Published in The Edge Malaysia, 27 Oct – 2 Nov 2013.
I recently completed the “Math Camp” portion of my program (Master in Public Administration in International Development) at the Kennedy School. Believe me when I say it is even more nerdy than it already sounds. That said, I have always loved Mathematics. I am not talking “Mathematics is my favorite subject” love. I am talking “Mathematics is my true love” love. Thus, you will forgive me for being slightly biased here, but I sincerely believe that a sound mathematical education is one of the keys to a mature (Malaysian or anywhere really) civil society.
I have strong concerns about mathematical education in Malaysia, particularly at the primary and secondary school levels. The 2011 Trends in International Mathematics and Science (TIMSS) study reported declining standards in Mathematics and Science among Malaysian students with Malaysia not only experiencing the largest drop in test scores among all countries for both Mathematics and Science between 1999 and 2011, but also declines in scores in all the various sub-indicators for Mathematics and Science. Consider as well the finding in the Program for International Student Assessment (PISA) that almost 60% of Malaysian students do not meet minimum benchmarks in Mathematics. I find these trends in Malaysian mathematical education deeply troubling.
To be clear, when I say “Mathematics,” I do not mean numbers and figures. A “Math” person is not somebody who has a head for figures (that would be Accounting) or who can perform arithmetic calculations in her head at warp speed. Neither is a “Math” person somebody who knows a lot of formulas. The best definition of a “Math” person that I have found comes from an academic paper by David Gale and Lloyd Shapley entitled, “College Admissions and the Stability of Marriage.” They state, perhaps tongue-in-cheek, that “…any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures, but because they are unable to achieve the degree of concentration required to follow a moderately involved sequence of inference.” Thus, by this, Mathematics really is about the construction of arguments based on logically consistent sequences of inferences.
This definition leads me to my belief as to why Mathematics is so important. The field of Mathematics is all about logical rigor. It is the ability to construct a solution based on a well-argued sequence of steps. This is why it is important to show your work in Mathematics exams. If you skip a step, it is not so much that you are taking a shortcut, it is that you are missing a logical point necessary for completing your work. The training in Mathematics is therefore about building sound arguments. Greg Mankiw, an Economics Professor at Harvard, hit the nail on the head in his blog post when he said that, “Math is good training for the mind. It makes you a more rigorous thinker.” Call me biased, but I say that more rigorous thinkers in civil society is a good thing.
Since Mathematics trains an individual in applying rigorous thought, it is not a stretch to contend that this training will permeate through that individual’s life, even outside the Mathematics classroom. Sure, at some point in life, one may forget how to differentiate the natural log of. One may forget what the Pythagoras Theorem states. One may even forget why 1 +1 x 0 is not 0. However, a solid training in Mathematics will ensure that the individual does not forget the logical rigor required to solve a problem. Whether the decision (or solution) is to marry a person now, or to buy a house in two years, or to forgo a lucrative career to pursue a life of art, a person well-grounded in mathematical training is likely to make a better decision because of the training in rigorous analysis.
From the perspective of civil society, the logical rigor that Mathematics builds will not only help an individual evaluate decisions in her life, it will also help her evaluate current issues in the world around her. She is able to see the strengths and flaws of an argument and decide if that argument is adequate or not. She can avoid common logical traps that lead to fallacious conclusions. Consider the case of the justice system, which is commonly predicated on the notion that an accused is presumed innocent until proven guilty. This forms the ‘null hypothesis’ of the justice system. A “not guilty” decision by the courts does not imply that the person is innocent; it simply implies that there was not enough evidence to prove the person guilty. This is often unappreciated with many confusing a “not guilty” verdict as an “innocent” verdict. A “not guilty” verdict simply means that we cannot reject the presumption that the accused is innocent.
All in all, while I believe that a solid mathematical training is one of the key components to developing a mature civil society, I should add that it is not the be-all end-all solution. In mathematical terms, solid mathematical training is a necessary but not sufficient condition in achieving a mature civil society. For instance, in addition to the application of logic, we need to apply reason. Logic may suggest, for example, that a society with one person making $1 million and nine persons making nothing is as well off as a society with ten persons making $100,000. To understand the difference between the two scenarios, we must apply reason in addition to the logic. Yet, the point remains that we must ensure a sound mathematical grounding for all Malaysians to move towards a mature civil society. The best part is that it really does not matter in what language we study Mathematics; to quote Lindsay Lohan in the movie Mean Girls, “(Math is) the same in every language.” Whether you say integration, pengamiran or integracion, a sound mathematical training will develop, in you, rigorous tools for dealing with nearly all aspects of life.