You Say You Want a Revolution…
I was recently reading A Mathematician’s Lament, an unpublished article by Paul Lockhart that was featured on the website of the Mathematical Association of America (http://www.maa.org/devlin/LockhartsLament.pdf). Dr. Lockhart’s story is very interesting as he left many years of studying and teaching college-level math at some of the nation’s top universities for a teaching position at a private K-12 school in Brooklyn. Homeschoolers have embraced his Lament as an insider’s view of how compulsory schooling has raped education and learning until all that is left is any empty shell.
The basic premise of A Mathematician’s Lament is that true mathematics is not taught in schools. Lockhart explains that true mathematics is a form of art, not a tool of science. True mathematics is about discovery and creation and trial and error; it’s not about “facts”. It is not a series of soulless definitions, theorems, and rote memorizations; it is about solving problems and pondering the universe.
These are truly revolutionary ideas for a teacher to express, but many homeschooling parents feel that this perversion of learning can be seen in all areas of schools, public or private. Many of us believe that schools have been inherently broken ever since they were made mandatory, because when they became mandatory that’s when they were turned into learning factories whose purpose was to create interchangeable cogs in the societal wheel. Before that most basic learning was done in the home, and school was an optional place to send children to gain extra knowledge. However, school was not seen as the only way that someone could become educated; there were apprenticeships, books to be read, and good old-fashioned trial and error. Education was something experienced not memorized.
Mr. Lockhart tries to allow his students to experience mathematics. He gives them a question and tells them to figure out the answer for themselves. However, the answer does not have to be a composition of limited definitions, theorems, and math facts that they have memorized from their text book. He compares what he does to allowing his students to create an original work of art rather than filling in a paint-by-numbers. And if he does need to use a definition, theorem, or math fact to get a point across he has his students explore where these things came from. How and why did Pythagorus come up with the theorem that bares his name? Is this definition correct? This approach offers relevance and meaning, as well as teaching critical thinking skills.
Lockhart further laments how sorry he feels for the majority of children who are forced to learn what passes for mathematics in schools. And he also feels sorry for the teachers who have to teach what passes for mathematics in schools because they just don’t know any better. The teachers themselves have been schooled into believing and passing on this lie. Most of them can repeat the definitions, theorems, and facts and plug them into exercises but most of them could not tell you what they really mean. Being accredited as a math teacher does not make one a mathematician.
Lockhart is trying to start a mathematics revolution through his teaching methods, but like most revolutionary (a.k.a. great) teachers he is lauded by parents and students and questioned by school administrators. Critics of homeschooling complain that rather than pulling their kids out of school, homeschooling parents should use their time and resources to revolutionize schools for all children. How do parents really stand a chance of changing schools for the better when teachers who really try are constantly slapped down and administrators treat parents who dare to question them as annoying gnats to be swatted? Critics really expect parents to put their kids on the Titanic and help re-arrange the deck chairs more efficiently?
I think many homeschooling parents are calling for the same revolution that Paul Lockhart is. They realize, though, that an educational revolution is going to take time and will have to come from the top down and can not be done at the expense of their own children. It may take ten or fifteen or twenty years but eventually politicians are going to have to realize that what is broken with the school system can not be fixed with more money, more testing, or more administrators. I believe when they realize that schools need to be rebuilt from scratch, they will look towards the methods and success of homeschoolers as a guide for the rebuilding. And maybe even former homeschoolers will be the very politicians leading the revolution…
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Box of Chocolates 
March 21, 2008 at 3:54 am
As I see it, Paul Lockhart’s essay would be much more powerful if it were not written in such a complete historical vacuum. Although Lockhart decries the sterile formalism in which mathematics courses have been and continue to be taught, he makes absolutely no reference to the fact that the traditional mathematics curriculum was demolished by the excessive formalism and abstractions of the School Mathematics Study Group (SMSG) new math, as incorporated in the Houghton Mifflin series of books co-authored by Mary P. Dolciani. This apparent ignorance on Lockhart’s part is likely due to the fact that he was educated with Dolciani-type books, and he may not be aware of the preceding textbooks.
The manner in which Lockhart ridicules Thales’ Theorem (which he does not name), on page 19 of the PDF file, is utterly unacceptable–and it raises serious questions about the rest of his lament about Euclidean Geometry. When I studied 10th-grade Euclidean Geometry in 1963-64, at Everett High School, in the factory city of Everett, MA, we used the textbook by William G. Shute, William W. Shirk, George F. Porter, “Plane and Solid Geometry,” American Book Company (1960). On page 25-27, the textbook contains a historical Note about Thales (640-546 B.C.), Thales’ demonstration that all vertical angles are equal (considered to be the first theorem ever proved), deductive reasoning, and the components of a proof of a theorem. According to the Note, when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as:
1. all straight angles are equal
2. equals added to equals are equal, etc.
At the top of page 10 on the PDF file, Lockhart writes: “So put away your lesson plans and overhead projectors, your full-color textbook abominations, your CD-ROMs and the whole rest of the traveling circus freak show of contemporary education, and simply do mathematics with the students!” Although this advice is quite sound, it is unfortunate that Lockhart conveniently makes absolutely no reference to the fact that all this rubbish has been produced and promoted by the self-styled math reformers of the past two decades.