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.
Friday, June 24, 2011
Tuesday, June 21, 2011
What's Math got to do with It ?
"What's Math got to do with It?" by Jo Boaler, 2008
Helping children learn to LOVE their least favorite subject -- and why it's important for America.
Jo Boaler is the Marie Curie Professor of Mathematics Education at the University of Sussex in England. She was previously a professor at Stanford.
Introduction
In 2005, an AP news poll showed that a staggering 4 out of 10 adults said they HATED math in school.
Twice as many people hated math as any other subject.
Yet the advent of new technologies means that ALL adults now need to be able to reason mathematically in order to work and live in today’s society.
This aversion to math is reflected in our popular culture as well:
- In an episode of The Simpsons, Bart returns his math textbook at the end of the year, noting that it is in perfect shape, “still in its original wrapping !!”
- Barbie’s first words were “Math class is tough”
(manny adds – I hear it all the time in TV shows and movies….I have even heard school counselors tell the students that math was their worse subject)
Mathematical know-how is not only one of the most important qualities for workers to possess in the future, it is critical to successful functioning in life.
“Today’s news is not only grounded in quantitative issues (budgets, profits, inflation, global climate change, weather probabilities) but it is also grounded in mathematical language (graphs, percentages, charts).”
21th century citizens need mathematics.
But the mathematics that people need is NOT the sort of math learned in most classrooms.
If young people are to become powerful citizens with full control over their lives, then they need to be able to reason mathematically – to think logically, compare numbers, analyze evidence, and reason with numbers.
Mathematics classrooms need to catch up – not only to help future employers and employees, or even to give students a taste of authentic mathematics, but to prepare young people for their lives.
“Traditional K-12 mathematics curriculum, with its focus on performing computational manipulations, is UNLIKELY to prepare students for the problem-solving demands of the high-tech workplace.”
What’s Math Got to do with It ? IT is a lot to do with children having low self-esteem as they are made to feel bad in math classes; it also has a lot to do with children not enjoying school as they are made to sit through uninspiring lessons and it has a lot to do with the future of the country, given that we urgently need many more mathematical people to help with jobs in science, medicine, technology, and other fields.
Children need to solve complex problems, to ask many forms of questions, and to use, adapt, and apply standard methods, as well as to make connections between methods and to reason mathematically – and they can engage in such methods at home and at school.
Helping children learn to LOVE their least favorite subject -- and why it's important for America.
Jo Boaler is the Marie Curie Professor of Mathematics Education at the University of Sussex in England. She was previously a professor at Stanford.
Introduction
In 2005, an AP news poll showed that a staggering 4 out of 10 adults said they HATED math in school.
Twice as many people hated math as any other subject.
Yet the advent of new technologies means that ALL adults now need to be able to reason mathematically in order to work and live in today’s society.
This aversion to math is reflected in our popular culture as well:
- In an episode of The Simpsons, Bart returns his math textbook at the end of the year, noting that it is in perfect shape, “still in its original wrapping !!”
- Barbie’s first words were “Math class is tough”
(manny adds – I hear it all the time in TV shows and movies….I have even heard school counselors tell the students that math was their worse subject)
Mathematical know-how is not only one of the most important qualities for workers to possess in the future, it is critical to successful functioning in life.
“Today’s news is not only grounded in quantitative issues (budgets, profits, inflation, global climate change, weather probabilities) but it is also grounded in mathematical language (graphs, percentages, charts).”
21th century citizens need mathematics.
But the mathematics that people need is NOT the sort of math learned in most classrooms.
If young people are to become powerful citizens with full control over their lives, then they need to be able to reason mathematically – to think logically, compare numbers, analyze evidence, and reason with numbers.
Mathematics classrooms need to catch up – not only to help future employers and employees, or even to give students a taste of authentic mathematics, but to prepare young people for their lives.
“Traditional K-12 mathematics curriculum, with its focus on performing computational manipulations, is UNLIKELY to prepare students for the problem-solving demands of the high-tech workplace.”
What’s Math Got to do with It ? IT is a lot to do with children having low self-esteem as they are made to feel bad in math classes; it also has a lot to do with children not enjoying school as they are made to sit through uninspiring lessons and it has a lot to do with the future of the country, given that we urgently need many more mathematical people to help with jobs in science, medicine, technology, and other fields.
Children need to solve complex problems, to ask many forms of questions, and to use, adapt, and apply standard methods, as well as to make connections between methods and to reason mathematically – and they can engage in such methods at home and at school.
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