By Dennis Martin
In my 35+ years of teaching math, I had lots of little stories to illustrate different points in mathematics. There is one mathematical habit that Miss Wright taught us and insisted on. It’s such a simple thing to do. On the first day of every math class I taught, after the initial roll-taking, syllabus explanation, etc., I would start off: “I had this battle-axe for a math teacher in high school.” (usually some laughter in the room) “She gave me the best advice I ever had in math. She insisted that we always work problems vertically on the page, not side-to-side. It will use up more paper, but believe me it is worth it.” Most students already had this habit, and after a few weeks of watching me work problems on the board, every student saw its advantage and did it.
Another habit Miss Wright preferred was that when working with equations, write the equal sign for each new line right under the previous equal sign. For example, X - 2 = 4 on the first line, +2 = +2 on the second line (this is how you are going to transform the equation), then X = 6 on the third line (the result.) For more complicated problems, there would be many more lines. The advantage to this is that it becomes an alternating sequence of equation, transformation process, transformed equation, over and over, until you reach some final result. If the equal signs are lined up vertically, it is also easier to spot mistakes. (Just in case you have to help your grandkids with math now.)
There is a principle in mathematics, illustrated above, called the principle of equality. Basically, it says that if you have an equation, you can do anything you want to the left side – add, subtract, multiply, divide, square, square root, whatever – and as long as you do the same thing to the right side, the equations will still be equal. Now I’ve taught probably 10 times more philosophy courses as math courses in my career, since my PhD is in philosophy with only a B.S. in math. The principle of equality in mathematics is only a specific case of the principle of equality in philosophy. So more generally, if any two things are equal and you do the same thing to both, then they will still be equal.
In both math and philosophy, there is a corollary to the principle of equality. If two things start off as equal, and then a transformation is made, but the two things are no longer equal, then the transformation itself was unequal, different, or discriminatory. If a woman takes a blouse to the cleaners and a man takes a shirt of the same material, but they are charged different prices after the transformation/cleaning, then there is discrimination going on.
Justice and fairness are fundamentally based on this principle of equality.
Miss Wright lived about two blocks from the WPHS campus. One morning in homeroom, someone yelled out, “We drove by your house Saturday night, Miss Wright. We saw you in your driveway. Was that your date?” She seemed both perturbed and embarrassed. Several guys in the room, including the one who asked the question, snickered. Nothing more was said.
At the time, naïve but ever-optimistic me thought – well good for her; she has a social life; no one should be single forever; maybe she’ll get married to her boyfriend; we’ll call her “Mrs.” someday. So, why were they snickering? I didn’t get it.
Later in life, I realized that a lot more was going on, for which I am now truly sorry happened. The snickering showed an implicit discriminatory assumption and judgement concerning who she could date or be with, held over from previous generations. Now, fifty years since high school, marriage equality acts around the world embrace the principle of equality, and snickering is on the decrease. In algebra, you may not have understood the principle of equality, but when your own child or grandchild emerges from that windowless closet, you get it.