When are we ever going to use this stuff?

When are we ever going to use this stuff?  Why do I have to study math? 


Common questions from students.  These questions usually come with at least a hint of disrespect, so I'm usually tempted by a snide quick reply, like: Probably never.  You don't have to study math...there's the door!   If my mood is more patient I might reply with some bizarre, artificial example the textbook, like: When will two trains meet? How much  is 5 hotdogs, 3 hamburgers, and a small coke, if 2 hamburgers, 1 hotdog and 3 small cokes cost $10? - or -  If you're in a rowboat 2 miles offshore, what heading should you take to get to the lighthouse quickest?  These are all good problems, but none of them really answer the student's question.


In general, instructors are quick to respond to these types of questions, and usually from a defensive posture. We've chosen mathematics as a career!  If the students are right, (that there's really not a "good" reason to take math), then we're sunk!  It's time for some real soul searching, and more importantly, a real meaningful answer to the question.  


There are as many answers to this question as there are people who teach or study mathematics.  My answer to this question is ever-changing and evolving, so check back with me in a few days if you want a different answer.  


Of course, if we do a little searching, we can find practical applications for almost any topic in mathematics.  The "why or when" questions will invariable pop up whenever we mention complex numbers.  One option here is to stand smugly in front of the class, strike the aforementioned defensive stance,  and state: "Complex numbers are used extensively  when working with partial differential equations, signal analysis, and quantum mechanics."  At this point it's best to quickly continue with the lecture before the students' eye rolling quits and they ask follow up questions.  My point here is that there really are real world applications for most math topics, but this won't satisfy many students.


This brings up another topic:  Do students really deserve a satisfying answer?  Is this one of those things "you'll understand when you're older"?  I think students do deserve, at least an attempt, at a satisfying answer.  It may be difficult to give a student, who just scored 12% on an Algebra exam, a satisfying answer, but I think they do deserve an attempt.


Here's my attempt:


I think it's a good idea to bring up some applications in different fields occasionally, but let's be honest....beyond arithmetic, a typical undergrad student just won't use mathematics that much.  According to the U.S. Department of Education, only 14% of post-secondary students were in science, technology, engineering, or mathematics.  100% of post-secondary students need to take some type of mathematics, and all 100% will need to use some arithmetic occasionally.  But what about complex numbers?  Algebra?  Calculus?  


People attend college for education, not for training.  The purpose of colleges and universities is not to train people how to do a job.  This is done at vocational schools or on - the - job.  There are parts of a university curriculum that might be considered as training, such as student teaching, practical nursing programs, physician residency, and others, but this is not the main purpose of the university or college.  The most important thing education can do for an individual, in my opinion, is to help that person become a better thinker.  If you can read, analyze, discuss, and think about an essay or novel, you'll be a better thinker.  If you can create a poem or painting, you'll be a better thinker.  If you can solve a problem using "non-real" complex numbers, you'll be a better thinker. 


Mathematics is a great tool to help teach critical and logical thought.  Even if mathematics had no practical application, a person who could understand and think about calculus or number theory has demonstrated an ability to think in a critical and logical way.  To be completely honest, other than arithmetic, which I try to avoid when possible, I rarely use mathematics outside the classroom, but I often use the critical and logical thinking I learned by studying mathematics.


We need to continue teaching and encouraging students to study mathematics, and we also need to continually remember why we're doing that.  I sometimes need to remember that my students and I are on the same "side".  I need to be completely honest with them and with myself.  "Good" math applications rarely show up in the undergrad classroom, so I make a big deal when they do, but more importantly, I often remind my students that we're here so we can learn to think, maybe learn to shift gears on our brains and think in new and better ways.


Too often I think we fail our students.  We teach them the steps involved in solving an equation, or which buttons to push to get an answer.  How can we help them to not worry so much about the steps, solutions, and answers, and help them become better thinkers?

Math; Suks or Doesn't Suck?

Math Suks!  
In 1999 Jimmy Buffett took some inspiration from graffiti he glimpsed in Key West,  Florida and wrote the song Math Suks.  Quick rebukes came from the National Council of Teacher's of Mathematics (NCTM) and the National Education Association (NEA), condemning JB's new song.  Also in response, an actress named Danika McKellar wrote a book Math Doesn't Suck to counter the damage done to young minds by Jimmy's song.


I quickly took Jimmy's side.  Although I'm a member of both NCTM and NEA, and I don't have anything against Danika McKellar, deep inside I knew that math really does Suk!  


To be fair, and with the risk of being a bit "Clinton-esque", I guess it depends on your definition of Math.  Math means very different things to different people.  Math to some means a classroom they were forced to spend time in while memorizing some arithmetic facts and a few formulas....I think most of us agree, that Suks!  We usually blame poor teachers for not making math fun, but that's a whole other can-o-worms that I won't open right now.  


Frustration is an essential part of any kind of real learning.  When you learn something new, the filing system in your brain sorts through all of your previous knowledge and experiences and tries to find a place to file this new info.  If it doesn't fit in to your current filing system, that means you don't "get it".  This means you need to rethink the concept, see it in another way, try something different.  When you do all these things, and you still don't "get it", you get frustrated!  This type of thing happens often when studying math, and it Suks!  


Teachers and professors are well known for quotes such as: "This is easy" or "Math is fun!".  Ms. McKellar, the Math Doesn't Suck author, has even said; "Math is sexy".  I agree, math can be fun and easy after you've made it through the frustration stage.  Sure it's easy, and sometimes fun, if you understand it!  I'm still working on the "sexy" part of math...I think I skipped that day...probably nursing a hangover after a Jimmy Buffett concert.


It's not my intention to slam NCTM, NEA, nor Danika McKellar.  They all have math students' best interest in mind, but shouldn't we at least attempt to be honest with our students?  Math does Suk!  Not "Math" the content, but learning math certainly does suk.  I enjoyed being a math student because I worked through the frustration, but the frustration Suk'd!  I have seen students in graduate school brought to tears, even Einstein has shared his frustration with math.  Did Einstein think math was sexy?  Does it really help students to tell them what they've been struggling with is easy or fun?  I guess this is a good idea if you really want to make them feel horrible, or if you're really trying to just piss them off.   Is a 27% on a math exam "sexy"? 
 Hell No!  Math Suks!...... and that's OK!  

Ten Arguments for Moving New Year's Day

My wife says I'm contrary and grouchy.  I plead guilty, so allow me to share:


1.) First and foremost, we should find a better day for "The first of the year" because there's really no good reason to have it on January 1st.  Our calendar is based on a solar year, so why not start it on a significant solar event?  The obvious choices would be an equinox or solstice, but I'm sure there's plenty of other good solar events.  Our calendar, for the most part, has been thrust upon us by Julius Caesar and then later tweaked by Pope Gregory VIII.  I'm sure they had good reason to start with Jan. 1, but it makes no sense today.


2.) We're a bit to overloaded with holidays this time of year.  This reason may also eliminate the Winter Solstice as an option.  


3.) My history's a little shaky, and the events are a bit confusing,  but some time ago, in a land far away, January 1st was "The Feast of the Circumcision".  Celebrating an event most of us would rather not think about, that occurred eight days after the birth of Christ.  An important event that would affect millions of Christian males for centuries to come, but it doesn't really conjure up the desire for a feast in my book.  This was also the day that Jesus was named, so at a later date, the Catholics changed the "Feast of the Circumcision" to the more palatable "Feast of Christ's Name".


4.) Generally we think of Winter as being the season that is at the end of the line with Spring being the beginning.  March 20th would be a perfect start to our "New Year".  Granted this causes several serious calendar problems....could we just shift our calendar ahead 79 days so that January 1st falls on what is now March 20th?  Probably not practical...but it would be better.


5.)  We've gone to great lengths to make sure our calendar coincides with the solar year.  Since the solar year is approximately 365.2425 days, we've invented leap years and even leap seconds,(as needed when we wobble),  to compensate for the fact that our Earth doesn't behave according to the integers.  So then why do we decide the beginning of the year as at some arbitrary day that doesn't relate to the solar year any any way?  


6.) Our main New Year's Eve custom has somehow become drinking excess amounts of alcohol.  Don't get me wrong...I'm not opposed to people enjoying excessive spirits.... What else are we supposed to do on the darkest coldest nights of the year?  I like the idea of the new year being a time for new beginnings, a time to look back on our shortcomings of the previous year and readjust for a better coming year.  For me, starting things out with a massive hangover doesn't bode well for the remaining 364.2425 days.  I propose we all continue getting drunk and nursing our hangovers during the short, cold days of winter, then resolve to sober up on a beautiful spring day, late in March...with a clear sober mind.


7.)  On a slightly different, but related topic, I would also like to propose that we start each day at sunrise.  Instead of the beginning of the day being Midnight, each day would start at zero O'Clock at sunrise.  Instead of driving to work in the dark during the Winter, we would always wake up at zero O'Clock and be to work by 1:00 or 2:00 every day.  This would pose some nightmares to clock and watch makers, but I'd guess it would eliminate early morning car accidents caused by darkness, and I would also suppose, eliminate quite a few sleeping disorders.  On March 20th, we would wake up a little early, and enjoy a fresh, sober, sunrise start to our new year, and promise ourselves we wouldn't drink so much during the dark cold nights of the upcoming Winter.


8.) Having traditions and customs are an important part of any culture.  New Year's Eve and New Year's Day are probably the most universal traditions on our planet.  But...If we forget the reasons for the tradition (If there ever was a reason), then it's time to move on.  


9.) This is really an extension of #2 (above). By the time Christmas is over I am sooooo sick of looking at tables and counters full of cheese balls, cookies, snacks, fruit cakes, and sausages, that I can't quite stomach another fattening feast.  New Year's Eve is just more of the same with potato chips, beer, and champagne added in.  On March 20th, we'll celebrate with a nice springtime breakfast shortly after zero O'Clock.


10.) I'm a contrarian.  I like to go against the grain.  I want a nice refreshing change!


Happy New Year!