Presenting Math as an Art

I was disconnected from the internet for most of the August and got a luxury of time to read a few deep-hidden non-fiction books from our library. One of these books was a shocker - a light, eloquent, captivating and constructive critique of the ways mathematics is percieved and presented at schools, universities and most of our households. It is a very refreshing and convincing analysis from a former scientist and experienced math teacher and I am going to recommend it to every teacher, parent and high school student. The book is: "A Mathematical Lament" by Paul Lockhart. It is subtitled: "How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form."

Dr Lockhart suggests that math is an art and should be treated exactly like music and painting. We should not be learning math because it is applicable to our daily lives or essential in our future occupations, but rather because the process and the result bring joy to our soul like listening to or producing music does. Forget all the bad math associations you have nurtured and think of a pleasure that discovery of any pattern brings to us. And the sweet mental game of attempting to explain this pattern.

Take for example this curiosity:

1 = 1

1+3 = 4

1+3+5=9

1+3+5+7=16

1+3+5+7+9=25

Fascinating! Sum of the subsequent odd numbers produce results that are all square numbers.

But why?

Can any square number be represented as a sum of subsequent odd numbers?

If we let our mind wonder about this for a while we may be able to come with an explanation, perhaps even as thrilling as this one:

Any square number can be drawn as a square, such as this big and colorful 5x5. Any square can be split into such colorful parts.

Count the number of little pieces in these parts. They are 1 (purple), 3(green), 5(yellow), 7(blue) etc. These are our subsequent odd numbers. Looks like any square can be split into such pattern.

Lockhart writes that in school "the rich and fascinating adventure of the imagination has been reduced to a sterile set of facts to be memorized and procedures to be followed." Being math expert, math lover and experienced math teacher he suggests a number of directions to improve such math education:

• "Mathematics is an art of explanation." This means that students should be allowed to pose their own problems, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble togather their own explanations and proofs."
  
• Math history is fascinating and provides a great base for captivating storytelling. Instead of handing kids formulas to memorize retell them stories of ancient and contemporary mathematicians and their search for solutions to the fascinating problems that are wrapped in these formulas today.
• Like other arts math should be subject to debate and critisize in schools. "Is this argument sound? Does it make sense? Is it simple and elegant?"
  
  
• Forget proper notations that are frequently a source of frustration. "Math is not a language, it is an adventure." DaVinci, Pollock,and Warhol each created art in their own way.

The author also cleverly warns that although math is and should be presented as an "art" subject, such shelving may be dangerous as "useless" art disciplines are frequently the first to be cut off from the curriculum in time of budget cuts.

This book will definitely change the way you think about math.

It may boil your blood from anger with the author or on opposite, the current math curriculum against which he convincingly stands.

It may explain you why you always hated math classes but liked riddles and puzzles.

It surely will inspire you and teach you a few tricks that you will rush to share with your kids as I did.