Math Education-Is There More To It Than Just Numbers?

Rasha asks: "I am taking a class this semester which discusses different models of the human mind. One topic that has caused much debate is the nature of math education and its goals. I am writing a paper for this class which will attempt to discover what exactly we try to accomplish by teaching math to young students. Are we trying to give them skills or is there more? Is math our attempt to access the more abstract parts of students' brains and develop them? I have sent a survey to a bunch of teachers (mainly elementary and high school) but I am curious what Slashdotters think. I think that most Slashdot readers are probably more mathematically inclined than the average and might have a greater insight into the issues that I'm addressing. Also if anyone knows any previous research on the topic let me know (this is not the focus of the paper though, I'm just curious)." (There's more...)

"Here are some of the questions I sent to the teachers so you can get a feel for what I'm looking for:

• Of all the subjects which is the most important for the development of the student? That is, which subject gives the most skills to the student beyond the actual information taught? Why? What is the goal of teaching Math to children? Is it to give them skills to manipulate numbers or does it accomplish something else (or maybe both)? What are those skills?
• People often say that math teaches abstract reasoning. Is this so, how and why? Could there be a better way to accomplish this?
• With the development of small computers and calculators do you see the role of math education declining? Why or why not?
• Why are children often forced to memorize multiplication tables and do long division?
• Why is it that students who have some deficiency in math are stigmatized as "not so bright" more often than children who fail to do well in other subjects? Conversely, why are children who excel at math considered gifted (more so than other subjects)?"

Comments

Elementary school teaches Arithmetic, not Math

[Louis_Wu]

We teach math to enable students to live in our society. Beyond that, it's just frosting on the cake. Some people (like my mom, who teaches math to junior high kids [11-14 years old]) maintain that kids do not have abstract thinking ability before ~13, for the most part. So teaching it would be hard in elementary school.

1)

Of all the subjects which is the most important for the development of the student? That is, which subject gives the most skills to the student beyond the actual information taught? Why?

Reading. Period. After that, she can teach herself. But "A, B, C" isn't enough, which is why English classes are so key, they give practice in reading. English class doesn't teach anything about reading; for that see "How to Read A Book" by Mortimer J. Adler.

2)

What is the goal of teaching Math to children?

So that "the future of America" will be able to live in the "America of the Future(TM)".

3)

Is it to give them skills to manipulate numbers or does it accomplish something else (or maybe both)? What are those skills?

Again, until high school, it's just coping skills. Then, higher thinking is slowly introduced. Slowly.

4)

People often say that math teaches abstract reasoning. Is this so, how and why? Could there be a better way to accomplish this?

Math teaches abstract reasoning, arithmetic does not.

From "Mathematics Dictionary" 5th Ed.

Arithmetic n The study of the positive integers (1,2,3,4,5, ...) under the operations of addition, subtraction ,multiplication, and division, and the use of the results of these studies in everyday life.

Mathematics n The logical study of shape, arrangemant, quantity, and many related concepts. Mathematics often is divided into three fields: _algebra, _analysis, and _geometry. However, no clear divisions can be made, since these branches have become thoroughly intermingled. Roughly, algebra involves numbers and their abstractions, analysis involves continuity and limits, and geometry is concerned with space and related concepts.

Thought that I would clear the definitions up a bit. Basically, you don't hit mathematics until high-school. So elementary 'math' doesn't teach abstract reasoning, though it may teach reasoning on some level.

5)

With the development of small computers and calculators do you see the role of math education declining? Why or why not?

You always need a gut-level check of whatever you are doing. If you don't know that 1882*1000 should be bigger than 1.9, you won't realize that you divided instead of multiplying.

In engineering we occasionaly finish a complex analysis which has many possibilities for making mistakes by doing a "sanity check" where we use a less precise but simpler method to check our answer. Stress analysis of a spring using elasticity methods is a good example. I had a 3/4" stack of paper for my analysis, with the pages covered in calculus and static analysis. When I was all done, I checked my spring constant equations against a handbook equation, and I was close. So I assume that I was 'right'. Without the sanity check, I wouldn't really know.

6)

Why are children often forced to memorize multiplication tables and do long division?

Because it is actually useful. Not just for engineering students like me, but for checking the high-school dropout who is ringing up your groceries: if he puts the decimal in the wrong place, your loaf of bread is $10, not $1. That is much easier to check if you know that $10 is 10 times $1, and that multiplication by 10 can be done by moving the decimal point. An ability to do basic arithmetic cannot be thought unnecessary when our society is ruled more and more by numbers. (Politicians use polls, we all use prices, homeowners use mortgages, nearly everyone uses credit cards. To understand all of this, we must understand arithmetic so well that we don't have to check to see if we did it right; arithmetic must be nearly second nature.)

7)

Why is it that students who have some deficiency in math are stigmatized as "not so bright" more often than children who fail to do well in other subjects? Conversely, why are children who excel at math considered gifted (more so than other subjects)?"

Because it seems that our society thinks that math is hard (to quote Barbie), so if you can do math, you must be smart. That one is mostly societal.

BTW,
Are the people in your class primarily from the sciences or the humanities? I ask because I have noticed a trend at my university that the students who use math in class regularly (physics, engineering, chemistry, etc.) think that math is an essential life skill for everyone to know, and the students in the humanities (psychology, english, history, etc.) see math as useful in balancing a checkbook, but beyond that, it seems to have little point. "Why did I have to take algebra? I've never used it?" When this comes up, the science types insist that math is an essential skill, but are hard pressed to find "real life" examples of how algebra or geometry could be useful. And we aren't even up to basic Calculus in the discussion! I would like to find a way to convince people that math is useful, not just arithmetic.

Louis Wu

Thinking is one of hardest types of work.