General Ideas for the Classroom

Getting to know you…

For the past few years, I’ve had students fill out an online survey for their very first nightly work assignment. It’s to help me get some of the logistics out of the way (their nicknames, making sure they read and understand some key things in the course expectations, making sure they know to have their name on the back of their calculators). But it’s mainly for me to learn about my kids.

I’ve found the questions on the survey are simple and nonthreatening enough that I get interesting responses. However I find that I do get way more extensive and thoughtful answers from the upper level grades than from freshman.

Here is a link to the survey if you want to check it out.

The thing is… I get tons of interesting information about my kids. They let me know about some horrifying thing that happened in fifth grade math that they still remember, or an amazing feeling they got once some abstract concept snapped into place, or about some lifelong passion of theirs that I wouldn’t know about. Perhaps the most important question — in terms of the information I get from it — is this one:


It’s kinda amazing. The phrasing of the question implies that there is something they are nervous about and are invited to write. (It’s so different than “Are you nervous about math this year? If so, why? And if not, why not?”… It’s like asking “What questions do you have?” instead of “Do you have any questions?”)

I’m not going to copy and paste responses, but I will share some types of responses:

  • keeping up with the material / keeping up with classmates / falling behind
  • test anxiety
  • fractions
  • coming across as annoying to classmates
  • memorizing formulas
  • explaining my reasoning in words

They really open up given the opportunity, especially considering I had only met them for 30 minutes before I asked them to fill this out. And if a kid came to you and had told you they were nervous about any of these things, you would know as a teacher precisely what to say!

So what I do, once I get these surveys, is I write back individually to each kid. The emails aren’t long, but they do talk about things that students specifically referenced in their survey. Here’s one from a couple years ago:

Howdy [Stu],

I’m reading through the surveys that you guys filled out for precalculus, and I wanted to respond to you, just to say hello! I’m thrilled that you’re going to be in our large band of precalculetes for the year. I’m excited about everything! We’re going to be doing a lot of exploring and making a ton of connections. I love love LOVE math and have since I was in high school, and I want to extend myself to you. If you ever feel overwhelmed or unclear about things, and they just are staying foggy, never hesitate to email me to set up a meeting. (Of course, I think you should first try to ask a colleague, because they often are better resources than I am.)

You noted that you’re nervous about keeping up with the workload. It is going to be a solid amount each night, but I very much try to keep it reasonable and I also try to make sure it is all relevant/important. I don’t assign 10 of the same types of problems, but rather I assign a couple of them and expect students to try extra problems if they need extra practice. But please let me know if the workload is getting to be too much for you. Last year I asked for feedback periodically on the workload and for the most part kids said it was fine, except in the third quarter when I think I accidentally asked for too much — and when kids told me, I was able to be more conscientious!

You also said that you don’t talk a lot at first, but you will. I saw you talking in your group! I think maybe because this is going to be a group-based class, you’ll find you’ll come out of your shell pretty quickly! But if you’re painfully shy, definitely talk with me. I’ve worked with kids who are shy before and we’ve come up with ways to help get over that so they can delve into the math!

Glad to have met you, and I’m looking forward to an enjoyable year.

Always my best,
Mr. Shah

It takes up a long time to write to every student. I have smaller class sizes that most of my friends, because I’m in an independent school. But still… I only get 5-6 emails written in an hour.

Why do I do this survey? Mainly because I love reading their responses. Especially to these two questions:


I also take the time to reply individually because I hope — though I never really know — that it helps make me more approachable. I pray that it implicitly tells my kids hey, I care. And early in the year, when I stumble through not remembering their names and want to crawl in a hole, this is such an important sentiment to get across.

So in this survey are some of my better questions, and how I deal with them.

[Cross posted on the betterQs blog]

Everyone Has To Raise Their Hands… and other thoughts

We haven’t started school year. But last week and this week I’ve done some brainstorming about things I intend to do this school year (which *ahem* has some aphorism involving a road and hell associated with it, right?), and so I thought I’d pull out those few concrete little bits that deal with questioning that I want to do this year.

  1. If your group has a question, everyone in the group must raise their hand to call me over… This is how I started the last couple years of precalculus (all my kids work in groups). The idea was that if a kid had a question, they needed to first talk with their group so that the math teacher (me!) was not the sole mathematical authority in the classroom. I quickly added on … and I will call on one of you randomly to ask me the question. That way everyone in the group had to be comfortable asking the question, and that it was a real group question and not just an individual question.Last year, for some reason, I didn’t keep up with this practice, and started answering individual questions. I need to remember to keep up with this practice, because it’s awesome  and it works to get kids really talking and explaining without you.
  2. I taught calculus for seven years, and when I started standards based grading, I used to put after each question testing each skill a little box:
    rateIt was useful when I met with students to discuss their tests. If they felt shaky and did poorly, that meant one thing to me. If they felt confident and did poorly, that meant another. If they felt shaky and did awesome, that meant something totally different. It led to some good conversations, and got kids to be more meta-cognitive. It also led to some interesting written feedback on the tests (even if I didn’t meet with the student).But I only ever did that in calculus, and I don’t teach calculus anymore. So I want to incorporate this on my assessments in my other classes — at least geometry and precalculus. When I’m asking a “mathy” question, this is a sort of different additional question that helps me put their response in some context.
  3. Questions can have different purposes for me, even though I don’t (in the moment) think of them this way. Mostly they are to either (a) to get a student to go from a place of not understand to understanding (through asking questions to get them to think and make connections), or they are (b) to help me understand what a kid (or my class as a whole) is understanding.If I’m asking a question to the whole class, and my purpose is to figure out what my kids understand and what they don’t, I’m not going to have my kids raise their hands anymore. I got to the point where sometimes I would call on kids with their hands raised, and sometimes not. I mean: if the kids all raising their hands to answer a question feel they know the answer, then why am I calling on them? Instead, I am thinking of stealing an idea from a friend who taught middle school: THE POPSICLE STICKS OF DESTINY. I am going to have my kids’ names written down on popsicle sticks and pull them out of a mason jar (because I’m such a hipster!) to randomly call on someone. Yeah, index cards work too, but INDEX CARDS OF DESTINY is way less fun to say dramatically.

    If I do this, however, I need to make sure that the kid who doesn’t know something or is confused feels like the classroom is a safe space. This year I’ll be teaching the advanced sections, so there is a lot of insecurity that these kids have about “being smart” (*cringe* I hate that word) and “appearing dumb” to their classmates. I have to brainstorm how I’m going to publicly reward kids for having good questions or being confused but doing something about that confusion or for being wrong but for owning it and saying “I NEED TO GET THINGS WRONG IN ORDER TO FIGURE OUT HOW TO BE RIGHT. AND I’M AWESOME FOR KNOWING THAT.” Heck, maybe I’ll have a poster made which says that, and have kids read it aloud occasionally when they’re wrong. And I should point to it and say it when I am wrong. Or maybe that’s dumb. I don’t know.

That’s about it for now. Hopefully more to come as I figure things out!

[cross posted on the betterQs blog!]

9th Graders Final Exam Prep / 11th Graders and College Recommendations

This is a two part post, but it’s going to be short. The first part is about final exams for freshman, and how to help them. The second part is about teaching students how to properly approach teachers for college recommendations.

First Final Exams in High School

I’m teaching freshpeople (9th graders) for the first time. And I’ve come to learn how important structure is for them. I’ve realized how useful it is to make topic lists for them (next year, I’m going to ween them off of them and show them how to create their own!). I’ve learned how important it is to be explicit with them about everything. And I’ve learned that many don’t quite know how to study.

In exactly a month, my kids are going to have their geometry final. So I whipped up a guide to explain how they might go about facing this daunting task. It’s not perfect. I hate the fact that it is so long and text heavy. But I want to get it out to my kids soon — so editing will have to wait for next year.

The truth is I don’t know if any of them are going to use it. But I’m going to at least provide them with some ideas — and maybe one or two things will resonate with them. Here it is below (and in .docx form). If you have any additional advice you give to your young ones that would go well in this, please throw them in the comments. Although I might not be able to add them for my kids this year, I can revise it for next year.

11th Graders Asking for College Recommendations

I am teaching a lot of juniors this year, which means I will be asked to write a lot of college recommendations. I never learned how to formally ask for a recommendation until I was in college — but when I was taught by a professor (who was helping guide me in the grad school application process) it was enlightening. I crafted a cover letter, got my best work together, and set up a time to meet with my professors who I was asking for aletting of recommendation from. At that meeting, I outlined why their classes were important to me, what I took away from them, and things I was proud of — and why I would really appreciate if they would be willing to take the time to do this huge thing for me. In other words, I was “pitching” this. It was thought-out, respectful, and professional.

When I first started teaching, kids would ask me for recommendations as a “by the way” in the hallway, or in a short one line email. I don’t allow for that anymore. I make sure they sit down with me and we talk through it. I ask them to fill out an extensive set of questions which often helps me frame the kids in my recommendation (if I don’t yet have a framing device in mind), and lets me learn about kids in a different way.

This year I sent an email out to my juniors, being as explicit as possible. It isn’t to make their lives harder. It is to teach them skills that are usually never explicitly taught. And all of this helps me craft a better recommendation.

Hi all,

I know it’s about the time that y’all are going to be thinking about soliciting college recommendations. If you are thinking of asking me to craft one, you should read this email. If you are certain you are not, you don’t need to read past this!

I know early in the third quarter I talked briefly about this in class, but I figured you should have it in writing too. First off, you should talk with your college counselor before approaching teachers about recommendations. They will be able to help you figure out if you’re asking the right people, who can write about the right qualities, for the colleges you are considering.

If you are going to approach me about being a recommender, there are some things you need to know. I am not a teacher who is grade-focused. I’m a teacher who values reflection, growth, hard-work, and demonstrated passion. If you’re a student who struggled but has shown a transformation in how you see and appreciate mathematics, or in your approach to effectively learning mathematics, or in how you communicate mathematics, or in your ability to work effectively and kindly in a group, or something else—all that is important to me. On the other hand, if you have done well on assessments, that is all well-and-good… but it is important that you are more than that… it is important to me that you have shown a passion to go above and beyond (inside and outside of the classroom and curriculum), or an enthusiasm for the material, or a willingness/eagerness to help others. In other words, it is important that you have thought about yourself, and can talk to me about how you are more than just grades.

That all being said, just a few reminders of what I said in class about recommendations:

· I do not write recommendations in the fall, so if you’re going to ask for one, you must ask me this year. Fall is a very busy time and is too far away; I like to have students fresh in my mind when I write. You also cannot approach me after our last day of classes (May 22).
· I never learned how to properly ask for recommendations until I was in college. So I want to help you learn that skill. (I’ve had to ask for recommendations in high school, college, grad school, and as a teacher.) If you’re going to ask me, send me an email to set up a meeting to talk formally about it. You need to plan this meeting, because you’re going to be in charge of leading it. Think about what you’re going to ask and how you’re going to pitch it.
· I said in class that you should start keeping a list in the back of your notebook of specific moments that you’re particularly proud of (large and small!), and things that you’ve done that might set you apart or make you unique or interesting! You should be sure to bring that to our meeting. If you have specific things you’ve done throughout the year that you are proud of (large or small!), you should bring those too.

As you might suspect, I write recommendations with great integrity—meaning I am honest and specific in what I write.

In the past I’ve been asked for a lot of recommendations from juniors. This year I may have to put a cap on how many I’m writing for, unfortunately, as each recommendation takes a number of hours from start to finish. After we meet, if I agree to write for you, you will be asked to fill out an extensive reflective questionnaire. I recognize that I ask a lot of students who request a recommendation, but I also know how important these recommendations are – and to do justice in the recommendation, these are important to me.

Mr. Shah

Two Organizational Things I Do

I don’t know if I’ve blogged about these things before. These aren’t Two Classroom Ideas That Will Completely Change Your Teaching or anything. In fact, I’m willing to bet that many of you have tried or currently do something similar. But for me, these two things have made my life easier and my classroom run more smoothly. So in case this helps…

The First Idea

In Geometry, I want my kids to learn to use multiple tools, and find the tools that are the most useful to them at any given moment. One moment they might need patty paper to trace something. Another moment they might need eraseable (this is key!) colored pencils to emphasize different things. Another moment they might want to pull up Geogebra on their laptops. And another moment, they might need a ruler to draw a straight line. Who knows. So what I did at the start of the year was create geometry buckets, populated with the tools that each group might need at any given time.


I have a different bucket for each group. I color coded most of the items in the bucket (with the exception of the protractors, because I didn’t want to cover any of the angles!). I store the buckets in the room. At any point, kids are allowed to grab them. Sometimes they have to, because they are asked to measure an angle, or draw a circle. When I have them use the giant whiteboards, they have their dry erase markers and an eraser in the buckets. But most of the time, when a kid needs some patty paper, or a ruler to make a diagram, or colored pencils to organize their ideas or annotate a diagram, they’ll just grab the bucket and bring it to their groups. And at the end of each class period, the kids will just put them back.

I thought things would get lost or mixed up. But it’s been a semester, and I just went through the buckets and have found only a few colored pencils were in the wrong boxes, and only a single compass migrated from one box to another. I love these buckets of geometry tools!

The Second Idea

I do tons of groupwork in my classes. And I try to switch up groups often enough for some spice, but let them work together long enough so they can learn to work together (I try to do it two times a quarter). However, when kids are in groups, passing things out and collecting things can be annoyingly time consuming. And if my kids know one thing about me as a teacher: I don’t waste time, not a second.

So here they are: something I’ve been doing for the past few years. Folders. Specifically, each group gets one folder.

20150226_175913 (1)

On the front (not photographed), I have a label with the kids’s names on it. Inside are two pockets. The left hand pocket is for things I normally would hand out. (Mainly: the packets that I make for kids to work collaboratively through.) The right hand side has two purposes: (1) I have kids turn in nightly work sometimes, so they will put it in there, and (2) when I mark up the nightly work, I put it back in there and students collect it the next day.* There are also some “The Dog Ate My Homework” forms for when a kid doesn’t turn in their work. Instead of them calling me over and giving me a story explaining what happened, I just have them fill out that form saying why they didn’t have their work.

One huge benefit for having these folders is that it allows me to mix up where the groups sit each day.** When I walk into the classroom, kids aren’t sitting down usually. They are waiting for me. I throw down each folder on group of desks, and then kids sit at the group of desks with their folder on it. That way: kids are in different locations each day, mixing things up. The group in back won’t always be in back! Sometimes I give a kid the folders to put down, and sometimes the power, the sheer power of who sits where, goes to their head. (“Oh, you’re standing by this group of desks? Too bad, I’m putting your folder waaaay over at that far group of desks.”) Fun times.

Now you might say: each day you have to put in the packets you’re going to hand out the next day? Nope.Well, sometimes. But usually not. In classes I’ve taught before, where I have my ducks in a row, I do a massive photocopying of the papers for the entire unit. I lay them out, and fill up the folders. Then I’m pretty much set for a week or two (or more!). Below is a picture of me doing that today!


That is all. Go back to your regularly scheduled lives now.

UPDATE: I forgot to say: I color code the folders for each class. So red folders = my geometry class, blue folders = one of my precalc classes, green folders = the other one of my precalc classes. I also use a lot of file folders to organize things for me. And for those, I use the same color folders for each of my classes. So, for example, when I give a geometry test, I bring a red file folder to class. And then I keep the taken geometry tests in that file — and when I’m going home, I just throw that red file in my backpack so I can mark ’em up.

*The fact that there is one folder per group also has the added bonus that when one kid forgets to put their name on their nightly work, you know exactly whose it is, because it is in the folder for that specific group (and usually all the other kids put their name on it).

**Someone, somewhere, told me that there was some ed research that suggested that kids sitting in the same spot every day helped them learn better. I have my doubts about that.

Intersections, 2013-2014

Today we had our launch party for Intersections, our school’s math-science journal. Last year a science teacher and I gathered interested students to produce this journal — and they worked tirelessly and did a spectacular job. This year, we have some new students and some old students who served as editors. Here they are giving their speech at the launch party (which was also a pizza-soda party).


More than anything, I have enjoyed watching the editors become independent leaders, organizing something involving so many people and moving parts, and presenting their creation to administrators, math teachers, science teachers, computer science teachers, and other students. I feel like I’m coming to understand the niche I play in my school: I find ways to make math exist outside of the formal curriculum for kids who want to get more involved. Intersections is one of those spaces — both for editors and for those students who submitted.

If you want to check out this year’s issue, please click on the cover photo (designed by a student) below and it will take you to the website.



(You can also click here.)

More than anything, if you have the time, just click around and see what cool things you discover!

Although it’s a lot of work, if you have any thoughts about starting something like this at your school, I highly recommend it.

Senior Letter 2013-2014

Every year I write a letter to my seniors. Each year the message is pretty much the same, though the way I deliver it may change a bit based on the class and what I’m feeling at the time. Each year I hate my letter when I’m done, but I decide I’m going to give it out because it’s a tradition and I don’t want to break it, and I convince myself it is not that awful. I hand it out. I’m grateful after I do, because… I suppose I need closure. I have worked with these kids closely for a year (sometimes more). And I have come to care about them all. And although it happens every year — they leave and I stay — and from this point on they slowly begin fading from my memory, right now they are in my life in saturated colors and I know I’m going to miss them and I want the best for them.

So even though I currently hate it, here is this year’s senior letter.

It came packaged with their “who I am” sheet that they wrote about themselves on the first day of class, and two cards I had printed.


“Explore Mathematics: Part II”

I felt like my first venture into “Explore Mathematics!” was so successful last quarter with my Advanced Precalculus kids that I wanted to build upon that. So this is what I’m doing for “Explore Mathematics!: Part II”

  • Last quarter students scoured the web and did 5 different mini-explorations which exposed them to all the neat math that exists outside of our standard curriculum. This quarter students will be doing up to two more in-depth explorations.
  • Because I don’t want this to be seen as busy work, doing “Explore Mathematics!: Part II” is going to be completely optional. I was glad to read that almost every kid who did the five mini-explorations last quarter didn’t end up finding it busy work, but I suspect doing it a second time would feel tedious.
  • To have some sort of incentive for those who do it, I am going to make each of the two explorations worth 12 points. These explorations will count as a mini-assessment (normal assessments are around 50 points). This is useful for kids because our fourth quarter only has 18 days of instructional time (seriously) — so there are only two major assessments and one minor assessment scheduled. Doing these explorations can act as a way to get another mini-assessment grade in there, that will be low-stress, high-reward. [1]
  • I’m not framing it around the grade boost it will likely provide, but around the fact that it’s an opportunity to do some awesome math explorations, for anyone who wishes to do so.
  • It is still pretty open-ended, but I’m now looking for students to write something to get others to see what they find interesting/intriguing/awesome about something.

Here’s the document I just emailed my kids:

Here it is in .docx form in case you want to modify it.


[1] Yes, I do SBG with my calculus kids. Yes, I know how ridiculous this sounds, me playing the “point game.” I almost wanted to make it so that there was no external reward, but our kids are so busy with so many things that I know even a little incentive will go a long way. I’ve been at my school long enough, and know our kids well enough, to know this is doomed to failure without a little external reward.