"Education is not the filling of a pail, but the lighting of a fire." William Butler Yeats

I've been hired to get a girl into college.

She's already done all the legwork, she's put in her application, she's been to the campus. She's got the tuition money. She's even been accepted. Accepted on the condition she passes her GED, and what stands in her way is two points on the math portion. Before she took that test, she'd never seen an algebra problem.

A twenty-year-old isn't exactly free to sit in on an algebra class in a public school. Nor are they really welcome in the college setting before they've been accepted. This is where I get the call. I'm not being asked to instruct a comprehensive Algebra class, but I am expected to divulge the content of such a course. And quickly-- because an individual doesn't attempt to get the GED until they're ready to commit going to school again--until they have a plan. Then they fail, and they start to panic. "I want to start school in the spring!"

The first time I saw an algebra problem, I was amazed to find that the little "x" did not just function as a place holder: "2x" was not "twenty something." I got to see the bewilderment in the eyes of a student realizing this. Not a "Eureka!" moment, more of a "WTF?!" I had eight weeks before she took the GED again. I squinted into the future. I had to come up with something that would be both comprehensive and just enough to get her to pass the test--her college algebra class would give her the proper education.

The experience isn't mundane, by any means. In one hour a day, two days a week, I have to swoop a mind from fractions and percents into the abstract of representational math. After hours of preparation--counting on the characteristic of algebra where everything builds on the previous--the projection looks something like this:

• the language of algebra (listing of all the properties, like commutative, distributitive, associative, negative, identity...)
• "things you can do to a number"
  
• order of operations
• one-step solve for x
• combining like terms
• distribution
  
• linear equations
• systems of equations
  
• plotting points and slope intercept form
• FOIL
• quadratic equations
  
• solving rational equations
  
• radicals and radical equations
• inequalities, scientific notation
• word problems
  

At each concept for one hour, it would take a dedicated student to pull this off. And an extremely time-conservative teacher. I do one example. I watch and guide while she plugs through for the rest of the hour. Then I leave extra problems. That's all I got. In sixteen blazing hours, she gets a pretty comprehensive Algebra 1 course.

It's totally worth the two points.



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For more on William Butler Yeats

"A mathematician is a device for turning coffee into theorems." Paul Erdos, Mathematician

The fascinating thing about mathematics is that everyone perceives it differently. My construction worker dad sees every mathematical computation as a concrete, real-life , unquestionable number. As a linguist, I see language as more specific and less abstract than math. I can make anything equal two. I can make two apply to anything. I can figure its differentials; I can manipulate it into a fraction, a circle, an imaginary number, even coffee. There is nothing concrete in how I deal with numbers.

As a tutor, someone who delves into the mind of another human being to figure out how it ticks and then teaches it what it wants to know, I mull over this revelation with an intensity reserved for how one finagles extra value into a dollar.

It's not the first slap-in-the-face I've gotten about the instructional aspect of mathematical concepts: I've recently taken on a student with a variation of autism who treats math as a series of processes, no end result necessary, not purpose driven, just a certain kind of machine that does a certain task. Perplexed, it took me two weeks to figure out how to teach her.

And then there's my own children, one in preschool and one in her second year. The younger one counts infinitely, knows implicitly the position of the fingers necessary to display numbers one through ten, and has a spacial recognition that puts me and my cognition in the dark ages. The older one is the opposite. Just in the current school year we've gotten her to count to twenty consecutively, though she reads at a nine-year-old's level. Neither think about math the way I do, nor do they follow any traditional math teaching method contained in my math books.

At a standstill with the home-schooled math student, I started looking at math not as a subject to be accomplished but as a region to be understood. What is math? It's not simply a series of figures with operation signs and the strategies to manipulate them. It's not necessarily purpose-driven, but it doesn't have to exist in an etherial realm, either. And it's far from being rote memorization. And it's certainly not as arbitrary as I might imagine.

Math is a perception. Like an artist who works in 3D but can't draw more than a stick figure, math is a process of interpretation. Logical and Spatial intelligence, on the IQ tests, but really, a way of integrating the world to one's imagination, and then communicating it.

For my beginning math student where words already exist in her psyche, teaching with language is the best option. Use units, use story problems. Find the perimeter kinds of problems. Write math equations instead of drawing them. Label graph paper with ones column and tens column and hundreds column. Speak of multiple digit numbers as a "six" in the ones place, a "four" in the tens place, and "add the ones column and any result with a digit in the tens place needs to be carried to the tens column." It's the language that will get her through the basics into the higher math. No pages of numbers and operations symbols are going to be sufficient. Rulers with numbers and units, polygons with units, and labeled graph paper for working the figures--these are the tools.

These are the tools, and I am the teacher. I pack my toolbox with the linguistic versions of all the mathematical concepts suitable for a "first grader," and I pull them out and carefully order them in story form. I line up the concept to the student, and walk away, because once I've done that, they have all they need to know. That toolbox isn't for me.

No, it is for me to do my job, this job to find out what math can possibly have to do with coffee. It is for me to find the psychology behind both what needs to be learned and the individual learner, and show that learner how those two things are the same.

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For more on Paul Erdos

Extra! Extra!: What Comes After Acedemia?

I spent a fair amount of time researching after-school activities for my homeschoolers. To begin with, I checked the homeschooling laws in my state which dictate that as long as the student complies with the requirements, then they may attend the publicly funded extracurriculars at the nearest public school.

Step two, I checked with the school district. Surprisingly, the elementary grades do not offer any extracurriculars, but instead outsource that job to the city Parks and Recreation department. Translated: you have to pay handsomely. Parks and Rec offers an enriched after-school babysitting program for the youngsters on both full and short days, takes your kid to field trips on teacher workdays, provides a full weeks' activities during winter break. No program is divided by grade, ability, or activity.

Next, I skipped into the city rec programs, which is really a catalog of private venues across the valley. The city does some sports programs, but so does the college. The kids' gymnastics gym also offers dance, the ice arena has kids programs, and there is a variety of swimming lessons at the city pool. A couple of individuals offer some martial training. As the kids get older, they can add fencing, golf, and dog obedience to the list.

When I was in grade school, the music teachers had after-school choirs and bands and music lessons. Every gym teacher and most academic teachers were athletic coaches and interscholastic sports could be started as early as first grade. And this for a teeny tiny portion of the price of the Parks and Recreation programs. I'm willing to bet more kids were in sports then. I have to admit, dog obedience and yoga are pretty cool options, though.

I begin to wonder, what we do with the youth of this community: where do they go? What clubs are they in? And the original question: what is available? Besides, of course, a new twist on the day-care.

The competitive spirit, it appears, is being streamlined in our elementary schools. Why is it we all despise "spirit dad" and his loud mouth at Little League or Powder Puff games but we all drool over the National Spelling Bee and the hushed tension? As an academic in linguistic and literary studies, I still cannot understand why our schools push our youth to comprehend esoteric vocabulary and obscure, borrowed syllabic constructions but shy away from cheering them on at the pool or on the field.

It's a matter of what one can accomplish in a classroom. A teacher cannot run a basketball practice in addition to the required readings, and there just isn't the monetary support to do it after school lets out. On the other hand, those borrowed syllabic constructions--you know, like -ology and pseudo- --can be taught in the classroom with no eyebrows raised.

It's up to the parents to do all the cheering, no easier illustrated than the event today: "Harder!" "Keep going!" "Get up!" "Finish third!" "First place!" "Keep it up!" "You can do it!" and multiple other exclamation points rising above a din of clapping and an unmistakable whir. And that was just for the four-year old. What loud, parent-driven, child-competen' event is this? Oh, it's just the weekend BMX meet. I can tell from all the quick-pop tents, the trailers, the bikes, helmets, and bottled water that this is no cheap organization to run or be a part of, but somebody has to give our kids the benefit of a hard-earned trophy. Power to the parents! Now, where can she sign up?