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Saturday, July 25, 2009

My Morning with ETS

So I got to spend my morning with Henry Goddard's present day disciples (i.e. the good people at the Educational Testing Service.) But that's starting in the middle of the story.

By the time I registered for my tests, all of the local testing dates had passed. The only date available prior to the start of grad school was at a center in Salem, MA. Unfortunately, it was a week before my wedding and on the day of another wedding I was to attend. Nonetheless, I felt it was the best choice in the long run. Plus it was months away, so I had plenty of time to study.

Without too much more adieu, this morning arrived. My alarm went off at 4:30am and I suddenly realized that I hadn't really studied as much as I probably should have. Still, I sharpened my number 2 pencils and hit the road. On the way, I dropped off my lovely fiance at the marine animal rescue center where she volunteers. Google Map print-out and toll money in the passenger seat, I tooled on down the highway.

I had planned to get there with time to spare, but after several wrong turns, I arrived with seconds to spare. If you have ever tried to navigate through New England as a visitor, you know my pain. These states seem to make a game of obscuring road signs. As you are flowing through traffic, you must somehow glimpse the tiny non-reflective sign hidden behind two hedgerows, one giant oak tree, and any one of a dozen quaint New England landscaping features that that seem to exist solely to frustrate visiting drivers. Still, in the end I prevailed and arrived at Salem State College on time.

Four hours and 120 lead-filled bubbles later, I headed back home. I really hope I passed, because I don't want to go through this again.

Friday, July 24, 2009

Praxis Makes Perfect

I have to drive down to Salem, MA tomorrow to take back-to-back Praxis II tests for math and physical science content knowledge. I've been brushing up a bit on all my trig identities and special factoring formulas and such. I feel pretty well prepared, especially considering that I only have to get 60% of the questions right to pass. Isn't it great that we have such high standards for our children's teachers? I'll let you know how it goes.

P.S. I'm getting married in a week. Woo-hoo!

Friday, July 10, 2009

The Dreaded Word Problem

All across this great country of ours, math students grapple to the death with their arch nemeses- the dreaded word problems.

Regardless of how they are dressed up or repackaged, most math textbooks are still pretty much the same. A particular lesson or skill set is explained, several examples are given, and then two to three pages of exercises follow. At the very end of these practice problems, buried in the back so they are easily ignored are the much maligned word problems. While the future mathematicians relish with excitement the chance to challenge themselves with these rhetorical abstractions, the average students find ways to conveniently skip over them, like peas being pushed around an otherwise empty plate.

Despite our efforts to reassure the students, to give them problem solving techniques and confidence boosters, we must admit that we are sending mixed signals. Anyone who truly understands mathematics realizes that word problems are not only a key part of math, they are the only part of math. Mathematics is a way of thinking about our world. Seldom does one find themselves confronted by a floating quadratic function demanding to be solved at gunpoint. Instead, we encounter normal, everyday questions or problems that can be illuminated using the tools of mathematics. This means translating the idea into language and translating that language into a mathematical construct. Thus, by hiding these problems at the end, we allow our students to skip the only problems that they really ought to attempt at all.

Rather than work umpteen practice problems, already laid out in clearly defined mathematical language exactly mirroring the guided examples, the students should skip directly to the world problems. Too often I hear my pupils tell me that they understand everything but the word problems. I politely respond that if they don't understand the word problems, they don't understand anything. Instead, they are confusing familiarity with understanding. They think because they can generate the expected answers with a series of repetitious algorithms, that they are preparing themselves for the exam and beyond. There curriculum is a mile wide and an inch deep.

What I would prefer is this: fewer practice problems investigated with greater depth. I would like the answers to come in narrative form, where the student explains to me and to themselves exactly why they made the decisions they made and what axioms of mathematics allow them to employ the techniques they chose. Take the following example:

An Internet service provider charges $9.95/month for the first 20 hours and
$0.50 for each additional hour. Write an expression representing the charges for
h hours of use in one month when h is more than 20 hours. What is the charge for
35 hours?

I don't want to see 9.95 + 0.5(h-20) = Cost (h) ; Cost (35) = 17.45. I want to see the following:

The Internet service provider is offering 20 hours a month of internet usage for
a flat rate of $9.95. This means that regardless of how many hours we use, our
bill will be at least $9.95. In other words, this value is a constant. If we go
over our allotted 20 hours, we will have to pay an overage fee of $0.50 for each
additional hour. Since the number of hours we use will change each month, we can
represent that value by the variable h. (We label it h out of convenience, since
hours starts with the letter h.) It is important to note that we only pay
overage fees on the hours we use beyond 20. An expression for those extra hours
would be h – 20. Therefore, our total bill will be $9.95 plus $0.50 for every
extra hour, or in algebraic terms,

Total Cost = 9.95 + 0.50(h – 20)

To evaluate the expression where h = 35 hours, we simply plug 35 in for h and solve.

Total Cost = 9.95 + 0.50(35 – 20)

9.95 + 0.50(15) = 9.95 + 7.50 = $17.45

That, ladies and gentlemen is how you solve a word problem, and until our students are able to clearly explain every step, they aren't mathematicians. They are walking, talking abacuses.

Thursday, July 2, 2009

Intro to Chem Lab

Last semester I was forced to endure the most painful chemistry lab. As is typical for labs, the amount of work required is disproportional to the one hour credit earned, but that was not the source of my frustration. A scientific laboratory is by its nature about discovery, but this lab was really just about pedagogy. We were really only there to learn how to run columns or pipet solutions, yet we were to write our lab reports as though we were conducting real science.

Evidentally, some of the faculty members shared my concern. This summer, the entire general chemistry curriculum is being retooled. A new textbook has been selected, one written by the American Chemistry Society and centered around the most abundant and familiar molecule on the planet- water. Subsequently, the labs must be rewritten as well.

I have been working for the chemistry department this summer, researching procedures regarding using titanium dioxide to remediate environmental contaminants. The work was done toward designing some new modules for the analytical chemistry lab. The idea was to give the students all the requisite data to design their own lab procedures instead of following a cookbook recipe. That way, they get to appreciate what science really is. Yesterday, I finished that project. The professor I was working with is also involved in retooling the aforementioned gen chem labs. When I was given the option to turn my attention toward those, I jumped at it.

Next semester, when students download their chemistry labs, they will be reading my words. Pre-lab questions, procedures, post lab review- all written by me. Hopefully, I can spare them from the boredom I experienced.