life like. And so we were asked to draw specific things. There was still room for creativity that personal expression on I want to have this here. There were some exercises to refine some skills like drawing circles. And there was guidance to help you as needed. I remember my teacher guiding me on color carefully closer to the edges so you don’t go outside the lines and then you can quickly fill in the rest of the body. Or using a cotton swab to get rid of the pattern from using a color pencil. And it was excellent advice to help me achieve the outcome I wanted from my art. Which was drawing helicopters and sports cars. Pro tip, having your people wear helmets made them 100x cooler and kept you from making faces.
In Math class on the other hand it was on to operations. Addition, subtraction, multiplication, division. Of course you memorize the time table. And are taught the algorithms for doing operations on two and more digit numbers. Having learned how computers work, I can safely say that I was as sentient about my math problems as the transistors in the calculator are when performing the same operations when I need an answer now.
Middle School
By this time our motor skills have become somewhat refined. So we can draw things that look somewhat realistic. But the powers that be thought that art isn’t really relevant as a subject any more. Probably for the better before they could destroy it too much. I do remember my 5th grade art teacher not liking that I had colored the tea pink. The sad part is, I wasn’t even trying to be very creative, just drawing from my personal experience. Since as a child the only tea I was allowed to drink was Kashmiri Chai which is in fact pink (Dear reader, to apologize for my rambling accept this humble gift of knowledge that there is in fact a pink tea.)
In math class however, they started trying to tell us that this stuff is relevant. We started getting the dreaded word problems. Is there a bigger testament to the failure of math education in its purported goals of teaching people the math needed for every day life than people find the thought of translating an everyday problem into an equation overwhelming. Maybe if Math had some connection to every day reality sooner we would have done better. They do however remember PEMDAS and judging by the number of social media riddles with only a genius can answer, apparently most think that is what Math is.
And Beyond
The experience continued. At each point in my Mathematics education from kindergarten locked up and held hostage to bad coursework, unsupported teachers, exams and societal pressures for achievement was something of profound beauty. Something both exciting in of itself and that allowed me to think more logically through every day life. Some of us dared to venture into the dungeon where she was imprisoned. We actually befriended her. Awed by her beauty, wisdom, power. Her laws, that make the universe bow to her will. We never had the strength to break her fetters but look at all the articles about mathematics on Medium. Many of us are adamantly trying to let others see her beauty and glory and spend some more time in her comfort. This same subject is what education makes so detestable that children’s toys complain about it.
But What Can Be Done
I feel the largest travesty is how Mathematics is reduced to a series of operations you do to numbers for the first many years of our education. Ideally we need to start being able to do proofs from kindergarten. No they wouldn’t need to be rigorous proofs complete with notation. But the first course where I remember actually talking about logic was discrete math in college. But it is a simple concept. And it is something that is accessible at a very young age. Otherwise it wouldn’t be the foundation of many children’s riddles. You can talk through outcomes of these with Venn diagrams and I bet they’ll understand.
And while we’re teaching simple addition and subtraction, why not right after asking them to do 3+5, ask them to do 8–3, followed by what number added to 5 gives 8? Even better ask them if there is only one number or can there be other numbers.
Why is probability a 6th grade subject? Children start playing dice based board games quite early. I remember I had been playing card games for quite some time. I would have appreciated my Math teacher helping me improve my Rummy game.
Back then Tic-Tac-Toe was actually exciting. You didn’t know who would win. A quick lesson in minimax trees and we could have been back to playing chess instead.
Would love to hear what mathematical problems you believe are accessible at a young age and can be used in encouraging Mathematical thinking?
