Is Math Really Important?

Welcome to the math for teaching program blog

Picture of Andy Engelward

Andy Engelward

As the director of the Harvard Extension School’s Mathematics for Teaching Graduate Program I have been able to work with hundreds of current and aspiring math teachers over the past decade. I’ve had many interesting conversations about math, math education, and the nature and art (!) of teaching and learning. In this blog I hope to share with you some of the thoughts, insights, and questions that have come up in these conversations. I will also ask friends and colleagues to share their thoughts on these topics too and to contribute to this blog as well. If you have an interest in adding to our discussion, please get in touch.

As a starting point, let’s pose a question

What is mathematics really about, and why do we make students study it at all? Over the summer a somewhat provocative article showed up in the New York Times, written by Andrew Hacker, questioning the need for studying algebra. My immediate reaction was, “Here we go again.” It’s easy to ask the question about any particular topic in mathematics, and we all have stories of when students ask, “What’s this good for?”

Anecdotally, this question seems to hit math classes more often than history or English classes. Part of my response to this is that math is critically involved in so much of humanity’s progress that it is almost impossible to conceive of how we would have gotten this far without mathematics. Unfortunately, that hardly makes any one student feel better if they don’t believe that they are going to be adding to that progress in a scientific way themselves.

Then there’s the strength of mind argument—that studying mathematics contributes to building one’s brain muscle in a particularly effective way. A counterargument to this is that there are many ways to exercise one’s mind. Why do we ask everyone to run laps on a track if some students would rather work out by swimming or rock climbing?

Mandelbrot image

Fractal images: math, art, or both?

And finally, one of the most fundamental reasons to study math is doing math, exploring math, and creating math can be among some of the most enjoyable things that one does with one’s mind, full of fun, interesting twists and turns, amazing vistas, and clever connections. Done with students in a way that’s unfortunately not necessarily the norm, (i.e., not as simply a repetition of facts and formulas aimed at a conquering a limited set of tasks) math can be a joyful, creative endeavor, one that can be shared with friends and strangers alike.

So, here’s your first question ...

Why do we ask students to study math? And if you’d like to stick more closely to Andrew Hacker’s original question, why do we ask all of our students to study algebra?

Please feel free to comment here, e-mail me, or come to a math for teaching class at some point and follow up with a discussion of your own with some of the teachers you’ll find there!

Eric Gorenstein replied:
Mathematics is a language. As is inherent in all languages (or at least most, as I am no linguist and cannot confidently make this universal generalization), Mathematics is a complex structure of subtleties and nuances, slangs and formalness, abbreviations and quantifiers. We can describe objects and occurrences in a myriad of ways using Mathematics in the same way we could do so in English, French or German. Mathematics can be blunt and concise, or flowery and graceful. It can be circuitous or it can be elegant. In the language of Mathematics, there exist distinguishably different accents and dialects. I would go so far as to say Mathematics is the only truly universal language. If I were to ask a person at random off the street in Harvard Square “Can you give me an example of a noun?”, it would be a safe bet that person gives a correct response. If I were to then ask, “Can you give an example of an antanaclasis?” the likelihood of a correct response undoubtedly decreases dramatically. One need look no further than the dialog between Viola and the Clown in the opening scene of the third act of Shakespeare’s Twelfth Night for an example of antanaclasis, though I admit it is a bit more of an obscure literary object than noun. The difference between a noun and an antanaclasis is that the noun is a necessary component of the language, while the antanaclasis is merely used to accentuate the aesthetics of the language. Mathematics holds the same phenomena. Consider what would be necessary in learning a language to develop the capacity to understand a poem. At the level of introductory algebra there exists but a mere shadow of the linguistic freedom that occurs in copious abundance throughout higher Mathematics. This can undoubtedly make the subject of algebra seem at times droll and purposeless. That said, how can we develop an appreciation for the limitless depths of beauty contained within the web of intricacies of a language without first understanding its foundational structure? Algebra is full of “nouns”, and nouns are one of the basic building blocks necessary to understand and create Mathematical prose.
Anonymous replied:
Hi. Why do you think that at schools: maths and science became more important than arts? Why more hours of maths and science rather than arts? Why having good marks in maths and science became a priority for most of schools?
Leo De Velez replied:
Why do we ask students to study math? So that they will understand and be able to properly use the common conventions for describing and communicating human activities as well as the physical and imaginary world around him.
Aonymous replied:

Studying more math in high school allows a student to do better on the sat and have a better chance to go to college. College graduates usually have a better and easier life than non college graduates. Students that study algebra 2 do better on the sat than students who don't. 

Anonymous replied:
good that.
Deyanira Salazar replied:
What would our world be without math! Math can be so interesting and fun, that just having the opportunity to truly invest some time in learning mathematics is such a gift. Of course, not everyone shares my viewpoint on this, particularly students who may not like math at all. However, math is important and useful in so many areas of our lives. And, in particular, getting this point across to those students who may not see the purpose in studying math should be the goal of schools. Who knows? There may some hidden potential in some students that can be uncovered by a lively teacher who enjoys what he/she does. And, in actuality, there are many such students in our schools. Students who are hungering for more than the typical teaching of formulas and facts. Without math, our lives would be so boring. Think of all the gadgets we use on a daily basis...cell phones, computers, cameras, iphones, ipads, and Nintendos, to name a few. How could we ever have access to these things were it not for mathematics? Impossible! So why do we ask our students to study math? Math is fun and makes our world an exciting place to live.
Mike Gilmore replied:

The Math muscle analogy resonates with me, though I'm not sure there are other exercises that develop this strength in your brain. Running, swimming, and rock-climbing are all valuable exercises, but if you want to improve your running you have to run. You can study numbers in an applied Physics context or logic in a philosophical context but if you want to develop your ability to process numbers you have to do Math. I do think we as teachers can do more to bring to the classroom examples of how this is valuable to people who aren't looking to do Math explicitly in their chosen career. It seems to me most people are under constant bombardment from marketing that often involves numerical claims, whether it be trying to sell juice, drugs, or the next president. These are things that most are dealing with on a daily basis, so it seems like these would be a useful basis for classroom work. Maybe most teachers are already basing their class work on examples that are likely represented in their students lives. When I took Algebra I remember a few examples with apples and oranges, but mostly just the numbers and letters themselves.

Oliver Knill replied:

Why do we ask students to study math?

  • Mathematical thinking helps all other sciences and is a foundation for them.
  • In daily life, we have to do decisions which are often mathematical.
  • We pass through an industrial revolution which turns more and more to mathematics.
  • Modern technologies are tied to mathematical theories and techniques. Examples: a thesis in photography, or a math for teaching thesis in 3D printing.
  • Managing upcoming climate, energy, financial challenges requires mathematical models.
  • Many successful companies today made their living from mathematical ideas. Examples are medical equipment which can scan bodies, search engines which become intelligent, or cameras which can do face recognitions or stitch pictures to a panorama.
  • Mathematics is part of our culture. It helps to understand our history. See E-320: Math and History
  • Much of art is inspired by mathematics: pictures, sculptures or movies or music. A page on Math movies, or Novels can illustrate this.
  • It is exercise for the brain like running, biking or swimming.
  • It is fun. Working on a mathematical problem can be a form of meditation.
  • Mathematics is eternal. It is a science which is many thousand years old. Its truth does not depend on opinion, fashion or belief. It will be done also in thousands of years.
Nguoi Phan Bien replied:
I like math. But the question here is: "Why do we ask students to study math?" First, I think we need to separate numeracy from math. Many accountants have excellent numeracy skills but in fact are afraid of math, if we understand math skills to mean the ability to deal with very abstract concepts (which is the nature of math), and the skills to solve these very abstract problems using particular techniques such as calculus, vectors, matrices, inferential statistics, etc. We muddle the water by lumping numeracy with math; these are two very different things. Case in point, many math professors do see a need to hire accountants to file their tax to the IRS. By the same token, many accountants do not see a need to learn much math beyond basic algebra. I don't have the answer to the question "why do we ask students to study math?" but I do think we can only start having a good conversation on this question by NOT lumping numeracy with math.
NELIDA replied:

Yes, Mathematics is one of the important subject to learn. We can use it and apply in our everyday life as well as in your own way of thinking. Its the practical way to learn and it will show how your thinking works.

Anonymous replied:

Hi, I agree it can be enjoyable but not to everyone. Math had a negative impact on me as a child. It was a nightmare that shook me. Schools should not be cruel in teaching advanced complicated Math. Thank you

edward r chaplin replied:
The question posed is why do we teach students math but perhaps we should not worry about the why but realize that in fact we do. With the reality that we do require each student to learn math, the more important question is not why do we do it? but rather can we do a more equitable job of teaching math. No subject in schools today have a greater negative impact on young students and their self esteems. Without any factual data at my disposal, I think everyone would agree with these generalizations: 50 years ago less than 10 percent of students had success in Algebra One before 9th grade, while today perhaps as much as 70 percent of students have success in algebra One prior to 9th grade. In fact maybe 10 percent or more of today's students have success in Algebra One in 7th grade. If this is true, then an outcome of 50 years of teaching strategies is that 90 percent of the students in the 1960 and 1970's perceived themselves adequate in math entering high school turned into 30 percent of our young students that feel totally inadequate in math entering high school and mostly left behind in our education system. If we tracked high school dropouts, would we find that 90 percent of them were part of the 30 percent that entered high school without success in Algebra One. What percent of our jails are populated with students who had success in Algebra One prior to high school and how does that percent compare with the percent that did not have success in Algebra One prior to high school. If the stated goal of 50 years of teaching strategies is to teach Algebra To All, then we must find a way to do it better. If society is saying that math is that important then we as educators are leaving students behind and at a much earlier age than 50 years ago.