# Nominations, Part I

At TMC this past summer, Kathryn Belmonte introduced an idea about sharing student work in the classroom. Something she termed “NOMINATIONS!” I loved the idea — and wanted to use it when kids do their explore-math project. But I saw it was so flexible, and pretty early on, the time was right to test it out. So I modified it slightly and this post is about that…

In all of my precalculus classes (I teach two standard sections and one advanced section), my kids are being asked to do tons of writing. A few who have had me before in geometry are used to this, but most are not. And honestly: getting down what mathematical writing is, and how to express ideas clearly, is hard.

So what do I do? I throw them into the deep end.

On day two of class, I ask them to write an answer to a problem for a seventh grader to understand. On the third day of class, they come in, and are given the name of the student who comes after them alphabetically (and the last person is given the name of the first person alphabetically). Then they read these instructions:

Everyone moves to the desk of the name they were given. Then I project on the board:

And I give students to read through a different student’s solution. They have to make sense of it — pretending to be new to the problem. And then they critique it. Eventually, probably after 3-5 minutes, I left them return to their seats. They read over the comments. I talk about why the feedback is important. And how specific feedback is useful (so “good explanation” is less useful than “your explanation of how the groups were made was easy for me to follow”). And then we continue on with class.

Here are examples of some post-its (front of a few, then back of a few):

To follow up: that night for nightly work, I gave students a writing problem — a simple probability problem. My hope was that this would help them pay attention to their explanations. I collected the problem and read through the writeups.

They weren’t so hot. Most of them didn’t talk about why and some didn’t have any diagrams or visuals to show what was happening with the problem. So I marked them up with my comments. (They got full credit for doing it.) The next day I handed them back and shared my thoughts. I also shared a copy of a solid writeup — one that I had created — along with four or five different possible visuals they could have used. (I realized –after talking with Mattie Baker about this — that I couldn’t really get my kids from point A to point B unless they saw what point B looked like, and what my expectations were.)

At this point, I wanted to figure out if they were taking anything away from all of this. So I created a page with three questions. A formative assessment for me to see what my kids understand and what they don’t about the content. But I also asked them to take all the feedback they’ve gotten about writing and explanations, and explain the heck out of these problems. Here’s an example of one of the problems (one I’m particularly proud of):

I collected them today. I haven’t looked through them carefully yet, but from a cursory glance, I saw some thoughtful and extensive writeups. And even from this cursory glance, I can see that these two activities — plus all the conversations we’re having about explaining our thinking in class — have already made an impact.

Yes, they’ve gotten some ideas of what a good writeup looks like. They know diagrams can be helpful. They know words to explain diagrams are important. They know the answer to why is what I’m constantly looking for when reading the explanations.

But more important to me is the implicit message I’m trying to send about my values in the classroom. I think a lot about implicit messaging to communicate my values, especially at the start of the year. And I am confident my kids know with certainty that I value all of us articulating our thinking as best as we can, both when speaking but also when doing written explanations.

# Notes on the Start of the Year

Today was my first day with kids. I can’t tell you how terrified I was to be back. I had about a zillion normal reasons (the standards: do i still remember to teach? so many kids names to learn and i’m terrible at it! what if I totally suck?). I also have a lot on my plate right now, a few of which are out of the ordinary, which have put me in a weird headspace. #cryptic #sorry

However I had a really good day today. I saw my advisory and two of my four classes. I even went to some of the varsity volleyball game after school!

This post isn’t about my kids or my classes. It’s going to be about some things I’ve done at the start of this year.

(1) Inclusivity. I read a book about trans teens this summer. We had a lot of conversations about pronouns last year. We as a school have taken gendered pronouns out of our mission statement. Last year I included this in my course expectations:

But this year, in my get-to-know-you google form that I give to kids, I asked for their pronouns.

Chances are, I probably am not going to get any different answers that what I expect this year. But I’m not including this question for the majority of kids. I want to be ready when that first kid gives me pronouns that differ from what I may expect. I want that kid to know they can find comfort (not just safety) in our room. And I want all kids to know things that I value. And I think this question sends that message — no matter who the kid is.

That’s the idea behind it. Who knows if my intention is how the kids will understand/interpret it?

(2) Mattie Baker and I were working at a coffeeshop before the year started, and he showed me his class webpage, which had this video (which I’d seen before) on it front and center:

I loved how *real* this video felt to me. Not like something education schmaltzy which makes me want to roll my eyes. I then went searching for a twin video that explicitly talks about the growth mindset. I had a dickens of a time finding one that I felt would be good for students to watch, but didn’t seem… well… lame. I found one:

So as part of the first set of nightly work, I’m having kids watch these videos and write a comment on them in google classroom. (So others can read their comments.) As of writing this, one class has already had two kids post their comments (even though I don’t see them until next week). I read them and my heart started singing with happiness. I have to share them:

Two videos aren’t a cure-all. But having kids realize how important having a positive can-do attitude, and how important it is to look at math as a skill to be developed (rather than something you’re innately born with and is fixed) is so important to me. I have to remember to be cognizant about how important this stuff is, and how important it is to reinforce daily.

(3) In both of my classes today, one student said something akin to “I first thought this, but then I talked with Stu (or listened to the whole class discussion) and I changed my mind.” I stopped both classes and made a big deal about how important that was for me. And how those types of statements make my heart sing. And why they make my heart sing. So they should say those sort of things aloud a lot. Okay, so I said it once in each class. How can I remember to say it a lot more? In any case, it was a teacher move I was proud of.

Oh oh another teacher move… I saw when one student was sharing their thinking with the class, but not everyone was facing the student. And I remembered Mattie Baker and Chris Luzniak’s training from this summer (on dialogue in the classroom). I told everyone they had to face the person that was speaking. I need to remember next week to make this more explicit — and talk about (or have kids articulate) what they should look like when actively listening to someone. And why it’s important to give this respect to someone. They are sharing their thinking — which is a piece of them — with us. They took a risk. We need to celebrate that. And try to learn from their thoughts. Doing anything else would be a disservice to them and to our class. (Okay, clearly you can tell I’m thinking through this in real-time right now by typing.)

(4) Robert Kaplinsky has created a movement around opening classrooms up. I personally hate being observed. Before someone comes, I freak out. Of course as soon as I start teaching, I absolutely forget that they are watching. Totally don’t even recognize them as an entity. In fact, I think I often teach better, probably because I’m subconsciously aware I’m being watched so I’m hyperaware of everything I’m doing.  But leading up to it is horrible. And I also hate the idea of “surprise visits” because… well, who likes them?

That being said, I know that getting feedback is important, and I know that in my ideal school, classrooms wouldn’t be silos. So I joined in. Not for all my classes… I need to dip my toe in gently. But I posted this next to my classroom door:

Next week or the week after, I’ll probably put this up as a “do now” and ask kids “what do they notice/wonder?” about it. Then I’ll tie it into a conversation about growth mindset and the videos they watched.

(5) For the past two years, I’ve been teaching only advanced courses. (In fact, because of that, I asked to teach a standard course… I have taught many, and it was weird to not have that on my plate for two years.) And I heard from someone that a few kids were nervous about having Mr. Shah because “he teaches the really hard courses? will he be able to teach us?”

I know that my first few classes with these kids need to show them that I am different than they expected. I also was proud of this paragraph I put on the first page of their course expectations…

(6) I met my advisory for the first time. Seniors. The thing is: we’re ramping up our advisory program to be more meaningful. Advisors are going to be with their advisees for four years. We are going to be the initial point of contact for many things. And we want to be there to support and celebrate our advisees in a way that we haven’t been able to in our previous set up.

But for all this to happen, I need to form relationships with my advisees. Relationships that go beyond pleasantries. In our training for our new advisories (amazing training… I think I should write a post to archive that thinking before I forget it… done by the Stanley King Institute) we did an exercise. We found someone we didn’t know (I found a new teacher at our school). We had to think about something meaningful to us, and something real (not something like our favorite sports teams… sorry sports fans)… and then talk about it with our partner for EIGHT MINUTES. Anyone who has been a teacher knows that speaking about anything for eight minutes straight is tough. It feels like eternity. While that person is speaking, the other person is actively listening. They can say a few words here and there, like “oh yeah…” or “totally,” but it wasn’t about having a conversation.

Normally I’d roll my eyes at something like this. But at the end, I felt like I got to know this new person at our school pretty well… actually, considering we only had eight minutes, amazingly well… and we bypassed all the initial superficial stuffs. That stuff, like movies and books and stuff, we’ll get to later. Yes, it was awkward. But yes, it worked.

So here’s how I adopted it for my advisory. I met with them today to do a bunch of logistics, and then I took them to a different room. I had cookies, goldfish, crackers, and a cold drink for them. And I explained this exercise. And I said: “I want to do this with you. I want to get to know you.” And so I took out the notecards I prepared, and I shared stuff about my life with them. And they were rapt. I told them about stuff going on in my family that was exciting and stuff going on that was tough, I told them “things I wish my students knew” (this is such a great way to flip “things I wish my teacher knew”). I told them my total anxiety for the start of the school year and why I had it, and I told them my total excitement for the start of the school year and why I had it. I even said: “I never feel like I’m a good enough teacher.” When I was saying that, I wondered how many kids think “I never feel like I’m good enough.”

A photo of my index cards are here… but I only used them as launching points. I didn’t want to be rehearsed.

I’m a guarded person, and I made sure never to cross the line between personal and professional, but when I finished, I sensed some (all?) of them were processing that a teacher opened up to them in this way. A few thanked me for sharing with them.

I wanted to set up an initial connection, and send the message I want you to know that I’m not an advisor in name only… I’m opening up to you because I want you to believe that when you’re ready, you can open up to me. They’re seniors. They have a lot figured out. But I hope they know I’m here for the stuff they don’t have figured out.

In the next week and a half, I have 10 minute meetings with all of my advisees individually. I told my kids they are going to talk to me about what’s meaningful to them for 8 minutes. I acknowledged it would feel awkward. I told them they didn’t need to open up in any way that made them feel uncomfortable. But I wanted them to speak about whatever is meaningful to them. We’ll do favorite books later. Now I’ll get to know them on a more personal level. [1]

(6) As you might have noticed from #4 above, I’m trying to be better about formative assessments. I want to make sure I know what kids are thinking, and where they are at, and use that to refine or alter future classes. I haven’t tried this out yet (today was just our first day!!! I only saw two classes!!!), but I made a google form for exit tickets.

This is a #MTBoS sample version, so feel free to click on it, and fill out fake feedback to get an idea of the form.

Pretty awesome idea, right? I didn’t want to have a bunch of pre-printed slips (something I knew I wouldn’t actually do).

(7) I took a page from Sara Van DerWarf’s playbook. I didn’t do this on the back of name tents, but I have a separate sheet that they’re filling out. For my two classes today, I asked them to share something about themselves that would help me get to know them as something other than a kid in our math class. Some kids gave a lot, some a little, but I learned something about each one of my kids. As I’ve mentioned, I’m terrible with names. But what’s nice is on this sheet I created, I put photos (they’re in a school database for us to use) and knowing something about them is helping me remember their names. It’s odd and unexpected and lovely. Kids interested in arts/photography/social justice/sports/debating-arguing/nature/etc. I liked writing that little note back to my kids. I don’t know what question I’ll ask next. I may ask them “Math is like…” (like James did). For the penultimate one, I should definitely take a cue from Sara and ask them to ask ME a question.

I have a few more ideas for posts percolating. I hope that I get the time and motivation to write them. But it’s nice to be back!!! SCHOOL IS IN SESSION!

***

[1] This is what I included in my email to my advisees:

I know it may feel awkward, but when you meet with me during this meeting, you’re going to speak for 8 minutes about things that are meaningful to you. So something more than a listing of your favorite books/movies. If you need help thinking about this: what makes you tick? what makes you gasp? what are your thoughts about senior year and the future? what could you not imagine doing? what are you feeling? what keeps you up at night? These are all questions that might help you find things that are truly meaningful to you. I found it really helpful to have an index card of things when I was talking with you, because I was nervous. I suggest doing that!

# Pitching college math courses

Ooops. This turned out to be a post with no images. So here’s a TL;DR to whet your appetite: I wanted to expose my seniors to what college mathematics is, but instead of lecturing, I had them “pitch” a college course to the rest of the class.

My multivariable calculus courses was coming to an end, and I got some questions about what college courses in math are about. It reminded me of a comic strip I read years ago, which I frustratingly can’t find again. It has an undergraduate going to meet with his math professor adviser, saying something like “I want to major in triple integrals.” Which is crazy-sounding — but maybe not to a high school student who has only ever seen math as a path that culminates in calculus. What more is out there? What is higher level math about? (These questions are related to this post I wrote.)

So here’s what I told my students to do. They were asked to go onto their future college math department websites (or course catalog), scour the course offerings, and find 3-4 courses that looked interesting and throw these courses down on a google doc.

It was awesome, and made me jealous that they had the opportunities to take all these awesome classes. Some examples?

After looking through all the courses, I highlighted one per student that seemed like it involved topics that other students had also chosen — but so that all the courses were different branches/types of math. I told each student to spend 10-15 minutes researching their highlighted course — looking up what the words meant, what the big ideas were, finding interesting videos that might illustrate the ideas — so they can “pitch the course to the class” (read: explain what cool math is involved to make others want to take the course).

I’m fairly certain my kids spent more than 10-15 minutes researching the courses (I’m glad!). Each day, I reserved time for 2-3 students to “pitch” their courses. And since some of the ideas were beyond them, after the pitches, I would spend 5 or so minutes giving examples or elaborating on some of the ideas they covered.

If you want to see the research they did for their pitches, the google doc they chucked their information into is here.

Some fun things we did during the pitches?

(1) We watched a short clip of a video about how to solve the heat equation (that was for a course in partial differential equations)

(2) I showed students how to turn a communication network into a matrix, and explained the meaning of squaring or cubing the matrix (this was for a course on network theory)

(3) A student had us play games on a torus (a maze, tic tac toe) (this was for a course on topology)

(4) I had students store $x=0.3$ on their calculators. Then I had each student store a different “r” value (carefully chosen by me) and then type $r*x*(1-x)->x$ in their calculators. They then pressed enter a lot of times. (In other words, they were iterating $x_{n+1}=rx_n(1-x_n)$ with the same initial conditions but slightly different systems. Some students, depending on their r value, saw after a while their x values settle down. Some had x values that bounced between two values. Some had x values that bounced between four values. And one had x values that never seemed to settle down. In other words, I introduced them to a simple system with wacky wacky outcomes! (If you don’t know about it, try it!) (This was for a course on chaos theory)

(5) A student introduced us to Godel’s incompleteness theorem and the halting problem (through a youtube video)

It was good fun. It was an “on the spot” idea that turned out to work. I think it was because students were genuinely interested in the courses they chose! If I taught a course like AP Calculus, I could see myself doing something similar. I’m not sure how I would adapt this for other classes… I’m thinking of my 9th grade Advanced Geometry class… I could see doing something similar with them. In fact, it would be a great idea because then they could start getting a sense of some of the big ideas in non-high school mathematics. Kay, my brain is whirring. Must stop now.

If anyone knows of a great and fun introduction to the branches of college level math (or big questions of research/investigation), I’d love to know about it. Something like this is fine, but it doesn’t get me excited about the math. I want something that makes me ooh and ahh and say “These are great avenues of inquiry! I want to do all of them!” I think those things that elicit oohs and ahhs might be the paradoxes, the unintuitive results, the beautiful images, the powerful applications, the open questions… If none exists, maybe we can crowdsource a google doc which can do this…

This year, our school adopted this weird rotating schedule where we see our classes 5 times out of every 7 days. And four of those times are 50 minute classes and one of those times is a 90 minute class.

I didn’t have a clear idea of what to do in multivariable calculus for the block. I still had to cover content, but I wanted it to be “different” also. After many hours of brainstorming, I came up with a solution that has worked out pretty well this year.

The 90 minute block was divided into 50 minutes of traditional class, and 40 minutes of book club. (Or 60 minutes of class, and 30 minutes of book club.)

Now, to be clear, this is a class of seven seniors who are highly motivated and interested in mathematics. I can see ways to adapt it in a more limited way to other courses, with more students, but this post is about my class this year.

## BOOKS

We started out reading Edwin Abbott’s Flatland.

Why? Because after they read this, they understand why I can’t help them visualize the fourth (spatial) dimension! But it convinces them that they can still understand what it is (by analogy) and makes them agree: if we can believe in the first, second, and third spatial dimensions, why wouldn’t we believe in higher spatial dimensions too? It’s more ludicrous not to believe they exist than to believe they don’t exist! A perfect entree into multivariable calculus, wouldn’t you say?

After reading this, we read the article “The Paradox of Proof” by Caroline Chen on the proposed solution to the ABC conjecture.

This led us to the notion of “modern mathematics” (mathematics is not just done by dead white guys) and raised interesting questions of fairness, and what it means to be part of a profession. Does being a mathematician come with responsibilities? What does clear writing have to do with mathematics? (Which helps me justify all the writing I ask for on their problem sets!) It also started to raise deep philosophical questions about mathematical Truth and whether it exists external to the human mind. (If someone claims a proof but no one verifies it, is it True? If someone claims a proof and fifty people verify it, is it True? When do we get Truth? Is it ever attainable? Are we certain that 2+2=4?)

At this point, I wanted us to read a book that continued on with the themes of the course – implicitly, if not explicitly. So we read Steve Strogatz’s The Calculus of Friendship:

What was extra cool is that Steve agreed to sign and inscribe the book to my kids! The book involves a decades long correspondence between Steve and one of his high school math teachers. There are wonderful calculus tricks and beautiful problems with explanations intertwined with a very human story about a young man who was finding his way. Struggling with choosing a major in college. Feelings of pride and inadequacy. The kids found a lot to latch onto both emotionally and mathematically. Two things: we learned and practiced “differentiating under the integral sign” (a Feynman trick) and talked about the complex relationship that exists between teachers and students.

After students finished this book, I had each student write a letter to the author. I gave very little guidelines, but I figured the book is all about letters, so it would be fitting to have my kids write letters to Steve! (And I mailed the letters to Steve, of course, who graciously wrote the class a letter back in return.)

Our penultimate reading was G.H. Hardy’s A Mathematician’s Apology:

I went back and forth about this reading, but I figured it is such a classic, why not? It turned out to be a perfect foil to Strogatz’s book — especially in terms of the authorial voice. (Hardy often sounds like a pompous jerk.)  It even brought up some of the ideas in the “Paradox of Proof” article. What is a mathematician’s purpose? What are the responsibilities of a mathematician? Why does one do mathematics? And for kids, it really raised questions about how math can be “beautiful.” How can we talk about something that is seen as Objective and Distant to be “beautiful”? What does beauty even mean? Every section in this essay raises points of discussion, whether it be clarification or points that students are ready to debate.

What is perfect about this reading is at the same time we were doing it, the movie about G.H. Hardy and S. Ramanujan was released: The Man Who Knew Infinity (based on the book of the same name).

Finally, we read half of Edward Frenkel’s Love and Math:

Why? Because I wanted my students to see what a modern mathematician does. That the landscape of modern mathematics isn’t what they have seen in high school, but so much bigger, with grand questions. And through Frenkel’s engaging telling of his life starting in the oppressive Russia and ending up in the United States, and his desire to describe the Langland’s program understandably to the reader, I figured we’d get doses of both what modern mathematics looks like, and simultaneously, how the pursuit of mathematics is a fully human endeavor, constrained by social circumstances, with ups and downs. Theorems do not come out of nowhere.Mathematicians aren’t the blurbs we read in the textbooks. They are so much more. (Sadly, we didn’t read the whole thing because the year came to a close too quickly.)

## STRUCTURE OF THE BOOK CLUBS

I broke the books into smaller chunks and assigned only them. For Flatland, it might have been 20-30 pages. For Love and Math or A Mathematician’s Apology, it might have been 30-50 pages. We have our long block every 7 school days, so that’s how much time they had to read the text.

At the start, with Flatland, students were simply asked to do the reading. Two students were assigned to be “leaders” who were to come in with a set of discussions ready, maybe an activity based on something they read. And they led, while I intervened as necessary.

For every book club, students who weren’t leading were asked to bring food and drink for the class, and we had a nice and relaxing time. On that note,  never did I mention anything about grades. Or that they were being graded during book club. (And they weren’t.) It was done purely for fun.

Later in the year, I had students each come to class with 3-4 discussion questions prepared, and one person was asked to lead after everyone read their questions aloud.

The discussions were usually moderated by students, but I — depending on how the moderation was going — would jump in. There were numerous times I had to hold back sharing my thoughts even though I desperately wanted to concur or disagree with a statement a student had made. And to be fair, there were numerous times when I should have held back before throwing my two cents in. But my main intervention was getting kids to go back to the texts. If they made a claim that was textually based, I would have them find where and we’d all turn there.

Sometimes the conversations veered away from the texts. Often. But it was because students were wondering about something, or had a larger philosophical point to make (“Is math created or discovered?”) which was prompted by something they read. And most of the times, to keep the relaxed atmosphere and let student interest to guide the conversation, I allowed it. But every so often I would jump in because we had strayed so far that I felt we weren’t doing the text we had read justice (and we needed to honor that) or we were just getting to vague/general/abstract to say anything useful.

## EXAMPLES OF DISCUSSION QUESTIONS

I mentioned students generated discussion questions on their own. Here are some, randomly chosen, to share:

•  Strogatz talks about how math is a very social activity. We see this exemplified in the letters between Steve and Mr. Joffray, but where else do we see this exemplified in math? (papers, etc.) How do you think Strogatz might have felt about Shinichi Mochizuki’s unwillingness to explain his paper and proof to the math community?
• What do you think about Strogatz and Joff using computer programs to give answers to their problems? Are computers props, and their answers unsatisfying? Or are they just another method, like Feynman’s differentiating under the integral?
• Do you like A Square? In what ways is he a product of his society? Does he earn any redeeming qualities by the end of the book?
• Can you draw any connections between things in Flatland and religion? Do you think Abbott is religious? Why/why not?
• When we first read about Mochizuki’s ABC Conjecture, we debated whether or not math is a “social” subject. Perhaps many mathematicians do much of the “grind” work on their own, however, throughout everything we’ve read this year, there has been one common link when it comes to the social aspects of math: mentorship. It appears to me that all of the great mathematicians we know about have been mentored by, or were mentors others. In what ways have Frenkel’s mentors – he’s had a few – had an influence on the path of his mathematical career? Do you think he would/could be where he is today without all of those people along the way? Can you think of any mentors that have had a profound influence on your life? (The last one can just be a thought, not a share.)
• Frenkel talks about the way in which math, particularly interpretations of space and higher dimensions, began to influence other sectors of society, specifically the cubist movement in modern art. This movement was certainly not the first time math and science influenced art and culture – think about the advent of perspective in the Renaissance and the use of technology on modern art now – however math and art are often thought as opposites and highly incompatible. Why do you think that people rarely associate the two subjects? Would you agree that the two are incompatible? Can you think of other examples of math/science influence art/culture/society?

## REFLECTIONS

In many ways, I felt like this was a perfect way to use 30 minutes of the long block. After doing it for the year, there are a few things that stood out to me, that I want to record before summer hits and I forget:

(a) I think students really enjoyed. It isn’t only a vague impression, but when I gave a written survey to the class to take the temperature of things, quite a few kids noted how much they are enjoying the book clubs.

(b) For the post-Flatland book club meetings, I need to come up with multiple “structures” to vary what the meetings look like. Right now they are: everyone reads their discussion questions, the leader looks for where to start the discussion, the discussion happens. But I wonder if there aren’t other ways to go about things.

One example  I was thinking was students write (beforehand) their discussion questions beforehand on posterpaper and bring it to class. We hang them up, and students silently walk around the room writing responses and thoughts on the whiteboard. Then we start having a discussion.

Or we break into smaller groups and have specific discussions (that I or students have preplanned) and then present the main points of the discussion to the entire class.

Clearly, I need to get some ideas from English teachers. :)

(c) I love close readings of texts. I think it shows focus, and calls on tough critical thinking skills. At the same time, I need to remember that this is not what the book clubs are fundamentally about. They are — at the heart, for me — inspiration for kids. So although for Flatland I need to keep the critical thinking skills and close readings happening, I need to remember (like I did this year) to keep things informal.

(d) Fairly frequently, I will know something that is relevant to the conversation. For example, I might talk about of the math ideas that were going over their heads, or about fin de siecle Vienna, or branches of math that might show how the line between “theoretical” and “applied” math is blurry at best. I have to remember to be judicious about what I talk about, when, and why. We only have limited time in book club, so a five minute tangent is significant. And one thing I could try out is jot down notes each time I want to talk about something, and then at the end of the book club (or the beginning of the next class), I could say them all at once.

(e) I usually reserve 30 minutes for book club. But truthfully, for most, 40 minutes turned out to be necessary. So I have to keep that in mind next year when planning class.

(f) Should we come up with collaborative book club norms? Should I have formal training on how to be a book club leader? Should we give feedback to the leaders after each book club? Can we get the space to feel “safe” where feedback could actually work?

And… that’s all!

# 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:
It 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.

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).