Crying About Mathematics

I recently saw this image posted on Facebook and then looked at the last 3 posts from Grammarly, the original poster.  We have a think piece on whether universities should require writing proficiency for graduation, a joke about precision and exactitude in grammar standards leading to vandalism (with indications that that's at least understandable) and a prettied up quote from John Dewey that, "Education is not the preparation for life; it is life itself."  That last one is particularly interesting in contrast with this image and it leads to the obvious implication that what they really mean is, "Education (in the arts, humanities, and soft sciences) is deeply fulfilling and enriches life to the point of making it worth living, but of course we know technical sciences and mathematics are just painful things to be suffered through."

This is probably a good example of why US culture is so innumerate (the numerical equivalent to illiterate, a term coined by John Allen Paulos) and inept at scientific thought.  This is where we get the reflex of credibility toward the phrases "experts say" or "studies show" or the news stories that butcher or manipulate statistics to serve whatever purpose hits the emotional agenda of the story.  I'll be the first to admit (and then probably go on a tirade about the problem for however long you listen plus ten minutes) that our mathematics education is just heinous and obsolete to a point that would be absurd if it weren't so damaging and dangerous.  With that said the solution is certainly not to perpetuate the idea that these things are hard, stressful, and just generally unpleasant.

I've written here before about the nobility and importance of mathematics, and this one won't be the last time I do, so perhaps I'm just belaboring an idea, but I'm going to list out some of mathematics' virtues anyway.

• Math is Mind Expanding: Mathematics deals with concepts that can go beyond normal human experience.  How often do you work with the infinite?  Did you know there were several different sizes of infinity, and that some infinities are larger than others?  I had a very serious discussion with some family and friends recently about dimensional figures and the nature of God.  I wear a metal Möbius band (a strip that has only one side, yes really) on a necklace that was given to me by my wife.
• Math is Humbling: The humanities are important largely because they teach us to think emotionally, form opinions, and understand the human experience.  Math, and the sciences (though perhaps to a lesser degree), teach us to think rationally, examine our ideas, and understand the world around us and, yes, the human experience as well.  In mathematics one thing must strictly follow from the last and we must learn to abide by the rules of the operations we're performing.  We can form and idea or an opinion just as easily as we can in any humanities class, but then we're told to really look at that, to see if it makes sense in context, and it can become starkly clear when it's not.  Humanities often remind us that how we perceive and judge the world around us matters.  Mathematics, and the sciences, remind us that the laws of systems (like the universe) don't just bend to our will because we think we have a better idea of how things should be.
• Math Teaches Self Awareness: Like my last point, the requirements within mathematics that we "stay within the lines" as we progress form one thought to the next in our process of proving, computing, or deriving new information means we need to learn to watch our thoughts, and see where they fail to stay consistent with our principles.  Learning how we think, how one thought in the mind springs from the last and whether that process is working properly or in need of reform is pretty clearly an invaluable skill that will better society if widespread.

So if math is so wonderful, why is it so often denigrated, like in the image above depicting it as something that is sure to spawn sadness and strife sufficient to stimulate sobbing?  Why is this far from the first post to the effect of, "Ooh math really sucks, don't you all agree?" that has gotten shared around?  Why do people flaunt their ignorance or lack of active engagement in mathematics with phrases like, "I totally forgot how any of that stuff works, but hey I'm never going to use it again, right?"  Why does that receive knowing chuckles and appreciative nods instead of the derision or contemplative sadness such ignorance or loss of talent should garner ("I can't remember a thing about the Civil War, but who cares?  I'm not becoming a historian," "I used to be able to play the oboe, but now I can hardly even remember the basic fingerings," "Why did I even do all of that reading in high school?  I never ended up being in a Shakespeare play or even going to one.")?

Well, there are systematic problems.  Like I said we teach math horribly (in the US at least), especially at the elementary level which means that when children are forming their emotional understandings they learn early that math is something hard and to be feared.  It doesn't help that so many who shape the culture are also the worst at mathematics and mathematical thinking.  Still, none of these jabs at "that painful and useless old field, math" seem to present solutions or even raise awareness about the problems of media misrepresentation or the need for educational STEM reform.

I've been told that it's about thinking differently, that the jokes are just trying to say, "Oh man, my brain sure doesn't work that way," but mathematicians and scientists aren't sharing Facebook memes about how useless writing and art are.  The most I've seen are more along the lines of, "Boy it's really frustrating how misrepresented we are and how poorly understood and distorted our work is when presented for public consumption."  Also, I don't really buy that our thinking is all that different.  When I tutored mathematics the problem really seemed to be more about attitude.  People didn't put effort into learning or doing mathematics because they thought it was hard, boring, or just not important to them.  With effort they picked up the concepts just fine, but the attitudes that surround math made them reticent in putting forth that effort.

Math students have often been taught in what one teacher of mine referred to as the GMTED or the "Give Me The Equation, D***it!" mindset.  Try to discuss the concepts behind the figures, the real meaning of the numbers and symbols and they shut down and demand you give them a simple formula so they can mechanically plug numbers in.  Math education is too often a "human programming" job, using drills, memorization, and routines to create humans that will carry out operations to compute a value.  This must change, but can't if people believe that actually thinking about math is something they're incapable of because, "their brain just doesn't work that way."

So I beg of you, respect mathematics.  Let's leave behind the antiquated views of math as prima facie unappealing as we leave behind the systems that have made thousands fail to understand the beauty and wisdom it contains.  Let's elevate our understanding of ourselves by doing meditative mathematics.  Let's elevate our understanding of the universe by understanding the language in which God wrote it.  Let's create a society that values this great field of human thought and endeavor that's gifted us the computer, engineering, and so much more.  Let's create an intellectualism that, to paraphrase the apocryphal inscription above Plato's Academy, lets none but mathematicians enter; not out of elitism or to exclude readers, writers, artists, and other so-called non-math people but in recognition that a complete philosopher will be mathematician in addition to artist, reader, theologian, writer, and more as he or she embraces all the many worthy areas of endeavor in the vast yet limited expanse of human knowledge.

Technology, cheating, and the Augmented Mind

As a student I've been taking plenty of tests lately.  My university has a pretty good testing system and convenient testing centers and I'm a pretty good test taker so none of this really bothers me, but I have found the testing center policies interesting.  The fact that I have to remove my hat before going in is one.  Recently they've also disallowed the wearing of a wristwatch, almost certainly in response to the new smart-watch technology coming out.  While this is the right thing to do, it does indicate a need for much grander changes in both the way we do things as well as our thinking, probably especially in education.  Changes we are woefully unprepared for.

Let's consider the testing center again, perhaps as if you were the director of these.  We made the change for smart-watches so that they won't be used for cheating.  What will we do if Google Glass, or a similar project where data is displayed on a pair of glasses worn by the user, takes off and starts showing up?  If that technology becomes integrated into people's prescription lenses?  What about if those smart watches become smart tattoos?  What about when students start having direct neural interfaces integrating computers into the brain?  These problems are coming, and I think we can quickly see there's no easy solution, and maybe no solution at all to make a our current testing systems compatible with the existence of these technologies.

As my neuroscience teacher put it, most testing today is a simple demonstration of declarative memory.  This is to say tests usually require a simple recalling of facts, figures, or other basic knowledge.  However, the need for this to be done in the human brain is dwindling.  Facts can be more easily stored, more quickly recalled, and more reliably maintained in computer systems than in nervous tissue.  Why would we keep using cerebral circuits (that weren't really designed to do this in the first place) when we can use electronic ones?  The go to example is memorizing phone numbers, something many of us remember doing before technology made it an exercise in pointless exertion of energy.

Lest you think this is the pie in the sky omphaloskepsis of a futurist and science fiction fan, let me relay a story I heard from one parent.  He wanted to have his daughter writing letters, and specifically to do so using some specific vocabulary.  Shortly after he heard his daughter speaking out loud while alone in her room writing the letter.  Listening closer he realized she was using the voice recognition feature of the tablet/smartphone to simply ask for the spelling of the appropriate words.  This was much to his disappointment, as he was expecting her to look the words up when writing them and learn the definition along with the spelling.  That's how big a change something as simple as voice recognition is making.

A future where traditional testing is pointless seems on the horizon.  How education will or even can deal with this is unclear.  The problem with leaving our traditional testing is that other methods require more work to evaluate, and usually are less objective which can be a big problem for admissions tests like the MCAT.  The only solution I've thought of is an increase in internships and apprentice work, but whether or not this is feasible is unclear.  I know the major reason the radiology or medical laboratory programs at my school can't admit more than about 40% of applicant students is because they only have so many slots for clinical rotations available.  It could be damaging to the economy to have the influx of cheap or free labor that having five interns or apprentices to every one trained employee might mean.  The problem is a big one, and sadly I haven't seen it given all that much attention.  Let's hope for and work toward that changing sometime soon.

Thirty Years

Yesterday was my thirtieth birthday. As I leave my thirtieth year of life and enter my thirty-first I reflect on the passed year.  Year thirty feels as if I've been a plane that's waited at the gate, taxied up the runway, and taken off for a new destination.  Here's the highlights:

• Working at inthinc : I continued my job at inthinc technology solutions for the first part of the year.  This time taught me once again the importance of good management.  Our last manager was very skilled at keeping the support team of which I was a part happy and feeling valued within the company.  During the first part of the year we had no manager and a number of internal conflicts arose within the team as well as numerous difficulties arising from a lack of effective interfacing with the rest of the company.  Our new manager, when hired, eventually turned out to make promises like a politician, fail to inform us about and connect us effectively with the rest of the company, and make the talent feel undervalued. I was the third person to leave the team as the burden on our team increased and feelings of valuation decreased.  After leaving the company I continued to hear of hardships and found the company was losing money and talent at an alarming rate, though it seems to have stabilized at this point. I have a number of good friends from my time there, but am happy to have gone.
• Returning to University : Leaving inthinc prompted an overall career change.  I had noticed that the career trajectory in technical support would take significant time to advance and might not lead to a place I really wanted to be.  Looking at what field might be related to my previous scholastic experience in physics I found that radiology is something that would probably take about as much time to train in as it would to advance in my current work, had similar job demands at higher pay, and ultimately would be more fulfilling and interesting.  I enrolled at Weber State University and started attending classes. I was reminded how much I appreciated the university atmosphere and learning new material.
• Entering Medicine : Preparing to enter the field of radiography I've been learning about the medical field generally as well.  I trained as a phlebotomist and am making arrangements to test for my limited x-ray machine operator's license.  I have been fascinated by the challenges and nature of the medical field. There's an intriguing intimacy to healthcare that makes me feel a great deal of responsibility toward patients. I never thought that biochemistry would hold any interest for me but after studying it (in part at least) for a semester I've completely turned the corner and am engaged by protein structures and metabolic pathways.  There's clearly a lot to learn and do in this field and I'm eager to continue exploring it in year thirty one of life and beyond.

On Campus

Four years after graduating with a degree in physics I'm returning to school.  I've always loved learning.  New facts, viewpoints, and skills are a thrill to acquire and I'm ecstatic about the opportunity I'm carving out together with my wife to collect a new bushel of these in the field of radiology.  I'm counting down the days until classes start, and have already read the first chapter or two in the books I've bought.  I'm excited to be back on the university campus.

The campus, in particular, has turned out to be something I didn't even know I had missed.  When I walked around the campus recently to fill out financial aid forms and speak with an academic counselor I took in with glee just being on a college campus.  I adored looking over artwork and artifacts displayed in hallways and lobbies of the health professions building.  I enjoyed the bustle of the student union and looked over message boards to see if any clubs, bands, or activities would catch my interest.

The college campus is a great reflection of the community made up by a college or university.  So much of community is ethereal these days that the physical presence felt on a college campus is refreshing.  Being 'at the office' has this too, but so few workspaces also include socialization, recreation, or relaxation spaces in them as well.  All is devoted to getting the job done, whereas on campus the goals of creating a positive culture and promoting student interaction also seem very present in the consideration of the buildings and landscapes.

I also love the diversity of a college campus.  Diversity often refers to a high degree of heterogeneity in skin colors, sexualities, and other traits with which the human race sadly divides ourselves into factions, but that's not to what I'm referring to here.  I love that the art building is on the other side of the student union from the business school.  I like knowing the computer science building is across the quad from the mineral museum.  I love the diversity of opinion, of interest, of passion, of expertise, or of study represented by having buildings devoted to so many varied pursuits together in one place.

The university experience and the role of post-secondary education is changing rapidly in our society.  Online classes are quickly gaining traction and more and more people are realizing that the bachelor's degree often doesn't carry the same value it once did and may not be worth the price tag it often carries.  I support this and believe that post-secondary education and career training  needs to be more readily available in an assortment of forms (and that high schools need to teach more career training and less academic fluff seemingly only to fill the time until you finally go to college and learn something useful...hopefully, but all of that is a different discussion entirely).  That said, I hope there will always be a place for the grand college campus that seems to include a park or two, community message boards and meeting houses, and building after building devoted to disparate intellectual pursuits.

The family and the schools

I was thinking about prayer in schools lately. For the record I'm not for it, though being a spiritual individual I wondered why. I am at the conclusion that what I'm for is prayer in the family and that's many times more important and beneficial than prayer in school.

One reason for this is that it means I'm afforded greater control over my child's development and involvement in his or her life. I want to be part of my kid's spirituality, rather than have it dictated by whatever principle, teacher, or school board member would do such things. When the schools teach my kids to pray, or any number of other things for that matter, my kids are taught what the school wants them to learn, rather than what I want them to learn.

Exposure to other ideas is important, but it's not unreasonable for a parent to wish to raise a child with certain values. It's imperative, actually, to raising a child with any moral compass who grows up to be anything other than, well actually just a child who grows up. Without learning to follow a set of principles rather than be tossed to and fro by every whim and impulse a child never grows up, but I digress. I want to teach my child values, and don't confide in the schools to teach my child the right values or even to do it well if they did.

The hand that rocks the cradle rules the world, and so the issue extends to who do I want as my ruler. As a strong willed individual I only want myself, with my family in positions of power. Leaving the individual to be free means that families raise the children. A friend of mine teaches at the local high school, which isn't a great school. He was once asked, "How can you trust the school to teach your kids," and his answer was a simple "It's not the school that's going to teach my kids." He then mentioned that he and his wife has already taught their children some basic reading and writing skills, and he never plans to surrender all the responsibility of teaching to the school system.

I've always agreed with that sentiment, and as such only expect the schools to provide a good supplement for the teaching I and my wife will provide for our children. On my part, I know that some grammer, history, and literature will be something I want my kids to hear from someone more expert than myself. Still, though, I hope to be a part of my kids learning all of this, sharing and discussing the ideas. I might learn something myself, I might provide an new perspective for my kid to think about, or I might just help my son or daughter to better understand something new to him or her but well known to me. One way or the other, my child will learn something and I will be a part of it. That's the kind of parent I want to be.