Lockheart proposes some exciting ideas regarding math education in schools, which I wholeheartedly support. Looking back at my high school math education, it has always been a monotonous cycle of lessons, reviews and exams. This rigid way of teaching has sucked away and made math boring to many students. As Lockheart points out, most students take math to improve their college application or get college credits to get math over with. Coupled with the need for marks or standardized testing in the US, I can see how the current education system emphasizes instrumental mathematics in the classroom, as detailed by Skemp.
While Skemp's argument of relational mathematics may seem similar to Lockheart's way of changing the mathematical education system, Lockheart's methods are more aggressive. Skemps's idea of relational mathematics still relies on the fact that there is a set curriculum that a teacher should follow, but rather than teaching the "hows of math," we as teachers should teach the "whys of math." Meanwhile, Lockheart argues that the rigid curriculum restricts the creative juices of math teachers. To truly embrace a new way of teaching math, Lockheart argues that we should thoroughly teach math without a proper curriculum so students can embrace mathematics and allow teachers to explore various topics.
While I appreciate Lockheart's view of dismantling the curriculum, he eventually still tied the dismantling of the curriculum to lead the students to take calculus in a formal setting. Yet, calculus is not all of math. Many different math disciplines still need to be more represented in our current math curriculum, such as discrete mathematics, elementary number theory, rings and fields, and many more. These math disciplines can be taught at a secondary level, albeit more conceptual, to introduce students to the abstract topics of these different math disciplines. Regardless of everything tying back to calculus, as a new teacher candidate, the best way to make math somewhat not dull is to break out of the current shell of classroom lessons and add more interactive activities for students to engage in and learn. Overtime, as we push for change in how math is taught in school, only then can we consider a proper reform, as mentioned by Lockheart.
Great observation that calculus is not the be-all and end-all of mathematics! I would love to see more discrete math, number theory, topology, group theory, etc. introduced at high school level -- and also more geometry (but for its own sake, and not only as a pretext for teaching proofs!) Lockhart is quite aggressive in his approach, and he is not a K-12 math educator, so we need to take his suggestions with a grain of salt. But he does offer a very dynamic vision of mathematics learning that is worth thinking about!
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