Read-and-Respond: Lockhart’s Lament
From Lockhart’s claim, I strongly support and agree with the point that he said, “nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic as mathematics.” Mathematics is a combination of patterns, numerals, debatable proofs, and spectacular geometric graphs. With mathematics, everything can be converted into music, the fine arts, painting, and the perfect ratio, resulting in beautiful and elegant drawings. However, I do not think what Lockhart said that “Mathematics is the purest of the arts, as well as the most misunderstood.” Math can be easy to understand as long as people or students are willing to dive into it deeply. There are numerous opportunities to understand and learn math through various means, including nature, people, and communities.
When comparing Skemp's instrumental and relational
understanding, the connection between the two passages is that relational
understanding is essential in building a basic concept and understanding of
math. However, Skemp also emphasized instrumental learning, which Lockhart
disagreed with. Skemp said that instrumental learning builds the cognitive
aspects of learning, but Lockhart thought that this limits the ability to
foster mathematics learning and ultimately loses the creativity of math.
Hey Snow! This is a thoughtful and passionate response. You capture Lockhart’s poetic view of mathematics beautifully — I really like how you describe math as something that connects to music, art, and nature. That shows creative thinking and an appreciation for the aesthetic side of mathematics that Lockhart celebrates. You also bring in an important counterpoint by suggesting that math isn’t necessarily “misunderstood,” but rather that understanding depends on people’s willingness to engage with it. That’s an interesting stance, and it could be worth exploring further — what helps people want to engage deeply with math in the first place?
ReplyDeleteYour comparison between Skemp (1976) and Lockhart is clear and well-reasoned. You’ve recognized the tension between relational and instrumental understanding effectively. I like that you note Skemp’s value in instrumental learning as part of cognitive growth, even if Lockhart might dismiss it. That’s a mature and balanced way to handle theory — acknowledging multiple perspectives rather than choosing one side.
During practicum, reflect on how students find meaning in mathematics — what draws them in or helps them see its beauty. Notice how teachers use structure and creativity together to build understanding. You might also consider how you can make mathematical ideas feel connected to the world — through art, patterns, or stories — so students see that math isn’t just about numbers, but about relationships and expression.