In Math You Have to Remember, In Other Subjects You Can Think About It
This captures the problem with mathematical education well enough:<p>> When Boaler would visit a class being taught in a Railside-like fashion and ask students what they were working on, they would describe the problem and how they were trying to solve it. When she asked the same questions of students being taught the traditional way, they would generally tell them what page of the book they were on. When she asked them, "But what are you actually doing?" they would answer "Oh, I'm doing number 3." [p.98]<p>The typical math education relies a lot on rote learning (just take a look at the cheatsheets here: <a href="http://tutorial.math.lamar.edu/cheat_table.aspx" rel="nofollow">http://tutorial.math.lamar.edu/cheat_table.aspx</a>). There are a lot of equations you just have to remember by heart to be able to be productive in solving the typical textbook problems. For a high-school student who does not have any insight on the beauty of mathematics, this is a huge turn off. They leave school with the impression that this is a cold hard subject with perfect proofs that you have to learn by rote, and nothing more. No one talks about why Math is beautiful. The most positive thing about Math I've heard from people is that it is the best subject to get a perfect score. The arts are subjective and there is no perfectly right answer, but Math, if you know how to solve these types of problems without missing a sign or a bracket here or there, you get a 100/100.<p>The problem, I think, is because we teach the results of hundreds of years of evolution of Maths. For example, most courses on Calculus start teaching it by talking about Limits, and from there moves onto Differentiation. Integration is considered to be the 'advanced' part of Calculus. It was very recently that I discovered Apostle's textbook on Calculus (students of universities who use that text are lucky) where he treats Integration first - because that is the right historical order in which Calculus evolved.<p>I could appreciate it a lot more when I understood what kind of problems were Newton and Leibniz trying to solve when they came up with the formalized notion of Calculus. Calculus was described by them using the concept of 'infinitesimals', not through Limits. Limits was a clever abstraction that was evolved later to better explain Calculus and keep it consistent. But when we start teaching students Calculus with Limits, show them the perfect way where Limits can be used to find the differentials of trigonometric functions, they do not know this background. For them, there is no moment of 'awe'. They are not even shown a glimpse of the amazing intellectual pursuit that was behind this fantastic subject. All you see are a bunch of equations, some proofs that are mathematically perfect, and you just learn them by rote.<p>The typical Math education needs to focus more on the evolution of the subject, the pains faced by mathematicians (or physicists!) to which they came up with these solutions. The logical gaps in new ideas and how they were filled later. Let the students understand that this is not a 'perfect' subject. There were  human beings who faced real problems who came up with these solutions. Even better, let them understand that some of the things they learn was the result an intellectual pastime for these mathematicians. It was imperfect, and there was joy when mathematicians brought it closer to perfection.<p>With the advent of computers, most of the evaluation criteria used in High School Math is becoming redundant. Moving from one step to another without making careless mistakes is priority number one now. If we reduce the importance on that manual aspect of the typical Math problem solving, and instead focus on teaching the more  interesting, insightful things about Math, the students will go away with a totally different idea about Maths. Like programming, it becomes a universe of abstractions where your curiosity drives you to learn more.