Think Thank Thunk makes me want to throw my hands up in the air. I’m not a good writer, but that sentence was carefully crafted to be pregnant with ambiguity. Because with every post Think Thank Thunk author Shawn Cornally writes, I rejoyce… and I despair. Reading him is like reading Dan Meyer again for the first time (although they seem to have slightly different *cause celebres, *they actually are saying almost the same thing). It’s all obvious common-sense things. Motivate. Have the kids come up with the questions. Once the hook or need is there, pounce. Capitalize. It doesn’t have to be “real world.” It just has to somehow get the kids *internally* invested, not just by grades. With a question. And a need for an answer.

**I feel inspired by what I could be doing, and like a total lame-oid for what I am doing.**

Or as David Cox twittered:

dcox21 .@k8nowak Problem is, I never sucked until I met all you guys. Thanks “everybody.”

*Yeah. Thanks guys.*

Recently I’ve been inspired enough that I’m going to try to get some curriculum money from my school to spend time coming up with (short) activities to “hook” or motivate my kids for each of the major topics we cover in my classes. That’s not going to be easy.

Reading Shawn and Dan just underscore something I’ve been feeling all year. I mean, I’ve felt this to some degree every year, but uber acutely this year. I became a mathteacher because I wanted to impart that feeling of exhilaration and accomplishment to my students… to show them the beauty and applicability and serious-honest-to-god-creativity that is implicit in math work… to see doing math as fun — a million little puzzles all connecting in these random and unexpected ways.

Or more succinctly: **I became a math teacher because I want my kids to experience the doing of math as inherently enjoyable. **So I’m asking myself:

**when did I lose that as a goal in my work, replaced by the singular focus on understanding?**Yeah, understanding is great, but that should only be the baseline of my teaching. My standards should be higher, and getting kids who don’t enjoy math to enjoy math (not just tolerate, or be able to do, but enjoy) should be the target.

I know, I’m already feeling sheepish now that all this is typed out. All my idealism is spilling out unfiltered. And tomorrow I’ll go back to the classroom and see that my Algebra II students still don’t know why is the same as , and my calculus students still don’t know why , and I’ll remember why I have such a singular focus on understanding, jettisoning fun for more immediate concerns.

But that’s still probably not going to stop my brain to keep on going to the place it has been stuck all year… asking ad infinitum the question “when do we get to have fun?”

Hear here!

Try teaching NEXT DOOR to one of these guys!….and no, I don’t teach in the same school as Dan. (How’s that for some late night deductive reasoning?!)

It’s true. It’s all true. Shawn and his students spend a lot of time living the math concepts, just not deriving them on the board or working problems from textbooks.

It’s draining just thinking about the necessary changes let alone being able to write about them regularly. Lesson for the day: teaching isn’t easy….again.

Um, dude, you ARE these guys. Have you looked at your blog? http://mctownsley.blogspot.com/

Standards based learning is central to all y’alls work!

That feeling (

Problem is, I never sucked until I met all you guys.), which I get from reading your blog as well those others (and talking to my partner and various other friends/colleagues) is why I’m so convinced thatone can learn good teaching.When talking something out makes me realize how shitty my previous thinking was, that vaguely bad feeling (which it turns out was ‘I suck at this’ all along and I just didn’t quite realize that) turns into a whole new world of possibility!

Well, I’m sure having fun! The question in the fall will be how to get more of my students having fun, when they don’t even want to be there. I’m hoping I can try out some of Shawn’s shenanigans, but he uses devices I haven’t used. My biggest problem may be how much energy it takes me to try a new bit of technology.

I’ve managed to get an easy schedule for the fall, so I’ll have lots of prep time to plot out new stuff. I’ve got two sections of beginning algebra, and one of Calc II. I’m hoping to come up with some real motivation for our topics. Maybe I should start asking around about the Calc II topics now…

If it helps you, I’ve always been fully aware of how much I sucked. That’s why I went looking online in the first place. Like DavidC said, it convinces me that I can eventually get good at this thing.

One of the joy of blogs is that it shows our progress and all the glorious failure that comes with it. What causes me despair is going into another classroom and seeing awesomeness going on and thinking that teacher has just got whatever gift I don’t have.

The blogosphere and twitter and such give me hope because I know that my teacher models struggle too.

Yeah, I’ll join your pity party here. Count me in. :) I still spend most of my time trying to compel students to practice stuff they don’t get and don’t see connected to the world. And even more depressing is when I do try lessons where they have to apply the stuff to solve/do/explore something real, they get the most upset/confused/give-up-y of all, or I get the “there’s obviously no way this stuff today is going to show up on a test, so I’m going to check out,” before they even try to engage. And then I feel like I wasted a day when I’m supposed to be bombing through these Alg2 standards. And the other teachers in the building think I’m nuts.

I feel like Shawn and Dan are talking to me from the other side of some wall of understanding, because their attitude is like it’s so easy and sensible to teach this way. And everyone should be able to come up with a compelling hook problem for every concept, AND be able to do that magic teacher voodoo that turns the activity into generalized abstract understanding, AND then the kids will automatically be able to execute the mechanics of the algebra that goes along with it. I don’t get it. I’m not there yet.

Thanks for all of the kind words. As Matt puts it so often, teaching is hard. Coming up with the ideas for lessons that are engaging but not obfuscating is super hard. Especially when you’re sick, tired, and you’ve had 100 kids ask for help with their science fair projects at the last minute…

I’ve been learning a lot from all of you, and I consider myself very very green. I almost stopped blogging altogether this week due to a deluge of negative comments that really sent me reeling. Mostly, the staggering misconceptions these people had about who I am and what I’m trying to do seemed to fly in the face of my mission as a blogger. Which is also why I’m commenting here, just like Dan Meyer, I don’t do this because I want every other teacher to know the “right way.” You should see my room, then you’d realize that there must be a better way. I just want people to know what happens when you try the things I’m trying, so that you all can take what works and make your already awesome rooms better.

Thanks again for warm reception into ye olde blog-o-net. I hope my greenness doesn’t disappoint.

Green my foot. You’re a hero! You are awesome and I definitely don’t think you are displaying hubris or anything. Who are these people? I’ll kick them. Please don’t stop. You’re a breath of fresh air and you are inspiring me. I can’t imagine how boring teaching would be if I didn’t have you (and the rest of my blog roll) to keep me thinking.

Two things:

1. I decided when I started writing that I would write for myself. To archive things that work, and sometimes things that don’t. To think about the state of things. But I swore that I would consider stopping (and finding a new lark) when I wasn’t writing for myself. So in case you hadn’t already decided that: write for yourself. Then it’ll stay useful to you. I think you stopped commenting on your blog. Good for you! But one day in the far future please consider starting it up again! I’d love to ask you questions about your activities.

2. I hope you don’t think that this post was in ANY way a knock at you (or even about you). I get in these funks about teaching. They just come and go, and I write about them here. I never feel like I’m awful, but I’m just waiting to get to that point where I feel I have something that’s amazing at my fingertips. I have lots of points when I feel I’m boring. That I’m making the material boring. That the rest of the world (of people I know in real life) doesn’t care about making math unboring, and that I fall in the trap of being okay with that. That I’m beholden to the curriculum. And a million other things. I’m also incredibly scared of venturing out of the comfort zone of what I do. Where I know I’m competent and what I do works in terms of student understanding, and sometimes I’m okay with that, and sometimes I am dying to be more than that.

Warmly,

Sam

I’m reminded of your post about how you’re a fraud. Now I’m not saying you, Dan or Shawn are frauds by any means, but that on the vast majority of blogs we’re seeing the best of what happens in each classroom. Even if someone were to post an incredible video of 5 minutes of an amazing lesson every week, you’d only be seeing 2% of what happens in their classroom.(See what I did there? With that math.) Everyone has their strengths and weaknesses, and there’s no reason to be hard on yourselves because your perceived weaknesses are the only ones you get a chance to see. So, what I’m saying is hold on to that inspiration and forget about that other stuff. All I know is that I’m inspired to think of ideas like this for my calculus class more and I’m going to have a killer lesson about product rule next year.

Okay, so who is going to be humble enough to start posting about their worst failures? (Maybe someone has already started?) A group blog…averagemathteachers.com or something like that?

@Shawn I hope you turn comments back on. Comments can be very productive and healthy. There are “people” (who sharpened their teeth on the Math Forum listserves, I think) who seem to put all of their energy into being condescending and just awful. I deal with them by either 1. totally ignoring their comments or 2. delivering a canned blogger smackdown like “The Internet is big place. If you think I’m such an idiot, there are lots of other people you could be reading instead.” Eventually they give up and go away and you can have normal conversations with non-rabid human beings.

@Matt, I’ve tried that (posting about failure), but it feels like fishing for an “Aw, there, there” or maybe a sympathy compliment. Or, even more maddening, people try to “help” by explaining math to me. (Not like I know all there is to know, but I know the high school curriculum pretty much inside out and backwards by now, so I get irrationally offended when people assume I don’t know something. I know – real mature.)

Wow! I love you all (in a mathy sort of way).

Next year, when I’m back in my classroom, and I’ve just tried one of these ReallyCoolLessons and it’s fallen totally flat, because I’m not as great as these young’uns, or I haven’t done a cool lesson in weeks, or …, when I’m feeling incompetent, I might just come back to this discussion (if I can find it), to remind myself that we all struggle with the dilemmas of teaching. (I know, run on sentence…)

Sam,

I am also going to be getting grant money to come up with activities to make students love math again and engage in all the thought necessary to understand and analyze these concepts (Thanks Dan and Shawn!!!). Mine are going to try to center on Algebra I and II curriculum, but we should join forces and show just want a bunch of inspired creative individuals we can be. Any interest (invitation is open to anyone that reads this)? let me know.

Sam, you have totally hit how I feel. I think it’s so easy to be locked in your own building, in your own classroom and never really compare yourself to others. While all of you (including you, Sam) have made me feel like I’m not living up to be the teacher I had planned on being, it is in that realization that I have suddenly become more inspired and passionate about what I do everyday. All of us who add to this digital network better ourselves and better those of us around us.

Thanks everyone for blogging. Keep up the good work!

i’ve posted about failure for years.

nobody reads it.

Sorry if this is silly, but is there anything you would have them know about why besides “you add the exponents because that’s the rule”?

@DavidC, I’m not sure about your question. In algebra II we talk about why the exponent rules work, and I even give an “explain in word — but you may use an example to illustrate — why the exponent rules/properties work” questions on their exam.

I just get frustrated that (a) they don’t know WHY and (b) they can’t use them properly. In calculus. Would I be happy if they can just apply that rule? Honestly, sure. Would I be happier if they already knew why? Sure.

The inability to distribute negative numbers properly, or the canceling of terms in fractions that can’t be canceled, or the sheer terror when students are given anything trigonometric or involving e, just highlights how compartmentalized our curriculum is before calculus. That they could reach my class, and not know how to simplify fractions or solve something like ? So that’s why I’m doing my Algebra Boot Camps (https://samjshah.com/2009/08/21/calculus-a-new-approach/).

But I hear the same stories from all calculus teachers.

Thanks. I think that’s pretty much what I was wondering…

Yes, yes! The same story from me too! In particular about exponents, it was supposed to be a neat punchline that ln and exp are log and exponential functions — but a punchline they would totally miss unless we reviewed those, first. Even if they had some facility with the exponent rules (not all of them did!), I think lots of them couldn’t say why they work, or (relatedly!) why exponentiation with fractions is defined how it is. But going through that (all the stuff in my reply to Sue below) was great fun for all of us.

I’m curious: Do you think your student who couldn’t solve knows that means “the cube root of x”?

@David C, re: cube root of x, the answer is: yes and no. They do know that fact, but they don’t know *why.*

I do teach it (and give another “explain with words and equations why x^(1/5) is the fifth root of x” or “explain what the fifth root of x means”) in Algebra II. My kids — for those couple weeks we’re working on exponents and other stuff — do *know* that fact. I harp on the *why* of it.

“because that’s the rule” isn’t the reason. The ‘rules’ come from patterns we can observe. I personally prefer calling them properties instead of rules.

If I asked a student why x^{1/2}x^{3}=x^{7/2} is true, I’d hope they’d say something like … x^{1/2} is the square root of x, x^{3} is the same as square root of x to the 6th, and multiplying all those copies of square root of x gets you square root of x to the 7th, or x^{7/2}. (Sorry I don’t know how to insert a square root symbol.)

Yeah, that’s the kind of thing I have in mind. I think answers could differ a little depending on which of various similar stories about exponents gets told, and what the student wants to focus on. For an answer very different from yours but still pretty reasonable, someone might say “Because when the exponent is an integer, we know that , and that’s really nice, so we adopted notation that makes that property hold for non-integer exponents also.”

Just for fun, here are some bits I think the full story about exponents should include (not exhaustive):

-It’s tedious to write , so we adopt as notation for that.

-That notation makes it true that .

-We can apply our other operations (like addition and multiplication) to other numbers, too. What could possibly mean?

-Well, if we want that nice property to keep holding, MUST be the cube root of 5.

-other fractions, negative numbers

-(Hmm, look how this only gets us as far as rational exponents. How can we extend it further…)

That last is in parens, since it probably only comes up once you get to a calculus course. Anyway, Sue, what you’ve written is important, and students should know that. I guess I just also think it’s important for students to see that the meaning of our notation is something we could make a choice about, and we why make these particular choices about this notation. What a long comment I’ve written trying to make that point!

Ahh, I misread (the tenor of) your question. I see now that we’re on the same page. :^)

And you’ve both just pushed me to realize that me explaining the why is a lot different than them explaining it back. I have not asked for that on tests, and I need to. Thanks!

@Sue: Ideally, I think it would be nice to have them (with guidance) discovering/inventing that stuff themselves rather than having it explained to them. But I know I’m naive.

Just had a conversation yesterday with a non-teaching friend of mine that reminded me of this post:

Him: So..are you good (at teaching)?

Me: I’d say I’m above average for my school, average for the teaching population as a whole, and in the bottom 1% of any teacher blogger.

Him: (WTF face…)

I so so so so often feel that way.

That convo is priceless. Thanks for sharing. It’s exactly what David Cox’s twitter sentiment was too. I don’t think I’ll ever forget that.

Sam

I loved this post; summed up my feelings about my teaching very nicely. But isn’t this the blog with the cover image that says “Don’t let other people’s success depress you?”

I wish that were my cover image, or a motto I live by. It’s noble.

I wish I could *just* be inspired by what I read. But I’m super self-critical and, naturally, when I read something I immediately put it in comparison to my own work. And I do kick myself at my own shortcomings — a lot. And reading blogs just highlights my own shortcomings.

So I get depressed, and then I get inspired, and the beat goes on. The cycle continues. It’s hard to change that super-self critical introspection that I’ve got going. I’ve had it for years, and it’s probably not very healthy.