Latest from Math Teacher/Author, Barry Garelick: Chapter 2. Making Concessions, Seeing What You Want to See, and a Feeling of Belonging
Having been part of the work force for 40 years, I’m no stranger to job interviews and particularly that old chestnut of a question, “Describe one of your weaknesses.” In one particular interview I responded by saying, “I have a difficult time dealing with jerks.”
A profound silence followed. This didn’t go over as well as I thought it would since the interviewer—a grim poker-faced humorless woman—was a jerk. So I said “What I mean is…” and explained how in consulting (the job was for a consulting firm) one has to deal with difficult clients, and so on and so forth. I was hired, but it turned out that the jerk of an interviewer was my boss. I was fired within six months (the one and only time in my life).
This interview experience comes to mind as I recall the apprehension I felt before my first meet and greet with my new parole officer, Diane. As I mentioned, Helen was no longer going to be my parole officer and though I was never overjoyed at meeting with her, at least I knew what to expect. Given my first meet and greet with Helen, and given my job interviewing experiences, I wasted time with imaginary dialogues such as:
Imaginary Diane: As educators, we are no longer instructors, givers of instruction, but designers and facilitators of learning. Do you think this is a fair description of what we do?
Me: Tell me what that means and we'll go from there.
Nothing like that occurred.
The first meeting took place in my classroom. Diane is in her fifties, has taught and been a principal, and then took on higher level administrative duties. She currently is in charge of the mentor/parole program for the county in which I teach.
We talked a bit about my classes. I have two this year; a 7th grade math class (non-accelerated unlike last year’s), and 8th grade algebra, most of whom were in my accelerated 7th grade math class last year. “This year’s 7th grade math class had a rough year last year so they’re coming in with an ‘I can’t do math’ attitude right at the start,” I said.
“That’s never a good thing,” she said.
“And on top of that, there are a lot of significant deficits. Like not being fluent with their multiplication facts.”
“Really?” she said, her eyes widening with disbelief. “How can that be?”
Actually, it can be and is in many schools across the US. I wondered how on earth she could not know this, being in education as long as she has.
“So how are you addressing that?” she asked.
“I’ll let you in on a secret,” I said. She looked intrigued.
“I’ve been giving them timed multiplication fact quizzes every day to start off the class. My principal told me that timed quizzes stress students, but these kids love the competition, plus I show them how their scores are increasing.”
“Of course!” she said. “Kids love to compete.” This was several points in her favor since current educationist dialectic dictates that kids should not compete since competition can be injurious.
She looked around the room. “I like the way you’ve set up your classroom.”
This was another hopeful sign, given that the desks were set up in rows, rather than grouped together as is the custom these days. I pointed out that the desks have a white-board like surface so students can do math figuring and/or doodle with dry-erase markers. Plus the desks are small enough to be moved around and fit together to accommodate collaboration.
(What I didn’t say: “Which doesn’t happen too often.”)
In addition to my appearance of concession to the “collaboration is good” catechism there was another important concession—or appearance thereof. Namely, a series of student-made posters adorning my classroom, and which explain mathematical principles such as why the product of two negative numbers is positive, how cross-multiplication works, and why the invert and multiply rule for dividing fractions works as it does. The posters speak to both collaboration (i.e., students worked in pairs to produce them) and “deep understanding”.
These posters were done last year by students in my accelerated 7th grade math class. As bright as those students were, however, the words on the posters came largely from my edits on their drafts. I doubt that any of the students could explain the “conceptual understanding” the poster described. This would be true of all students in my class: even though I taught the concepts, and went over the explanation of “why” for various procedures, the students focused more on the procedure than on understanding. And while this is a fairly well known phenomenon among math students, there are those who hold firmly to the belief that understanding must and always take precedence—otherwise students are “doing” and not “knowing” or some such catch-phrase. For those people, the student posters allow them to believe that I am teaching students to “think like mathematicians.” For the rest of the world, I’m teaching them math.
Diane also liked various quotes I had tacked up on my walls; random things uttered by my students that I felt worthy of making into a quote. Like “In real life, all math is a word problem” and “Variables don’t make sense and make sense at the same time”.
I keep the ones from last year on the wall, as well as new ones from my current crop of students. “Seeing quotes from previous classes gives students a sense of belonging,” I explained to Diane. “Knowing that future students will see what they said gives them a sense of legacy and tradition. This is what I try to create in the classroom. A sense of belonging. An esprit de corps.”
“That’s great,” she said.
There were other quotes as well, that I didn’t point out to her. These are at the front of the room, half hidden by a table with computer equipment piled high on it and are from math teachers and mathematicians—some famous, some not. A few samples include:
“The biggest problem we have in talking about math teaching is the belief that ‘conceptual understanding’ means something”
And
“It is quite possible to use mathematical concepts correctly without being able to say exactly what they mean. This might sound like a bad idea, but the use is often easier to teach and a deeper understanding of the meaning often follows of its own accord”.
These quotes represent a different legacy, a different sense of belonging and esprit de corps. Who makes up this corps varies though many are parents of the students I teach. One parent of a student in my 8th grade algebra class last year gave me a card around the Christmas holidays. It said, “Thanks for bringing math back.”
They see what they want to see as well.
A profound silence followed. This didn’t go over as well as I thought it would since the interviewer—a grim poker-faced humorless woman—was a jerk. So I said “What I mean is…” and explained how in consulting (the job was for a consulting firm) one has to deal with difficult clients, and so on and so forth. I was hired, but it turned out that the jerk of an interviewer was my boss. I was fired within six months (the one and only time in my life).
This interview experience comes to mind as I recall the apprehension I felt before my first meet and greet with my new parole officer, Diane. As I mentioned, Helen was no longer going to be my parole officer and though I was never overjoyed at meeting with her, at least I knew what to expect. Given my first meet and greet with Helen, and given my job interviewing experiences, I wasted time with imaginary dialogues such as:
Imaginary Diane: As educators, we are no longer instructors, givers of instruction, but designers and facilitators of learning. Do you think this is a fair description of what we do?
Me: Tell me what that means and we'll go from there.
Nothing like that occurred.
The first meeting took place in my classroom. Diane is in her fifties, has taught and been a principal, and then took on higher level administrative duties. She currently is in charge of the mentor/parole program for the county in which I teach.
We talked a bit about my classes. I have two this year; a 7th grade math class (non-accelerated unlike last year’s), and 8th grade algebra, most of whom were in my accelerated 7th grade math class last year. “This year’s 7th grade math class had a rough year last year so they’re coming in with an ‘I can’t do math’ attitude right at the start,” I said.
“That’s never a good thing,” she said.
“And on top of that, there are a lot of significant deficits. Like not being fluent with their multiplication facts.”
“Really?” she said, her eyes widening with disbelief. “How can that be?”
Actually, it can be and is in many schools across the US. I wondered how on earth she could not know this, being in education as long as she has.
“So how are you addressing that?” she asked.
“I’ll let you in on a secret,” I said. She looked intrigued.
“I’ve been giving them timed multiplication fact quizzes every day to start off the class. My principal told me that timed quizzes stress students, but these kids love the competition, plus I show them how their scores are increasing.”
“Of course!” she said. “Kids love to compete.” This was several points in her favor since current educationist dialectic dictates that kids should not compete since competition can be injurious.
She looked around the room. “I like the way you’ve set up your classroom.”
This was another hopeful sign, given that the desks were set up in rows, rather than grouped together as is the custom these days. I pointed out that the desks have a white-board like surface so students can do math figuring and/or doodle with dry-erase markers. Plus the desks are small enough to be moved around and fit together to accommodate collaboration.
(What I didn’t say: “Which doesn’t happen too often.”)
In addition to my appearance of concession to the “collaboration is good” catechism there was another important concession—or appearance thereof. Namely, a series of student-made posters adorning my classroom, and which explain mathematical principles such as why the product of two negative numbers is positive, how cross-multiplication works, and why the invert and multiply rule for dividing fractions works as it does. The posters speak to both collaboration (i.e., students worked in pairs to produce them) and “deep understanding”.
These posters were done last year by students in my accelerated 7th grade math class. As bright as those students were, however, the words on the posters came largely from my edits on their drafts. I doubt that any of the students could explain the “conceptual understanding” the poster described. This would be true of all students in my class: even though I taught the concepts, and went over the explanation of “why” for various procedures, the students focused more on the procedure than on understanding. And while this is a fairly well known phenomenon among math students, there are those who hold firmly to the belief that understanding must and always take precedence—otherwise students are “doing” and not “knowing” or some such catch-phrase. For those people, the student posters allow them to believe that I am teaching students to “think like mathematicians.” For the rest of the world, I’m teaching them math.
Diane also liked various quotes I had tacked up on my walls; random things uttered by my students that I felt worthy of making into a quote. Like “In real life, all math is a word problem” and “Variables don’t make sense and make sense at the same time”.
I keep the ones from last year on the wall, as well as new ones from my current crop of students. “Seeing quotes from previous classes gives students a sense of belonging,” I explained to Diane. “Knowing that future students will see what they said gives them a sense of legacy and tradition. This is what I try to create in the classroom. A sense of belonging. An esprit de corps.”
“That’s great,” she said.
There were other quotes as well, that I didn’t point out to her. These are at the front of the room, half hidden by a table with computer equipment piled high on it and are from math teachers and mathematicians—some famous, some not. A few samples include:
“The biggest problem we have in talking about math teaching is the belief that ‘conceptual understanding’ means something”
And
“It is quite possible to use mathematical concepts correctly without being able to say exactly what they mean. This might sound like a bad idea, but the use is often easier to teach and a deeper understanding of the meaning often follows of its own accord”.
These quotes represent a different legacy, a different sense of belonging and esprit de corps. Who makes up this corps varies though many are parents of the students I teach. One parent of a student in my 8th grade algebra class last year gave me a card around the Christmas holidays. It said, “Thanks for bringing math back.”
They see what they want to see as well.
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