Technical Enrollments and Mathematical Pedagogy

ProblemsIn order to make critical decisions about issues such as global warming, health care and pollution, everyone must understand obvious functional relationships.Issues of functional dependence, continuity, rate of increase, concavity, tops and bottoms, all must be understood by more people in a technical democratic society.It is irresponsible to introduce these concepts in terms that are not clear and not student friendly.It is pedagogically unethical and unsound to place delta-epsilon arguments as roadblocks to the study of calculus.At professional meetings, we are told there is a shortage of engineers and technicians.At the same time, it appears that too many K-12 students are acquiring an aversion to mathematics 5,16 .The excessively high number of students graduating high school finding mathematics distasteful indicates we are doing something wrong.If we aim to increase enrollments in technological studies, and if it is true that youngsters choose technical studies because they like math, then mathematics must be introduced in a more attractive format.The study of numbers and shapes should be emotionally neutral.There is no reason for either liking or disliking any particular scientific fact.But the discovery of natural facts and patterns of facts is an exhilarating activity and more children should be excited by this exhilaration of discovery.If they are not, we are at fault for failing to provide an effective and more inspiring introduction.Mathematics in itself has nothing to do with memorization.Calculators and computers can perform general fault-free calculations.Sensitive students must certainly dislike the unnecessary pressure to memorize disconnected and meaningless facts and the pressure to perform calculations with dire consequences for making mistakes.In fact, computational ability does not represent either intelligence or analytical ability.It represents the ability to execute an orderly sequence of rules that obtain the fastest answer even if the student lacks any understanding of the rules.The student really learns that if he just follows the rules, his teacher will reward him with a high grade and the associated praise.In the student's eyes, the entire point is to get it right and continue on to the next question.In the eyes of the teacher and in the eyes of the principal, the system provides well-defined performance goals, which can gain community praise and rewards.However the drill and test environment does not foster creativity or the questioning scientific attitude that should be acquired by students in the STEM disciplines.Any exhilaration in the drill and test system derives merely from the competition and outperforming classmates.This momentary, vicarious thrill is trivial compared with the enduring satisfaction and pride of scientific discovery. HistoryIn 1807, Fourier published his iconoclastic paper on representations of periodic functions as an infinite series of harmonically related sinusoids.Fourier's paper drastically challenged fundamental concepts of mathematics and resulted in changes including the redefinition of the