The Meaning of Math, Problem-Solving, and Great Education

I would like to thank Larry, who writes the blog, Maximize Productivity with Industrial Engineer and Operations Research Tools, IEOR Tools, for pointing out, in his latest blogpost, the wonderful essay written by Dr. Robert H. Lewis of Fordham University, entitled: Mathematics: The Most Misunderstood Subject. In the essay, Dr. Lewis takes us on a journey through the education system over time (beginning with Dick and Jane readers) and illustrates effectively the relevance of mathematics not only to a liberal education but to today's highly technological world, in which math and accompanying implemented algorithms, through computations, make our high tech world operate.

In his eloquent essay he states:

Americans like technology but seldom have a grasp of the science behind it. And the mathematics that is behind the science is regarded as even more mysterious, like an inner sanctum into which only initiates may gain entry. They see the rich and nourishing technological fruit on this tree of knowledge, but they see no deeper than the surface branches and twigs on which these fruits grow. To them, the region behind this exterior of the tree, where the trunk and limbs grow, is pointless and purposeless. "What's the use of math?" is the common query. "I'll never use it." When a nation's leaders are composed primarily of lawyers, administrators, military men and stars of the entertainment industry rather than statesmen, philosophers, the spiritual, and the men and women of science, then it should be no surprise that there is so little grasp of the simple reality that one cannot dispense with the trunk and limbs and still continue to enjoy the fruit.

He concludes his piece with words from another essayist, David R. Garcia, which I find especially appropriate as many faculty from around the country are turning in their final grades for the semester:

Teaching is not a matter of pouring knowledge from one mind into another as one pours water from one glass into another. It is more like one candle igniting another. Each candle burns with its own fuel. The true teacher awakens a love for truth and beauty in the heart--not the mind--of a student after which the student moves forward with powerful interest under the gentle guidance of the teacher. (Isn't it interesting how the mention of these two most important goals of learning--truth and beauty--now evokes snickers and ridicule, almost as if by instinct, from those who shrink from all that is not superficial.) These kinds of teachers will inspire love of mathematics, while so many at present diffuse a distaste for it through their own ignorance and clear lack of delight in a very delightful subject.

Interestingly, at the final exam for my undergraduate Transportation & Logistics, which I flew back early from Chicago (where I was speaking at the Measuring Systemic Risk Conference) to proctor, one student, after he handed in his exam, told me the following: Professor Nagurney, I was working on some of the practice exam problems that you gave us and I figured out how to solve one of the problems (which was mathematical) in a different way and I got so much satisfaction from this experience and was on such a high that even if I did not do as well on this final, I feel so good!

By the way, this student aced the final and the course, and, as importantly, experienced the joy that comes with creating a solution to a challenging problem!

Learning Experiences, Face-to-Face, Service in an Orphanage in the Dominican Republic

Coincidentally, yesterday's New York Times (Sunday, January 25, 2009) had an article on trips to the Caribbean, just as my daughter was heading out at 5:15AM with her 9th grade class from The Bement School, with a few teachers and coaches, to the Dominican Republic. The caravan of Bement School busses left Old Deerfield in sub-zero weather to JFK airport and JetBlue flew them all down to Santo Domingo. The service adventure has begun. The students have been preparing for this trip for weeks and had assembled suitcases filled with clothes, games, and toys for the children at the orphanage where they are now staying for the week to help out.

Planned activities at the orphanage include educational activities such as math exercises, assisting with building projects, and, most of all, sharing with those who have no families in face-to-face time, basketball and baseball games, and just showing that others care.

These kinds of experiences cannot be obtained through "virtual connectedness." The group of 9th grade "Bementers" includes children from Massachusetts and Vermont, plus boaders from China, South Korea, and Singapore. They will speak in the language of friendship, kindness, and play, and, hopefully, will engender memories that will last a lifetime.

Updated -- January 27, 2009: Today, The Recorder, a newspaper based in Greenfield, Massachusetts, ran an article on this service trip.