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Thursday, January 26, 2023

Book Review-A Mathematician's Lament By Paul Lockhart

In the forward to this monograph. Kevin Devlin of Stanford University, a well renowned mathematician, tells the story of how Paul Lockhart, someone who had given up his career as a research mathematician to devote himself to the mission of improving K-12 mathematical education, turned an earnest but obscure essay into a resounding statement.

The first genesis of this book is as a 25-page document that was passed around in the mathematical education circles. It became a sensation because many felt that Paul Lockhart had hit the nail on the head with his observations; observations and beliefs that resonated with mathematics educators; indeed, he struck a very sensitive nerve. As this document was passed around, it became a clarion call to mathematicians, mathematics teachers, and anyone who has a passion for how mathematics is taught.

A Mathematicians Lament is short and compact. Paul Lockhart had a lot to say, and he says it with urgency and alarm. Part I of  the book is the lamentation, he goes into everything that he feels is wrong with mathematical education. He makes his argument progressively starting with a discussion on mathematics and culture,  then a discussion on mathematics in the school, a dive into the national mathematics curriculum — a chapter in which he was unsparing in his criticism. In the last chapter in Part I, Lockhart zeroes in on a well-known and well reviled target: high school geometry.  Lockhart gave it a subtitle: Instrument of the Devil. This is his coup de grรขce, his pronouncement on the abysmal state of mathematics education in the United States.

He expounds on the insidious practice of limiting mathematics education to just computation, while emphasizing the mechanical and uninspiring practice of training skills without giving the students a vision of what true mathematics is. We don’t give the students enough credit for being perspicacious enough to sense the immutable and deep beauty of mathematics. We don’t give the allure of the mathematical abstraction enough credit for being able to inspire and elicit  passion from the students; we think that the average student could not fathom the depths of meaning of mathematics; and that the student can only appreciate mathematics in its most utilitarian and unimaginative incarnation. It is an insult to the students and to mathematics.

As an engineer by training, I managed to survive my formal mathematics training with my love of mathematics intact, even though I knew my talent for theoretical math is limited.  I recognize all the stated pitfalls and shortcomings of how mathematics is taught because I had experienced it firsthand.

Although I  appreciate the beauty of mathematics, as I had aspired to be an applied mathematician; unfortunately, I had made a mess of the higher math that I took as a grad student in engineering, I didn’t have the patience nor the curiosity to sustain my interest because I was studying to gain a degree rather than studying for the love of a discipline. I was resigned to take enough applied math to help me become an engineer even though I was always curious about doing pure mathematics. Even as I have  resigned myself to the fact that I won't ever be a pure mathematician nor  even be a good applied mathematician, I have come to appreciate and love the subject.

In the second part of A Mathematician’s Lament — titled Exultation — Paul Lockhart made his elevator speech  to  anyone and everyone reading about the beauty of mathematics. He assiduously avoided the equations, a smart decision in my estimate. He dealt with mathematics as a holistic entity. He is much more eloquent in stating his case than I will ever be, so I will let the reader  read the book rather than dilute his passion and his narrative.

He discusses the common sensical instinctive aspect of  mathematics. There are crude but effective sketches about the points that he wanted to make, adding to the intuitive charm of the narrative.  He refrains from delving into the dreaded and unwelcoming geometry that he wrote about in Part I;  he uses simple sketches to ease the reader into mathematical thinking.

When he hit his stride talking about mathematics, it is a beauteous expression of passion he speaks of the raw beauty of mathematics that makes it so attractive, intoxicating,  and habit forming for so many. It is as if  mathematics is some kind of addiction. And to mathematicians that I know, and to a much lesser degree to me, that addiction is very real.

The second part of the monograph reminds me of the passion exuded by another book written by a mathematician. Francis Su wrote Mathematics for Human Flourishing, (Su 2020). I reviewed it in 2020. (https://polymathtobe.blogspot.com/2020/02/book-review-mathematics-for-human.html) Prof Su had the advantage of having a book to make his point about the allure of mathematics. It is perhaps a good companion book to buttress the second part of the argument.

The monograph is an extended essay identifying the problems with the way we have taught mathematics, how the math that is taught is contrary to what the mathematics lovers love about mathematics; what mathematics is in the eyes of those that are knowledgeable in the art; while  proposing in broad strokes what need to be done to change that paradigm. It is a timely and necessary clarion call to our society and our educators that we are irresponsibly squandering our opportunity to educate our society in the art of thinking, questioning, and creating. It is an attempt to reverse the trend, and more broadly, it is a valiant attempt to convince a math deficient public that they are missing the boat, and our society will suffer.

I hope that this is not just preaching to the choir, but the obstacles to universal understanding of the importance of the subject is quite high. I hope that Paul Lockhart is not too late.

Works Cited

Su, Francis. Mathematics for Human Flourishing. Yale: Yale University Press, 2020.

 

 

 

 

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