Big Teaching Questions

Inspiration and Mathematics

In my multivariable calculus class this year, we’ve been holding a regular “book club” during our long blocks. (Don’t ask… we have a rotating schedule and every seven school days we have a 90 minute class.) Right now we’re reading Edward Frenkel’s Love and Math: The Heart of Hidden Reality.


In the introduction, Frenkel criticizes the teaching of math:

What if at school you had to take an ‘art class’ in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it. [1] … There is a common fallacy that one has to study mathematics for years to appreciate it… I disagree: most of us have heard of and have at least some rudimentary understanding of such concepts as the solar system, atoms and elementary particles, the double helix of DNA, and much more without taking courses in physics and biology. And nobody is surprised that these sophisticated ideas are part of our culture, our collective consciousness.

So many whirling thoughts came up while I was reading these passages. One thought led to another to another to another. Writing this post is an attempt to start recording them and to get them a little more codified in my mind! It is still going to be a hot discombobulated stream-of-consciousness mess. #sorrynotsorry

I wonder if I asked my kids “what is mathematics?” right now, what they would say. I am doubtful that their answers will include the adjectives and verbs that I personally would say.

I wonder if I asked my kids “what is is going on in the field of mathematics?” right now, what they would say. I’m guessing a lot of blank stares.

I wonder what my kids would say if I asked ’em “what courses exist in college for mathematics?”

I wonder what my kids would say if I asked them to name a mathematician who is alive?

I wonder if the word “mathematics” was changed to “astronomy” or “physics” or “biology” if their answers would be different.

There are ideas that my kids learn about modern physics (in popular culture, in classes) which spark their imagination, blow their minds, make them curious and full of wonderment at the weirdness and strangeness of the world. Special relativity. Quantum mechanics. Quarks and the structure of atoms. They are exposed to these ideas, even if they don’t have the mathematical capabilities or abstraction to attack them rigorously. And these ideas have a powerful effect on some kids. (I know I wanted to be a physicist when I first learned about these ideas!)

But what do my kids learn about modern mathematics — from school or popular culture? Are there any weirdnesses or strangenesses that can capture their imagination? Yes! Godel’s incompleteness theorem. Space filling curves. Chaos theory. The fact that quintic and higher degree polynomials don’t have a general “simple” formula always works like the quadratic formula. Fractals. Higher dimensions. Non-euclidean space. Fermat’s Last Theorem. Levels of infinity. Heck, infinity itself! Mobius strips. The four color theorem. The Banach-Tarski paradox. Collatz conjecture (or any simply stated but unproven thing). Anything to do with number theory! Anything to do with the distribution of primes! But do they capture students’ imaginations? No… because they aren’t exposed to these things.

Where in our curriculum do kids get inspired? Where does awe and beauty fit into things? When do we ever explicitly talk about beauty in mathematics? When a kid has a rush of insight and makes a visible gasp, what do we do in that moment? What has to already be in place for a kid to make that gasp?

We need to expand how we frame mathematics in high school so it isn’t seen as “Algebra I, Geometry, Algebra II, Precalculus, and Calculus.” These course names aren’t mathematics.

We need to consciously and regularly introduce a bigger and more modern world of mathematics to our kids. How? Having kids read when the New York Times publishes an article about a mathematician or mathematical result! Using resources like Numberphile and Math Munch and Vi Hart videos. And… I don’t know.

We need to provide space and time for kids to explore an expanded vision of what math is, and have choice in having fun and playing with this expanded vision of math. (My explore math project is an attempt to do that — website here, and posts one, two, and three here.)

We need to have mathematical lore, stories we can tell students. Galois duel! Ramanujan’s inexplicable genius! What are mathematical stories that can be passed down from generation to generation? (Does a good resource exist for this? Tell me!) [Update: The internet went down when I was going to edit this post by mentioning we need stories and people who aren’t just white men!]

Do we have Feynman or degrasse Tyson-esque figures we can point to? Dynamic popularizers of the subject that have entered the public consciousness?


Maybe what I’m trying to say, if I had to distill everything down to the core, is:

(1) Can we find a way — in our existing schools with our set curricula and limited time — to expand kids notions of what mathematics is by exposing them to notions external to the Alg-Geometry-Alg II-Calc sequence. And if we can do this well, will it help inspire more kids to be interested in mathematics? 

(2) Are there ways for us to keep an focus on beauty, the unexpected, awe, and wonderment in our classes? And find ways to record, highlight, and amplify those moments for kids when they happen? Why I love mathematics is because of all of these moments! Maybe focusing on them would help kids love mathematics?



[1] This notion has so many resonances with Paul Lockhart’s A Mathematician’s LamentWhich I highly recommend.



Mulling things over

Tonight at school we had our inductions into Cum Laude (like national honor society) and Mu Alpha Theta (the math honors society). And our guest speaker gave a rousing speech about his life, and how it’s okay to have fear, but the biggest hurdle to doing something significant with your life is accepting the fear and moving on in spite of it. Accept it, own it, be afraid, and then still forge forward.

At the end, he said something powerful. The first thing one needs to do to when leading a purposeful life is to say what it is that you want to do. Articulate it aloud. And that is scary. Making it public so you can hear yourself say it, but also so someone else can hear you say it. So it becomes real instead of this thing that bounces around in your head but never gets out. And so at the end, he told everyone to be quiet, and he was going to say something he wanted to do, and then afterwards there should be silence… and when anyone else wanted to say something they wanted to do — something they would declare out loud — they should stand up and say it, and then remain standing. This was an open invitation to the students in these honors societies, but also to the parents and teachers there as well.

The speaker said: “I want to change the world.”


A little more silence where everyone looked around and felt uncomfortable.

Then a student — one courageous student — got up and said something. And remained standing.

And then another. And another.

The head of the upper school said something. Then more students. Then a parent. Then me. Then another math teacher. Then more students.

At the end, every student made a declaration, and a few adults too. It is scary. But it also showed me how much courage our kids have. Their declarations ranged from showing others that girls can do math and science to spreading love to making people laugh to promoting peace to inventing something to becoming a biochemist to making a mark on the world. Big things and small things, lofty things and concrete things, but all things that share with the room a sense of self and a sense of purpose.

I loved watching this.

I also loved and hated how hard it was for me to come up with my thing. My purpose in life. I said:

I want to make it so that kids see math as an artistic and creative endeavor.

And I meant it. Because you know what has been bouncing around in my head that I have been having trouble articulating? I am now pretty good at coming up with deep and conceptual approaches to mathematical ideas. And I’m okay at promoting mathematical communication. And I’m transitioning to having kids do groupwork all the time, to learn from each other — so I am not the sole mathematical authority in the room.

But all of that said: I don’t think I teach math in a way to shows how it is an art form, how deeply creativity and mathematics are intertwined. And I know that this is one of my charges as a teacher moving forward. It’s going to be an uphill challenge, and one that will likely take me many years to wrap my head around. The hurdles are significant. Having a set non-problem-solving-based curriculum which doesn’t allow time for much mathematical “play,” nor for the inclusion of rich problems with multiple entry points, is the largest hurdle. But there must be ways — activities or units here and there — that can illuminate the artistry and creativity of doing and discovering mathematics. And I want to be involved in finding ways for this to happen. Yes, this happens at math circles. Yes, this happens at math clubs. Yes, this happens at summer math programs. That’s where the love and excitement and understanding of the beauty of mathematics unfolds for many students. But I want to find a way for this to happen in a normal classroom, with normal students, with the normal constraints. That (one of) my purposes.

Projects and Project Based Learning: HELP! AAACK!

What I’m going to ask you at the end of this post: I’d love any links in the comments to examples of awesome projects and examples of project based learning for the math classroom. I’d love any projects that you think are actually really good, and any and all examples of project based learning (good or bad).


This isn’t a post about something I’m doing in the classroom, but rather me soliciting resources from all y’all so I can do something different in the classroom.

But my basic sentiment at the moment is: AAACK! HELP! AAACK!

Setup: My school is jumping on the Project Based Learning bandwagon. However, no one has been able to give me good examples of what real Project Based Learning in the math classroom looks like. However, no one has yet been able to give me a satisfying example of Project Based Learning in math.

I found this online (thanks twitter) which appears to separate Project Based Learning from Projects:


It’s all very good sounding. But I am a concrete thinker and I haven’t been able to come up with a hundred examples of Project Based Learning. Honestly, I haven’t even seen one that I’d say “hey, this is awesome.”

Also, I am not really good with doing projects in general. I don’t do a lot of them (for a variety of reasons).

So, as I said: I’d love any links in the comments to examples of awesome projects and examples of project based learning for the math classroom. I’d love any projects that you think are actually really good, and any and all examples of project based learning (good or bad).

Mainly I’m just trying to wrap my head around this. I still am unsure what to think about this move my school is making, and if it makes sense for the math classroom. But for now, I am keeping an open mind.

An Open Letter to New Teachers

A response to Bowman’s post. Read other letters to new teachers which are cataloged here.


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.)

Now some background on me. I was only a first year teacher once, at a school that is in all likelihood not your school. And my kids are are certainly not your kids. And all of this colors my thoughts. So take everything with a grain of salt, and I’d say if anything resonates with you in your gut, maybe that’s the thing that worth listening to. So you have some context, my school is an independent (read: private) school in Brooklyn. The class sizes are small (usually 12-16, rarely more), and the kids are fairly well-behaved. I have been here for five years, and it’s the only school I’ve known as a non-student-teacher teacher. Still, if this doesn’t sound similar to where you’re going to be starting and your gut tells you to stop reading, first: just for now, ignore what I said about going with your gut. Second, there are truisms for all schools and all students, which is why I have had so many awesome conversations with zillions of colleagues in all parts of the world in all sorts of schools.

Introductions over, and let more be added to the heap of unsolicited advice you’ve already gotten. There is something to be said for the fact that so many people are giving you unsolicited advice. Let’s talk about going out on your first date. It’s awkward and uncomfortable and when you tell your friends/parents/strangers/stuffed-animal you’re nervous, they all want to stroke your hair calm your nerves and tell you how they know everything is going to be alright. And then, to show you that they know everything is going to be alright, they’ll tell you some awkward and embarrassing story to make you feel better — because the hidden truth that they’re trying to say without saying it is: it won’t go at all the way you have pictured it a thousand times in your mind, and you’ll be too self-conscious, and the illusion of that perfect date will shatter. And they give you a ton of unsolicited advice. But they say this because they care, and because alright means you’ll survive.  And you will. (And in case this wasn’t clear, that is what your first year will be like. It’s an analogy  simile analogy-simile-metaphor-thingie.)

You: “How annoying! Yet another jerk telling me that the first year of teaching is going to be hard and is going to suck. Hooray, thanks for that.” But what I want to say is: everyone is saying the same thing, which means that everyone went through it, and everyone is saying it to you out of lurve because they totally want you to succeed. We all do. And we don’t even know you. So I’ve said it now officially. The first year of teaching is hard.

Unsolicited and Probably Unhealthy Tiny Piece of Advice #1: Work a lot.

It pays off. Seriously. The more time you put into your lesson planning, the better your lessons will be. The better your lessons will be, the more respect you’ll get from your students (and colleagues). I don’t know if this is healthy advice or not, but I’m giving it anyway. I remember working everyday until 9pm or 10pm each night. I thought that was normal. (I had three different courses to prepare for, and had very little material given to me, so I don’t know if I had much of a choice, honestly.) But it paid off with relatively good student behavior and a fairly productive classroom. I learned that students reserve respect for teachers who constantly demonstrate that they care about student learning. And there is no way to better demonstrate this care than by planning good classes. And more importantly, I had learned to create two curricula on my own. And there is almost nothing that will throw you into the deep end, and have you coming out of the other side stronger, than doing that. It was also super intellectually stimulating, and I thoroughly enjoyed doing it. The best part: the next year I had a lot less work to do because I had created some strong core materials, and I was able to stop working so late.

Of course I don’t want you to burn out, so find some balance. But push yourself, and recognize that it will pay off in the short-term and in the long term.

Unsolicited Tiny Piece of Advice #2: Be passionate, even when you’re not.

I don’t care if you’re teaching what you consider the most useless and boooooring topic in the universe (rational root theorem, anyone?). Go into class with a smile, with energy, and be excited about this really cool thing about polynomials. Fake it, if you can’t make it. One of the pieces of feedback that I continually get from students is that my passion and excitement for mathematics comes through, and some students even say it is infectious. Um, honestly, the quadratic formula or the y-intercept do not an excited Mr. Shah make. I mean I know these things and have for years… yawn. But your students don’t, and you can capitalize on that freshness!

And if you aren’t someone who is naturally good at showing excitement, one thing you can do: inflect your voice. Modulate it. If you don’t know what I mean: say “this is a really exciting sentence” in monotone. Then say it again but raising and lowering your pitch randomly. THIS IS HUGE (even if I called it a tiny piece of advice). It is the difference between having students hang onto your every work, and having students with their heads on their desks. At first, this faux passion might seem like you’re not being yourself. Get over yourself. You can be a better self, at least when teaching.

Unsolicited and Important Piece of Advice #3: Don’t make a mountain out of a molehill

If you’ve gotten this far, good on me! I figure now everything is solicited, because the browser tab is not closed. Anyway, I wrote more about this before, so read it.  And actually, here’s a follow-up post.

Solicited and Important Piece of Advice #4: VENT

I wrote about this before too, but I’m going to copy and paste it here. I don’t know why I didn’t do that for #3, but I’m too lazy to fix it.

Okay, I think venting is one of the most important thing you can do as a new teacher. You’re going to be facing a lot of things and you’re going to get frustrated. With students, with administration, with other teachers. I mean, you have to keep it professional, but you should find a few trustworthy friends (preferably new-ish teachers) and complain your heart out.

Not conventional wisdom, I know. But one of the things that happens to first year teachers is that there are periods when you get dejected. You feel like you suck. Heck, you may even suck. (I feel that way all the time, and I totally crash and burn often enough.) And kids are getting to you. Maybe one in particular. And the pressure is building up. And your systems that you so carefully thought out aren’t working. The worst thing you can do is keep all this inside. It’ll start eating you up. You’ll start crashing and burning, and feeling trapped and alone.

The best thing you can do is VENT to some close friends. Because as soon as you say it aloud, it stops being your private shame. Think about it. When something bad happens, like you go to the mall and  you try on pants and realize, oh! that size doesn’t fit you anymore. You can either internalize it, be ashamed, and go about your business obsessing over it. Or you can make a joke about it and tell your friend who you’re shopping with. (As long as your friend isn’t a judgmental jerk.) It stops being this horrible thing, and it just starts being this thing. Okay, not a terribly good analogy. But trust me on this: venting is healthy. Keeping things to yourself, going it alone, being afraid to talk about problems, is the foundation for failure, methinks.

(Just a caveat: vent with those you trust who aren’t judgmental jerks, and be somewhat professional when you vent.)

Completely Stolen Advice #5: Think About Why

Approximately Normal has advice for student teachers, which I think is superuberamazeballs… even though it is for student teachers, the ultimate message about understanding hidden norms in the classroom is key. And figuring out how to make your own (hidden) norms is important. You are cultivating an atmosphere, a small culture. You should think intentionally about the culture you want.

Observe, observe, observe. You might be thinking, “DUH…” but it’s more than that. If you begin student teaching after the first days of school, there are hidden norms in the classroom than an unobservant person might miss. Don’t think about what YOU’RE going to be doing for lunch, or after school, or the coming weekend. PAY ATTENTION TO EVERYTHING!!! How do students enter the class? Are they “bookin’ it” to get there on time or is it more like, “meh, whatevs – be thankful I showed up”. Does the MT have a “do now”/”bell activity”, but more importantly, WHAT KIND? How is it done? Is it review or a challenge to get them thinking? Is it multiple choice? Do kids start right away or socialize before it’s started and how do they complete it? What happens when students are late? What if a kid has to use the pencil sharpener? Is talking during class allowed? And if so, under what circumstances? How do kids let the MT know a bathroom/water break is needed? Are kids allowed to “zone out”? How does the teacher let kids know when they’re doing what he/she wants? Or more importantly, what he/she DOESN’T want? How does the lesson flow? Are there “brain breaks” for students to collaborate? If there is technology (calculators, voters, etc.) available to students, how is it distributed to the students and collected? What is the attitude with kids about learning? Is it engaging or the attitude “whatever – just tell me what to write down”? Do kids talk when the MT is talking? Are kids trying to sneak text? Do kids pack up before the bell rings? This is just a fraction of the things you need to look out for before it’s YOUR turn to take over.

So I said you should think about the culture you want in your classroom. The question you should have is how? And you know I can’t answer that. It’s so specific to your school and your kids. But I can tell you how you can answer that question. Find a couple teachers in your school that you look up to. Invite them out to coffee (on you! and let them get a pastry too, okay?) and ask them. They’ll let you know. Who can say no to coffee?

Short Linked Advice #6: Beg, Borrow, and Steal Curricular Materials

Obvious Advice #7: Don’t Try to be Kate Nowak

… because she broke the mold. (Bonus points, Kate? EXTRA CREDIT?)

You want to be amazing all the time. You have a crush on Shawn, Bowman, Kate, Dan, whoever. You are a polyblogist. I get it. Me too. Me too.

But I want you to know that your lessons don’t all have to be interactive and flashy and you don’t need to do projects for every unit. People post their best stuff on blogs a lot, and you think they’re all amazing, but you don’t see what’s really going on in their classrooms. I’ve talked with enough bloggers to know that for most of us, we lecture a lot. I personally sometimes feel like a fraud because if people came into my classroom and saw what I did on a daily basis, it wouldn’t compute with what they read on the blog. Not because I’m trying to deceive, but most of what I do isn’t flashy or innovative. I probably lectured exclusively for the first three years of teaching. My sister (who is also a teacher, and is extraordinary at what she does) gave me some good advice whenever I would call her telling her how I felt like I didn’t measure up. “Go small, make baby steps. Decide you’re going to try to do one interactive thing in one of your classes each week.” I liked her philosophy of baby steps. Whenever I feel boring, I get out of my rut by actually making a small baby-step goal and doing it. It works.

Advice #8: Ignore the Echoing Voice

A kid says something offhanded. Mutters something under his or her breath. I remember in my first two years of teaching, I took everything personally. A student would say something, and it would bounce around in my head for hours. I can’t even tell you the number of nights I couldn’t fall asleep because my mind would wander back to this or that remark.

I don’t have a solution for you, if you experience this like I did. Ambien? For me, the only solution was time. After two years of teaching, I realized that almost everything that a kid said that I took personally was not about me. It took me a long time to grow a thick skin. It went hand in hand with my realization that being liked is not the same as being respected. And you can’t do nada in the classroom if you aren’t respected.

Important Advice #9: Be Consciously Building Your Reputation At School 

You made it down here, which means you get my most shiny gems. Here is one of them. You want to be thinking very consciously about how you act in your first year.

I’m not only talking about how you teach in the classroom. I’m talking about everything else. Whether you think about it or not, everyone you work with (this includes maintenance staff!) is going to have to file you away in some category in their brains. Decide what you want to be known for, and then go for it. If you want to be considered reliable, then be don’t only do what’s asked of you but do a little bit more. If you want to be considered kindhearted, randomly bring in cookies for people — just because. If you want to be considered friendly, make sure to make eye contact with people when walking in the hallway and make a sincere “hello! how are you?” and then listen to the answer without interrupting and making it about you. (You jerk.)

In the classroom, if you want to be considered organized and prepared, have everything ready everyday you enter the room. If you want to be considered approachable, reach out to students early on. If you want to be considered funny, build jokes into your lesson (if you aren’t good off-the-cuff… I’m terrible off-the-cuff).

First impressions are important. Cultivate good impressions in your first year, and you will reap the rewards every year hence. (Did I just use the word “hence?” Thine brayne needs to reste soon, anon and all that.) Your reputation is all the capital you have at your school. That is so important that I will repeat and italicize that: your reputation is all the capital you have at your school. And it gets pretty firmly set in your first year.

I love what I do because I love what I do. But I also have come to love going to work each day because I have colleagues who have become friends, and we have so much fun twirling around in our chairs, singing Sound of Music, and laughing at all our daily mishaps and adventures.

My Final Advice Gem #10: You’re Going To Have Problems, Lots and Lots of Problems

I’m coming full circle year. I started out by saying teaching in your first year is hard. I noted that everyone who is going to give you advice is saying the same thing. People talk about “surviving” their first year, and then a couple years later, how they can’t imagine leaving the classroom.

What can you do to have a smooth first year?


Here’s why. In your first year, you’re going to be in reactive mode. You don’t know what the problems are going to be, so you can’t anticipate them and fix them. You don’t know if you’re going to have an issue with students not bringing pencils to class, or not doing their homework consistently, or cutting class, or whatever. You don’t know what problems to expect so you can’t prepare for them. You’ll be reacting. And I promise you that you’ll be asking everyone around you for help and advice and that is good.

But I can also promise you (okay, not like I’ll put money on it, because as I pointed out, I don’t have much, but you know what I’m saying) that your second year will go better, and your third year will be infinitely better. You won’t be reacting, but you’ll be proactive. You’re not only going to be able to anticipate the problems, but you also will have a repertoire of moves you can make to deal with them.


I’m not a gloom and doom type. I lurve you and all that, remember?  I can honestly say that I thoroughly enjoyed my first year of teaching. I have hilarious memories of my classes and my kids. I remember when I was teaching my first 7th grade class and I held up a notebook as an example of what they should have for class, and I got three questions: “Does it have to be red?” “Does it have to be xx pages?” “Does it have to be from Staples?” How cute was that last question? But I who had never taught thought that my sweet 7th graders were mocking me! Ha! (They weren’t! They were just that clueless.) Or when the skylight in the hot small room my calculus class was crammed into had the sun shine on the bottom of the SmartBoard screen, and slowly crept up, making part of the SmartBoard unusable? That was fun, because each day we had a race with how much I could cover before I had to switch to the whiteboard. And the student who wanted to become a teacher, and did her final project creating and teaching a lesson in class. I have great memories. I also have some painful ones, which included taking a student into my office and yelling at him. I… I don’t yell, and I yelled at him how I cared about him but he didn’t care about himself, and that I didn’t know what else to do.

So not to pull a Dan Savage on you, but It Gets Better… even when you think it’s going well. And when it isn’t going well (and there will be times when you will feel dejected and like a failure), It (too) Gets Better.

Teaching rocks. You will rock.

Remember why you came to the classroom, because it’s easy to forget in the day-to-day. Let that guide you.

Sam Shah
Unsolicited Advice Giver and Unicorn Enthusiast

Senior Letter 2012

Each year at the end of the school year, I say goodbye to my seniors. And each year, I’ve written a letter to the seniors with some imparting thoughts as they go off in the world. And each year, the message in the letter stays fairly constant, even though the way I say my message might slightly change. It always goes something like this:

Knowledge is precious and vast, it keeps us curious and engaged in the world, and simple ideas can — when taken to their thoughtful conclusions — be extraordinarily powerful. And thought it may seem like we have forever to cull this knowledge, we don’t, so take advantage!

Without further ado, my letter to my seniors. I know, it always comes across as hokey. But when I get sentimental…

A Time Capsule

I had this idea, and I wanted to throw it down before I lost it. It may be nothing, or it may be something awesome.

I have been mulling over if I should do a project in calculus in the fourth quarter. And I had a thought. I have been really trying to focus on the fundamental underlying ideas in calculus, and shooing away the algebraic gobblygunk. Why? Because my kids aren’t taking AP Calculus. Most won’t be taking math in college. So I want my kids to leave calculus saying: “Yes, I understood the ideas. Calculus is about ideas.”

I wonder if a good final project, which would force them to grapple with the Big Ideas, might be having students create a collective time capsule, which will be stored in some deep underground facility, and will be the only remnants of “Calculus” that may exist after some horribly apocalyptic disaster.

I’m not sure what would go in the capsule, but I like the idea that all students would be asked to contribute a few items. Maybe we’d break the course into chunks, and each student would be responsible for writing an accessible explanation of each chunk — and we bind these together into a book? And each student would create set of drawings/graphs/photograph/images that (for them) represent the Big Ideas of Calculus, and they have to explain each one of them… What’s the idea, and why is it so important?

In addition to these required items, students could have their choice of what else to contribute… Things like:

1) A video of the student explaining the weirdnesses/paradoxes/strange ideas of (or relating to) calculus
2) A short research paper on the history of calculus
3) A letter to the future explaining why calculus is an important swath of knowledge that shouldn’t be forgotten (including uses / applications of calculus)
4) A challenging calculus problem, and it’s solution
5) A “concept map” for calculus
6) Audio recordings of students reading quotations about calculus that resonated with them, and then students explaining why it resonted with them.
7) Designing a cover to the collective calculus book we bound together, and on the back cover, an explanation of how the cover exemplifies the course

Or other things?

I don’t know. It felt like a cool idea when it jumped in my head a few minutes ago, but now that I’m writing it, I can’t quite picture it … yet. Any ideas of how to take this idea and turn it into something good? Throw it in the comments!

An important question: how do you plan?

I don’t think I’ve seen this asked before, and … well, I need to crowdsource something.

Tonight, on twitter, I asked:

For the past few weeks, I feel like my teaching hasn’t been that good. It’s okay, but not near the level of goodness I know I could achieve. My big limiting factor is time and energy — I’m overextended with commitments. But I also think I could be doing better if my planning process were better. If it were more efficient, and I reoriented the way I thought of how I plan…

So I’m wondering from y’all, on a regular basis for a normal class

… and before you answer, this is a judgment free zone! If you wing it and don’t plan most days, just say that! I just want to get a sense of what people do to see if I can’t steal some great ideas and be a more effective planner … and I guess I’m also just plain plum curious!

(1) How do you plan? Like… um… what’s your process (if you have a formal one), or what do you do (if you just sort of do something)?

(Things like: what sort of things do you think about when you’re planning? Do you pre-script questions? Do you pick specific problems? Do you design some conceptual walk-through for the kids? Do you always build in formative feedback? Do you always try to switch what kids do 2 or 3 times a class? Do you start with a unit or week-long plan and then go down to the individual class level, or vice versa?, etc.)

(2) What does your completed plan look like? Is it written on paper, or a SmartBoard file, or a computer file, or in your head, or something else — and what sorts of things are on it? Questions? Objectives? Problems?

(3) How much time does it take you (again, for a normal class, on a normal day) to make a plan for a single day’s class?

(4) Other stuff that didn’t get caught in the net of the first three questions, but you wanted to say?

Throw your answers in the comments! Help me out!