Week 14: Carrying on a Conversation

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An educated populace finds common ground and moves forward; an uneducated populace, paralyzed by divisions, stagnates and dies. Our nation’s founders knew this.

Citizen: What kind of a government have you given us?

Benjamin Franklin: A Republic, madam, if you can hold on to it!

James Howard Kunstler, in his book “The Geography of Nowhere” noted:

"For [Thomas Jefferson], the temple represented the culture that had first conceived of democracy (Greece), and that which had first devised a republican form of government (Rome), and it carried for Jefferson deep associations with his own classical education and his feeling that a democratic republic could only flourish if its citizens were educated.”

My heat transfer professor, Ralph Greif, once said to me:

Don’t worry that you’re not learning how to do or build anything. You’ll have plenty of time for that later. That’s what graduate school is for. That’s the easy stuff. Right now, focus on your literature classes, your social sciences. Relish your humanities—that’s what an education is about. 

Which reminded me of a soul-tingling dialogue between Captain Jean-Luc Picard and Ensign Wesley Crusher in the Star Trek episode Samaritan Snare (TNG 2x17):

Picard: Did you read that book I gave you?

Crusher: Some of it

Picard: That's reassuring.

Crusher: I just don’t have much time.

Picard: There's no greater challenge than the study of philosophy.

Crusher: Well, William James won't be on my Starfleet exam.

Picard: Important things never will be. Anyone can be trained in the mechanics and the piloting of a starship—

Crusher: but Starfleet Academy—

Picard: —takes more. Open your mind to the past—art, history, philosophy—and all this may mean something. 

In the midst of lectures, midterms, finals and projects—it is easy for the goal of education to get lost in the process of education: it is easy to mistake going to school with getting an education.

When we condition ourselves to think that learning only happens in school, we close our minds to so much more.

For me, once I realized that it was education for the sake of education, and not education for the sake of a job; once I realized to look beyond the specialized knowledge of an engineering education to see the universal truths driving all interaction—I was able to recognize my true, limitless potential.

Week 13: Your World. Delivered.

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In the process of education, we immerse ourselves in different fields of study, laying down a sample size of data in our brain large enough to illuminate a coherent pattern. The more we learn, the more this pattern is refined, reinforced, and strengthened. This pattern then lifts us up, allowing us to see the world not as a forebodingly complex jumble of dissonance, but as infinite variations on a singular theme: the world becomes one. 

Through education, we are empowered to infer beyond the world of our five senses, beyond our perception of reality. Through education—we find faith.

In Week 11, when Billy tried to sound out the word “mathematics”, he was transforming a single, ominous and impossibly complex “sound” into a logical sequence of more familiar, easy-to-spell syllables. He took a complex word, framed it as a collection of syllables, and used this new perspective to decompose the word into smaller, more manageable pieces.

This is the exact same approach we take to add any multi-digit sum, such as 88 + 66. The down and dirty approach would be to start at 88 and then count a collection of 66 sticks, rocks, fingers, toes or some witches brew of all the above in order to arrive at the sum. But nobody does this—not anymore; modern mathematics allows us to sense and manipulate numbers more efficiently than that. In school, we all learned how to take a multi-digit addition problem, frame it as a collection of place values, and then use this new perspective to decompose it into a series of easy-to-calculate single-digit sums. The algorithm is simple: start at the ones place, carry over if necessary, move on to the next place value, and repeat.

Taking a complex problem, orienting it around a familiar frame of reference, and then decomposing it into more manageable components: this is problem solving! Through education, we expose ourselves to so many different frames of reference and familiarize ourselves with such a diversity of viewpoints that no problem is too complex.

Education: the entire world—decomposed at your fingertips.

Week 4: Know Your Place

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The Mathematics Content Standards for California Public Schools, adopted by the Board of Education in 1997, exemplifies my ideal of what government's role in society should be. The standards define "what" a student must look like at each grade level, but leaves it up to the teachers, the parents, the Sylvan Learning Centers, the ACI Institutes, and the indie math tutors (locally grown and organic, like me!) of the world to figure out "how" to actually go about creating those students.

One of the larger categories within the standards is something called "number sense". I interpret number sense as being able to understand numbers abstractly: what numbers mean, what they symbolize, and how they are related. A primary requirement for number sense, (1.0), states:  

Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000.

The sub-requirements are:

Count, read, and write whole numbers to 1,000 and identify the place value for each digit. (1.1)

Use words, models, and expanded forms (e.g. 45 = 4 tens + 5) to represent numbers to 1,000. (1.2)

I've been struggling with how to teach Billy the concept of place value. He can identify the place value of each digit in whole numbers up to 1,000, per (1.1) but I know he doesn't really "get" it, because he's still struggling with (1.2). It's great that he knows how to identify the ones, tens, and hundreds place of a number, but it doesn't do him any good if he can't use this knowledge to get a "sense" of what the number actually means, abstractly.

Today, I tried introducing a game involving different colored poker chips. I would give him a number and ask him to create that number using a combination of various green (1), blue (10), and red (100) chips. He started getting very fidgety after about 1 minute of gameplay. I was losing him, and we were both getting frustrated.

I decided to give up on the game when I realized that, while it was a functioning game, it wasn't functioning to teach Billy what he needed to learn. The poker chip game was teaching him to express abstract quantities through color, when it should have been teaching him to express them through number. Hippies would argue that both are equally valid forms of expression, but I say hippies be damned. The reason we have standards is to ensure that, at some basic level, we can all speak a common language.

I think next week, I'll replace the poker chips with monopoly money. I figure, if the kid is gonna gamble, it's better he learn to gamble on something that the government is almost guaranteed to subsidize, to prop up, to perpetuate as a false promise--an opiate of the masses.