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.

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.” Future Teachers: Why take this course?

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!