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Lockhart's Lament Math Education Is Wrong


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Many of the best programmers I have ever hired were math majors, and I think it's because they learned how to break down math problems into pieces and then solve those pieces -- one of the most critical skills for becoming a successful software engineer. Is that how we teach math to most kids though?

Unfortunately, Lockhart is right. Most kids don't like math.

I had to go back and read Lockhart's "Mathematician's Lament":

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

The BI article summarizes the gist well:

Lockhart begins with a vivid parable in which a musician has a nightmare in which music is taught to children by rote memorization of sheet music and formal rules for manipulating notes. In the nightmare, students never actually listen to music, at least not until advanced college classes or graduate school.

The problem is that this abstract memorization and formal-method-based "music" education closely resembles the "math" education that most students receive. Formulas and algorithms are delivered with no context or motivation, with students made to simply memorize and apply them.

Part of why many students end up disliking math, or convincing themselves that they are bad at math, comes from this emphasis on formulas and notation and methods at the expense of actually deep understanding of the naturally fascinating things mathematicians explore. It's understandable that many students (and adults) get frustrated at memorizing context-free strings of symbols and methods to manipulate them.

This goes against what math is really about. The essence of mathematics is recognizing interesting patterns in interesting abstractions of reality and finding properties of those patterns and abstractions. This is inherently a much more creative field than the dry symbol manipulation taught conventionally.

My favorite part of the article is when they talk about The Soul of Mathematics:

At the heart of mathematics is a need to understand structures, real or imagined. This is a profoundly speculative and creative exercise: a strange type of higher dimensional shape might hint that it has some interesting properties; a data set describing Ebola infection rates could roughly fit the same pattern as uranium atoms undergoing atomic decay. The job of the mathematician is to find and, far more importantly, explain these kinds of properties and relationships.

While it is important for students to work through a few basic problems at every level of mathematics they encounter, we live in an era when, once an understanding of the underlying concepts is mastered, one can turn to calculators or computer programs to do the mindless symbolic manipulations needed to get an answer. Pedagogy needs to move away from finding the answer, and toward understanding why this is the answer and why we care about the answer.

Mathematics is unique among human endeavors because it combines our most "right brained" creative, abstract, imaginative instincts with our most "left brained" logical, evidence-based, focused instincts. Math is about making a poetry out of pure reason and about abstractions based on seeing patterns in our world, and it is very sad that so few people ever get to experience this.

Lockhart's entire essay is a beautifully and passionately written plea for a better way of educating students to truly understand the wonderful world of mathematics. Anyone who has any interest in math and math education should read the whole thing.

I went into computer science to avoid math.  :-)

You can do that? How did you get through algorithms without math?

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