Mathematical Intuition: The Cyanide of Standards-Based Curriculum

Mathematical Intuition: The Cyanide of Standards-Based Curriculum:

I just finished reading a 25 page paper titled "A Mathematician's Lament", by Paul Lockhart.
This document, more than anything else, speaks volumes about what exactly is wrong with our modern school educational systems. The problem is we kill all creativity, all intuition, all beauty, from the subjects we teach.
Of course the abstract concepts we teach have their importance and place, but they should be taught in the context of, and as a derivate of, the natural creative and explorative processes inherent in the actual subjects themselves.

It never ceases to baffle me how we teach Math. Even as a Math tutor, I have found my fellow tutors, and especially the students, telling me that we don't need to teach them the WHY behind anything: simply HOW to solve their problems, irrespective of the reasoning behind it.
This does not lead to them knowing or even understanding math, and only compounds their issues when they get to higher levels of math.

If you are only taught how to solve specific problems without THINKING yourself then of course you will find you can't solve all the problems on your exams! The secret is that solving all the problems requires CREATIVE application of the concepts taught in class, and yet in that very class you are not taught to creatively apply or use those concepts!
What a contradictory way to learn math!
No wonder so many students fail, they are prescribing to the teaching model while the testing model is a vapid shell of the creative process that is inherent in REAL mathematics, and they cannot comprehend how their rote memorization, what they are taught and encouraged to do, has failed to land them in good graces.
It's sad, it's troubling, and it is completely unnecessary and is a really bizarre and abnormal model for teaching.
Oh, except it is not abnormal: it's the standard! Ha!

The fact that I can find people in higher level math courses, math majors, who do not know where the double angle formulas or half angle formulas come from, who don't understand the beauty and interconnectedness of everything we do in math, continues to shock and baffle me.
Do students simply rote memorize everything in High School?
The answer is: yes, yes they do.
And is it their fault? No, they don't know better, and everyone knows your GPA takes precedence, particularly before you get into your dream college.

The problem is the way they are taught and the fact that teaching has been largely reduced into a passive activity for students.
Sure, they can do assignments and use what they are taught, but they aren't engaged, there is no dialogue, no active suggestions or explorations to get people thinking.
They aren't even taught in the historical and exciting context from which all this "Math stuff" comes from!
How many opportunities for original mathematical thought have been passed over in favor of the standard model of passive teaching and note taking?
Or, rather, in favor of lecturing I should say, the current model hardly passes for "teaching".
How much originality and creativity does note-taking really involve anyway?


Our students are never taught or told to play with math, to discover interesting and cool things for themselves, to have fun and gain a sense of intuition for where everything comes from and what place everything has in the greater context.

The only reason I was so excellent at math in High School, and continue to be quite decent in college, is that I actually understand and care about where things come from in Math, I love the history and context, but most importantly of all: I play with math and as a result am accustomed to creative interpretation and intuition when it comes to math.

When I understand where a lecture is headed before we reach there it is not because I read the textbook ahead of time, it is because I have developed my sense of mathematical intuition and mathematical creativity.
I have yet to meet a student who does math for fun as I often do.

I love math and find it to be extraordinarily fascinating and fun, as I do English, History, and the sciences.
People are always shocked when they find out I am a math major, largely due to my passion for writing and my love of poetry and English.
Hahahaha, people have such screwed up perceptions of everything, especially math.

I'll tell you what I told my English professor,
Once you get far enough out (abstract) everything blends together, the differences are artificial.
Math is beautiful and so is English(Or language and literature for that matter, to be more broad), and the ties between them and between any subjects are interesting.
Most notably, in the right context, every subject is beautiful and gorgeous in its own right.
This is where we often fail in teaching: we fail to provide that context, to provide that context so desperately needed and to provide a platform that is both engaging, natural, and inspiring.

These failures are what, I am convinced, above all else, differentiate excellent teachers from horrendous teachers, and are what make or break an excellent education.

I understand why the system is the way it is: it is easier to measure and rank students the way the system is now.
Easier to teach from a prescription than from the soul, easier to try to mechanize and remove the humanity from the experience than to make an organic and authentic, high-quailty, natural experience for students to learn from.
Schooling and Education is largely based on ranking students for some God-awful reason, not about learning or about passion or about making discoveries never before made, nor about creativity.
This is why school often kills the natural interest and joy students have in subjects, why it fails so epically to actually do what it theoretically is supposed to do, and is why I intend to create my own nonprofit entity for learning that does everything the school system does wrong right, without any of the pressures or baggage the educational system has.

Learning for the love and sake of it.
I am a purist, make no mistake.
I believe in doing things for the sake of the things themselves, and being a philomath and bibliophile, I intend to make an entity for learning that actually cares about learning itself, not ranking individuals pointlessly and/or grubbing money to perpetuate an antiquated and shitty system of education.
We all think that college and school is about learning, but no there are ulterior reasons for why things are the way they are, and believe me: things are not optimal if these institutions are actually here to help us learn.
These decaying and horribly inept systems in which we compete and memorize have little to do with learning and everything to do with ranking and competition, things that are, true, american, but things that do little to augment or improve the learning process. (Well, sure you can measure and track "improvement", but you, and I am certain your students, can surely tell when a student is struggeling? And if the dialogue in class was truly bi-directional, you wouldn't an abstracted way to measure and analyze students and their issues: they would tell you what they need help with.)


Until things change we will just have to grit our teach and form clubs that attempt to augment and counter the passion-killing modern educational system.


I will write more on this, this is far from over.

~James

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