Where do I start?
This book gave me a whole slew of emotions as I read through it. In fact after I read it, I am still unsure of what kind of star rating that I would give the book, because I agreed and disagreed with the author about so many things that were addressed in the book.
So...I guess I will start with this. I read the book "Mathematician's Lament" by Paul Lockhart and forwarded by Keith Devlin. I first read the forward, and it gives a nice summary of the purpose behind the book itself and the publishing of the book. Lockhart had originally wrote this Lament as a way to just lament about his frustrations of the ways mathematics is taught and presented nowadays. He had no intention of publishing it for public viewing, but had shared it with some fellow mathematicians. Devlin had came across a copy of it, read it, and thought that there was such good information in the piece that he shared it with some other fellow math teachers. They all agreed and felt mutually about the frustrations Lockhart emphasizes in the book. So, naturally, Devlin decided it needed to be published, and got it published so that it could be shared with the world. Whether that was a good decision or not, I am unsure based on how I felt after reading the book.
I can see why Lockhart had never intended for this to be published for public display. The way that the book is written is almost like one of those letters that your mom, dad, or friend had encouraged you to write to someone who you were really upset with, but then never send it. You basically write it to get your frustration out, yell at the other person(or in this case, object), and give them a piece of your mind, in hopes that it settles the anger that you have about whatever had happened, and never send it to the person. If you were to read this letter aloud to someone else, parts might not make sense, you could contradict yourself at different points in the letter, and it would probably be more like word vomit expressing anger and frustration, but never offer a solution to make your frustration into something that is productive.
I would say that this is a pretty accurate explanation of the layout and context of this book.
I first started reading this book, and I agreed with just about everything he said. He explained the problems with the way that math is taught in school, how there is no understanding, and students are forced to memorize and mindlessly go through the process of finding an answer in math. They don't get to see the mind-blowing components because there is a lack of discovery and exploration of mathematics in classrooms today. He explains that math is a creative topic, and we are teaching it without the creativeness. I really enjoyed the metaphor he gives for the way that math is taught in school and how much is lost by teaching it this way. He compares the way we teach math to the way we teach art. We all know art is a subject solely based on creativity. So imagine if we taught art by only allowing students to do paint by number paintings, and that is what they do the whole time they are taught in school. They are never giving the freedom to paint what they want, try out different medias and ways of creating art, or shown cool art that has been created by artist in history. So, they got through school thinking that art is this boring subject where all they do is think "number 3...that's purple. I need to paint all the 3's purple, and then I am done and can move on to the next number to do it all over again. Yay." How is this fun?! Well, it's not. We know that. So, Lockhart poses this idea that if we are teaching one style, one way, and never allowing ourselves to teach students math outside of that structure, how are we expecting them to be interested and see deeper understanding behind mathematics? You wouldn't have interest in art without creativity, or any subject involving creativity for that matter, so why do we expect students to be interested and understand math when we are teaching it without its creative components?
Personally, if the book would have stopped after this section, I would have been able to give the book an awesome review. This is an awesome point! and the point that needs to be seen by all teachers who are teaching mathematics at some point. Can you imagine if we made math fun, meaningful, creative, and purposeful how much more excitement students might have for math?!
However, the book continues, and he continues on his rant of anger and frustration.
He continues with other points in the book about this lack of creativity when teaching mathematics. At the end of each chapter, he provides this little summary/argument/discussion between two people, Simplicio and Salviati, where one person, Simplicio, is questioning some of the statements that Lockhart has made in the chapter, and the other person, Salviati, is explaining his reasoning (so Lockhart's actual reasoning for his statements). I know, it sounds weird and confusing, but it is also nice to have this bit of dialogue at the end to clarify some of his thoughts. At one point he brings up that there should be a curriculum for math, and that we should simply allow students to work with it, explore, and discover the concepts themselves without the teacher teaching them any of it. At one point, Simplicio asks what he suggests we do with students in younger grades as far as math then, and Salviati responds with have them play games and explore. To me, I am agree with Simplicio here. This solution doesn't make sense. What do you think would happen if we gave a bunch of kindergartners games during a math lesson and told them to figure out how to count? Can you say "Chaos"?!! These students have no sense of numbers, what counting is, or how to even do it, and you expect them to figure it out on their own through games? I would like to see these games he would have them playing, because I don't think it would happen. In fact, when he made this argument, my first thought was that this guy must not have an experience in teaching mathematics and must be a pure mathematician. Throughout the a majority of the rest of his points I continued to think the same thing based on what he said, until I was later reminded in our class discussion that he was indeed a math teacher for many years.
Students need structure. I agree with the fact that we need to implement more creativity and discovery into our current mathematics curriculum, and that unless something is changed, students are never going to have the understanding we desire for them to have, but that can't be done without actually teaching them things and having the teacher structure the learning. The teacher needs to be the mediator of the learning. It is our responsibility as a teacher to give the students the tools they need for learning, and help them successfully grasp a concept. For Lockhart to basically claim that we need to just step back as a teacher and let them discover alone, doesn't make sense to me. We need to be there to help push them in the right direction when they are going astray. Also, if we don't teach them the basics of math, like counting, place value, etc, how are they supposed to discover things in math?
This pattern of agreement with points of frustration, disagreement of how to handle it or how we really need to do things, and what he is suggesting just doesn't make sense, continued for me throughout the first part of the book. I won't even start with the second part of the book, because it is just a continuation of him complaining, not making sense, and never offering a solution to anything he was complaining about.
Overall, my feelings towards the book are, if you want to listen to a lot of venting and get riled up about problems in mathematics, this is a good book for you. But, if you are like me and are looking for a book that points out issues in mathematics curriculum and teaching and offers ways to fix these problems or suggestions to teaching math with more creativity, then you might want to pass because you will probably get frustrated with the authors points and get sick of him complaining and not doing anything to solve the problem he's complaining about.