Ch. 1 What is Math ?

Chapter 1 What is Math ? (and Why do we ALL need it ?)

(Introduction section is posted way BELOW....the nature of Blogs)

In my different research studies I have asked hundreds of children, taught traditionally, to tell me what math is. The will typically say such things as “numbers” or “lots of rules”.

But ask Mathematicians what math is and they will more typically tell you that it is “the study of patterns” or “a set of connected ideas”.

Students of other subjects, such as English and science, give descriptions of their subjects that are similar to those of professors in the same field. Why is math so different ?

The math that millions of Americas experience in school is an impoverished version of the subject and it bears little resemblance to the mathematics of life or work or even the mathematics in which mathematicians engage.

What is Mathematics, Really ? Mathematics is a human activity, a social phenomenon, a set of methods used to help illuminate the world, and it is part of our culture. (manny adds - a nice a little discussion about rabbits and Fibonacci sequence and golden ratio follows).

Ask most mathematics students in high school about these relationships (Fibonacci and Golden Ratio), and they will not even know they exist. They have never been taught about them. (manny adds – I DO !!)

It is also a powerful way of expressing relationships and ideas in numerical, graphical, symbolic, verbal, and pictorial forms. This is the wonder of mathematics that is denied to most children.

A discussion of Fermat’s Theorem follows and its proof by Andrew Wiles of Princeton. (Simon Singh wrote a book about it “Fermat’s Enigma”)

It is hard for school children to enjoy a subject if they experience repeated failure, which of course is the reality for many young people in mathematics classrooms.

Problem solving is at the core of mathematicians’ works, as well as the work of engineers and others, and it starts with the making of a GUESS. And yet when children who have experienced traditional math classes are asked to estimate, they are often completely flummoxed.

After making a guess, mathematicians engage in a zigzagging process of conjecturing, refining with counter examples, and then proving. Such work is exploratory and creative…

Devlin states, “Mathematics is not about numbers, but about LIFE. It is about the world in which we live. It is about ideas, And far from being dull and sterile, as it so often portrayed, it is full of creativity.”
(Devin, The Math Gene)

As George Polya, the eminent Hungarian mathematician, reflected:

“A teacher of mathematics has great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity.

But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve the problems with stimulating questions, he may give them a taste for, and some means of, independent thinking.”

Bringing mathematics back to life for school children involves giving them a sense of living mathematics.