After reading Lockhart's Lament, I really agree with his point that math should be about curiosity and creativity instead of just following rules. I like how he describes mathematics as a kind of art, and that part really stood out to me. I also don't agree with the idea that students should only memorize formulas or follow the exact steps shown in practice exams. When students only plug numbers into formulas, they lose the chance to actually think and see patterns. I think giving students space to explore and even make mistakes is what makes math meaningful.
But I don't fully agree with how strongly Lockhart dismisses the practical side of math. I understand his frustration with "usefulness" being overemphasized, but I still think connecting math to real-life examples or applications is beneficial for students. In my own experience, my professors and classmates often say that math is the foundation of all sciences. I actually developed my mathematical thinking by exploring how math connects to the fields I am interested in. I think that a physics student, a statistics student, and a computer science student would each look at the same math problem differently, and that to me is also part of the beauty of mathematics.
This also reminded me of Skemp's idea of relational and instrumental understanding. Lockhart clearly values relational understanding, knowing why something works instead of just how to do it. Both authors care about genuine understanding, but Skemp seems more balanced. He admits that instrumental understanding can sometimes help students build confidence or make progress, while Lockhart mostly rejects it. From my perspective, I find myself agreeing a bit more with Skemp's view.
You clearly understand Lockhart’s argument that mathematics should center on curiosity and creativity rather than rote procedure. Your reflection on how overemphasizing memorization limits genuine thinking is well articulated.
ReplyDeleteI appreciate your balanced critique of Lockhart’s rejection of practicality. Connecting mathematics to real-life applications while maintaining space for exploration shows strong critical awareness. Your example of how students from different disciplines might approach math differently is insightful and demonstrates appreciation for diverse ways of knowing.
Your link to Skemp (1976) is accurate and thoughtful, especially your point that relational and instrumental understanding can coexist.
Helin, you have more to say and I can see your voice in glimpses through out this blog entry. Do you think Skemp's view is one you align with or is it closer than Lackhart's viewpoint? You and those around you are the future of math teaching, be bold and tell me how you feel about these arguments. Do you really think they get close to your wonderful idea of beauty in understanding different approaches to mathematical problems? These authors can be brought with you into the classroom, but you, you are the one who gets to work with young people. On practicum, please learn from the teachers but also remember that you are exploring how to make this career work for you to. What is it about a lesson that takes it from a good lesson to an excellent lesson to observe? Is it the lesson plan? Is it the interactions in the classroom? Or maybe something else?