Identification

There are many ways to identify a person.  Your place of work usually issues some sort of ID card, most folks get driver licenses, upon birth we all get a birth certificate and generally a social security card.  Any time I apply for a job, I have to produce these documents to prove I am in fact who I say I am.  Each of these cards is filled with a certain set of information about me.  Name, address, position I hold, sometimes a picture, date of birth, height, weight, all different facts that explain in a small way who I am.  I wear a bracelet with my personal information when I run, so if something happens, folks know who I am.

Each of these represent a superficial way for someone else to identify me, but none of these traits are as important as how I identify myself.  There are a plethora of ways that I do so, ranging from my intellectual pursuits to my hobbies and the people I spend my time with.  Sometimes life pushes us to identify ourselves with a group of people with whom we would not ordinarily be associated.  This can be both bad and good.  I've spent the last semester identified primarily as a student teacher to a group of high school students, which has been an interesting mix of pleasant and frustrating.  Other times, folks are pigeonholed based on a single physical characteristic that misrepresents who they really are.

One of the difficult things in life is striking a balance among all of the groups and traits I identify with.  Running is a stupendous stress buster and physical challenge, but if I give all my time to it, I will more than likely be injured and will lack time to pursue other interests.  If I only read for pleasure, I will get to experience fantastic stories and see the world through others' eyes, but I won't learn anything that I can use to sustain my physical life.  As much as I want my students to succeed, I cannot spend all my time for them, or I won't have time to personally grow and learn.

Another tricky part of leading a happy and fulfilling life is finding ways to identify myself within my comfort zone but outside complacency.  I began my college career as a computer science major, but realized after two years that I would be miserable if I pursued that line of work to retirement.  Inspired by teachers in my life, I switched to mathematics teaching.  About a year ago, however, I began to become discouraged by the politics poisoning the atmosphere of public education.  I have tremendous respect and hope for the future, because I know there are still brave souls battling on the the face of negativity, but I again realized that my current trajectory would not end in my happiness.  A burgeoning love of the study of mathematics caused me to begin to research graduate schools, and after a year more of classes, mixed in with recommendation letters, statements of purpose, and one standardized test, I was accepted to Bowling Green State University graduate school for the purpose of studying mathematics.  They also offered me a position as a Teaching Assistant, which will feed my satisfaction from helping others to learn, and I have accepted.  Beginning July 1, I will be happy to identify as a BGSU Falcon!

And so my friends, how do you identify yourself?  How do you challenge and change that identity to continue an upwards path to happiness?  I know that in this human life I will never achieve complete satisfaction, but the joy is in the journey, I've heard.  Let's journey on!

Support

This being the reflective time of the year that it is, and being close to the thankful time of year, has naturally got me to thinking about what I am thankful for.  I could fill a book with everything that I'm thankful for, though, so I'll just hit the biggest one.  I am thankful for my family.

I titled this post "Support" for a reason, you see.  Everything has to have some sort of support to do things, to exist.  Even invertebrates have to be able to support themselves enough to move around.  And everything I do, I know I have the full support of my family.  I ran a marathon this year, and who was there to help me hobble back to the car and drive me home?  They have a wide range of experiences to draw from for advice, and I know they'll give the advice and then support me whatever choice I make.

I can't say I always express my sincere and deep appreciation for each of them, and I may occasionally get angry with them, but in the end, I trust them and love them beyond anyone else.  My mum and dad bring the wisdom of years and experiences beyond my own.  My sisters grew up together and know each other better than anyone.  Having a little brother means I get to do all the things I wanted to do at his age now, and he's smart enough to keep me humble.  I don't see my extended family very often, but I know I can count on their support too.

As we bring another calendar year to a close, remember why you are where you are and who helped you get there.  Go give them a hug, just because.  I know I am incredibly lucky to have such a wonderful family.

Performance

I have been thinking about assessment recently due to discussions in my classes and my field experience at a middle school.  Educators split assessment into two general categories: formative and summative.  Formative are quick, informal checks of understanding, i.e. "can you evaluate this derivative?"  Summative are the more traditional quizzes and tests that occur after a unit of learning and result in something to be turned in and graded.  Most overall grades are decided by these summative assessments, but I have a problem with them.

Any assessment is really a snapshot of what people know at a specific time and place.  Students may know how to translate graphs for the test, but forget by the time Labor Day rolls around.  So can we truly say they know what they were tested on?  Assessments for nonacademic pursuits are the same way.  Sports stars are judged based on game-time performance, runners on race times, and artists on the critical reception of their work.  The issue is that these specific times don't show the full picture.  They don't include the hours of sweat, tears, and sometimes blood poured into an endeavor, just an end result.

I don't think anything can be put in a neat box like that.  As a runner, I compare myself to other runners via race times, but just because I am faster than a runner doesn't make me a better runner.  You can't see the failed runs, the physical pain, the rearranging of my schedule to accomodate a run in my race times. I can't see the years of consistent running, joy in finding a new place, or interest in running pushing a personal boundary in another runner's race.  As humans, we like quick and easy comparisons, for decisions to be a binary yes or no, black or white, good or evil.  But real life is never like that.

As a student, I have never seen what goes into a single lesson that I attend.  I don't see the written plan, the caffeine consumed, and the snap decisions made to break away from the plan.  I have a new appreciation for it as an almost student teacher.  As a teacher, I don't know if my student is focused on what I want them to learn.  I can't even be sure that they're starting with the knowledge base they're supposed to have.  So we both have to go under the assumption that the other has some idea of what's happening.

Real life is messy.  Maybe a student's personal life is going through some upheaval, or they couldn't get breakfast that morning, or they were ill and missed school for three days.  I guarantee they'll do better on an assessment if all those things went away.  Maybe the athlete just lost someone close to them, and they drop the game-winning run/TD/goal.  Maybe the runner next to me has been fighting an Achilles injury, and isn't running at 100%.

So why do we put so much weight on these snapshots of ability?  There is so much that happens underneath the surface of a single performance, from time spent to other responsibilities ignored to obstacles overcome.  Perhaps that's just the way we're wired.  Regardless, we need to appreciate that we can't fully see anyone else's perspective, and accept that for the most part, we're all just trying to do our best with the hand we were dealt.  Let's try to get the full picture before we make any assessments.

Mathematics

This semester I started tutoring for math at my university to maintain at least a little income.  Between that experience and most of the conversations I have with people when they learn what my major is, I have noticed a common trend.  It's something I was already semi-conscious of, but the idea has been hammered home in courses I'm taking now as well.  It is that apparently, no one likes math.  If I had to put a number to it, I would say 90% of the people I talk to in tutoring and about my major say, and I quote "Oh, I never liked math."

Obviously, this makes me a little sad, because I like math.  Shoot, that's not enough.  I think math is the bee's knees.  I think math is (or at least can be) the most beautiful thing in the world.  I want everyone to see math the way I do, but I know that's not possible.  So the question I must ask in return is, what do I see that this 90% doesn't?

As a senior in a mathematical education degree, I have taken more and higher level math courses at the university level than a great majority of people, but I don't think that is enough to explain why I like math when so many others don't.  I recently had to read an article for one of my courses that went along really well with this line of thought.  Paul Lockhart's "A Mathematician's Lament" is the article, and it is a fantastic read if you are interested by this topic, but I understand if you don't read it.  My own thoughts and Lockharts are pretty close together from here on out, so bear with me if I'm repeating what the article says.

Essentially, the reason why people don't like mathematics in our public education system is because they are not learning math.  "Hold the phone, SRC.  I learned math in school.  I mean, it has math right in the title of all the textbooks and the class itself," you may respond.  That's a fair reaction.  I stand by my statement nonetheless.  The "math" we are taught in school is a series of rules and formulas to follow.  We are given some "real world examples" in which the rule or formula of the week is always needed, but next week we might as well forget it, because this new week has a new rule.  We don't get to explore problems in which a whole variety of rules can be discovered simply by exploring the situation.  We are told what mathematicians of previous generations have discovered and given examples of where it works, so the what of math, but we never learn where those mathematicians got their ideas, or the why.

To me, public education doesn't ever move beyond arithmetic.  Arithmetic is built on simply adding one to itself (more or less), and subtraction, division, and multiplication are applications of that adding process.  Arithmetic is the machinery of all the rest of mathematics, the foundation upon which the towers of geometry, algebra, number theory, statistics, and many more are built.  So it is necessary to be familiar with arithmetic, but it's no fun to be drudging about in a basement when there are beautiful views to be seen from immense towers.

It's the equivalent of a builder being handed all the tools of the trade, but never getting the opportunity to, you know, use them to build something.  They are presented in a discrete manner (separated from each other) and only seen in use by themselves.  The builder gets a hammer, a nail, and a board, and drives the nail into the board.  Then that board is tossed out and forgotten, and the builder gets a saw and a new board, and cuts the board in pieces.  And so on and so forth with each tool in the toolbox.  The builder is tested to see if he can use each tool by itself.  Then he is expected to appreciate all the work that goes into making a house and to appreciate the beauty of how the house looks, but without actually building one for himself, just using the same tools as whoever built the house.

If we can't expect a builder to make a beautiful and sturdy house without some experience actually building, how can we expect students to appreciate and apply mathematics if they never get a chance to use it on a situation in their own lives?  Clearly, the builder needs to have a working knowledge of the tools needed (the basics, i.e. arithmetic), but they will build best and use the tools most effectively if they use them to achieve a means that they desire, not what someone else has designed.  No student of any discipline should enjoy being forced down a single road of understanding.  Why has mathematics been so cruelly curtailed?

People and Numbers

As a mathematician, I have numbers on my mind pretty often.  Even so, I find it interesting that in today's world, people are often assigned and identified by numbers.  Social security numbers, patient numbers, telephone numbers, employee numbers, bank account numbers...it seems every company wants to give us a unique number identification, because on a macrolevel, it's easier to manipulate and analyze numbers rather than letters.  E.g. we owe employee number 7 $52.28, to be deposited in bank account number 4, and we know it's #7's account because it matches his social security number.  I know I would fall into this trap of thinking of people as numbers at the carwash.  It was very easy to treat every customer interaction as another iteration of the same conversation.  "Hello, customer number (previous customer # +1).  You want that wash?  Great, and have a nice day!" (Repeat until end of shift)

Or when I'm running, I can fall into the dangerous habit of running by the numbers (mile splits or distance) rather than how I feel.  I've caught myself being disappointed I couldn't hold a certain pace for some distance before realizing that numbers are not why I run, but emotions are.  I decided to write about this, however, because of what I heard at my little bro's back to school night.  The new principal was talking to all these parents about how excited she was to work at this school, and how everyone should glad to be in this school system.  So, you know, typical please-don't-desert-us-for-private-schools stuff.  That's a whole other thing that I won't get into though.

She also talked about how she planned to improve the school in her term.  Most of this talk was focused on increasing the percentage of students who pass our annual standardized test.  And this is the part that made me a little angry.  Like I said, I understand this particular tendency, but that doesn't mean I like to see it.  I feel like she lost sight of the purpose of schools, which is to educate students.  I like to think of that as individual students, not just increasing a percentage or other metric.

One of the responsibilities of a good person is to see other people as, well, people.  I've recently started tutoring at IPFW, and the biggest thing the director of the tutoring service pushed on us tutors is to get our tutees' stories.  That is, connect with them on a more personal level than just someone we talked to to make our hourly wage.  I feel like this applies every part of our lives.  Don't talk about improving your school with a lot of numbers, because it makes me think that's how you see your students, as numbers.  Don't think about your performance at a job or hobby based on the number of hours you put into it, or the number of miles you've run.  Remember that we humans are an emotional being.  Appeal to that emotion and connect to each other (and ourselves) on a personal level.  It's not a question I like to ask myself, but a good question to ask is "How do I (or you) feel?"  Have I learned from this class?  Did I enjoy being outside on a beautiful day running?  Numbers have their place, don't get me wrong.  Nothing summarizes better than numbers, but don't let numbers sit in between you and other people.  How do ya'll feel today?

Adultness

There is no certificate for adulthood.  As a kid, I always figured that once you reached a certain age, you just knew things.  Like how to fix things when they’re broken, how to cook food for yourself, and what to do in every situation you face.  I don’t know how I was supposed to learn all this, maybe a big book or a long conversation with my parents.  Or maybe the government sent you a pair of sunglasses on your 18th birthday and all that knowledge was downloaded into your brain, Chuck style.  If you don’t get that reference, that’s a shame, because it’s a good way to be entertained.

As a toddler, I always wanted to be a little older so I could stay up “late” with my sisters and play games with, well, the older kids.  As a pre-teen, I wanted to be older so I could drive and play sports and have money to spend.  Now, when I thought I’d have my life all planned out, I’d like to regress a bit to around my brother’s age, when all my needs are cared for and my biggest worry is who I get to play with next.  Maybe I’m just a 9-year-old stuck in a 21-year-old’s body.

I’ll go ahead and confess that all this is rattling around in my brain because my sister, Blondie, just got married, and I just plain don’t feel old enough to be a brother-in-law.  It feels weird just to give myself that label.  Then there’s my 21st birthday, which occurred this past April.  According to most folks, this is an absurdly exciting day, as it’s when I can legally drink alcohol and gamble.  But again, these activities don’t fit with my definition of leisure time, or even what I should be allowed to do.  I also believe that if I’ve survived for 21 years without either activity, I should be okay for at least another 80.

However, 21-year-old me feels like I still have the knowledge and skills of a teenager, so why should I be deciding the course of the rest of my life (i.e. grad school? year-long road trip? get a teaching job? stay at the carwash? to name a few questions that frequently come up)?  It turns out that all those people I’ve looked up to my whole life face some of the same questions and fears and concerns I do, but as an adult, you just handle it.  My dad didn’t know how to act while participating in his first wedding as a father, my mom still has to look up recipes online, my grandparents sometimes struggle to keep abreast with news among the family and what the daily plans are.  The thing of it is, none of us have a playbook to read or consult, and we’re all just muddling along, making the best decisions we can based on what information we have.  So here’s to the dark, foreboding future, and being a help and example to each other as we walk on.

Today

I would like to share with ya'll something I've learned through observations of people at work, school, and just in general.  A couple recent events have got me thinking about, well, human mortality.  Which is a rather depressing topic of thought or writing.  But I'm not here to be a downer.  I have this theory about life.

It's actually pretty simple.  Each day, it's up to you to make that day a good day.  Don't get me wrong, not every day can be a great day, because some things happen in life that completely bring you down a notch.  However, on most days, the relative goodness of the day depends on you.  I read a quote once, a really long one I don't feel like reposting, that said "Life is 1% about what happens to me and 99% about how I react to it" or something to that effect.  I think those are words to live by.

I had a (former) coworker that one day was just in a terrible mood.  I don't know what was happening in his life outside of work that got him in that state, but he was bringing down the mood of the whole team.  I tried my level best to maintain an upbeat attitude, but it was difficult.  I don't always realize how my mood is affecting those around me, but if I'm always positive, I know I am a help and not a hindrance to my coworkers, friends, and family.

I think the biggest difficulty in staying positive is because it will involve change.  When I'm in a bad mood, that signals to me that I need to change something.  This can be range from going for a run, to moving my work to a different room, to eating a treat, to getting to bed early so I'm well-rested for tomorrow.  The problem with change is that very few people actively seek it out.  Most change is not as drastic or sudden as people expect though.  For example, the change from a couch potato to a fit, healthy person is not the flipping of a switch, but the sum of a thousand healthier choices.  The choice to eat an apple instead of cheetoes, to walk the stairs instead of the elevator.

That's really getting into a whole other subject, but it serves as a good example.  Being positive can help out another.  When I'm running, I make an effort to wave and greet the people I see, even if my eyes are crossing from exertion (a real thing, I promise).  I know I feel better when they smile and wave back, so why do the same?  I love the customers who talk to me as a person, not as a faceless carwash employee, and I love watching the kids light up when I draw a smiley face on their window.  So go out and be cheerful!  Smile at a stranger, give a thumbs up to the guy running on the side of the road, ask your checkout person how their day is.

A quote from Ghandi to close: "Be the change you want to see in the world."