Something that nearly every adult has wondered about, but is scared to say it out loud is “Is knowing math really that important?”
They don’t say it out loud because they fear that someone, possibly a math teacher like me, or someone else who knows better, will put them in their place with a long explanation about the importance of math in everyday life, in the sciences, and in the development of minds.
I love math. I realized I was good at in when I was in 6th grade and have progressed through the levels, majoring in it as an undergraduate. I’ve spent most of the past 20 years as a math teacher. So when I write what I’m about to write, it will certainly shock most people. Here it is: math is overrated.
Nowadays, with high stakes testing, we are told that the only two things that really matter, in equal amounts, are reading and math. Schools are praised or shut down for their scores (or ‘gains’) on these subjects. Some schools, particularly charters, have realized that if they focus on math, at the expense of reading, they can get better combined results than if they try to focus on both, equally. This implies that proficiency in math is somehow as important as proficiency in reading, and I’m here to say that this is completely absurd. I’m one of the few people who is not scared to say this since I will hold my own in a debate against anyone on this topic, as I’ve been pondering it, nearly daily, for about twenty years. In this post, I’ll try to summarize why I think this.
First let me distinguish between two types of math, which I’ll call Mathematics and ‘math’. When I say I love math, I’m talking about Mathematics. The word Mathematics is derived from the Greek, meaning ‘knowledge.’ It doesn’t say anything about adding fractions with unlike denominators or about the area of a triangle. I study Mathematics in my spare time, subscribe to a journal called Mathematics Magazine, and really pursue it in the way that people pursue art or music. I will give an example in a bit about what I mean by Mathematics and how it relates to its distant, and inferior, relative which I’ll put in quotes and start with a lowercase letter, ‘math.’
‘math’ is what is taught in school. Kids are subjected to twelve years of boredom, memorizing math facts and formulas, and churning out solutions using algorithms, without the slightest idea of why the formulas or algorithms work. Students are told (lied to really) that they will ‘use this’ someday, when they are building something or balancing their checkbooks or shopping. For those students who manage to get a year ahead, they are rewarded, after twelve years, of taking Calculus in their senior year. Unfortunately, what was once regally known as The Calculus could now only be described as ‘calculus’ since it is also a mindless set of algorithms which would make Isaac Newton flip in his Westminster Abby grave.
The high stakes ‘state tests’ are about ‘math’ which is too bad since doing well on such state tests does not mean the students know anything about Mathematics. It is more a measurement of how obedient they are. This is something that most thinking adults probably suspected, but didn’t feel they could defend these thoughts against someone who is much better than them in math. The fact is that the ‘math’ that students learn will not help them much in later life. Over the years topics kept getting added and added until poor ‘math’ teachers had no choice but to teach each topic in a superficial way in order to ‘get though’ them all. As a result, all the Mathematics was stripped from the ‘math’ leaving something that, for the most part, is a waste of time. What they ‘learn’ about ‘math’ is quickly forgotten after the test. That which isn’t will rarely be used again, not by scientists, not by engineers, not by bankers.
But true Mathematics, I think, is worth studying. I still don’t think that it is nearly as important as the skill of reading, but real Mathematics, when experienced properly, is something uniquely human which makes the mind flex in ways it cannot in any other discipline.
Here’s an example of what I mean by Mathematics. And, believe it or not, I’m going to pose it as a multiple choice question, but one that requires an explanation.
Here it is, and I’m going to ask the reader to spend a few minutes thinking about this.
3 is an odd number and 7 is an odd number, but when you add them together you get 10 which is an even number. Which of the following do you think is correct? Justify your answer.
A) An odd plus an odd is never even.
B) An odd plus an odd is always even.
C) And odd plus an odd is sometimes even and sometimes odd. It depends what the numbers are.
Take a few moments and see if you can experience a mini ‘Aha’ moment.
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The correct answer is B.
A beautiful ‘proof ‘ of this can be done with something called a ‘proof without words.’ Look and ponder for another minute.
This is what I mean by Mathematics. This is way mathematicians call a succinct proof in Mathematics, ‘elegant.’
So how is this concept covered in ‘math’? Well students are asked to memorize the facts: even+even=even, odd+odd=even, even+odd=odd, even*even=even, even*odd=even, and odd*odd=odd. Some justification might be presented, but there is not enough time to really allow students to think about why these rules are true because we have to get to the way these are presented on the standardized test. This is a question from a practice test for the SSHSAT, which is the test eighth grade students in New York City have to take to qualify for one of the specialized high schools.
If x is an integer, which one of the following must be odd?
A) 3x + 1
B) 3x + 2
C) 4x – 1
D) 4x – 2
E) 5x – 2x
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The answer to this one is C, but if there was a choice that said ‘Who Cares?’ that would also be right.
I hope you’re beginning to see the difference between Mathematics and ‘math.’
One reason we are stuck with ‘math’ instead of Mathematics is that there are not enough teachers who are qualified to teach Mathematics properly. And of course I’m not attacking teachers and demand they be fired for not being trained properly. It’s just that there is a real shortage of highly qualified math teachers so they have to do the best they can. But the bloated curriculum is the main culprit. Each year new topics get added, but things rarely get taken out. The only topic I can think of which used to be popular and now is out of the curriculum is taking square roots by hand.
If it were up to me, I’d gleefully scrap about 40% of the topics required by most curricula. Out would go the word problems where people work together to paint a house and we figure out how long it will take, or the famous train leaving Chicago at 80 miles per hour …, and a whole lot more.
The Common Core Standards in math have, in many ways, made the situation worse. They added many more topics and removed very few so that some of the topics had to be moved down to lower grades to make room for the new topics in the upper grades. So topics that kids are not ready for developmentally are now taught too soon.
But the crazy thing about all this is that so many policy makers believe that this ‘math’ is so important that schools need to be closed and teachers fired when students are not proficient in it. This is also why I cringe, knowingly, when I hear of the success of the ‘no excuses’ charters of getting math scores up, despite having little or no improvement in reading. Most recently, Houston tried to take the KIPP model and create something called the Apollo 20 program, which pumped a lot of money into math tutors, so they got their math scores up but nothing in reading.
As you suspected long ago, ‘math’ is not very important. It doesn’t measure intelligence. It doesn’t make countries ‘globally competitive.’ It’s mostly a waste of time.
As a professional ‘math’ teacher for nearly twenty years, I’ve found ways to sneak Mathematics into my ‘math’ course. Sometimes this means that I give a very cursory treatment of certain topics so I can have time for what I consider important. I’m fortunate to teach one section of something called ‘math research’ where I get to choose the topics so I can ensure that it’s all Mathematics all the time. Sometimes I feel like I’m a trained Chef who is forced to work in a McDonalds. I have to do my job and make those Big Macs and fries, but I search for opportunities, even within my constraints, do things the way they are supposed to be done. It isn’t easy since there are just way too many topics to be done in so little time.
Feel free to browse my youtube channel if you want to experience a bit of what I consider Mathematics.
I am not alone among math educators about the sorry state of the imposter that we currently call ‘math.’ Just a day after I started working on this post, the cover story in the magazine American Educator written by professor Hung-Hsi Wu identified the same contempt for what he calls Textbook School Mathematics or TSM. He, like me, thinks that the current math curriculum has developed into something that serves little purpose. He feels that things will improve if four things happen: 1) If the Common Core Standards for math are good, 2) If textbook companies get behind them, rather than just slapping a sticker on their old books and calling them ‘compliant with Common Core.’ 3) If schools of Ed get on board training math teachers properly, and 4) If the mathematical community invests some brain power on the problem. He believes that the Common Core was well created so there is a chance that things will get fixed. Though I agree with his assessment of the problems that have led to this math crises, I don’t agree that the Common Core were appropriately developed. His defense of the Common Core includes a lengthy description on page 7 of the new way to teach that -1*-1=+1 for 7th graders, and it will make your head spin if you read it. I agree that IF Common Core was good, that would be a good, and necessary, start. For the same reason that ‘math’ is in the state it is in, the Common Core fell victim to the same problems — too many people with too many favorite topics.
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Hi Gary, I’m a 2011 CM teaching math in a high school with very low math achievement (even by TFA standards). I agree with your assessment that most curricula teach mathematics rather than Mathematics (to use your formalism). However, in your criticism of this fact, I feel as though your background as a Mathematics major may actually limit your perspective. Even among generally “successful” individuals, there are few who, at least initially, appreciate Mathematics for the reasons that you do–the beauty of elegant proofs, the foundations of number theory, etc. As an astronomy and physics major, I certainly didn’t need to understand integrals down to a fundamental level in order to apply them in answering very important questions about the universe. Econ majors don’t need to understand derivatives beyond “mindless algorithms” in order to figure out marginal rates of return for real businesses (though in the process, they might just pick up a conceptual understanding). Social scientists don’t need to understand the details of how statistical analysis software works in order to draw valid and valuable conclusions from data (though it would probably help a little).
In short, I think it’s rather unfair to say that lower-case mathematics is a waste of time. Certainly, the more rigorous and conceptual, the better, but that doesn’t mean it’s impossible (or even particularly difficult) to show students that the more mechanical stuff they’re learning can be very useful and relevant in the real world, and not just for buying groceries or paying bills.
Perhaps I’m just arguing semantics?