I’m thrilled that Sam Shah is the first math teacher to be featured on this site. Sam teaches at Packer Collegiate Institute in Brooklyn, NY and writes the math teaching blog, Continuous Everywhere Differentiable Nowhere, which was nominated for two Edublog awards.
Type of School: independent K-12 school
Years taught: This is my 6th year teaching.
Number of students this year: 49
You were a straight-A math student at MIT and received an M.A. in History of Science at UCLA. What led you to teaching at the secondary level?
I used to play “school” when I was young, and make tests for my parents and sister to take. Like, really hard tests. But I wasn’t good at school: I used to get Cs in junior high. It wasn’t until eighth grade that I finally saw school as something I could do, and junior high is when I started falling in love with mathematics.
Then, in high school, I had a triumvirate of three amazing teachers: a math teacher, a history teacher, and most significantly, an English teacher who started broadening my horizons. And because I respected them so much, I knew teaching high school was what I wanted to do with my life.
While I was taking math classes in college, I also took some history of science classes to fulfill the general requirements for a degree. And I fell in love with that subject — head over heels. And so I decided to check out academia and see what it was all about, thinking maybe I wanted to teach at the college level. But no, even though I loved learning, I hated academia and my favorite times in grad school were planning and leading my discussion sections with undergrads. But teaching is not what academia rewards. So I decided that wasn’t the life I wanted, I left, and here I am!
What excites you about math, and how do you get students excited about it? What’s your favorite topic to teach?
There is this inherent beauty and connectedness to math. It’s creative, because there are often many ways to get from question to solution. For me, it’s conceptual depth, or deep understanding, that keeps me invigorated.
Even though it’s “just” high school math, every year I have these random insights that will totally upend how I look at a topic. For example, just recently, I had a moment where I said: “Wait, what is an instantaneous rate of change?” when I was planning a calculus lesson, and then: bam! New lesson plans, investigating just that idea.
Not all my students love math. But one piece of feedback I get is that just being enthusiastic about what we’re doing is super helpful to get them interested. I try to show them what I find stunning/unexpected/interesting/weird, and hope that they get a little taste of what I see. But I should say that I tend to teach fairly traditionally – without many projects or applications.
My favorite topic to teach is anything that involves students coming to a deep conceptual understanding rather than a surface-y, robotic understanding. It could be inflection points and the shape of a curve in calculus, or completing the square in Algebra II. Those lessons that I have which get at the ideas — those are what I really go gaga for.
How do you handle stereotypes in your classroom, such as ‘Asians must be good at math,’ and ‘Girls are bad at math’?
I wish I could say I have a good answer to this. I realized I used to judge students based on their handwriting a little bit (!)… And if I taught siblings, I would often expect them to be alike. As I’ve matured as a teacher, though, I have learned to take each student as an individual, and we start our relationship from scratch at the beginning of the year.
That said, I have noticed that many girls in my non-advanced classes tend to suffer from what I call “learned helplessness.” This is when a student hits the first moment of frustration, and her method of dealing with it is to raise her hand and ask for help.*
To combat this, I ask students to ask each other for help first. Then I’ll come over and ask a random group member what the problem is. I also won’t allow students to say, “I don’t know.” I have them say something they do know, and try to pinpoint exactly what their blocking point is.
*The opposite of this is with boys who tend to not ask any questions. They hope all will work out via divine intervention or something. I don’t have good strategies for this, other than encouraging question asking and students to be proactive.
Last August, 140 teachers signed up for your Math Blogging Initiation. They wrote once a week for four weeks based on prompts you created. How did it go? Why did you start the project, and what have you learned from it?
I started the initiation because I had created a “Welcome to the mathtwitterblogosphere” website to help people get involved with our community, and I wanted to capitalize on that momentum.
The feedback we got was overwhelmingly positive! Although it was a lot more work than I imagined since so many people signed up, I had a ton of help from a great crew of bloggers.
What I learned was that there are a lot of people out there reading blogs, but not writing! I used to think of the math teacher blogosphere as this really tiny sparkling star with a set number of people on it, but it turns out there is this whole glowing penumbra of people around the star. Okay, that might not make so much sense. Sorry. You get the idea, right?
If you could change one aspect of your job, what would it be?
Freedom. I would like to really have complete control over my classroom, my pacing, my grading, everything. In order to grow, I need to take risks, fail here and there, and just be trusted to do what I know I can do well.
What’s the biggest misconception about what you do?
I think most people think teaching is an 8-3:30 job. I mean, when I was in high school, even though I was surrounded by teachers all day, I assumed teachers just (a) taught classes, (b) graded papers, (c) photocopied worksheets, and (d) prepared for class by coming up with a few example problems and do a lot of winging it. But that’s nothing like what teaching is.
I start at 7:30 and go until 7 or 8pm every day (if not longer). And I work on weekends. And over breaks. It’s just a lot of work, and is physically and emotionally draining, but most people don’t see that. And that’s hard to get across to people. The fact that we’re dealing with kids, and not “classes,” is also hard to get across to people. That’s why my friend Tina and I have created A Day In The Life.
What teacher made the most impact on you and why? What would you tell him/her now?
There have been too many (including the few I listed above). I want to tell them all: thank you. As teachers, our students constantly leave us, and we never really know if we changed their worldview a little bit…or if all we did came and went and nothing but dust remains. That endemic uncertainty to our profession, that sucks.
I would tell my teachers they inspired me to become a teacher because I love learning, and I value knowledge. Those are things they inculcated in me, and I want to do for others what they did for me.
What advice do you have for aspiring or beginning teachers?
I’ve written An Open Letter to New Teachers. Here’s an excerpt:
Dear person about to enter the classroom as a fulltimeteacher,
I love you. Okay, fine, not quite true — maybe respect, like, or lurve is more appropriate — but you have a passion for something and you’re following it. I don’t know if that passion is for the subject you teach, or for working with kids, or the deeply interesting intellectual puzzle of how to get someone to understand something, or for (in the booming Wizard of Oz voice) the Betterment of All Mankind. Regardless, this thing that brings you to the classroom is wonderful, because it puts you in the same ranks as those wonderful teachers that loom large in your past who inspired you and who helped you recognize that what they do has some worth. (Unfortunately, it also means you’ll probably have a bank account similar to those teachers. Sigh. Yeah, that will continue to suck, newteacher.)
Those Who Teach 