An espresso-based job interview, a 1962 algebra book, and procedures vs understanding

Editor’s note: This is the second piece 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.” The first piece can be found here.

An espresso-based job interview, a 1962 algebra book, and procedures vs understanding

In the remaining two weeks at my previous school, I applied for the few math teaching positions that were advertised. I had the typical non-responses except for one—a high school that specialized in problem-based learning. I had applied there out of desperation never expecting a response. I received an email saying they were interested in interviewing me. Despite my skills at making my teaching appear to be what people wanted to see, I knew that this one required too much suspension of disbelief on both sides of the aisle.

I cancelled the interview saying something along the lines of having to wash my hair that day. Shortly after that, I received another email from St. Stevens, a K-8 Catholic school needing a part-time math teacher. A fellow math teacher from another school had put in a good word for me. Like the school where I had been, this school was also part of a small community and had about two hundred students.

A few days later I was at the school for a 2 PM interview. I tend to get a bit logy in the afternoon so I thought I’d have an espresso prior to coming in. The principal, Marianne and assistant principal, Katherine, interviewed me and asked the usual questions: What does a typical lesson look like, what are my expectations and so on. My inner voice tried to keep me from extended caffeinated responses.  I emphasized how I leave time for students to start on homework in class, do the “I do, we do, you do” technique, and in my controlled ramblings managed to get across that I am, by and large, traditional.

But when the assistant principal asked me what my approach was in teaching algebra the espresso kicked in big time and my inner voice was having a hard time keeping up. I said that I taught using a 1962 algebra textbook by Dolciani. 

Inner voice: “You shouldn’t have said that.”

“I bought about fifteen of them over the internet when they were selling for one cent a piece about four years ago. So I was basically paying for shipping. But now the prices increased because of Amazon’s supply and demand algorithm, so they’re selling for about $60 a copy last time I looked. Which tells me a lot of people are buying them.”

“Please shut up.”

I talked about how I liked the sequence, structure and explanations of Dolciani’s book much better than the official textbook. As it turned out, so did the students despite the increased amount of word problems—and the word problems were yet another plus for using the book.

“But did you cover what was in the Common Core standards?” Marianne asked. I assured them that I did, supplementing with topics that weren’t in Dolciani, like exponential growth and decay.


I hastened to add that I did not spend inordinate amounts of time on exponential growth and decay functions.


“Did you cover exponents at all?” Katherine asked. “Because students generally are weak on those.”

“You mean like products and quotients of powers? Oh yeah, big time. The Dolciani book is very big on those.”  I was about to repeat that I didn’t spend time on exponential growth and decay, but the caffeine was mercifully wearing off.

They did not seem perturbed by any of my ramblings. Then again, it was during the last week of school and I imagine that they were so exhausted that they were probably amenable to anything I said.

They asked about my classroom management techniques. In any interview or evaluation process, one has to have some weakness to talk about and I freely admitted that classroom management is not my strong suit. I mentioned that my seventh grade math class had behavior problems even though there were a total of 10 students in the class.

“How did you handle the problems?” Marianne asked.

“I had a warning system; two warnings and they got a detention.  I wasn’t too faithful in carrying that out though.”

“Why was that?”

“When I gave a detention, the two main troublemakers were really good at carrying on about it and crying.”

“They cried?”

“I hated giving detentions. I always got talk-back, like ‘But I wasn’t talking’. And then the crying. Which they did with all the teachers, I found out.”

“So how did you deal with them most of the time, then? What did you do?”

I explained how this group had large deficits in math skills and most of the boys in the group had given up at believing they could learn math.

“I used an alternative textbook, which my school let me use: JUMP Math. It was developed in Canada and broke concepts down into very small incremental steps. It scaffolds problems down to incremental procedures and builds on those.”

I went on about how procedures can lead to understanding and you can teach understanding until the cows come home, but most students are going to grab onto the procedures.

“Did it work?” Katherine asked.

“Well, let’s just say that it would have been even worse had I not tried to fill in their deficits.”

They had no response and then the usual niceties ensued and the interview was over.

They called my references, as well as the principal of my school as I found out the next day. “Marianne called me about you.  She sounded excited,” the principal told me.

“What did she ask?”

 “She wanted to know more about the seventh grade class; she was curious about their behavior.”

“Oh,” I said. “I thought she might.”

“I told her they were really a tough bunch of students but you handled them well.”

“Did she ask about the algebra books I used for my algebra class? Or about procedures versus understanding?”

“No; just about the seventh grade class,” she said. “She sounded positive.”

And a few days later I was offered the job at St. Stevens.  “I think you’ll like it there,” the principal told me. 

I hoped so. There are always doubts about starting any new job, particularly in teaching. I had given them fair warning in the interview about how I taught. I hoped I would be allowed autonomy, but for the most part, I was glad they brought me in out of the rain.