Friday, March 13, 2009

The Mathematicians and Math in School

From Paul Dunham, Professional Mechanical Engineer and now certified Math teacher:

Before I headed back to school to re-tool as a math teacher, I wouldn't have considered myself a mathematician. To earn two engineering degrees, though, I studied and mastered more math than the vast bulk of the populace, including most K-12 teachers. It just isn't possible to learn the principles of thermodynamics, solid mechanics, vibrations, circuit theory, or any of a host of other engineering sub-disciplines without having first learned basic number theory, algebra, geometry and calculus as a solid foundation to build on. I consider myself a practitioner of applied math.

I have always known that there were people who worked with mathematics in a purely abstract way, without concern for applications. I have always been interested in applications, though, so I chose the engineering route. I never imagined that there was a third group who focused on math education until I spent a year in a teacher seminary. They don't know the math the way the pure guys do, nor to they appreciate it in the same way that those of us who apply it do. I get the impression that most members of the math-ed based community of mathematicasters would consider Rachel Ray a chemist, or Jesse James of "Monster Garage" an engineer. To be fair, how could they know otherwise? The very real world of applied mathematics is outside of their experience. But if they consider themselves mathematicians, then I certainly will stand up and declare myself one, too.

Key questions are and will remain these: Relevance - Why should people study math? Our culture has become corrupt in this area and teaches many of our kids that they shouldn't bother. That's a larger issue. Content - What math do they need to know to prepare for their future lives and careers? This depends on just what future they imagine for themselves, and where one size will never fit all.

Mastery vs. Appreciation - How well do they need to know it?
Authority - Who are in the best position to offer answers to these questions?

If we are to train people to be pure mathematicians, then the pure mathematicians are in the best position.

If we are to train people to apply math as engineers, scientists, technicians, etc., then people who have trained in and mastered these fields are in the best position.

If we are to train more mathematicasters, then mathematicasters are in the best position.

For all the big talk about the value of collaboration and differentiated instruction, though, the math ed community goes out of it's way to shut out diverse input and narrow the scope of what is taught to what little that their isolated culture of group-thinkers has trained them to appreciate. In essence, they only know how to train more of themselves.


Sudhakar Kudva said...

Looks like Paul has created three categories of "mathematicians" to help explain the status quo. I like the explanations he has given for the different mind sets. I do want to take his argument to its logical conclusion.

First, let me articulate how I see the picture he is trying to paint. There are those who do pure, cutting edge math for a living. They are pushing the envelopes of the science of mathematics. We probably need a few thousands of the people who will be future college professors and mathematicians working in national laboratories. Then there are people who apply advanced mathematics in other sciences like physics, chemistry, medicine, engineering. We probably need a few million of those. And then we have those who teach mathematics to K-12 students. We need a few millions of thousands of these.

Now if the math professors called the shots on how K-12 educators should teach math, then we get one version of K-12 curriculum, which would be rigorous and purist. If the applied scientists called the shots, we get another, maybe a little less purist, more applied and relevant. If the last group called the shots, we get another version - an interpreted version of watered down mathematics that only a non practitioner can appreciate.

The problem comes when the decision makers are in the last category, and the economic needs are in the first two. The times call for encouraging most students to get into STEM fields, because there is a consensus in the nation now that we need more of them to rebuild our shattered economy. We need more mathematicians and engineers and scientists, and the preparation needs to start in KIndergarten. If these kids do not memorize their multiplication tables by grade 3, we have lost them. Every year delayed in laying the groundwork in math is a year delayed in creating a lasting economic engine.

If we are really serious about bringing back the American dream, and resurrecting the middle class, then we must let those who drive the economic engine make the decisions on what math skills our kids must have, and let that drive the decision of what and how to implement them in our schools.

Anonymous said...

The great deception continues. Despite assurances to parents, TERC continues promoting nonstandard computational methods. It is a major misdirection for elementary school children. TERC's methods are substituted for the standard methods that children need to master. TERC confuses children by claiming to offer several "strategies" for each operation.

Why so many? The approach is based on the writings of Mortimer Adler, who created a learning model for curriculum using Aristotle’s ideas. In a TERC world each child chooses their own personal way to do math and communicate math ideas. According to Adler, the child’s transformation occurs in three stages, so students rise to their own level of potential. You will notice that there are three algorithms taught for each operation. Its historical roots can be traced back to 19th century theosophical ideas.

If standards are essential for effective communication in math and science, then shouldn’t TERC be concerned about how their "graduates" will communicate math ideas with others? Although, TERC no longer claims students "invent" these methods. So what? Like every other reform math program funded by the NSF, TERC is teaching computational methods that are cumbersome, inefficient, and only work for carefully selected simple problems. Once again, we should consider the ethics that are guiding our policy makers.

TERC’s methods seriously mislead children because they avoid fundamental concepts like carrying, borrowing, and common denominators. Using Math Investigations, students will never have the possibility of gaining automaticity. By avoiding ideas like carrying, borrowing, and common denominators until the end of fifth grade, TERC eliminates the advantages gained by learning arithmetic in the first place.

Writing about thinking is regularly required for both TERC method selection and TERC method execution. This is another theosophical idea and has nothing to do with ‘constructivism’. TERC believes maximum conscious thought indicates maximum conceptual understanding. Based on all the current research in bilingual education and linguistics this is profoundly biased and shows a childlike grasp of what learning is in general.

concerned said...

I am a high school math teacher who majored in applied math. This conversation is right on target from my perspective.

There is no reason that the US should be so far behind in math and science, other than the fact that in many districts the curriculum does not contain the appropriate content needed to prepare students for success in college.

Mathematicians would have never taken us down this road. Only those who do not know what lies ahead could possibly think that NSF programs are appropriate.

I left a comment about NSF math programs on the Education Equality Blog this morning.

The essence was that we need to stop accepting the idea that some children need an inferior curriculum and immediately eliminate mediocre NSF math programs.

(It stayed up for about an hour before it was removed. In fact, NO comments have been keepers, but I bet they are getting an ear full!)

Thanks for the post!