From: Johnny Hamilton
Subject: Questions about math needs
Date: 30 Jun 1995 15:57:45 GMT

I have some serious questions to ask and would like to hear from anyone on the subject.

How do we get people in our work force mathematically educated?

Every training program I know is clogged with young and mature workers who can't do fractions and decimals, much less the geometric calculations. The problem is compounded each year by many of the young people entering our work force. From a societal standpoint, we need every person to have a reasonable functional foundation in mathematics.

What level do you think that should be?

What can we, in the work force, do to help you?

What can we, in the publishing industry, do to help you?

What can we, at the local school level, do to help you?

I know that pressure is being placed on you to teach real world problems and applications. I know that your education probably does not include "real" experience out here.

Do we need programs by industry to give you experience in our work places during the summer?

What can we do to help you integrate academic math into vocational programs?

We have to solve this problem in our country if we are to have a stable, growing society. We must produce our replacements in the whole work force in such a way that they improve on what we have accomplished. By whole work force, I mean everyone. We need pure mathematicians, college math teachers, high school math teachers, and elementary math teachers, as well as engineers, technicians, and skilled crafts people.

We have to stop this trend of math phobia. It is not possible to have excellence in any school, industry, or work place without good solid foundations in mathematics. The very basis of any civilization is good groundwork in the language of the culture and mathematics. Math phobia does not just exist in the blue collar work force. Some programs avoid math because many people who make the decisions about training programs don't like math themselves. Math has to be provided as a foundation for learning the other necessary information.

In general, what can we do to start this dialogue or process?

If you need to be convinced, what can I do to convince you of the criticality of the problem?

Can we start now, this summer? I know it is the time of year that most people in the forum are away, but what can we do before the next school year starts?

From: Clem Padin
Subject: RE: Questions about math needs
Date: Fri, 30 Jun 95 18:25:47 EDT

John,

> >... How do we get people in our work force mathematically educated? > Whoa! Have you a 'serious question'! I hope this will start a lively discussion...

I have a lot to say on this topic. Here are some things that I think need to be done.

Talk to people like me! I got a C in algebra in the 7th grade. Although my brother has never admitted it, I believe he threatened my instructor with bodily harm if he did not pass me! I failed my first math class in college - Calculus I, even though I had taken a pre-calc course in high school. But after a few years, I had established a math tutoring business, got my BS in physics, and after graduation was working for a theoretical physicist, solving some equations for him. A couple years ago I was offered a full time teaching position at a local community college after teaching a few math classes and a physics intro course.

For people who have a natural propensity for math, why math is difficult to learn most seem unfathomable; for those who can't do math, how it's learned is completely obscure. There are many in the middle, I think. We can help point out where the stumbling blocks are and how they were overcome. And teachers need to take copious notes of where students got snagged and how the problem was resolved. And those notes need to be shared and analyzed so that new teaching techniques can be developed. And the development of these techniques must be dynamic, by a kind of 'Just In Time' process.

Now here are some things I learned in the process of bootstrapping myself into 'numeracy'.

• Language

  Teachers and students MUST be aware that words used in everyday language mean something different in math and the sciences. You can't just throw out a term like 'real number' or 'rational number', give a couple of examples and go on. Time is needed to map words like 'real' and 'rational' into another internal 'space'.

• History

  Until I began investigating the history of math, I didn't realize that it wasn't a linear progression from cuneiform numbers to modern topology; that there was a time before the decimal point; that Galileo did not use algebra; that 'algebra' is derived from Arabic; that the collection of mathematians throughout history includes every kind of person: brilliant, mundane, mad, fools, jokesters, bastards, the sickly, heros. These insights make math feel accessible, since human beings (like me) did these things.

• Methods

  For the longest time I thought math was done by mathematicians the way proofs are done: start at step one and continue to completion. I didn't realize there were guesswork; intuition; morning shower revelations; many blind alleys; a lot of time spent. People need to make math a human endeavor, with all the human emotions and motivations. (This ties directly to History). There is a perception that math is a cold, unfeeling chore because that's the image presented by ALL involved.

• Technique

  One subtle problem which a lot of teachers are completely ignorant of is the assumption by students that they need to learn the technique. By this I mean that many students attempt to memorize a way of solving the problem because they think that is what they are supposed to learn; that that is what math is about. This is reinforced by teachers who refuse to accept alternative ways of solving a problem -- they teach the technique, not problem solving.

• Time

  It may take longer for certain concepts to sink in than the time that is alloted in the classroom. I think it took me a first run through calculus, before I 'got it'. With so many other things going on in a student's life, this may be a fact of life.

• Style

  We need images of popular people engaged in thinking activities AND in 'cool' ways. We do NOT need to see a poster of Sting, stoic, holding a book open, with a caption like, 'Read'. We need to show him at a table laughing while a white board in the background is filled with mathematical equations. The images of kids' heros, engaged in intellectual persuits, need to be dynamic and fun. Math has to be 'cool' for it to appeal to kids.

• Relevance

  There is much discussion on the use of 'real world problems' as a technique to engage a student's interest. But I think that that is a false prophet and a bit disingenuous. Most of what is learned in math classes is never used (that of course depends on your line of work). For an algebra class, I used a math book from the 1890's. It was fun to see word problems with horse and buggy prices (real world problems were used back then, probably for the same reasons). It was not 'truly' relevant, but it was fun! I remember spending hours learning how to solve differential equations. Then I spoke with someone in the aerospace field and he told me he had never used Calculus or DiffEQ in his entire career! That dampened my drive!

• Aesthetics

  I always try to emphasize how 'neat' or 'cool' a result was, no matter how trivial. I get some strange looks but I want them to see math from a different perspective, as something that can be admired for its aesthetics and grace. That is one basis for an internal motivator - one which many (if not all) mathematicians share -- you are not going to engage someone if they think the subject is boring and dull.

I could keep going, but... I don't know if any of this makes sense, if it resonates with anyone else's experiences out there. -- Clem

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| Clem Padin                     |
| PADINCX@LLDMPC.DNET.DUPONT.COM |
| Dupont Merck Pharmaceuticals   |
| Dupont Experimental Station    |
| Wilmington, Delaware           |
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From: Lou Talman
Subject: RE: Questions about math needs
Date: Fri, 30 Jun 95 22:00:16 -0600

Clem Padin wrote:

For the longest time I thought math was done by mathematicians the way proofs are done: start at step one and continue to completion. I didn't realize there were guesswork; intuition; morning shower revelations; many blind alleys; a lot of time spent. People need to make math a human endeavor, with all the human emotions and motivations. (This ties directly to History). There is a perception that math is a cold, unfeeling chore because that's the image presented by ALL involved.

(This wasn't the only important observation that Clem made--just, IMHO, the one that I think is most overlooked.) --Lou Talman

Thanks for your thoughtful observations. I'd like to add some personal observation as well.

I teach science, mostly, and the first thing I have to tell students is that in science, "words mean exactly what I want them to mean", or whatever the correct quote is... You can't use words like motion, speed, acceleration, force,etc., without a specific context, and we spend a lot of time on language. In fact, I occasionally tell them that it's a language course. I can't remember any math teacher ever spending time developing a language.

I found long ago that students - especially the people-oriented ones - remember science concepts better if we wrap them up with the people who discovered them. They remember Van Allen's belts because they remember that no one wanted to send up the Geiger counter except Van Allen, and there are several other areas that have been made more real by adding the very abbreviated biographies or humorous stories associated with them. As you say, this humanizes a subject and helps students to realize that it's all just people like us - well, sort of like us! I started adding science history because there was some research that suggested that girls learned science better if there was a human context, and I found it to be true. Wouldn't this be true of math, too?

My high school math teacher was Dr. Baldour, a recent refugee from Castro's Cuba and the author of math books then in common use in the Spanish-speaking parts of South and Central America. His English was poor, and that's why he couldn't get work anywhere prestigious and ended up in our little private school in Hoboken, N.J. We never had the usual "If I have x apples and you have y oranges" problems - all our problems were oranges and mangoes! This was wonderfully exotic to us and somehow made the problems themselves more personal. We had long debates as to whether that was a "spear" or an "arrow" that pointed to the answer.

It's really a bit sad, now that I think about it, that such a simple thing made our math class unique from everyone else's, and that I remember it 30 years later. Why is math taught in such a sterile way? Why don't we share the delights of the personalities involved? The most delightful reading I've done in a while is the two "Mathematical People" books (ed. Donald Albers et al.). Yet students are rarely exposed to people who "do" math as a lifestyle and find it to be FUN. How do we change this? Is anyone out there doing this?

Of course, there is one more thing underlying our current failure with teaching math. When I went to "teacher school" about 7 years ago, intending to teach middle school, I was in the K-8 preparatory section. Out of 120 students, there was 1 math major and 1 science major. (I was the science major, because years ago in Hoboken, the administration wouldn't let me take the calculus class because "girls don't need calculus". And that's as far as my math went.)

There were 2 math classes required: one was to teach the teachers-to-be some actual math - and the enrollment in that had at least a 50% dropout rate. It was a wonderful challenging course, and the teacher who taught it never taught it again, because he weeded out too many students. The other class was supposedly a teaching math methods class, but the entire quarter was dedicated to overcoming math phobia in the teachers! If these are the people teaching fractions, percents, decimals, etc., is it any wonder that students don't learn them? It would not be an exaggeration to say that 75% of my classmates did not actually understand what place value is. They are teaching the children that you get in high school, and then college. The mind reels, doesn't it?