In reading Lockhart's "A Mathematician's Lament," I found that I agreed not so much with one thing or statement; rather, I found that I agreed with the sentiment that (creative) aspects of real mathematics have been removed from mathematics education. In this regard, mathematics and mathematics education are two different things. At times, I feel like teachers try to share this sentiment with their students through opportunities like open-ended questions or comparing approaches/responses to questions. However, this can be a challenge when, as Lockhart cried, politicians step in and tell teachers what to teach, or, for example, in the case of AP or IB programmes, that they are so content-heavy and assessment-driven.
In saying this, I do feel that it is not as bad and gray and lifeless as Lockhart's rhetoric might suggest. Classrooms -- not all of them, I grant -- can be places for flourishing. Mathematical ideas and relationships might just be present, sought, and celebrated. There are instances where real mathematics is being done. So, in defense of the practitioner, sometimes these ideals are fostered (even if it might not look like the creative utopia that Lockhart imagines).
Two more thoughts. The first regards the use of AI. This tool may really help to promote mathematical ideas in classrooms/mathematics education as Lockhart sees it. Do people have to know how to balance a chequebook? (1) What's a cheque? (2) No. There are other tools to do that, and, in a practical sense, as long as people can appropriately interpret the information that is provided by that tool, then the "mere" calculations might not be of the utmost importance to the human. And AI might just be one of those tools that really give teachers (maybe politicians/policymakers/curriculum developers?) the impetus that they need to focus on mathematics-as-flourishing.
Consequently (and secondly), I feel this ties in with Skemp's views on relational mathematics as a priority over instrumental mathematics. Skemp is interested in the relationships present within mathematics and maybe the relationship that we have with mathematics. Skemp doesn't think that understanding necessarily arises from the rote application of algorithms or the memorization of facts. Lockhart, I feel, would agree with this statement by saying that the former is not even really mathematics.
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This is a thoughtful and well-developed reflection. You engage with Lockhart’s argument in a balanced way, agreeing with his sentiment about creativity being stripped from mathematics while still defending the reality that many classrooms do create space for genuine exploration. That balance shows real insight—you’re able to see both the critique and the good that still exists within the system.
ReplyDeleteYour point about policy and curricular pressures is spot on. You capture well how external forces—politicians, exams, and rigid programmes—shape what teachers can do. I also really like your addition of AI to the conversation. You’re right that it’s changing the landscape of what “doing mathematics” looks like and could shift our focus toward understanding and interpretation rather than rote calculation. That’s forward-thinking and relevant.
Your link to Skemp (1976) is clear and considered. You accurately connect relational understanding to the kind of meaningful engagement Lockhart advocates, while recognizing that understanding doesn’t grow out of memorization alone.
During practicum, use this time to reflect on your practice from your previous teaching post. How do teachers make space for creativity and relational thinking (and how would you use this to influence your practice?). Notice how they use tools—digital or otherwise—to deepen understanding rather than replace it. Reflect on how you might balance accountability with curiosity in your own teaching, creating space for students to experience mathematics as something alive and connected. AND i want you to add something to the department you enter... You can decide what that is.