Why do I have to study math?

     “Why do I have to study math? I’ll never use it.”
      I’m sure every math teacher has heard this question. It’s not easy to answer. I have heard several possible answers, but I’m not completely satisfied with any of them. I have a somewhat different reply, which I learned from - of all people - an English teacher.
      One possible answer is how important math is in the real world. Each of us has our favorite real world problems that illustrate the importance of math. But these problems seem contrived, and are not the problems ordinary people encounter. The book When Are We Ever Gonna Have to Use This contains math examples from nearly 100 occupations, but most of these merely use arithmetic or pre-algebra.
      Another possible answer is that many occupations require math, and a student limits his future options by avoiding math. My reply is that most students are not going to choose such occupations.       A third possible answer is that math helps us to think logically. But many people who are quite logical thinkers and good problem solvers know minimal math. If the purpose is to teach logical thinking, maybe we should teach logic.
      Here is my reply, which I discovered during a team project in an education course. I was teamed with an English teacher, and we were trying to find some common ground between us. To my surprise, she explained that when she analyzes a poem, she searches for various patterns in the poem.
      Searching for patterns? As the math person, I thought I had exclusive rights on searching for patterns. But then I came to an epiphany: We’re all searching for patterns. The toddler who tries to learn which behaviors will elicit attention. The physician who tries to investigate the cause of an illness (think of the TV show “House”), who is similar to the police detective who tries to solve a series of crimes. The art critic and the movie critic. (I once heard a movie critic explain that when the major character travels across a bridge, there is about to be a personality change.) The plumber who searches for the leak. I’m sure you can think of many others.
      We are all searching for patterns in life, and we do this with our own unique lens on we how we view the world. As math people we look for quantitative patterns. It seems to me that the more tools we have to discover patterns, the richer our lives are. I think students should study math to give them one more tool in their toolbox to discover life’s patterns.

Saunders, H. 1988. When Are We Ever Gonna Have to Use This. White Plains, NY: Dale Seymour Publications.

Math is math, except in social science

"So how are the eggs?" "Eggs are eggs." "Eggs are eggs. That is very profound. By the same token, couldn't you say fish is fish? I don't think so." 

So goes a Seinfeld dialog.  Similarly Sigmund Freud is alleged to have said, "Sometimes a cigar is just a cigar," although researchers question whether he really said it.

And by the same logic, math is math, whether it is taught in high school or college, a 2 year community college or a 4 year college, etc. Right?  I found a counter-example of this in statistics.

I recently taught an intro to statistics class in a psychology department using a statistics book for the behavioral sciences.  This book defines the sample standard deviation for descriptive purposes as S_X with an N denominator while defining the sample standard deviation for inferential purposes as s_X with an N-1 denominator.  I found a second statistics book for behavioral sciences that agrees with this.

Is there a recent textbook in the math or statistics world that defines the sample standard deviation with an N denominator?  I haven't seen it.  And not only will the student of this psychology class find this definition conflicts with the math world, but she will also find (and did find) it conflicts with the Excel world, not only for the Excel standard deviation function but for the Excel statistics Data Analysis add-in functions.

Why can't we all just get along?