How We Teach Math and How They Teach Math

I just heard again on the radio about how the United States is falling behind other countries in mathematics. I found an anecdote about a guy from India who thinks he knows why.


In the military, I was a Field Artillery fire direction chief. Over the course of my career, we moved from manual, slide-rule gunnery to various stages of electronic ballistics computing. But through it all, we still understood the manual basics. If you don't understand that, then the computer makes no sense, and when it goes wrong, you don't know why.

I think mathematics is a lot like this. Do we rely too much on our computers in our United States math classes? This guy seems to think so:

It reminded me very much of a conversation that I had a few months ago. The person I was speaking with was a programmer visiting the U.S. from India. This gentleman and I had gotten to know each other fairly well, and he has been programming for quite some time, probably around as long as I have. He and I got onto the topic of education. It is a well-known fact that India, China, and a number of other countries are beating the U.S. in math scores. So I asked him how they teach math in India. He was almost baffled by the question, as if there was more than one way to learn math and this was the first time someone had let him know. “From a book, with examples on the blackboard, how else?” I queried him about the use of calculators and computers, two tools quite common in U.S. math education. He explained to me that calculators are forbidden in their version of high school and that, in colleges, the calculators allowed are basic models (think add, subtract, multiply, divide, exponents, square root, log 10, and natural log), and their usage even then is frowned upon to the point where using a calculator will be the cause of ridicule and humiliation. This sure sounded like a far cry from the educational environment in the U.S., where 7th grade students are now being required to own TI-85’s, a calculator that’s probably more powerful than the guidance system on a cruise missile.



Comments

  1. I don't necessarily think there's anything wrong with using an advanced calculator so long as you understand the principle behind the button-mashing. After all, I don't need to know how a CPU works to plug one into a motherboard now do I?

    At some point, low-level knowledge of the task before you doesn't really end up helping you do the job any better. In some cases, it'll actually impede you from getting the job done. I watched a UNIX guru immediately start trying to modify the source of our software to fix bugs (taking sometimes upwards of an hour) when we had known 5-minute fixes.

    I have no problems making the computer do the work and I have no problems teaching kids how to make the computer do the work. Our economy is build on making machines (or outsourced workers) do all of our grunt work so we can focus on higher-level concepts and jobs.

    As an aside, the TI-85 uses a Z80 processor, the same processor that powered the old TRS-80 computers in the early 80s. These are now used (in a cheap and low-power version, of course) in every major appliance from dishwashers to ovens to microwaves. (My GE Profile washer and dryer each have their own Z80.) I don't doubt that those cheap and well-supported chips also support cruise missles.

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  2. When I took math 1010 at UVSC they had a no calculator policy....for anything. I never learned more and had a better understanding of why.

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  3. Hey, thanks for the link and the quote! People seem to blow off the lag in math scores as "no big deal". After all, what is the ratio of people who took Calc I at some point to the number of people who ever used it outside of school? Probably at least 1000:1. I can never recall using an integral, derivative, or even a series explicitly in "the real world". That being said, the ways of thinking that I learned in higher math has been invaluable to be. The idea of, "this is my universe of rules to find solutions, this is the problem at hand, so let me figure out what tool in my box handles this" applies to every facet of my life. Additionally, as a programmer I found found that many of the goals I wish to accomplish have already been solved by mathemeticians ages ago. For example, I am working on an application that requires some very complex search systems. Where most programmers would create a huge ball of LIKE clauses, I am opting for a vector search system using some fairly simple linear algebra. Without awareness of math, I would be working on a system as slow and inaccurate as our competitors. Thank goodness for my math teachers who made us learn math instead of calculator operation!

    J.Ja

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  4. Justin,

    You're welcome. I look forward to reading more of your stuff on Tech Republic.

    I appreciate Jesse's point that sometimes we spend time trying to invent the wheel when we don't need to, but Justin makes a great point that if we don't know the undergirding knowledge some very profound understand and innovation will easily pass us by.

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