Tuesday, September 19, 2023

Thoughts on Lockhart's Lament

I think that Paul Lockhart's, "A Mathematician's Lament", hit the nail on what mathematics education looks like from K-12. The examples of the musician and painter felt eerily familiar and I completely agree with him that students are generally taught to analyze the qualities and properties of concepts, without getting a chance to experience it in its full glory. The Fibonacci sequence, for example, is often blown over or briefly introduced as a series of numbers, but rarely is there a dedicated lesson highlighting the presence and applications for it in real life. The same thing can be said about prime numbers, where students understand that primes are defined as having factors of (1, P) - but they may not understand why that is important or what primes can do for us! Students learn about calculating the area of a standard parallelogram, but have they ever seen the application rhombs have to tilings? There is a significant disconnect between the mathematics that is taught in schools and the mathematics that many mathematicians interact with. This distance seems to deter students from the beauty of this study. 

I disagree with him however, that "school boards do not understand what math is neither do educators, textbook authors, publishing companies, and sadly, neither do most of our math teachers." To an extent this is true, but the hyperbolized statement nullifies the work some educators do, and appears as though no educators are trying. There is an importance to understanding the properties of mathematics; even musicians must learn to read and write sheets, play music, practice for symphonies, follow a conductor- and painters likewise have to learn the brushes, strokes, properties of different paints, mixing of colours, preservation of substances, and so forth. In regards to textbooks, there are some very engaging and eye-opening ones, however they are not utilized properly by educators for various reasons. At this point, Paul Lockhart's critique blends seamlessly with Richard Skemp's discussion on instrumental and relational learning. Paul Lockhart is arguing the importance of relational learning, while Skemp proposes many factors as to why instrumental learning is favoured more often in schools. It's not necessarily the fault of the educator/textbooks, it become a fault of the school board and the systems in place that do not put policies in place to facilitate this type of learning. That said, it is also upon the math teachers to try their best to provide the most wholesome learning experience given the many constraints on our department. We fortunately now have many avenues of support available to facilitate a better experience for learning mathematics, and have the positions and awareness to make a difference, even if it's just one student at a time. 


1 comment:

  1. Lovely! A balanced and thoughtful assessment of Lockhart's piece and its connections with Skemp's paper.

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