Why Study Mathematics?
By Mr. Stephenson
First, please read these articles:
Then, here are my reflections:
Mathematics is used to model, and then solve problems. In our mechanical
universe (the "real world"), mathematical models are used to
properties of objects or to reconstruct past properties. Some, but by
no means all of those properties are location,
speed, acceleration, and temperature, etc. Mathematics is a kind of crystal ball that's used to peer forward or
backward in time.
Some students will need to master mathematics to pursue careers in technical or scientific fields. But even fields that do not contain mathematics still have problems to solve. Successful people solve problems. People who do not solve problems will work for those who do -- if they can find work at all. So all students striving for success need to develop an ability to solve problems. High School Mathematics is, if you will, a well outfitted "gymnasium" in which students can learn and practice the techniques of problem solving.
Teaching to solve problems is education of the will. Solving problems which are not too easy for him, the student learns to persevere through unsuccess, to appreciate small advances, to wait for the essential idea, to concentrate with all his might when it appears. If the student had no opportunity in school to familiarize himself with the varying emotions of the struggle for the solution, then his mathematical education failed in the most vital point. (Polya 1957, p. 94)
In no other subject but mathematics can students be given such [...] challenge[s] and such emotional experience[s] on a daily basis. This kind of experience is of life benefit. Remove the stress, remove the high standards, remove the unforgiving challenges -- and mathematics loses much of its educational value. (Stueben 2003, p.392)
I promise to try very hard to maximize the educational value in the
mathematics courses I teach.
Students need to understand that mathematics is not a spectator sport. They cannot learn to solve mathematical problems by watching the teacher or other students solve problems. They must struggle to solve problems themselves. They must fail, and analyze why they failed. Then use that knowledge to solve the next problem.
A basketball team member does not learn how to make baskets by watching others make baskets. She learns by unrelenting constant practice. By modifying her throw based on errors made. By practicing until successful throws are almost automatic, and then continuing to practice to keep the skill. She understands that she must use it, or lose it.
So too, mathematics students learn to do mathematics by unrelenting constant practice doing mathematics. Classwork and homework is that practice. Students should expect to do a lot of it. Note too that mathematics is very sequential. Missing any parts of the sequence seriously handicaps the student for future mathematics learning. Students should constantly review the mathematics they learned in the past. Use it, or lose it.
Finally I would make an observation on character. Employers look for indications of a potential employee's character in the work place: how well she handles stress, what her work ethic is, what personal goals she makes for herself, and how persistent she is at achieving her own, and employer assigned goals. The mathematics courses taken and grades achieved are good indicators of how well potential employees will do in the work place.
Polya, George. How to Solve It. 2nd ed. Garden City, N.Y.:
Stueben, Michael. "A Way of Teaching." In Mathematics Teacher, Vol. 96, No. 6 (Sept. 2003), pp. 390-392. National Council of Teachers of Mathematics.