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 AtlanticEducation NextEducation 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 7Chapter 8Chapter 9Chapter 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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