I really enjoyed this TED lecture by full-time ninth grade math teacher Dan Meyer. His main point is that modern math textbooks do so much hand-holding that they fail to inspire students to think through the problems. Instead of teaching math, they teach students to “decode” the problems by all-too-apparent reference to the exemplars.
As a result, many math texts cultivate impatience. Dan argues that we’ve got to stop thinking about math as merely computation skills. In support of this point, he quoted a man named Albert Einstein: “The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.”
Dan is doing his best as a teacher and a blogger to change the way students look at math class. I should not be something students resist, but rather embrace. His approaches to teaching math are easy to understand, and he offers many creative applications along the way.
Meyer’s work brings to mind the writings of John Paulos, who bemoans rampant American innumeracy (and see here).
I totally agree with Meyer. Math is taught entirely the wrong way. The emphasis should be placed developing skills of problem solving.
What Meyer describes is a form of immersions learning. Immersion techniques have been proven effective over the years for teaching foreign languages.
The idea behind immersion is to create an environment that encourages the student to want or feel a need to learn the subject.
What I found pointed up in this lecture is the thing that used to drive me nuts in school. All this stuff was shoved at us and all I ever wanted to know was "What are we going to use this for?"
Simple question. Never got an answer. Made swallowing it all rather difficult.
To underscore that, I learned and absorbed more practical math skills my first year in retail sales than in 12 years of public education. For a time I could do percentages in my head. When I went into professional photography, multiplying and dividing by fractions became second nature. Geometry came into play in architectural photography.
It should be a sobering thing to realize that kids who deal drugs often do double-entry bookkeeping in their heads.
The problem with school is it treat kids like empty vessels into which information is to be poured, later be shaken and stirred and hopefully a college graduate pops out. Not just in math, either.
Education uses subjects to teach people to think. Training teaches skills needed to perform specific tasks. These are different and parallel goals in the school system. Most people are happy just to learn the minimum necessary, and no more. Some weirdos just like to learn.
Math is both a subject and a set of skills. Depending on how much of it you learn, it has exponentially many uses. Most of those uses are not apparent — can't even be explained — until you've learned the skills. To what use you might put it depends on how well you are educated, rather than how much you learn.
Dan
I think a large part of the problem in teaching many subjects is a lack of context. Without the context, math is taught as a rote memorization drill, but the really inportant piece needed is teaching the students how to apply math in the real world. Application context gives meaning to the subject.
Unfortunately, since our schools are belabored by the current social experiment of NCLB (No Child Left Behind), the situation is worsening as schools are "teaching to the test".
in the real world, the formulae are never laid out for you. You have to determine what to measure.
For example, I once had to solve this problem:
Layout a tract of land on the corner of a larger property. The tract has 250 feet frontage along the east side being bounded by a road running due north. The northern property line runs 270 degrees from the eastern property line and the southern property line runs 274 degrees alung a fencw from the eastern boundary. the western property line runs 180 degrees from the northern property line to enclose 1 acre. what is the length of the northern property line.
I worked it out with pencil and paper in about 10 minutes, and verified the answer.
The problem is not as simple as it seems.