What I Learned In College
Yesterday, the University of Washington finally mailed me my diploma. A Bachelor of Science in Applied Computational Math and Science: Discrete Math and Algorithms. I learned a lot of things in college. I learned how to take tests and how to pinpoint exactly what useless crap a particular final needed me to memorize. I learned that math is an incredibly beautiful thing that has been butchered so badly I hated it all the way until my second year of college. I learned that creativity is useless and all problems have one specific right answer you can find in the back of a textbook somewhere, because that's all I was ever graded on. I learned that getting into the CSE major is more about fighting an enormous, broken bureaucratic mess than actually being good at computer science. But most of all, I learned that our educational system is so obsessed with itself it can't even recognize it's own shortcomings.
The first accelerated program I was accepted into was the Gifted program in middle school. I went from getting As in everything to failing every single one of my core classes. Determined to prove myself, I managed to recover my grades to Bs and Cs by the end of 7th grade, and by the end of 8th grade I was back up to As and Bs. I didn't do this by getting smarter, I did it by getting better at following directions. I got better at taking tests. I became adept at figuring out precisely what the teacher wanted me to do, and then doing only that, so I could maximize both my free time and my grades. By the time I reached high school, I would always meticulously go over the project requirements, systematically satisfying each bullet point in order to maximize my score. During tests, I not only skipped over difficult questions, I would actively seek out hints in the later questions to help me narrow down possible answers. My ability to squeeze out high grades had more to do with my aptitude at filling in the right bubbles on a piece of paper then actually understanding the material.
I fantasized about attending college, where I would be judged on my intellectual prowess, and not on my test taking skills. I longed for the pursuit of knowledge in it's purest form, only for this dream to be completely and utterly crushed. Instead of a place free from the endless battery of tests I had been subjected to during high school, I quickly realized that college was nothing but tests. I once had a math course where 95% of my grade was split between a first midterm, a second midterm, and a final. By the end of my second year of college, I simply stopped attending lectures. I could teach myself the material out of the textbook, and went to class only to take a test or turn in homework. I earned my degree by becoming incredibly adept at memorizing precisely which useless, specific facts were needed to properly answer questions. I was never asked nor told how to apply these to real world scenarios.
Thankfully, in one of the last classes I actually attended lecture in, the TA teaching the class said something that sparked a epiphany in me: “Math is simply repeated abstraction and generalization." Suddenly, I was able to connect math and programming, and began to realize that I had loved math all my life. What I hated about math was the trivial nonsense they taught in middle school. I signed up for the most advanced math classes I could get away with, even when I could barely pass them. I began to realize that the most important thing these classes taught me was what I didn't know. Once I knew what I didn't know, I could teach it to myself, but only after I found the holes in my knowledge. You can't fill a hole if you don't know where it is. I didn't know what combinatorics was until it was mentioned to me by that TA; Chrome still doesn't think combinatorics is even a word.
Everyone finds the beauty of math in their own way, but we teach it like an automated assembly line of cars. Math is taught as some kind of rigid tool, when it is really a language for expressing logic, one with multiple dialects, each with their own personality. We invented music to express emotions that cannot be described; we invented math to express logical abstractions that defy explanation. Every tool in math is like another instrument in a grand orchestra, each note echoing off the others, reflecting a whole that is greater than the sum of its parts. Some composers prefer the string section, others prefer the woodwinds. There is no single right answer, only different ones. Instead of giving our children a brush and telling them to use their imagination, we give them a coloring book and grade them on how well they stay inside the lines.
I mean, we all know creativity is overrated. It must be, since we systematically destroy it even when we try to encourage it. It doesn't matter how many programs we fund for encouraging things like art and music when the kids are still ultimately judged on how well they follow instructions and fill in little scantron bubbles. Kids are not stupid. I cannot believe how many adults still think they can get away with telling kids one thing and then doing another. They know what you're up to. They know the only thing the school system cares about is their grades, and that their grades are based entirely on how well they follow directions. They know that answering a question “almost right” doesn't matter. They know all problems have one answer in the back of the teacher's textbook, and their job is to figure out what it is. The vast majority of them have absolutely no idea how to approach a problem that has no correct answer. They don't know how to judge the correctness of a solution, because in school, everything is either right or wrong. All they know how to do is guess how likely it is that their solution is the solution the teacher wants, not how well the solution would actually work.
This is, of course, completely contradictory to everything in life. Life does not have answers in the back of the book. Life does not have a single correct answer to any problem. There is no right way to do anything, there are simply pros and cons. The fact that many people continue to delude themselves into thinking otherwise is a sad symptom of this issue. Our obsession with tests has trained a generation of robots, not engineers. They're more skilled at working their way through a bureaucracy than designing rockets. Then again, considering that colleges have now turned into enormous, obstructive bureaucracies, perhaps this isn't entirely a bad thing.
After all, with only 160 (now 200) spots open in its CSE major program each year when it has over 27000 undergraduate students enrolled, the University of Washington gets mighty picky about who they let in. After getting a 3.7 and 3.4 in my first two calculus classes, I slipped and got a 2.8 in my third math class, so despite the fact that I got a perfect 5 on the AP Computer Science AB exam and was qualified to skip both introductory programming courses, they rejected my application and demanded I take Matrix Algebra before letting me in. So I got a 3.9 in Matrix Algebra (a grade that was exceptionally good, according to one professor), and then… they still didn't let me in. They complained that my entrance essay sounded “too cocky” and had me take the second introductory programming course even though I already had credit for it. When I failed to get an exceptionally good grade in that class for all the wrong reasons (like being graded down for having both too few comments and too many comments in my code), I simply could not bring myself to compete in a hyper-competitive environment where the only thing I was judged on was how many irrelevant details I could regurgitate. So, I majored in Applied Mathematics and simply took all the condensed, non-major CSE courses instead.
This obsession with tests extends into the evaluation of the educational system itself. One of the reasons nothing is getting better is because we use the very thing that is wrong with the educational system to judge it. We fill out ridiculous polls made out of those same interminable bubbles that are destroying the curriculum. We introduce more standardized testing. The entire system is completely obsessed with tests, and yet the only place that tests actually exist is… inside the system itself. Education has become so enraptured with this imaginary world it has constructed, it's completely forgotten about the reality it's supposed to be teaching kids about.
Kids know this imaginary world has nothing to do with reality. We lament about how to teach kids math when they refuse to understand it, without realizing that they are simply applying the same method of learning they use in everything else - memorize useless facts, then regurgitate them on a test. The reason our math curriculum is failing so badly is because in math, you can't simply memorize things, you need to understand them. Consequently, Math acts as a canary in the coal mine for our entire educational system. Kids make no effort to understand anything, because they aren't graded on how well they understand concepts, they are graded on how well they memorize random, useless details and follow directions.
We live in a world being overrun by automation. Any task that can be reduced to simply following a set of instructions over and over is being done by robots and software. This constant attrition of jobs involving menial work and physical labor will continue at a steady pace for the foreseeable future. We are teaching our kids skills that are being made irrelevant in a modern economy. We are preparing our children for a world that no longer exists. At the same time, while I could write a series of blog posts outlining an effective educational system, it will never be implemented in public schools. The establishment is too deeply entrenched. Foolish startups repeatedly and continually attempt to “disrupt” the educational system without realizing just how laughably outmatched they are. This is not something you can fix with a cute website. People complain about global warming, space travel, all sorts of adorable little problems, but miss the elephant in the room.
The greatest challenge our species has ever faced is the educational system itself.
That was one of the most succinct, forward thinking posts I have ever read. I wasn’t even through the second paragraph and I had already told Tanner I wanted him to read it.
Spot on post. It was magnificent.
I'm flattered :D
Found your post on Reddit. I'm a university math professor and I would like to share this with my calculus classes this fall, if that's OK with you. Please know that there are a lot of us profs out here who totally agree with you and are trying to do something about it.
It's totally ok with me for you to share this with your calculus classes.
I've had professors and teachers who have worked against the system. I had one teacher in high school who got fired because of it. I don't believe that the teachers and professors can actually fix a system that is working against them when the system itself is so fundamentally broken. There are very deep, fundamental issues with society itself that must be addressed, and I fear those are things that teachers alone cannot fix.
So what do u propose as a possible alternative?Dont just bash the system without offering a possible alternative.Your like those logging protester who go on protesting with signs made of wood or occupy wall streets folks yet they barely offer a possible alternative!Not that am bashing u or anything...i mean the system is fucked but offer an alternative...something like the venus project..i hope ur familiar with that.Nice article either way!:)
I do have alternatives, but they are too complicated to accurately explain in just a few paragraphs, and as I mention in the article itself, they don't matter because the current system won't allow them.
I don't disagree with you, but do a follow up. My view is that the current 'educational system' has too broad a mandate. How can the any system offer equal opportunity to all while also adressing the 'needs' of individuals. Seeing a problem is a first step, and since I believe that the answer to this particular problem is many solutions with narrower scope, every answer may be part of the solution. I'd love to research and discuss the issue with you and post an alternative or opposing position whatever the case may be.
do you think you will write about your alternative ideas later on ? I'm deeply interested in the subject (although not knowledgeable) and would enjoy reading other people point of view. Maybe you know some references or essays too.
Anyway thanks a lot
I too would appreciate your ideas for a better educational paradigm.
We must bring great ideas into the forefront of our thoughts in order to begin navigating towards those ideals, however slowly they come to fruition.
I am a recently graduated public high school refugee attempting to negate the negative aspects of my schooling. It really all comes down to curiosity, creativity and imagination.
I am hesitant about publishing my alternative ideas, because they are just wild theories I have, and ideally I would want to do actual research into their effectiveness before advocating any of them. I'm a scientist, I want to work with experimental data, but obviously I just got out of college and am nearly broke, so I can't really do any real research towards this.
I may publish a number of my alternative theories later with a big fat "I HAVE NO IDEA IF ANY OF THIS WOULD ACTUALLY WORK BUT MAYBE WE SHOULD TRY IT ANYWAY?" disclaimer on them.
My main comment is below but I wanted to cut and paste it here so I can tell you something very important: please read this( and thr linked pages within): http://lesswrong.com/lw/c3/the_sin_of_underconfidence/ . You DO know something so you ARE justified in being confident about your ideas, don't be afraid to present them. Yes you are going to be wrong and naive about this and that but a guarantee anything you can spit out will be a whole much less crappy than the current system.
Great post, but I'm finding myself understanding a lot about what's wrong and not a lot about what should be done instead. I have read that Mathematicians Lament PDF that you probably know about and came out with the idea that math is the "art of ideas" which summaries some kind of warm fuzzy feeling, but even with his and your writing, if some one asks me "alright, why is math great then?" I'd be startled and not know what to say. I have a few minor things like explaining that "X is made of waves" is confused, since to say something is a wave is a purely mathematical statement about X's behaviour, but it's not much on it's own. So could you please provide some examples of ways to improve the system, or perhaps make that blog post anyway, since it would be valuable to me in my efforts to "enlighten" my friends. Don't just give up because you can't fix everything at once. enlightening 100 readers so that they can go through life with and passing on these understanding. It's easy to rant, but hard to step up and lay out a series of improvements, so do it if you can! What's trivial to you others are obvlivlious to.
Great post man! I would recommend to watch the documentary "Waiting for Superman" to discover some alternatives methods of education.
*I learned that creativity is useless and all problems have one specific right answer you can find in the back of a textbook somewhere, because that's all I was ever graded on*
I feel like this has more to do with the courses (and professors) you selected than anything else, because this certainly wasn't my college experience. I still remember the first professor who told me that "If your plan is to repeat the case study back to me across five pages, you're probably going to fail. I have 80 students and I don't like to read the same paper 80 times. You don't learn anything, and I get bored. If you want an A, your paper will be a truly original thought, something that could be developed into a publishable thesis."
Sure, I also had some profs where education was a self-service affair, who cared about educating only so much as it paid for their graduate studies, but I also had great professors who cared about a true education.
I'm slightly exaggerating so I can make an effective point here. I did, occasionally, have some really good professors, like that TA I mentioned who sparked my love of mathematics, and one brutally difficult english class that had absolutely no standard "tests" of any sort (but I still managed to get a perfect 4.0 in that class because I actually remember how to do things other than take tests). However, the vast majority of it was just a sickening regurgitation of concepts, even in classes like comparative literature, where we were "studying" surrealistic art as an expression of creativity in the most un-creative way possible.
I understand your frustration, yet can never empathize with you as much as I'd like. I went to design school, a different beast, but one still constricted by getting students across the line. The resources are just not there a lot of the time. The faculty's hands are tied, by strings reaching higher than one would either like, or imagine.
I feel if you can't succinctly get your alternative ideas across, then perhaps they're not as considered as they could be. Infact, if they're alternatives that you're admitting won't work, then aren't they just pipe dreams? Nothing wrong with publishing these: dreams have their uses, banners to form under, but maybe energy would be better spent on baby stepped agents of change instead of elaborate idealist overhauls and restructuring. As a adamant idealist myself, it's a thought I never like to admit. Never the less, the world is always hungry for new ideas, especially ones that beg questions.
I think a possible vector of interest would be education about education. Give students an awareness of the issues at the ground level, something as simple as having 1st graders asking the teacher "why are we doing this?" ad nauseum
until the teacher themselves are filled from toe to brim with the same burning question. Kids like me and you often don't care about these things until we're through the gauntlet; the blinders are on when we're running it. But I remember a time when no blinders were on, when I was an obnoxious questioning youth at an age where grades and performance didn't all that much matter when my future was concerned. It's that time, I feel, when you can rile up a bit of care in students about what they're actually doing and participating in daily. Put the pressure on from the ground up, the top is too strong, yet without the bottom, they're gone.
I am hesitant about publishing my alternative ideas precisely because I haven't had time to develop them as much as I'd like. I'm not confidant that they will work, they're just directions to investigate. You have already brought up many of the things that I would suggest, but I don't have a single coherent solution, because I don't have the experience necessary to figure it out. It's a really big problem, and I don't think I could solve it myself.
Overall: great post, and I agree with you on most points.
That said, you are way, way too dismissive of global warming and space travel as serious issues. Yes, you can make the argument that education is a blocker on these issues because without educated individuals we can't solve global warming or space travel. However, you can make the exact same argument about, e.g, campaign finance reform, without which it's highly unlikely that we can reform our educational system. You can even make the same argument in the opposite way by saying that if we don't solve global warming we won't be around long enough to solve the education problem. I think it is unreasonable to claim that any one of those four issues is the most important, and that's not even bringing into consideration other issues like nuclear proliferation, structural employment decline due to automation, etc, etc.
Is education a hugely important issue? Yes, absolutely. Is it the greatest challenge our species has ever faced? Probably not, and your hyperbole there is likely to cost you potential allies.
I seriously, honestly think that education is a bigger problem than global warming and space travel because we are currently unable to make significant progress towards those problems because of the educational system itself. A bad educational system hinders our progress in EVERYTHING, and consequently it is by far the most pressing problem we have, even if we refuse to recognize this.
I just wanted to say that I really enjoyed this.
Hi Erik, I shared your sentiment in early high school. In high school, all anyone cared about were the three acronyms: GPA, SAT, ACT. I don't think classes really fostered a whole lot of creativity.
However, this did not discourage me from attending classes and achieving good scores, because I realized that the classroom environment's primary purpose is not to improve one's creative thinking, but to either 1.Develop one into a well rounded individual, or 2.Give tools that can be applied with creative thinking. Because I understood the goals of the classroom environment, and having experienced the Japanese education system (which is much more test centered - search "juku" or "yobikou" or "ronin"), school was something I looked forward to.
I am reading the comments and I notice that these folks are asking you to offer up an alternative solution to this so called "Race to Nowhere". You don't have to, because you are trying to address a problem that does not exist in the way you think it does. As I stated above, the classroom environment is not there to foster creativity. Creativity is encouraged, fostered, and expanded in the project environment. In middle school, high school, and undergrad education, that means clubs, like the FIRST Robotics Competition, Odyssey of the Mind, Engineers Without Borders, Formula SAE, and many, many other clubs. In grad school, that means research as you and your team try to expand the frontier of human knowledge.
What we learn in school is useful. Tests are good at determining whether you have at least attempted to understand the material they gave you. Clubs, teams, projects, and research opportunities demand that you know the material, and will teach you how to use the tools learned in lecture to solve real world problems.
Creativity isn't something one learns in lecture. It's something one practices in producing an end product. And unless people understand that fundamental difference, they will never be satisfied with their academic education.
My entire point is that what we learn in school is becoming increasingly not useful. We *must* teach kids creativity in school because as computers become ubiquitous, the only useful tool we have as human beings is creativity itself. Everything else can and will be automated. When jobs or activities demand we know the material, we can just look it up on wikipedia. We don't need practice memorizing things anymore because we don't need to memorize anything. We have the internet. We need to learn to solve problems and apply creative thinking, not simply memorize reams of facts.
If you don't think the current school system has a problem, you need to think about where we are headed in the future.
Recently, I think there's some mathematical reawakening amongst the engineering majors (myself included). It always excite me to see how other engineering majors view pure math, since on the outside, they seem like the opposite end of the spectrum. The two opposing views are: the majority "pure math is useless and I don't care about it", and the minority "I am finding myself drawn toward this seemingly useless endeavor because it's so logically beautiful and God help me apply this to the messy world we live in." The minority are probably people who wound up in a pure math class because they got too curious (myself included).
Very refreshing read and I look forward see more of your views! /)
I dislike doing pure math because it's proving things and I have no interest in this. What I like doing is investigating what mathematicians have already proven and try to find useful things to do with it, which is why I consider myself an Applied mathematician.
I really enjoyed reading this piece.
While it's nowhere near a complete solution to the problem, I'm going to rephrase something you brought up in your article as a possible improvement. Once students are made better aware of how relevant and useful mathematics and abstract science theory really is, they'll be willing (perhaps eager!) to slog through the material. Future classes (and evaluation) on these topics need to move away from rote memorization and regurgitation of facts, to creative uses of the theory in solving interesting practical problems.
And as an applied mathematician by training myself, I'm trying to follow through on this idea. I’ve started working seriously on an applied math and mechanics education resource that tries to use interesting applications to motivate abstract theory. If anyone is interested in helping out or have ideas to share, I’d be delighted to hear from you.
I've been working on ideas for teaching abstract math concepts to very young children that introduces them to concepts in such a way that it builds a much better framework for things like algebra and calculus. I may detail them in a later blog post.
This is the best post I've read this week. I admit that I never got as high as you in the education system, I just couldn't take all the negative points you listed and I ejected myself as soon as possible in order to program in the real world and I only look back because sometimes I get mighty hungry for some math or algorithms, but then I remind myself that I can teach those to myself. There's so many options to do so.
Your post should be read on national television morning, noon, and evening until more people see how something so very fundamental to society is so rotten.
My parents wanted me to get a degree so I would have something to fall back on, and were willing to pay my tuition.
I'm glad you've written this. I have just recently graduated from a university in UK with a BSc in Computer Science and I was working on a blog entry that was pretty much saying the same stuff you've mentioned here; except, I'm not a terrific writer and it wasn't coming along smoothly.
I'm now putting my thoughts together on what a solution might look like (for higher education) from a very abstract point of view. But the scale of the problem, in my mind, is astronomically large. The solutions needs to dig deep and go all the way down to kindergarten level. It needs lots of money and great people.
Anyhow, I'd be interested to discuss the problem/solution-space if you're ever up for it.
You are approaching this problem from the wrong direction. Any reconstruction of the educational system must function on a bottom-up approach if it's going to get anywhere. Find a better way to teach the fundamentals (which is what i'm working on), then build on top of that.
This was a great read! It hits on all of the points that I've been reading and hearing lately about how our school system is not designed to create smart people, but rather worker bees -- people who do what they're told.
I felt the same way as you all throughout school -- it wasn't challenging, I learned quickly to put in the minimum effort to get As so I could go about the rest of my life -- only going to class as necessary. Never had problems until grad school, and even then I just had to learn to manage my time differently. Now I work in a large corporate environment, and it feels like I'm back in high school -- mandatory attendance, do what I'm told (without feeling the full impact of anything I do), and nothing remotely challenging. I just come in and do what I'm told each day.
I'd love it if we had an education system that encouraged creativity, entrepreneurialism, and independence -- at least for the individuals who are interested!
I could never work in that environment. I'd rather live in poverty than put myself through that.
Haha, for a job it's not so bad. The people are nice and my boss is pretty cool -- he's always trying to make sure that the projects are interesting and everyone has enough autonomy and that sort of thing.
Still, though -- I do have to agree. Some people are into it, but I'm just not the type to be happy stuck at a job like this -- I told my girlfriend at the time when I started the job that I'd be depressed about doing this for the next 40 years!
But it is a blessing. It finally gave me the kick in the ass I needed to come up with a good business and get out there to start making it happen -- plus the steady funds each week from my paycheck to fuel my endeavors. I don't plan on being here forever -- just long enough to make something better happen.
I agree that their are major flaws in education as a whole but I think far too many people over generalize the way you are. I think that many schools are crappy and should be avoided but some are amazing and awesome places to learn.
My biggest issue. Is the way you say higher education doesn't foster creativity. At my university creativity is huge and in high level math and cs classes teachers openly encourage students to come up with new and unique ideas and ways of doing things. I agree that their are many schools that dont do this but as a student or parent its your job to recognize when a school is not doing a good job and to find a better one. If a student actively believes that they are only learning how to fill in bubbles and make good guesses they need to man up and find a better school. Also on a sude note I've never taken a scantron test at university.
If parents and students stand up and refuse to attend schools that work the way you claim yours have the system will correct itself. Great schools will get more money and grow and bad ones will wither and die out. Blaming the system is just a way of pushing the blame off yourself.
Hello great article,
I'm really curious about what of if the teachers see the wholes in the education and know about the problem but they are working for the university and they want to help but somehow they are afraid to lose they job or don't want to get to troubles.
Richard, this is what tenure is for. Tenure more or less guarantees teachers their jobs. They're supposed to challenge the status quo and do something outrageous.
A lot of times at research schools (like UW) that shows up in their research more often than their teaching. But many faculty members bring their research into their classrooms, and most (if not all) involve students on some level, though this is sometimes restricted to graduate level students.
My advice for anyone pursuing an education at a research university is to get involved with a research project that excites and interests them. It's a -great- way to learn, and also a good way to help you score a job after your tenure ends.
Erik, what are you doing now? May I use this as a guest blog post on my blog...great topic for a bigger discussion.
I'm working on personal projects.
Sure, you can post this wherever you want, so long as it's reproduced in its entirety.
Thanks for putting this out there.
Good observations. Recommended reading: The Aims of Education by A.N. Whitehead and A Mathematician's Lament by Paul Lockhart.
I also recommend teaching in some capacity (inside or outside the system) before embarking on a project of educational reform/reconstruction/revolution. My opinions about what's *wrong* with the system have been essentially the same as yours for a long time, but my ideas for change--and more fundamentally what sort of experiments should be done to figure out what works--have been altered drastically by my experiences teaching.
This is why I am extremely reluctant to discuss possible ways of reforming the system. I don't trust anything unless I've had a chance to experiment with it. Anyone who just says they can up and fix the educational system has missed the part about this being an extremely complex and difficult problem.
As somebody working to change educational systems through school leadership, I would agree that just rattling off random thoughts about how the system could get better without the background knowledge would probably not be that effective (as you've pointed out). That said, what WOULD be very helpful to people like me and other educators actively trying to improve on a faulty system would be to start writing on concrete ways that we could TEACH MATH DIFFERENTLY. I was a math teacher. I taught it horribly for years until I realized that math was simply a tool for understanding abstractions - a "tool that helps you do cool, useful things" - and that changed how I teach. That said, few math teachers actually have the depth of knowledge that you might have about the subject - and all the useful, creative pieces that exist - so if you could start posting thoughts on how we could teach math in a fundamentally different way . . . THAT would be helpful. Because that's something individuals could implement in their own schools and classrooms, in spite of larger issues with the system.
So. We have plenty of people making sweeping generalizations about "improving education" without doing the work, themselves, and that's great, but not always helpful. What we do need, though, is more folks with real expertise focusing on specific chunks of the system that could be changed piece-meal without requiring sweeping, whole-level change. Because those are the things that might legitimately gain traction and start to change how we think about and DO education - which is what it will take for change to take place. Change is not impossible. The system is entrenched and there is a lot working against us, but patience is necessary. We have to begin enacting change in our thinking NOW, so that we can hope that a generation after us, the system is improved.
There are a lot of us trying to do things differently, but we don't even know what "different" could look like, half the time. You seem to have some thoughts on what "different" could look like from a math teaching perspective, and we need to know what that would look like, so we can try to implement interesting, new ideas. I, for one, would love to read that - and am in a position where I could actually push to implement it in real schools with real kids if it's realistically doable (and makes sense). So - no need to veer out of your expertise to try to "fix" a system that's currently beyond your (or probably anybody's) current knowledge or abilities - just focus on what you ARE qualified to speak on, and try to make a real impact.
While I have ideas on how to teach math differently, I haven't had any opportunity to actually test them to see how effective they are.
I'd suggest something like the Harkness Method used at Phillips Exeter Academy. This is when 12 students are seated around an oval table designed so that everyone at every seat can see all the other students easily, and learning happens through discussion. The teacher is only a facilitator, who can sometimes step in to ask a specific question or push the discussion in a different direction.
As a PEA student, I loved my classes -- especially my math classes. There was no textbook -- we solved word problems only, deriving complex theorems only to be told later what they were officially known as (Kepler's Laws for example).
The problem is, I don't think this is feasible at a school like UW. It's a giant public school. It would be impossible to divide a school with over 30,000 students into small classrooms. More importantly, UW is strongly research focused, so many faculty don't consider teaching as a priority. All high school students applying to college should research those colleges -- and should know stuff like this before you enroll. There are other, much smaller schools which would be able to offer a creative thinking environment.
I think one important thing to take away from this is that no one method is going to work. There is no magic bullet. We need a multitude of solutions if we are going to effectively teach students.
I think the actual root of this problem goes deeper than just education. It's clearly an inevitable fact that the majority of people will not need to work for our society to flourish in the future. Automation will replace a great majority of jobs. Teaching people how to be good workers (which is what traditional education does) or teaching them to be great thinkers (which is probably what we should be doing) isn't going to change the fact that there won't be jobs available for a large majority of people in the future (be they workers or thinkers). In fact, teaching people to be great thinkers now will only make that jobless future come more quickly. Though it will probably also help more people be capable of accepting such change.
It seems at least partially likely that education hasn't shifted wholly toward teaching creativity and thinking because people who are complacent with the daily grind are easier to pacify and so long as we can keep enough remedial jobs to keep them employed, the status quo stays. I personally don't think the status quo is all so hot, and perhaps we should be pushing for change, but a whole lot of freethinking people have found ways to fit into this life, have found happiness, and got comfortable.
For a more short-term view of the problem, I think society needs to stop over-valuing a university level education and appreciate folks who choose not to go to a university and instead go to a trade school, community college, or directly into the workforce. University level educations are expensive and there is a clear problem with student debt in our nation. There’s also a problem with using the least common denominator when teaching at the university level; I don’t think this should ever happen. If a student can’t keep up, then they don’t belong in the program they’re in. Alternatives need to exist, but dumbing down a subject isn’t the answer.
It also seems that the large volume of students who now enroll in college because “it’s what comes after high school” has diluted what used to be a highly scholastic environment. But in all reality, college offers a lot of opportunity to go as deeply into the academic side of things as you want. Sure, you have to take the tests, and memorize the facts, but there's still plenty of opportunity to have the sort of experience you sought, at UW and elsewhere, if you seek it out.
As you will ultimately find out life isn't going to just hand you thought provoking challenges that fulfill you. Nobody is going to just walk up to you and take you under their wing and say “hey kid, you could be the catalyst that changes the future for the better, let me teach you how to be the best you that you can be”. Based on this essay, I would say that you have somehow, in-spite of the less than awesome education system, managed to become a freethinking person who can think critically and analyze big problems and even come up with ideas that could contribute to fixing them.
The thing is, life is exactly what you make of it, and you get out of it what you put into it. Like everything else in life, if you want a great education that challenges and fulfills you, you need to go get it and not expect someone else to hand it to you.
It's funny, because one of the things that most frustrated me about college was that I approached the professors about doing research into problems I was interested in, and they simply weren't interested because those problems weren't related to the ones they were working on in the CSE graphics department. I was frustrated because I saw lots and lots and lots of problems with everything, but school served only to get in my way. I wanted to learn [x] and had to wade through immense amounts of crap to get at it, which is why I eventually became adept at finding precisely what I needed through my own research.
I have been putting a lot of stuff into life. I have several projects i'm currently working on, the most advanced of which is a generalized n-dimensional trajectory optimizer using a beam search algorithm. College mostly just got in the way.
Two perspectives on your post.
I also had a grad student open my eyes to calculus toward the end of my stint at UW. As a biology / biochem major I didn't have the concentration of math that you did, but I did experience the standard calculus series (taught from the "Koblitz notes" at the time I believe) which consisted of a prof reading and writing these notes in front of a class verbatim. This was terrible teaching and student suffering was palpable. I only saw the light when I had to retake one of these calc classes in the summer, from a grad student who was allowed special privileges to teach from notes he developed on his own. This special grad student wore all blue clothing and published his notes on blue paper. We called him the blue guy and he was truly fantastic! All applied math, with tons of discussion and examples. That 'blue guy' rekindled my interest in math AND taught with overt passion for the topic he clearly lived for. Terrific!
In contrast to the staid standard calculus series, most of the rest of my UW experience was fantastic, and I wonder why you didn't seek out interesting and challenging opportunities yourself. One quarter I took a class (1/3 undergrads, 1/3 grads, 1/3 profs) to develop the plan and degree framework for reintroducing a department that had been mothballed decades earlier; no scripted moments or scan-trons there! Got a lot out of teaching skiing with Husky Winter Sports (not for credit, but for the fantastic experience, fun and resume fodder.) Lab classes in the sciences certainly had some element of reaching expected conclusions, but originality, perspective and exploration weren't actively discouraged. Similarly, courses that required summarizing and presenting published research articles to small groups were a fantastic insight into 'real' science for an undergrad, and had no script or expectations. For-credit research in actual labs was also a great option for undergrads that provided real world experience and all-application all-the-time. Another nice option for exploring careers and gaining experience was a program that paired undergrads with a grad student or working scientist, and placed them in a high school class to teach hands on labs. This was an awesome, eye-opening experience where I was able to see the massive difference between a resource poor West Seattle HS science class (one electrical receptacle per room, few students anticipated college) vs Eastside HS classes (abundant resources and the inevitability of college.) So much opportunity.
I got a ton out of my time at UW and I'm sorry you didn't. Your degree focus was different of course. But, that's not the only factor that defines a stint a college, anymore than placement in a department or workgroup in a professional setting necessarily defines your scope and experience in that environment. As I read your comments, it is clear that you intentionally opted out of a college experience, inside and outside the classroom. Had you turned up in a language, history or science department and indicated you wanted to apply you math skills in order to get more out of your time at school, I can only imagine you would have found a plethora of opportunities. Sure, the calc instruction may be abysmal. But, that's a far cry from legitimately generalizing the whole institution as broken.
Education will evolve with Coursera, Khan Academy, etc and universities will have some growing pains / contraction as free education resources proliferate. But, I'm certain there's still a place for applied / hands-on learning and that universities will continue to fulfill this need for years to come.
I am not only criticizing universities, I'm criticizing everything. The entire educational system is focused on taking tests. This is a systemic problem, not a few minor issues with colleges.
Hello Erik. As a current student at UW I'd like to submit my thoughts on this post. I've given a lot of thought to the many questions you address, and have discussed these with many students at several universities (including fancy places such as Harvard/MIT/Stanford).
First of all, I agree with you entirely about the flaws in primary and secondary school education. Unfortunately, many high school and elementary school teachers simply _do not know_ what mathematics is - they learned it much the same way that you describe: via memorization. They can only teach what they know, and this is indeed a fundamental flaw of the system. Many more math-focused countries have mathematics graduate students and PhDs teach at primary schools, but this requires an infrastructure and culture that we do not have here. However, I would like to mention the growing movement of "Math Circles" - small classes of middle school students that teach proof-based abstract mathematics. The goal of these to to supplement primary school mathematics education with a more rigorous proof-based approach studying topics such as combinatorics, graph theory, and number theory. UW hosts one too, by the way.
All that said, must disagree with about what you say about our UW education. Yes, there is certainly a route to a degree that does not require anything more than memorization, but there are also many routes that involve minimal jumping-through-the-hoops. The beauty of college (and America in general) is that you can customize your education _however you see fit_ - there is a plan set in stone for those who want to follow it, but you are more than welcome to carve your own path. I, for instance, managed to convince professors to let me substitute many of my required courses in physics and chemistry for their graduate equivalents because the subject matter of the courses was fascinating to me and I wanted a more challenging environment. These graduate courses were indeed extremely challenging and demanded a tremendous amount of thought - they would have been impossible to succeed in if I were to simply memorize my way through them. The mathematics department, contrary to what you say, offers very difficult undergraduate courses. Yes, to find these you have to seek out the courses with long, difficult-sounding names ("Honors Accelerated Advanced Calculus" or "Special Topics in Differential Geometry") - but it's unfair to say that courses do not exist or do not make you think. I don't think you can memorize your way through any of the upper-level courses.
The kernel of my argument can be summarized as follows: college is an opportunity. Most people enter college to obtain a degree - a piece of paper that says that they have a particular set of skills - and this can certainly be obtained by memorizing away (one could argue that this is sufficient for most post-bac applications!). Many other students have the goal of pursuing science and mathematics into graduate school and perhaps further, and such people seek out courses that prepare them for the kind of thinking and problem solving that is required in graduate school. From my limited experience at other universities - this is very much the case everywhere in the US.
Finally, I would like to point out that you have completely ignored the concept of academic research: the heart of scientific thought and problem solving. Undergraduate students are actively encouraged to approach professors with requests to join their academic group and work on the frontiers of science and mathematics, and this is arguably one of the best ways to obtain the "thinking" component of college that you discuss in your post.
For the sake of not dragging out this response, I will end my argument here. Please let me know if this is something you would like to discuss further.
I did approach professors about doing research. They didn't want to research what I wanted to do. I decided to go do it on my own.
I did take the hardest math courses I could. Sometimes I learned stuff from them, but the tests were always the same, banal, ridiculous tests.
I am a 53 year old math/science nerd who 12 months ago decided to close my successful technology consulting firm (over $150k) to teach public middle school science in a school with the majority of children on free/reduced lunch (under $40k) I have complained bitterly about public education for decades and finally decided to try and do something about it. I recently completed my first year of teaching 8th grade science and was awarded "teacher of the year" by the school. Here are some of my thoughts and ideas on our deeply flawed public education system.
Rigor. Expectations on students are much, much too low. State standards are a complete joke - you can easily teach everything required in the standards in 2-3 months. The only equation you are required to learn in all three years of middle school science is: Distance = Speed X Time. Obscenely low learning targets start in elementary school where the entire school culture is based upon things being "cute". The only challenging courses in K-12 education are AP courses. A child with an average IQ and bare minimal effort can NEVER do homework and easily pass the required state exit exams and graduate with a decent GPA - just avoid AP classes and public school is a cakewalk. In my school no homework is assigned. I asked why... The answer, "kids will not turn it in, our parents don't care."
Teachers. Over 90% of middle school science teachers do not have a degree in science. To be a poor teacher is incredibly easy - almost no effort is required. To be a great teacher will sap every ounce of energy, ambition, talent and free time you possess. Your principal will judge you on only three things - your ability to "manage" the classroom (keep kids sitting quietly in desks doing mindless busy work) your ability to do all the non-teaching tasks (help monitor the halls, turn in grades on time, etc.) and the percentage of students who pass the ridiculously easy state assessment.
Society. Those who can - do. Those who can't - teach. When I told my friends / peers / family members that I was quitting my business to teach middle school science they immediately assumed I had lost my mind. Several seriously contemplated an "intervention" on my behalf. Our society does not look favorably upon public educators. A huge percentage of our populace considers the great majority of government spending a complete waste of funds. "We have dumped billions of tax dollars into education and our schools are still broken - why give them more?"
Pay. Your pay as an educator depends on only two things - years of teaching experience and your total number or college credit hours earned. Horrible teachers get paid the same as the best teachers. All teachers (except successful football coaches) are paid poorly. Gifted and credentialed math / science teachers who work 70 hour weeks get paid less than the person who drives your garbage truck or city bus and has no college degree. We will never have more than a handful of truly excellent educators until we pay them a decent wage based upon performance not seniority.
Teachers Unions. Bad teachers NEVER get fired unless they commit a serious crime. Over 50% of educators do not belong in front of students but can't be fired because of unions. Unions help teachers negotiate pay raises = good. Unions protect bad teachers from getting fired and fight merit based pay systems = criminal.
College and University "Schools" of Education. I recently completed a master's degree in education. Complete and utter waste of time. Mindless edubabble. Taught me absolutely NOTHING about successfully teaching in public schools. We should immediately eliminate ALL university based education classes. Math teachers should have math degrees. English teachers should have degrees in English. Elementary teachers should have university degrees with significant coursework in both the hard sciences and social sciences. All teachers should complete a full year of student teaching under the close supervision of a team of master teachers. The bottom 25% of all student teachers should never be allowed to teach. Not everyone can sing on key or dunk a basketball... You can't teach everyone to teach.
Culture of learning. Virtually all public schools lack a strong culture of learning. The only exceptions are elite private prep schools and a handful of truly exemplary charter schools like KIPP Academy. These schools have incredibly high expectations for both students and educators. KIPP takes poor inner-city minority kids and turns them into motivated scholars with the confidence and ability to pass the high stakes tests that (rightly or wrongly) determine success in America. Long school days, tons of homework, a balance of rote memorization and higher level thinking skills. Teachers so dedicated they spend many nights on their cell phones tutoring students.
High Stakes Tests. Success in higher education is primarily based upon your ability to effectively memorize and regurgitate facts into little bubbles. Law, medicine, engineering, math and advanced business degrees are exclusively granted to those who can quickly and competently memorize and regurgitate. Wikipedia and smart phones apps have completely eliminated the need for this skill. We now have free and instant access to virtually all known factual information 24/7/365 regardless of our physical location on earth. We should value the worth of humans on their ability to collaboratively search, filter, manage, integrate and implement factual knowledge to prioritize and solve real problems. Modern capitalism is relatively successful at this. Public education is not. Sadly, students are completely excluded from the highest levels of the game (MD, PhD, MBA, JD, Computer Science) unless they master the memorization / regurgitation in high stakes testing trick (or have wealthy relatives who can make a "call" on their behalf, i.e. George H W Bush)
Textbooks / Technology. All modern K-12 textbooks are very expensive garbage. All printed textbooks should be banned. All students should be given a $250 Chromebook and do almost everything digitally. Yes, schools should have regular activities that are "technology free" and require getting hands-on dirty... But, almost everything from fine art to frog dissection to group projects can be done better virtually. FYI - almost every public school teacher over age 40 has HORRIBLE technology skills. This is a huge impediment to meaningful change in education over the next two decades. 50 year old CEO's either have technology skills or hire people who do to work for them. By the time all our techno-dinosaur teachers retire our schools will be even further behind the rest of the world.
Flip the Classroom. Kahn Academy and self learning through YouTube videos eliminate the need for a "Sage on the Stage" teacher in the classroom. A "guide on the side" teacher/mentor is a better model. The responsibility of learning needs to be removed from the teacher and placed upon the student from a young age. In fact, get rid of classrooms - it's an obsolete concept. Humans live and work collaboratively in small groups with shared abilities and interests. Organize schools in the same way - let the kids who are obsessed with a given topic collaborate with other like minded kids in other parts of the world. Kids should learn fact hard facts on their own and practice problem solving in "class" with a trained teacher mentor to enforce high expectations.
Education is NOT one size fits all. Not every kid deserves a trophy for just showing up to the games. We need to embrace the fact that not every child is going to be a college graduate. The modern American High School is very successful at sending kids out the door with NO marketable skills. Not ready for college math or English. Can't code a program. Can't cook a meal. Can't fix a leaky pipe or change a tire. Can't tell the difference between facts and opinions on a Google search. Can't think independently. Can't write an effective argument. Turn half of all High Schools into "magnet schools" with a strong career track. Start training plumbers, electricians, mechanics, machinists, etc. in 1/2 day High Schools with a 1/2 day working. You go on a college track or an apprentice track starting in 10th grade. All AP level classes in the college track. Prom is over rated. Every non-college bound high school student I know wants to be a chef or a dolphin trainer. Let them start working in a commercial kitchen or mucking stalls for 4 hours a day at age 15 - that's education.
Close all for profit "colleges" (ITT Technical Institute, Culinary Art Institutes, etc. - any school who runs TV ads during Springer) These "schools" are simply scams to burden poor memorizers / regurgitators with government backed student loans. These institutions are criminal.
Did I enjoy teaching for a year in a public school. Yes! Incredibly rewarding, challenging, exciting, thrilling. Amazing students. Became friends with many dedicated and talented teachers. Learned you can change a life forever.
Did I hate teaching for a year in a public school. Yes! Low pay. Apathetic parents. Long hours. People assume I'm stupid or lazy or a loser because I teach in a middle school. Mean students. Students with hormones raging. Apathetic teachers. Recognizing that you can't change the system.
I look very forward to teaching next year. I can't wait apply what I learned in year one. I know I made a ton of mistakes can't wait to try a ton of new things. I already miss the daily interactions with the students. On the other hand, I might relax and take the easy $90,000 job that will pay the bills and let me enjoy my last 15 years of employment. That is why I wrote this post - to decide if I am teaching next year....
After reading your blog, I feel a little guilty for talking my daughter out of becoming a teacher. The reason I did was precisely because of the reasons you stated for hating teaching and, specifically, recognizing that you can't change the system. Being a teacher is tantamount to working for the Federal Government. I know my daughter has no idea what that would be like. Having worked for a large corporation for several years, I have some idea. Knowing my daughter, she would hate that aspect of it. Who would like it? I'd be interested to hear any comments you might have on Common Core.
An ability to identify and denounce the fundamental flaws of a system is a good thing to have. More specifically, your identification of math as the "canary in the coal mine" is very insightful. But, in the spirit of pointing out holes that need filling:
First, your tagline "the greatest threat to our species..." seems like an effort to aggrandize the problem you're interested in so that nothing less than the future of humanity rests on your shoulders. The assertion that the educational system is the reason why we can't make progress around problems such as global warming is a flight of fancy that can't be backed by evidence.
Second, you don't acknowledge the existence of entire fields of knowledge about a) the problems inherent to the educational system b) methods of teaching, in general or for math in particular. There are a few people who have been dedicating their life's work to the latter right under your nose in Miller Hall on the main quad. This is not to say that your thinking about how to teach math concepts is not a valuable exercise, or that you don't have anything to contribute to the field, but talking as if you are the first person to have observed the problems you identify is rather presumptuous. Hard problems are not meant to be studied in a vacuum; the loneliness of feeling like the only one who "gets it" is an indication that you're doing something wrong.
I'm far from the first person to observe this problem and I'm not entirely sure how you got that out of the essay. I'm not the only one who "gets it", I'm just providing a perspective from inside the educational system itself. Everyone I know also "gets it". The people who don't get it are the people in charge of the educational system, which is the problem I was trying to point out.
I will proclaim myself as the grande dame of this discussion. I have been in the education system since the 1960's. I started school when I was 3 years old in 1964 and just finished a class in June. I have taken classes at a the UW, various community colleges, self-study (remember when they used to call them correspondence courses?), online college courses, and professional training courses. I happen to be very good at regurgitating information. I am also a very creative person. There are times when it's right to stick to the facts and times when we should be thinking freely. My job does not support free thinking so I don't even go there. But when I am talking about music, for instance, I think in terms of aesthetics and interpretation. One can compartmentalize these two modes of thinking and survive very well. However, when the two come together, it's a beautiful thing. Important contributions are attributable to those with the ability to combine facts and data with visionary thinking. Is that what we call genius? If so, will revamping the educational system create more geniuses? I think not. Geniuses are born, not created. I don't like our current educational system, but I also think that most children and parents don't care. Parents will go along with just about anything in exchange for the babysitting service. As far as secondary education goes, the best classes I've taken are online college courses that cater to working adults. These educators know that the students are not high school kids on their parents' dime. They are using their own money to get an education, so it had better be good. These instructor-led online courses are the only classes I've taken that have attempted to link the curriculum to actual application in everyday life. Erik, I feel your frustration, but remember two things: Sometimes there IS only one right answer, like the math solution in the back of the book. The learning opportunity is in the path you carve out to get there; and free-thinkers will always be marginalized. Your choices are to infiltrate the system and try to change it (like the Rookie Teacher), or work around it like you are currently doing. You'll find a way and you'll learn a lot getting there. Good luck!
My entire point is that the number of situations where there is only one right answer is shrinking because of modern technology. Maybe that used to be the case, but it won't be for much longer.
Great article! "Instead of giving our children a brush and telling them to use their imagination, we give them a coloring book and grade them on how well they stay inside the lines" represents the whole idea of the article, IMHO.
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