Faulty Assumptions, the Best of Intentions, and a Croaking Frog
Editor’s note: This is the thirteenth chapter in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. Also, to my devoted readers, I decided to name the first school I taught at as Cypress School rather than “my previous school” to reduce confusion and irritation with the author.” The previous chapters can be found here:Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5Chapter 6Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11 and Chapter 12
Ch 13 Faulty Assumptions, the Best of Intentions, and a Croaking Frog
In planning my future classes during the summer before the upcoming school year I proceed from an undying faith in my expectations of how things will be. During the actual school year, I then deal with the reality. In the end, it is always astounding to me how some intuitions turn out surprisingly well.
My Math 7
class at Cypress my second year was the non-accelerated version. I had taught
accelerated Math 7 the year before, but was now faced with a challenging group
of students who I knew were disheartened about math and likely dreading the
next year. While planning my lessons during the summer using the JUMP Math
teacher’s manual, I had a vision that the students would upon succeeding and
getting good grades on tests and quizzes, eventually discover that the math was
actually interesting and that they could manage it.
The reality
was slightly different as I was finding out and as I’ve written about in
preceding chapters. I knew that something
was happening. Just not in the manner I had envisioned.
The next
year when I started at St. Stevens, I found that my Math 8 class was similar in
some respects to the Math 7 class. I had assumed during my planning for it that
the ability level would be high, thinking that was the norm for private schools.
I therefore sought to overcome what I called the vast wasteland of disparate
topics and dearth of algebra that is typical for Math 8. I thought that I might
introduce more algebra than is usually included, drawing upon the simpler
problems and approach in another book authored by Dolciani called “Basic
Algebra”. I selected some topics that I
thought would provide a basic grounding in algebraic concepts that would help
them when they took the regular algebra 1 class in 9th grade. These
topics included multiplying polynomials, factoring, algebraic fractions and
various word problems.
As it turned
out, my Math 8 class struggled with the various topics we had covered. I
realized that my plan for trying to squeeze in the basic algebra might not
work, despite my having worked out lesson plans for the same. On top of that, the two girls with whom I had
been doing intervention work were on a separate track. I had them work on
homework for other classes during the Math 8 class, and worked with them two
days per week during their first period on bringing them up to speed on very
elementary equations, percents, decimals and fractions—and insisting they learn
their multiplication facts.
In the case
of my Math 8 class, I realized that however mistaken I thought my initial
expectations were I would have to go through with my original plan. This
realization came after a bout of rainstorms that left puddles throughout the
campus, waterlogged green areas, and a tree frog next to my Batcave
classroom. I don’t know for sure that it
was a tree frog, but it was definitely a frog—and it croaked. Its croak was distinctive and almost as loud
as the crows that used the palm tree next door as their resting place.
One day, as
the class was starting to work on the homework I had assigned, the croak of the
tree frog filled the room. This provided a distraction that the eight students
quickly took advantage of.
“Can we look
for the frog?” they asked. “Jared is really good at catching them.” Jared had an albino snake at home, and was
known for being proficient at catching lizards which also populated the school
campus at times.
“Let’s do
it,” I said, despite the admonition of educrats these days that all teaching
must be done with “intention”—that is, nothing left to chance. I decided that if
anyone asked about my intentions, I would say I meant for that to happen.
Alternatively, I’ve toyed with the idea of talking about God’s intentions, but
have decided not to go there.
The class
ran out, looking around for a misplaced frog. Jared scaled up a hill on the
other side of the narrow outside corridor that led to the classroom. They looked
in vain for a frog that croaked when least expected and somehow made it sound
like it was coming from the narrow corridor—where it was not. Most of the time, however, it knew when to
keep its mouth shut.
It was
during the futile five-minute search for the frog I decided that I had no
choice but to go ahead with my original plan to teach the basic algebra.
My reasoning
had more to do with the remaining months of school than anything else. The
textbook the school used for Math 8 was one of those which had one day devoted
to a “discovery” type activity, and the next day a “direct instruction” type
lesson. Book publishers tout this as a balanced approach, usually on their
front covers. I tend to skip the discovery type lessons and teach the
traditional style lessons, supplementing heavily from older textbooks. There
wasn’t much left of the book, leaving me with a lot of time to fill until end
of school.
The next
day, I announced my plan to the class.
“We will be learning some more algebra,” I said. “In fact, it is the
same algebra you will learn when you take algebra next year.” They became strangely quiet.
“This will
have an advantage,” I continued. “When
you take algebra next year, some of the concepts will be familiar to you.” The
croak of the tree frog then filled the room.
“It’s back,”
I said. “Let’s try this one more time.”
I opened the door and Jared scaled the hill
again to no avail. When we got back, we started on the algebra. I felt deep
down that the tree frog’s croak was intentional and he approved of my decision.
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