The Mathematician's Lament is broken into two parts, the first part titled "Lamentation" and the second titled "Exultation". First, let us discuss what a "lament" is. Although this may be common knowledge for some, there are still a few of us who need to widen their vocabulary. According to Dictionary.com, lament can be defined as "a passionate expression of grief or sorrow". This definition perfectly aligns with the mood of the first part of Lockhart's book.
Lockhart starts this portion of the writing by introducing his views that math is an art, and by saying that our culture does not view the subject in such a way. He states that mathematics has been transformed from adventure and imagination to facts and procedures. And while I agree with his statement, I would also like to point out that the "facts and procedures" and the rigidity of the subject are what many people enjoy about math. Personally, I find comfort in the structure of mathematical topics such as algebra. However, I also like the freedom of a proof. A particular quote from Lockhart in the book struck a nerve with me because I can relate to his claims. It says "Many graduate students have come to grief when they discover after a decade of being told they were "good at math", that in fact they have no real mathematical talent and are just very good at following directions. Math is not about following directions, its about making new directions". I connected to this statement in the text because as I progressed through my mathematics courses at Grand Valley, I was presented with new challenges that required a new way of thinking. It continues to be a struggle to this day because of the fact that I used to view math as "black and white". While I do not feel that my K-12 mathematics education is completely to blame, I do feel it plays a vital role in this situation.
In The Mathematicians Lament, Lockhart refers to teachers and educators as two different things. What does he mean by this? This brings up an interesting segway into the key issues that Lockhart believes are part of our K-12 educational system, in regards to mathematics. The issue he discusses most is the mathematical reform that is taking place in schools today. Lockhart voices his opinion that "math doesn't need relevance, it's already interesting", when referring to the way teachers try to relate math to students lives in an effort to keep them engaged. His opinion does not sit too well with me, but more on that later. He also says that the problems we are doing with our students in schools are merely exercises, not real mathematical problems that are good with our brain. However, Lockhart does make a valid point when he poses the question: Why do we let people who don't have a passion for math teach the subject? He states that "If teachers themselves are passive recipients of information and not creators of new ideas, what hope is there for their students?" Lockhart also said in the book that "You learn things by doing them, you remember what matters to you". This point is contradictory to his comment about relevance earlier in the text. If students remember what matters to them, then why does he say that math does not need relevance? By making the student's experience with math relevant, we are making it matter.
Lockhart then goes on to discuss the issues behind high school geometry, which he refers to as "the instrument of the devil". I believe his most significant point in this section was that a students first introduction to mathematical arguments is not the place for formal proofs to be taught. This idea goes hand-in-hand with his argument that most teachers do not give there students the opportunity to create mathematics, only practice the procedures with drills and tests. I think that this could be why many students, myself included, struggle with mathematical arguments, because we never had to explore the "why" of so many topics.
The Mathematician's Lament closes with Lockhart's second official part of the book, which is titled "Exultation". Exultation means a feeling of triumphant elation or jubilation. In this section Lockhart proceeds to tell the reader all of the fascinating discoveries that his vision for mathematics can uncover, as well as giving examples of how easy it is to explain math in a simple, elegant, and logical manner. He also states a less-than-inspiring quote that probably makes some teachers question their career choice, which was "School has never been about thinking and creating, school is about training children so they can be sorted. Its not surprising that math is ruined in school, everything is ruined in school."
Overall, the main idea that Paul Lockhart was trying to convey to his readers in The Mathematicians Lament was that teachers and people in general just "need to play!" His wish is that students are able to discover mathematical concepts on their own, and play with the numbers and topics until they feel comfortable. But my question for Lockhart is: what is your solution to our current system? I agree that the joy of math needs to be reintroduced into our schools, but what suggestions does he have to ensure that students are meeting the grade level standards and developing the skills necessary to pass the standardized tests we have in place? This book was eye-opening to the issues we have throughout the math education system, and although it was difficult to read at times, I would recommend it to any future teacher so that one can have the opportunity to reflect upon their own teaching methods.