Mathematics and critical thinking


The more classes I take in the social sciences or the humanities, the more I hear the term “critical thinking” being thrown around. A lot of educators seem to harp about the alarming lack of critical thinking skills among young people today and that we need to be taught them if we are to have any hope of thriving in a pluralistic, multicultural society: one that is ripe with the potential for disagreement and argument.

The philosophy department is the loudest advocate for this. Its course offerings and quarterly lectures are geared towards teaching students critical thinking skills by helping them identify fallacies in arguments and arriving at conclusions based on logical, orderly thinking. In fact, taking a symbolic logic class at Bellevue College will satisfy your symbolic and quantitative reasoning credit for your transfer degree, thus allowing you to circumvent the dreaded pre-calculus class that many students take for the same credit.

I have known several students who thought it would be a great idea to take logic instead of pre-calculus. Those who didn’t withdraw said it was one of the hardest classes they had ever taken. Make no mistake; this article isn’t an attack on philosophy but rather an offering of a different way to approach its study.

In my opinion, all human beings, by their very sentient nature, are born with the ability to think critically. How well they can do so in their adult lives is a direct result of how well they cultivated and matured this innate ability through rigorous mental exercise. I believe mathematics play a key role in this mental development.

Mastering algebra, trigonometry or calculus requires a methodical, orderly logic to one’s thinking. The student of math learns to break up a problem into its component parts and to accept conclusions based on assumptions that have been proved to be true. Most importantly, math students are taught always to remind themselves of what exactly it is they are looking for thus preventing them from losing sight of the objective of their query. All of these skills are basic philosophical concepts, but taught in a more readily applicable fashion.

I think that the farther along a student gets in math, the sharper his/her critical thinking skills become. They are more able to solve problems and to formulate arguments by drawing on a wide base of knowledge that they can prove to be true. Math students acquire these basic logic skills without realizing it though, through constant and rigorous application of concepts rather than being told that they lack critical thinking skills and are going to learn them.

I don’t really think most are students are ready for a philosophy class like symbolic logic until they’ve taken at least one college-level math class, not because they lack critical thinking skills, but because they haven’t trained the skills they already have.

A lot of the great Greek philosophers like Plato and Aristotle were themselves brilliant mathematicians and, at least as far as I understand it, they deemed a healthy familiarity with math an essential prerequisite for philosophy. In fact, I don’t think any of them would deign to wax philosophic with you if you had the chance to meet them and they knew you hadn’t taken Math 141.

If it were up to me, even 100-level philosophy classes would carry a prerequisite; if at not at least a recommendation of Math 141 with a C or better. And philosophy majors in my world would be required to minor in math. The skills of logical reasoning that are perfected in math by finding x and y again and again can be directly transferred to a more philosophic discussion where the objective isn’t the slope of a line but rather the definition of justice or some other elusive concept. Successful math students can follow reasoning step by step, and most importantly, they don’t get distracted by tangents, pun intended. They stay focused on what it is they are searching for by way of well accepted truths.

The well trained mathematician is the best critical thinker and for that reason I believe that the focus for our students should be shifted more towards math in order to foster the thinking skills that the faculty and staff have deemed to be lost in us. Only then can students who are so interested choose to continue on to philosophy classes to further hone these skills.