A Mathematician’s Lament: The Final Reflection

I have finished “A Mathematician’s Lament!”

The final section of the article was about high school geometry and how its twisted, distorted ways (mainly proofs) drain students of all mathematical curiosity and inventiveness. I admit, I did not enjoy proofs in Geometry. They were terribly difficult, frustratingly annoying problems because I had to include every possible theorem, definition, or property that could have possibly contributed to the situation being proved. Ugh! I like structure, but man, proving was much too structured for this girl. However, this section was actually my favorite to read; Lockhart is certainly is an entertaining writer.

“A Mathematician’s Lament” is a contemplative article. Lockhart, with a courageous effort, revealed his opinionated thoughts to teachers, students, and parents everywhere on the mathematical education in today’s society. Lockhart makes the reader consider what should really be the purpose, the meaning, behind a child’s (and young adult’s) mathematical education. And actually, what should be the groundwork for all areas of education. Should children learn through discovery and curiosity or through definitions and memorization? In my opinion, after reading this article, a well-balanced mix of the two ideologies would be most beneficial. But, everyone has different opinions, and everyone always will.

P.S. I wonder if Lockhart is related to Gilderoy? ;-)

A Mathematician’ Lament: The Mathematics Curriculum

Part 6 of “A Mathematician’s Lament” was about the mathematics curriculum of today, and how Lockhart, predictably, disagrees with it. Lockhart does not agree with the “ladder myth.” The ladder myth explains how math is arranged into subjects, each sequential subject more advanced than the previous, i.e.: Algebra to Geometry, Geometry to Algebra II, etc. The ladder myth creates math to be a race. The ladder myth creates a race, which in turn creates a  silent competition among students. How many math classes can you take before you graduate high school? How many formulas can you have memorized (because the ability to memorize certain formulas certainly dictates how smart a person is).

Because certain students may be more “advanced” in mathematics than others, parents may feel that their children are falling behind, when  in reality, they simply grasp math concepts (I will get to math concepts in a second) at a slower rate.

During the summer, I tutored two elementary-aged students in math. I covered multiplication and division facts with the younger student and decimals and fractions with the older student. I explained to the younger student that basic facts were important to know, but I presented this information by “drilling” the poor child with endless multiplication and division timed-tests. To the older student I gave definitions of mixed numbers and improper fractions. How I tutored these students is an excellent example of what Lockhart believes teachers should not do: give definitions, enforce the memorization of these definitions and facts (without prior exploration), allow no creativity. Teachers should allow students the freedom to explore certain areas of math and to make discoveries, while providing guidance along their mathematical journey.

“A Mathematician’s Lament” describes the crooked ways mathematics is approached in today’s society (of course, in the author’s opinion).  Reading the article is a bit overwhelming, as Lockhart discusses many, many “faults” in the math classroom. I may not have touched on all of his musings, but I hope that you can get a sense of the article from my reflections. Additionally, as I continue to delve into the article, my opinions change and develop.

Here is the link again if you wish to read the article.