The example of music and painting education in A Mathematician’s Lament reminds me of a poem I recently read called The Little Boy. In the poem, a young boy is in his painting class, where the teacher dictates every step of the process. The teacher controls when the students may begin, which colors of crayons they must use, and even what subject they should draw. Even when the chosen theme is something as simple as “dishes,” the teacher restricts the size and shape of the dishes. Under such rigid instruction, the boy is “manipulated” into suppressing his imagination and curiosity. Later, when he transfers to another school where creativity is encouraged, he struggles to break free from these limitations. He has already become accustomed to listening carefully for what the teacher wants and cautiously following the rules, instead of expressing his own ideas.
I highly agree with the Lockhart's idea that what really need to be done to improve education situation is to hear from our students. This aligns with building an inquiry-based classroom, and it also enhances students' creativity and curiosity. As Lockhart describe, mathematics should involve "wondering, playing, amusing yourself with your imagination." As a teacher, we should leave a big enough space to students to imagine, experience and play with mathematics concept just like how art teacher should give students freedom to create their own paintings. In this process, the teacher becomes a guide and supporter rather than a strict director.
Lockhart criticizes about the giving directions in learning math without discovering by themselves. However, in Skemp's article, he argued about relational understanding and instrumental understanding that both of them has advantages. Skemp acknowledges that instrumental learning can have benefits, such as giving students immediate success and confidence, and sometimes serving as a stepping stone toward relational understanding. At this case, while Lockhart argues rigid direction is largely harmful to students, Skemp suggests that even instrumental learning has potential value when used appropriately.
Hi Elvie!
回复删除You make a creative and engaging connection between A Mathematician’s Lament and the poem The Little Boy. This analogy powerfully reinforces Lockhart’s argument about how rigid instruction suppresses imagination. Your retelling of the poem effectively illustrates the loss of curiosity and autonomy in traditional schooling, echoing Lockhart’s concerns with clarity and emotional impact (love this).
You demonstrate strong understanding of Lockhart’s central message that mathematics should be about “wondering, playing, amusing yourself with your imagination.” Your reflection on how teachers can create space for exploration and act as guides rather than directors captures a meaningful, student-centered philosophy of teaching.
Your discussion of Skemp (1976) is also well handled. You clearly explain the distinction between instrumental and relational understanding and use it to offer a balanced critique of Lockhart’s position. It’s thoughtful how you note that instrumental learning can provide confidence and serve as a bridge to deeper understanding.
To push your reflection further, you could consider how an inquiry-based classroom might practically balance this freedom with structure—what strategies or activities would make this philosophy work day to day? Think about this when you are observing a variety of different approaches on practicum, what are the benefits of teacher led instructional lessons vs inquiry focused lessons? Is it clear when a lesson is rigid or inquiry based? What are the key differences? What are the similarities? (Linking to you thoughts on providing more freedom to students)