A commenter wrote in what I consider a classic example of misrepresenting what he or she is commenting on. The argument is so full of holes that are all too often repeated in schools and other institutions, that I thought I’d better stand up for students everywhere in order to protect them from the kind of rhetoric that is so often used to make them  obey “rules” that either aren’t rules, or if they are, are not adequately  explained at to  why they are necessary.

The commenter wrote in:

The use of the word “and” to indicate the decimal point is an agreed-upon “rule” in math. Math has many of these “rules,” which try to clarify mathematics. This is a standard rule taught in most elementary schools. PLEASE don’t confuse the students by saying they can do as they please. Then can 2 + 3 x 5 be equal to both 25 and 17? NOT. The order of operations “rule” says multiply first, so 2 + 3 x 5 = 17.

Professor Homunculus sez:

I’m afraid you’re going to have to show me where that “rule” is. I think what you are calling “an agreed-upon “‘rule’ in math” is just a convention made up for the convenience of elementary schools and is not a mathematical law.

Click here to view the embedded video.

Great logic, Dick!

Regardless of how much you want to believe you are right, your argument is full of logical holes. It is a good lesson to students about one of the things that is so wrong about some schools and teachers, though. Using bad logic to bully students into accepting anything just because you say it’s “agreed-upon” is a crime against education. Unfortunately it is the  ”agreed-upon” crime .

Here are a few things readers can keep in mind when making up their minds concerning what is valid and what isn’t. When someone uses the words “agreed upon” in an argument, you should ask yourself the question, “agreed upon by whom?” The above argument does not address that. That fact doesn’t negate the above argument, but it certainly weakens it.

Also, keep in mind that no matter how strongly someone feels about an argument, it does not make their argument any more or less valid. What does make it less valid, though, is when someone unfairly and untruly twists the other side’s argument to try to make it sound wrong. This is exactly what the commenter here has done. His or her insistence that I , “PLEASE don’t confuse the students by saying they can do as they please,” is a disingenuous ruse. Go back and read the article if you want. You won’t find that I said “students can do as they please.” I didn’t even imply it. I even say the “and” rule is a good Idea, but it’s just a convention, and not the final law. It’s a good Idea not to fart in class, but there’s no law against it (no matter how strongly we both may feel about that).

Another disingenuous tactic is, “Then can 2 + 3 x 5 be equal to both 25 and 17? NOT. The order of operations “rule” says multiply first, so 2 + 3 x 5 = 17.”

To put it bluntly, that is a crap argument. I don’t say or imply that you ignore mathematical laws. I LOVE mathematical laws. The order of operations is necessary, doesn’t contradict anything else. It is a convention that grew into a rule. It’s not an axiom. It’s not even an actual “law”. But it is a valid rule. So, no, I don’t say or imply that 2 + 3 x 5 can be equal to both 25 and 17, and it would be lying imply that I am.

To put a fine point on it, that ruse is a very pernicious one, and is often used by people to promote ideas that are just idiotic. “Oh, so you think it’s good to help poor people? So you’re saying you’re a communist?” See how dumb that would sound? Of course the commenter is not the same point, but he or she is using the same form of argument. It’s not valid in either case, and to visit this kind of BS argument onto children, and say they should abide by it, is an injustice.

To be fair, maybe the commenter isn’t intentionally twisting the argument and using logical fallacies just to prove a point that he/she believes in. It may be ignorance, not intent. Either way, regardless of how strongly one feels about a subject, they don’t get to make the rules for you to have to obey, unless they make sense, are necessary, and don’t contradict existing laws.

Unless the commenter can prove that it is a mathematical law, you can dismiss his/her argument. It doesn’t mean it’s wrong – there might actually be a proof – it just means his/her argument is meaningless without the proof.

It’s hard to believe that a person in the twenty-first century can still come out with an argument like, “This is a standard rule taught in most elementary schools.” That is an argument? It’s still standardly taught that “multiplication is repeated addition.” That doesn’t make that right. (It isn’t. See this article by Keith Devlin, and this article by Keith Devlin)  Does any self-respecting human think that something is right just because it’s a standard rule taught in most elementary schools? For pete’s sake, segregation was a standard rule in most elementary schools up until the point when someone figured out how bogus it was. Sheesh.

 I recently read an article about Srinivasa Ramanujan. He was one of the greatest mathematicians who ever lived. He died in 1920, aged 32.  Mathematicians still study his notebooks today, trying to understand the brilliant insights he came up with. According to the chapter “The Formula Man,” in Ivars Peterson’s wonderful book, A Mathematical Mystery Cruise, “Ramanujan’s work reveals a genius for finding numerical patterns, hidden laws, and relationships in the wilderness of numbers. No one really knows what led him to his astonishing array of mathematical discoveries or how he proved his results. He spent most of his life far from centers of mathematica activity, and working in his own way, drawing formulas and theorems from mental landscape unconnected with the frontiers of contemporary mathematics.”

Until Ramanujan was 17, he was mostly self-educated. He had no teachers to tell him he was wrong for thinking the way he did. Can you imagine if he had a teacher who was fixated on an imaginary law like “and?” Yikes!

I’m not saying that everyone is a Ramanujan. What I am saying that O.D.-ing on what people tell you “are the rules” is a sure-fire way to make sure you will never be a Ramanujan.

I think this whole issue is a clash between mathematics and school rules. You are not doing mathematics unless you are thinking. You need to understand why certain things are accepted or not, and it is part of the duty of those who “make the rules” to prove that the rules make sense, are necessary, and don’t contradict existing laws.

The biggest reason for people “hating school” is that the rule makers tend to be ill-advised school boards, the administrators who have to kneel before them, some uninformed teachers, and text-book lobbyists. Real teachers are usually too busy trying to teach, or buying materials that the schools won’t supply, or trying to fill out lots of unnecessary paperwork to be making the rules. And real mathematicians are seldom understood or consulted by elementary schools. (Does your school have a mathematician – and I don’t mean a math teacher , or math-ed consultant – on it’s staff?)

Mathematics is an invitation to think. Elementary math education is more and more becoming an order to obey. There are exceptions, but I think one reason that a lot of people seek help from Math Mojo and other alternative sources is because the exceptions are too few and far between.

What do you think? Please leave a comment.