Transcript History of Mathematics Introduction to Course History in the Mathematics Classroom • • Where did mathematics come from? Has arithmetic always worked the way you.

History of Mathematics
Introduction to Course
History in the Mathematics Classroom
•
•
Where did mathematics come from? Has
arithmetic always worked the way you learned it in
school? Could it work any other way?
Who thought up all those rules in algebra, and
why did they do it? What about geometry?
•
•
•
Mathematics is an ongoing human endeavor,
like literature, art, physics, economics, or
music. It has a past and a future, as well as a
present.
The mathematics that we use today is very
different than the mathematics of 1000, 500,
or even 100 years ago.
Learning about math is like learning about
another person. The more you know of
someone’s past, the better able you are to
understand and interact with him or her now
and in the future!
•
•
To learn mathematics well at any level, you need
to understand the relevant questions before you
can expect the answers to make sense.
Understanding a question often requires knowing
the history of an idea: Where did it come from?
Why is it or was it important? Who wanted the
answer and what did they want it for?
•
Each stage in the development of
mathematics builds on what has come
before. Each contributor to that
development was (or is) a person with a
past and a point of view. How and why they
thought about what they did is often a
critical ingredient in understanding their
contribution.
Future Teachers: Why take this course?
• The report of the Conference Board of the
Mathematical Sciences, “The Mathematics
Education of Teachers,” published in 2001 states
“Prospective teachers need mathematics courses
that develop a deep understanding of the
mathematics that they will teach.”
• The report recommends “Prospective high school
teachers of mathematics should be required to
complete the equivalent of an undergraduate
major in mathematics that includes a 6 hours
capstone course connecting their college math
courses with their high school math courses.”
•
This course should bring together all the
strands of school mathematics, algebra,
number theory, geometry, analysis, and
probability and statistics, considering the
basic ideas involved from an advanced
standpoint, and “explicitly tracing the
historical development of key ideas,
identifying questions that were challenging
for mathematicians and will be difficult for
students.”
•
•
•
•
Teachers: To teach mathematics well at any
level, you need to help your students see the
underlying questions and thought patterns that
knit the details together.
This attention to such questions and patterns is
the hallmark of the NCTM standards.
Most students, particularly those in the early
grades, are naturally curious about where things
come from.
With your help, that curiosity can lead them to
make sense of the mathematical process that
they need to know!