Big Teaching Questions

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!


A guest lecturer…

Last year I had this student who struggled in Algebra II. And then, one day, he decided he hated struggling. He was frustrated and didn’t want to be frustrated anymore. He wanted to get math. And so… he did. To the point where he was getting almost perfects on assessments.

This was a student who I always thought highly of (I knew him both inside and outside of the classroom), and when he was frustrated, I felt for him. And when he made a dramatic turnaround, I couldn’t have been more elated. I have to say, there are some students who you just want to ask you to write college recommendations for. And these college recommendations just roll off the keyboard. He asked me, and I remember sitting down, and going at it. I think it ended up being two and a half pages, and I had to edit it down to be that. He exemplified the transformation that I hope all my struggling kids go through, but his transformation was the most dramatic of all my students last year.

Because I wanted my kids this year to know that they can struggle, and come through the other side, I invited this student to come talk to my class for a few minutes and talk about his frustrations. And how he made his transformation. I want to show my kids that they can be more successful, but there is no royal road to mathematics. The way to be successful is to work hard.

The key points that my former student made when talking to my kids:

  • One day, one moment, he said “enough’s enough.” And he made a decision to do well in math. He was sick of that low grade on his report card, year after year. It was this moment that changed it all, because he changed his mindset to “I can’t do it” to “I will do it.”
  • He said that doing well in math has a lot to do with confidence. He didn’t have a lot of confidence, but slowly when things began to turn around, he became slightly more confident. And then more confident. And now, this year, he is overconfident in math.
  • He said that those annoying “explain this” questions that Mr. Shah asked were… annoying. But once he learned why I was asking them, that I was trying to get him to understand more than procedures, but to draw connections and see everything fit together, they made sense.
  • He stopped looking at each test as something that needed to be crammed for the night before. Instead, each night he would work on understanding the material. And when doing this, he saw connections.
  • He entreated my kids this year to try to draw connections between everything we’ve learned. Because that’s how it all hangs together. That’s what made everything click for him.
  • He also said that even though he failed the first five binder checks, he finally figured it out. And he could be organized.

I don’t know if his message got through to any of my kids, but I do know that me saying these things isn’t going to do as much as a kid who went through the trenches and came out a hero.

So if you want to honor a kid who was awesome, and maybe (possibly?) get through to your class, think about inviting a former student to give a short guest lecture!

PS. I have former calculus students stop by all the time, and I always make them come to class. Sometimes I’ll leave the room and have the student talk to the class alone, about what recommendations they might have for my current students, sometimes I’ll stay, and sometimes I’ll have ’em talk about college life, and how everyone gets through the college application process, and how truly there is light at the end of the tunnel (even when it may not feel that way).

Next Semester

You know my philosophy about blogging… blog only when you want to blog. If you put pressure on yourself, it becomes a chore. And why would I make myself do a chore? More than that, it would be like a chore I created just to make my life harder. Like: every day, make sure you windex the windows to your apartment. (FYI: I have never windexed the windows to my apartment since moving in two and a half years ago.) (That’s what rain is for.) (And curtains.)

However, now that it’s been over a month since I’ve blogged, I wonder what’s going on?

We did have two weeks off, so it’s not like I could blog about school stuff when we didn’t even have school…

True. But that’s me rationalizing. Or how about…

I don’t have time because I’m just so busy…

I think. But this year I’m no busier than previous years. In fact, I might be less busy with school stuff. (However, I should say that I’m making good on my school year motto this year: “I’m doing me.“)

Actually, I think that is the problem. I wonder if I’ve gone stale, like that moldy bread in the back of my fridge? I only think it’s moldy, actually. I keep on putting things in front of it, because I’m scared to take it out, but I don’t want to look at it. It’s like smelling milk that might have gone bad. I don’t do it. I just throw it out, because the mere thought of smelling rancid milk makes me want to puke. Where was I going… oh yes, feeling stale. I’ve grown accustomed to having my SmartBoards that I slaved over years ago, and my worksheets and packets that I created ages ago. I’m tweaking. I’m not inventing. Or really even reinventing. I don’t have much to post because I haven’t been doing a lot of creation. And that’s always when I feel excited about posting. Invigorated about what I’m doing. 

Now that I know this, I have an easy fix. Recreate. Invent. Reinvent. I’m also meeting with my department head on Friday to talk about course assignments for next year, and I’m going to ask to teach a course that will be new for me next year.

With all this mind, I’m going to keep a list (that I will update) with possible ideas/goals for next semester, which will be starting in a little over a week.

  • In Algebra II, remember to do group work, and do more “participation quizzes” during that group work.  I did a bunch in the first quarter, and then the groupwork dropped off in the second quarter. Booooo, me! Keep it going, and strong!
  • In Algebra II, remember to utilize the Park School of Baltimore curriculum, especially when working on Quadratics, Transformations, and Exponential Functions. It didn’t quite fit in with our 2nd quarter material, but it will align with our 3rd and 4th quarters.
  • In Algebra II — since we don’t have a midterm for students to see a broad view and get a review of all the 1st and 2nd quarter’s material — have the 3rd and 4th quarter problem sets include “review problems” from topics from the first semester. Or if not, have review problem assignments, in addition to the problem sets.
  • In Algebra II, do a written “final exam study guide” project again, to continue having kids work on their writing skills. Provide feedback, and an opportunity to do revisions, and fix errors. (Video study guides from years ago, paper study guides more recently.)
  • Create this “pencils and eraser” station for kids who forget pencils.
  • In Calculus, continue having kids work in groups on challenging problems every so often.
  • In Calculus, do problem sets in the 3rd and 4th quarters, but make them shorter and give less class time than the 2nd quarter. Continue to make the problem sets have a “group” component and an “individual” component.
  • In Calculus, consider creating a “reading group” where students are asked to read chapters from books, or watch videos that I find online, dealing with calculus (from Charles Seife’s Zero, from David Foster Wallace’s Everything and More, from … well, I have think of the resources!), and we discuss them every other Friday in the 3rd and 4th quarters. I’m not sure how this would work. The point would be to add a more “cultural” component to the class, and a lot of my kids love reading and learning about tangents. But I don’t know how to make it interesting enough that kids will actually do it. (At my school, kids are so busy that they don’t really do things that won’t impact their grades, and I don’t want grades to be a threat to make kids do this… I need to come up with a way that they will do it because it interests them. One thing that’s buzzing around is having kids do the reading, but if they come to class not having done the reading/viewing the video, they don’t get to participate in the discussion/activity, and they have to do something else that’s calculus related and not busywork, but much more boring than whatever we’re doing.)I don’t know. This is tricky for me, because I don’t have a vision for it yet. That has to be clear to me first: the vision, the purpose, and then how to achieve that comes next. I don’t want to do it just because it “seems cool.” I want kids to buy in. Maybe I give them a choice: book/video club, an independent final project, or regular class?
  • I finally got large whiteboards for my students. I’m struggling to use them. So in the 2nd semester: use them. Even if it doesn’t go well, I need to keep using them. I need to have some practice and experience with them, even if to show me what works and what doesn’t work.
  • Now that we’re starting the 2nd semester, have built in time to review the course expectations, and collaboration guidelines for all of my classes.
  • Consider making changes with my Binder Checks in Algebra II? More frequent? Have kids leave their binders in class, and have time set aside for them to organize themselves? This year their binders are not improving much. It may be that I need to baby them. Some things might include: putting “correct the home enjoyment that we went over today” each day on the course conference (the place where I post the nightly work), having binder checks every two weeks instead of every five weeks (or random “homework correction checks” in addition to the five week binder checks), making test corrections a homework assignment (instead of just telling them they need to have it done by the binder check date), and showing kids how to create their own “checklist” to make sure they have everything in the binder done. I am a little surprised that sophomores and juniors are still finding this so challenging.

Some things I need to do regarding this blog:

  • Blog about problem sets in Calculus and Algebra II
  • Blog (briefly) about the change I made to Standards Based Grading in Calculus (scale is now out of 5). And also how this year is going compared to last year (read: better). And what still feels like it’s missing…
  • Blog about talking about Early Action/Decision with my seniors
  • Blog about achieving my goal from last new year’s… to read 52 books. And how I did it (short answer: I don’t know. It feels kind of miraculous.)
  • Make a new Favorite Tweets (even though I haven’t been on twitter lately so it will be short)
  • Update the Virtual Filing Cabinet

That is all.

Another “How To Fix Math Education” Article

One of my students sent me a Slate article, yet another piece of tripe with an attention-grabbing, gag-inducing headline: “How To Fix Math Education in High School and College.” Barf.

And the article is short and doesn’t really say how to fix math education in high school and college. So there ya go. But my student asked me for my thoughts. And I gave myself 20 minutes to compose a response. I had to give myself a time limit because I know myself. I’d obsess, second guess, and then think: well, that’s not precisely right, and then get diverted to go into this or that tangent, and never actually send it. And if I did, I wouldn’t be happy with it and it would be maybe 5 pages of things I wouldn’t be happy with.

So I did it under time constraints. And I figured I’d share it here. It is not precisely what I believe, and it is a lot of broad strokes. And it certainly is choppy (because I didn’t having time to proof). But here you go…

Hi [Stu],

I think this article brings up a lot of good points, and I know at all the math conferences I attend and all the conversations I have with math teachers (at Packer and around the country), these are the discussions we are having.

When it gets down to it, there are two claims that I think are worth discussing.

First, that our kids are being pushed on a “calculus” track, while the real action and usefulness is elsewhere. I do think that there is this standardized curriculum in high schools, where kids are being put on a track where calculus is the pinnacle of their math studies. It’s not just Packer, but everywhere in the US. And I think that is not always the appropriate track — and we could come up with alternatives. We could have multiple tracks, culminating is statistics, discrete math and number theory, alternative geometries, or something interdisciplinary. Of course there are about a zillion things in the way, including staffing (who would teach these courses, how would they get paid, when would they have time to write the curriculum which would have to be something untraditional) and colleges (which look for calculus on a transcript, or so I’ve been told… I don’t really know much about that world). But I think most math teachers would say that calculus is just one possible, and not always the best, ending to a high school math career (depending on who the kid is and what the kid’s interests are in math). Very deep-seeded cultural, social, institutional, and even political barriers get in the way of revolutionizing what math is taught and how it is taught. On the other hand, I disagree with the argument that calculus should not be pushed because it doesn’t have as much “practical” “applied” use to most people. If we only cared about pushing the things that would be useful for students in the real world, why teach Shakespeare and Pynchon and hydrogen bonds and what makes a rainbow — if most students aren’t going to be working in a lab or becoming writers or critics? I think there’s a value to calculus for the sake of it being calculus, for it showing (for many, the very first time) the abstractness and beauty that a few simple ideas can bring to the table — and how these simple ideas can be stretched in crazy and amazing ways. (Given that a student has the algebra tools to accomplish it.) But to be clear, I honestly believe most math curricula in high school aren’t solely bent on helping kids understand calculus. If that were the case, I could come up with a curriculum where we elminiate geometry, and combine Algebra I and Algebra II into a 1.5 year course… and students would have the background to do calculus afterwards. That’s not the goal. The goal is building up ways of thinking, putting tools in your mathematical toolbelt, and leading up to abstraction and reasoning… with the hope that the structure, logic, and incredible beauty and creativity of it all come tumbling out. Now whether that actually happens… let’s just say it’s not easy to accomplish. We teachers don’t get students as blank slates, and we aren’t always perfect at executing our vision under the constraints we have.

Second, there is the claim that ” that schools should focus less on teaching facts—which can be easily ascertained from Google—and more on teaching them how to think.” I think most teachers would agree with that. But then the article goes on to claim: “mathematical education will be less about computation—we’ve got calculators for that!—and more conceptual, like ‘understanding when you need to do integrals, when you need to do a square root.’   This is a much bigger issue and it can’t be simplified into these two sentences. There is a large discussion going on in the math education community about the use of graphing calculators, and if they can be the panacea for math education. That students who struggle with basic algebra can still explore and discover using their calculators. I half-agree with that. Pattern-finding is great. It invites creativity and expression, this sort-of calculator-based discovery-learning. But if the calculator is used as a black-box, and we don’t know what it’s calculating for us, or how we could calculate what it’s doing (but just much slower, and possibly with different algorithms), we’re in trouble. If you can find patterns in pascal’s triangle, but you can’t prove them or at least have some plausible argument as to why they exist, then you’re just finding patterns. It’s cool, but has very little depth. If you let a calculator factor for you (the new ones can! like wolfram alpha!), but you don’t know what it’s doing, then I fear math can easily turn into magic, where the magician is the calculuator. And that’s one thing I big thing I worry about as a teacher: math being seen as a bag of magic tricks, where there is no logic or structure to it. And if the calculator is the magician, and the student is the audience, the student might marvel at the trick, be excited by whatever pattern is found, but never really understand what makes it all hang together. That’s why you hear me harping on understanding so much. And why when you found the power rule pattern, you did the first step, but the real learning came when you went off to prove it. It stretched your mind, and you spent a long while working it out. You wanted to understand the pattern, the logic, the conjecture. When technology helps with understanding, I LOVE IT. When technology helps generate questions, I LOVE IT. But when it replaces understanding, I’m a bit more wary.

So there are my very quickly typed two cents. They might not make a whole lot of sense, but they just sort of poured out. My thoughts change in subtle ways on these issues all the time, so ask me again in a few months and I might have switched some of my thinking.

Mr. Shah

To be honest, I’m posting this as part of my desire to archive my evolution as a teacher. You’re welcome to comment, and have discussions, if you so wish, but I probably won’t engage too much. I’m tired.

In other news, explaining why I’m so tired, I spent the last week and half writing narrative comments on all my students. I think they are better this year than in years past (each year I try to improve a tiny bit), so maybe if I have the time and desire, I’ll post about my process. But who knows, school is like a train and time just keeps whooshing by. I can’t believe a quarter is already done. It feels like we just started, and I barely have scratched the surface of my kids.  (Right at this moment, that is. You know, by Thursday or Friday it’s going to have felt like this year is turning into a piece of taffy that keeps getting stretched out, the end getting further and further away while my grip on reality is getting as delicate as the taffy is getting thin.)

PS. On the views of math:

Compiling A List Of Posts

Hi all,

I need some help, if you have a few minutes. I am looking for some quality blog posts and/or websites which offer the following:

Stories from the Front: On the ground experiences of teachers teaching problem solving in the math… the good, the bad, the ugly

War Strategies:  Different ways teachers actually do problem solving in the classroom, and maybe some hints/tips/technqiues (e.g. whiteboarding, Moore Method, Harkness Table, problem sets, grouping ideas, hint tokens, etc.)

Weapons:  Good websites (or books) which contain good math problem solving problems (e.g. Exeter problem sets, AMC questions, etc.). My personal thought on questions is that they don’t need to be hard to be problem solving… In fact, the harder the problems are, the less accessible and fun the problem solving will be, and the more my kids will be turned off.

What I’m not really looking for is Polya’s How To Solve It, which is great reading but lacks in the day-to-day practicality and concreteness I’m looking for. I don’t need to know what problem solving is (like Potter Stewart, I know it when I see it), or read philosophical exhortations about how important it is in promoting meaningful and deep learning. I want practicality. Stories, resources, tips, etc.

If I get some responses in the comments, I will compile them into either a comprehensive post, or if there are a lot, I’ll make a new page (a la the Virtual Filing Cabinet) for it.

The reason behind this is selfish, but I’m hoping the output could be collectively useful. My department is thinking seriously about how to integrate problem solving into our curricula… and I wanted to show them: “hey, there are a ton of good ideas from teachers who do it!”

So if you could help a teacher out…

PS. Not to make you jealous, but yesterday I designed and ordered these buttons! (You have to recognize I don’t know what I’m doing with Photoshop, so the pictures aren’t all that great. And these buttons have a large bleed area, so the text will actually be just near the outer rim of the button instead of with all that blank space between the text and the outside of the pin.)

A Positive and Healthy Approach to Learning

A few weeks ago in Algebra II I had students fill out a series of questions… questions which was going to lead to a discussion about mathematics and intelligence. I cribbed this sheet from my friend and teacher extraordinare Bowman Dickson.

I didn’t capitalize on it immediately, but I think I can still get some good mileage out of this. The thing that brought me back to this sheet was that yesterday in Algebra II, I gave an assessment that students didn’t fare as well as thought they would.

With one section, today, I had a heart to heart with them about what I saw, and this disconnect, and I talked a lot about the difference between active learning and passive learning. I think I got through to them. And I said: take what I said to heart. Be an active learner. And I’m going to give you an assessment on the same material next week. Show yourselves that you are capable. Because I know you are — but you just need to learn and implement the right strategies to be able to do it and make a lasting change.

Or something like that.

So we’ve had the talk about the concrete things… and I think next week, after kids take the reassessment (and hopefully — HOPEFULLY! — do much better), it would be worth it to have a talk about the more abstract side of things… attitude. The way students approach math, think about math, think about intelligence.

I’d love for any ideas about how to structure/have this discussion. I’ll throw my class data below, but if I’m going to do this, I want whatever I plan to be as powerful as possible. I want it to really get kids to think about what learning is, and how important having a growth mindset is. I have a few thoughts, but nothing great. So any brainstorming you might have, awesome.

As linked to on Sonata Mathematique:

Yeah, I want that DOUBLE POSTER SIZE in my classroom.

Without further ado, here’s my (fascinating) class data…



The Messiness of Trying Something New

It’s now more than halfway through the first quarter, and things are … messy.

I’m pretty much going through Calculus like I did last year, except for the fact that everything is so much easier because I have standards based grading down. [1] I know what works. While Calculus was hell for me first quarter last year, it’s cake for me now. So calculus is not messy. [2]

So while Calculus is going smoothly, I’m finding Algebra II to be messy. Not in terms of my kids. I love my Algebra II classes. But like last year — when I vowed to really focus on Calculus and leave my other courses well-enough alone — this year I vowed to focus on Algebra II and leave my other courses alone.

Specifically, I’m working on two major things: making groups and groupwork a norm, and having problem solving be a regular (and non-special) part of the curriculum. (As you can guess, the two go hand-in-hand.)

I haven’t written much about my inclusion of problem solving into the curriculum, but right now we’re doing a day of problem solving before each unit (related to the unit), I have slowly started including problem-solving problems in our home enjoyment (our supremely corny term for homework), I have been putting simple problem-solving problems on each assessment, and we so far have had a single problem set (something which I may or may not continue with). Still, I should be clear that most of my curriculum and my classes are traditional.

Now, if you’re a teacher who teaches more traditionally and uses a standard curriculum, you know that this a huge change. Because there’s a huge activation energy involved in switching teaching modes. For me, I kept on saying “next year, next year” and I never did. It’s daunting! And why screw around with something that works well?

And if you’re a teacher who teaches with lots of groupwork, and uses problem solving regularly, you probably remember the year you went through the transition. And how it got easier each subsequent year, as you picked up more tricks of the trade. Tacit knowledge.

And if you’re not a teacher, what the heck are you doing reading this blog? Seriously?!? GET OUTTA HERE!

Switching to this mode has played havoc with my emotions. You see, it’s not healthy and I try to avoid it, but my self-worth is tied up with how well I think I’m doing in the classroom. When I feel like I’m doing things well, I walk around like I own the world. I have confidence. My head is held high. And when I feel like I’m doing a poor job, my head hangs low. I question my desire to teach. I wonder what I’m doing in the classroom. And I’m depressed.

This year, I’m playing emotional ping-pong.

There are times when I feel like I’m killing it in Algebra II. These are usually days before each unit, where we spend the entire period working in groups and problem solving. I love watching kids think and discuss, and they’ve gotten how to work well in groups down. I’ve never had it work so seemlessly. It’s amazing. They’re independent. They’re identifying their own misconceptions and fixing them. I leave these classes wondering why it took me so long as a teacher to get to this point… I feel like my kids are finally and truly grappling, and I love that. (And I’m starting to do this successfully when we’re not problem solving… I made an “exponent lab” which was just 20 “simplify this” problems… and I was seeing great things when they worked together.)

And then there are times when I feel like I’m being killed. I have classes where I want to crawl under my desk and hide. Some of these classes happen the day after kids problem solve, and they present their solutions. Kids put their work on the board, or under the document projector, and present. Or if we don’t have time, I’ll have them put their work up, and I’ll talk through it. These classes have never worked for me. It’s like pulling teeth. Kids don’t know how to present. They don’t know how to engage if they’re in the audience. It takes forever. I don’t think anyone is getting much out of these days. [3] Or there are the more frequent regular classes (where we’re not doing problem solving), and I find I’m standing at the front of the classroom the entire class, cold calling and explaining. And it’s ugh. I feel ugh. There’s no spontaneity. It’s not fun. I don’t mix things up or have different ways of introducing/practicing material to break up class.

What’s interesting is that I feel my kids think that I’m doing a crappy job. I know they — in actuality — don’t think our classtime sucks. (I had my kids anonymously answer some questions, including the what two or three adjectives would you use to describe our classtime question.)

But even though intellectually I know that my kids don’t think I’m doing a crappy job teaching, it doesn’t change the fact that I feel they think I’m doing a crappy job teaching. It’s a slight distinction, but maybe others of you out there know what I’m talking about.

So as I said changing things is messy. Because you don’t know what works yet, and what doesn’t. It’s taking a risk. It requires more work. And you feel like you’re constantly flailing and failing. And that’s not a good feeling. Here’s a recent Facebook “convo”:

I know this is sort of rambling. I’m just trying to work through some things, but I still don’t know where things are going. Which is why there isn’t a real point to this. Just a state of affairs, from an emotional vantage point. I’m not looking for sympathy or advice. I just wanted to try to get my thoughts down — and just let you know that if you’re going through a similar transition, you’re not alone.

[1] I have a list of standards I can choose from, I have good exemplars of problems for each standard, I learned how to effectively introduce it, and I know how to set it up so I don’t die with all the extra work that comes along with reassessments.

[2] But yes, there are lots of things I could do to improve it. Always, always…

[3] I’ve talked with a teacher who does a lot of group work and presentations, and she gave me some excellent suggestions (revolving around using giant whiteboard) which I’m going to take on board.