Mathematical Problem Solving in the Real World
Imagine you are the head of a research division for a world renowned IT content delivery firm, providing a hugely popular web portal that reaches every corner of the globe and you are given the following challenge: a country in South America under an autocratic regime that censors the content of your company’s publication on anything political about that country, but it has a strong populist subculture that supports freedom of speech and wants radical political reform. You have the company’s well being in mind: you can conceal the information on the regime’s past atrocities and current corruptions or you can publicize them on your portal. Kingmakering is intoxicating, after all, if a coup d’etat succeeds through the social media provided by your company, your stocks will go through the roof, not to mention it is also an ETHICALLY JUST undertaking. But here is the cliff hanger: is the electronic subscription to your company’s social media in that country and out connected enough to support a political change of blood – can the web of connectivity be fast enough to carry it out, or is it too localized such that any attempt would be detected, contained, and quickly extinguished like those before? You are dealing with a Marxist autocrat known for his iron fist and his cunning wit. You know him and he knows that you know him – checkmate, Kissinger.
All seriousness aside, not too surprisingly, this is also a math problem. There is a branch of mathematics that specifically addresses such problems: graph theory. This particular application is no joke, it’s real, and you are relying on the advice of your research team. The CEO, the chairman, and the board of trustees of the company are looking to you for answers. Times like this truly put your learning and your wits to the test.
In problem solving, there are two types of solvers: those who solve problems laboriously and those who solve them with the grace of a master, making the solutions enlightening and easy to understand. I have observed students in both camps. Education can enlighten someone or it can blind him. This is why when I solve a problem, I like to solve it again in different ways. Teaching a student solve a problem in different ways helps him to see the connections between the various solutions. Problem solving is not just important, it is critical in education. Perhaps Asiala will be permitted to have the last words:
“An individual’s mathematical knowledge is his or her tendency to respond to perceived mathematical problem situations by reflecting on problems by constructing and reconstructing mathematical actions, processes, and objects and organizing them in schemas to use in dealing with the situations.”
– Asiala et al. in A Framework in Research and Curriculum Development in Undergraduate Mathematics Education: Conference Board of the Mathematical Sciences: Issues in Mathematics Education. Vol. 6. American Mathematical Society. Retrieved at http://www.math.kent.edu/~edd/ICMIPaper.pdf