Memories of Writing Times

In a post on January 26, 2017, Barmerding asked if the participants in this quarter’s blogs on teaching and learning would consider writing a post as a “literacy narrative about their community college (or university) days?”  Barmerding also gave an initial prompt:

“What is one of your most prominent memories of reading and writing when you were in college? Why do you think this memory stands out to you?”

I’m a math teacher, but I’ve always been a reader of novels (old and new).  I read all the assigned texts in high school, thoroughly, and many others as follow-on—not extra credit, just interest.  When I enrolled as a freshman at a Chicago community college on the south-side of the city, I did not have a life-goal in mind.  My friends all went to four-year colleges or universities, so I was adrift in a new sea.  I was advised to take fundamental courses that would transfer.  That’s what I did.  I don’t carry many memories of the classes; they were in English literature, writing, analytic geometry, calculus, chemistry, philosophy (logic) and art history.  I remember only dream-like images of the instructors—the bus rides to and from class are more vivid in my mind.   On one particular ride I saw a public service ad with a quote by Mark Twain.  The quote was something akin to, “If you want to be a writer, write.”  I don’t remember wanting to be a writer, but at that point in my life writing became another dish on my buffet of possibilities.  I was eager to taste many experiences and experience many tastes (I couldn’t resist; we are covering commutative laws in my current math classes).  With that preamble, I’ll answer the question.

My most prominent memories are of the writing course.  I don’t remember the title of the course but we wrote short, fictional stories.  I found that I liked to write and I liked what I wrote.  I remember writing and rewriting on a small desk wedged into a large closet in the bedroom I shared with my older brother.  I typed the hand-in version; no home computers then.  I’m sure I never planned the structure of the stories; they just flowed from current topics.  It was the time of the Vietnam War and I remember one of my stories set in a car traveling down a highway with a driver and one passenger, a hitch-hiker.  I no longer have the story so I only remember its tone and its ending.  If I had analyzed it then I would have said that the hitch-hiker was suffering from ‘combat fatigue,’ what today they call PTSD.  I grew up in a blue-collar neighborhood, when that classification could be taken literally, and many of my neighborhood friends went off to the war—and returned damaged in many different ways.  The story ended badly (both content and form I’m afraid).  I never became a writer.  Math took its place.  But the exploration of trying to express emotion in words has stayed with me.  My fears and uncertainties of life unfolding—it’s good to remember how empty and lost young students can feel.

Bon Voyage

Week two has ended.  The roster is final.  The census is confirmed.  The ship has left the dock.  The students have tested their oars.  They almost know the tempo.  I can already guess who will pull steadily; who will take breaks; who will move to the edge of the oar to gain leverage.  It’s not a slave galley; they are all here by choice (if only by family proxy).  I’m playing the role of captain, navigator, and first mate.  I even get to pick which Scylla and Charybdis to steer between.  Will I lose some of my crew to the dangers?  Unfortunately, yes.  Will I lose most of my crew and return to dock powered only by the tide?  If past experience is a predictor of future returns, no.  I’ve sailed this ship before, several times, and have always returned with a majority of crew, well-weathered, but hardy.  I’ve even had students signup for new voyages (sometimes to the same destination).

I am, in fact, the captain of two voyages right now: one to the land of continuity and change and one to the land of discrete computation.  The inhabitants of the two lands are different species in the same genus and are related in the limit.  We row past many cities on the shores of the lands and we take time between rowing sessions to enjoy the sites.  Unfortunately we have too little time to become true citizens; we can only absorb some of the culture.  It’s dangerous in fact to go too deeply into the interior; the lure of undiscovered treasure and the urge to map the wilderness can cause a crew member to mutiny and not return on the charted course.

But now I must assume my role as navigator and chart course corrections to give to myself as captain.  The voyage must progress.  It has to converge before infinity.  After all, I have the ship owners to answer to on our return.

Always New

A new winter quarter started this week at my community college and with it a new round of reflection on teaching and learning.  I teach math in the evening and this quarter I am participating, again, in a seven-week, multi-discipline exercise in blogging on all things academic.   There are no rules on what to write or how to write, but the blogs will hopefully be worth the time to read.  All participants are required to review the blogs of other participants so there is some hope for more than monologues.   Let the game begin.

Every time I prepare for a class I learn something new about what I already knew (don’t you love English and its homonyms).  For example, I have taught on exponential equations many times, but in reviewing for a review of the topic I marveled at how exponentials, well before the long run, magnificently outpace polynomials.   Nothing really profound—I was comparing a simple quadratic function and a simple exponential function, the two topics for the lecture.

I used a TI84 for demonstrations so I’ll include some screen shots.

Here we have the two equations.


The first graph and its window settings is shown below.  The leftmost curve is the quadratic.  The quadratic seems to handily outpacing the exponential.  The graph was created with the ZOOM 1ST QUADRANT command. Increasing the height of the viewing window, by about a factor of four, shows that the exponential is catching up to the quadratic (below). Increasing both Xmax and Ymax, but only doubling Xmax, it becomes very clear that the exponential leaves the quadratic forever behind starting at about 10 (below).




square-versus-exponential-1w1  square-versus-exponential-2w square-versus-exponential-1w


Admittedly, some of the effect of the graphs relies on the shallowness of the first two windows, but it still is exciting to see the power of an exponential growth.  Whenever I teach about exponentials, I try to emphasize to my students that any use of an exponential growth model must require the determination of a practical domain—going too far is going too far.

Since I’ve shown some calculator graphs, let me reflect on the use of a graphing calculator, such as the TI84, in a math class.  Why should an instructor require a graphing calculator when there are so many more visual, easier to use, graphing packages available for free on the internet?  Here are two reasons.

First, the TI84 is a readily-available, common-denominator tool.  Many students already own one, or can borrow one, and for those students who don’t own one, there are usually a pool of them available at the school library.  The calculator has sufficient capability to draw graphs of equations or create equations of scatter plots.  And it is not hard to master the basic commands.  As an alternative, requiring all students to bring a laptop, tablet or phone with appropriate app is not always possible.  And not every community college class can be equipped with student-available computers.

Second, a calculator is generally needed on math exams to help with at least arithmetic operations on decimals, fractions, or irrational numbers.  If the course is also teaching regression of data points to best fit curves, this level of calculator is also needed for exams.  Allowing students to use a laptop utility, or their phone, with substitute software, is just too much temptation for students to move beyond graphing/calculation software to symbolic manipulation software.  This is also a reason to not use higher-function, symbolic manipulation calculators instead of graphing calculators.

That’s my reflection for the week of January 9, 2017.