One thing I agree with Lockhart is that we kill enthusiasm and interest in a subject by making it mandatory. Once mandatory, there are fixed standards and timelines to adhere to, and this forces rules onto people, which can be a way to kill self-motivation. In an ideal world, we would want to ignite interest in subjects first and then lead their curiosity to learning more.
One thing I disagree with Lockhart is the "problem of no problems", he argues that we should present problems that students do not know how to solve. Obviously, solving difficult problems provides challenges and, in the process, leads students to research math concepts and methods in their exploration. But this ignores the fact that the public education system is not catered to the prodigies like Gauss or Euler, who can attempt truly difficult problems at a younger age. In fact, most people without the absurd math talent, interest, or needs would not be able to tackle some of these "true problems" in their entire life, but they still have meaningful ways of life that require little math. Math as a tool is very much essential for a great range of career paths, and basic math is absolutely necessary in our current world filled with information and technologies. Forcing the "unsolvables" onto the average person can quickly snuff out however much curiosity or motivation in math is in their spirit. Then their reluctance to learn basic or application math can severely cripple their life in modern societies.
Similar to Skemp, Lockhart also loves to praise math as some sacred art where learners should approach with religious-like devotion and only learn in the true meaning of this art. While it has its merits, and we sure have benefited from masterminds like Euler, some of these talents are impractically impossible to be taught by a public system. Instead, building a system where prodigies can be discovered and focused, while the average people who benefit greatly from utilizing math as a tool are still carefully helped, is necessary for our civilization to advance. Gatekeeping math, seizing its spread to strengthen a small group of scholars' authority, and profiting from authorizing the "true ways of math" is a great way to line their pockets at the cost of average people's life quality.
Hi Yikang! You’ve written a really thoughtful and well-argued response. I like how you immediately identify the tension between enthusiasm and compulsion — your point that making something mandatory can change its meaning is a strong one. You’re already thinking about the realities of teaching within systems that are structured, timed, and standardized, which shows a good awareness of the limits we work within.
ReplyDeleteYour challenge to Lockhart’s “problem of no problems” is clear and grounded. You’re right to point out that not every learner has access to, or interest in, the kind of abstract problem-solving Lockhart celebrates. You’re asking the right kinds of questions about for whom his vision works — and for whom it doesn’t. That’s an important critical stance to keep developing.
I also find your comments on gatekeeping powerful. You’re starting to look at the relationship between knowledge, privilege, and access — that’s not easy thinking, but it’s necessary work in math education.
During practicum, keep exploring how curiosity and challenge can coexist with accessibility. What does it mean to create a math classroom where students can experience both success and struggle without being shut out? And how can you, as a teacher, hold onto rigor without reproducing the same kinds of gatekeeping you’re critiquing?