Math is argued to be something that one must wonder about, play with, and imagine to create anything he/she wants in the book Mathematician's Lament. The book uses an example about a triangle that fits into a rectangular box. It states that one can make this triangle as big as he/she pleases and the edges can be perfect because it is what he/she imagined. Although this person comes up with the triangle and rectangle, he/she cannot choose the amount of space the triangle takes up within the rectangle. Therefore, using math to try and figure it out. Paul Lockhart discusses how he used thinking and trial and error to decide to put a line down the middle of the triangle. He realized that there was the same amount of space inside the triangle as well as outside of the triangle, meaning that the triangle took up half of the rectangle. Because Lockhart had had experience with mathematics and has engaged himself with different ideas about problems, he was able to think of drawing the line to solve the problem.
Students nowadays in math classes are being deprived from imagination and creative thinking, leaving no room for engagement with the subject. Teachers are told to have students memorize formulas and apply them to problems over and over. The mathematics education as is needs to be scrapped and rebuilt into something new, rather than just coming up with new texts books to clarify material. Instead of focusing on what math really is, teachers are more focused what material to teach first and what notations to use to meet criteria. Teachers are always trying to relate mathematics to everyday life, when instead it should not be, it should be a fantasy that relieves children of his/her everyday life.
The way Mathematician's Lament discusses how math should be taught is by teaching its history first. It states that no other subject is taught without background information, where math throws out formulas and algorithms to memorize without any back story. It also discusses how it is okay to have formulas and algorithms, however being able to think creatively is a large part of math that should be brought back to the classroom. Students should struggle and be frustrated with a problem, this is when he/she comes up with new ideas that lead to other questions about the problem. If a student is really struggling, that is when a teacher should help, but not too much, only enough to make the student think about new ideas regarding the problem. Teachers should give students problems that are suitable to the students level of experience and give he/she time to come up with conjectures of his/her own. A good math classroom is one where healthy criticism is given, and teachers are flexible as well as opens to change in curiosity. Finally, math should be taught by solving puzzles, playing games and problem solving. Students should be put into a situation where deductive reasoning is necessary and creative thinking is involved.
After finishing the book however, I realized why people may be skeptical about why Paul's ideas may be a little far off. While I do believe that the math department should reconsider the way they are teaching mathematics, there is still a curriculum that needs to be followed. I do believe that teachers could switch up the way they are teaching the curriculum by doing fun lesson plans, playing games, doing puzzles, and having math be more hands on while still covering topics needed. For example, the book discusses how geometry completely kills mathematics and makes students hate it. Instead of learning formulas to solve problems about shapes, teachers could provide 3D manipulative for the students to play around with, then provide the formulas for the students to discover about the shapes. There are many ways to keep the curriculum in tact, and still make learning math fun.
All in all, math is not a language that can be learned, it is an adventure. Math is an art done for pleasure, it is not memorizing formulas to complete problems out of a book. Teachers are more concerned with following the curriculum and having the students memorizing algorithms to solve problems, that math is essentially being taken away. Students do not have room to critically think, instead he/she applies a formula to solve the problem and moves on to the next. Students should be able to think creatively and independently and not be "trained" to do something. The book Mathematician's Lament does an amazing job discussing what math really is, and how it should be taught in k-12 classrooms.