Blogging as Therapy

My Inflated Sense of Awesomeness

I used to suffer from an inflated sense of awesomeness. I blame my honors students. Now, stay with me for a moment. I don’t dole out blame like this too often, but I think I have a case here.

Picture this daily routine from my not-so-distant past: I bring mediocre to a classroom full of awesome kids on a regular basis. The experience is, well, awesome. Such regularly fantastic interactions lead me to believe my teaching is, well, fantastic. Little do I know, the awesomeness is often in spite of my efforts, rather than a result of them. Things only go swimmingly because my kids are so swell.

Reality Settles In

I mentioned that I used to suffer. No longer. In fact, my sense of awesomeness has been plummeting for a couple of years. I’m so mixed up right now that it’s about to crash into the floor. Here’s a graph of my current crisis in confidence:


Good News, Bad News

So the bad news is this: I’m not half as good at this teaching thing as I thought I was, and that’s more than a little discouraging.

Here’s the good news: I’m not a quarter as good as I think I could be, and that’s more than a little exciting.

More good news: I’ve realized that my primary teaching style (I’d call it “conversational direct instruction” with a lot of “What do you see? Why does that happen? How can we generalize?” in an all-eyes-on-the-front-of-the-room style) is seriously limiting my students’ potential.

I think the “What do you see? Why does that happen? How can we generalize?” elements of my teaching are incredibly valuable. I don’t plan on throwing those out, and I only hope to get better at creating opportunities for students to ask and answer questions like these.

But the all-eyes-on-the-front-of-the-room style is starting to kill me. What’s worse, I expect it’s been killing some of my students for a while. The delay in seeking a remedy is because my mostly-honors students have been so amicable and cooperative that they haven’t pushed back through bad behavior, inattentiveness, or poor learning results.

Enter this year’s course load. The pushback is alive and well. I have a few classes this year that are helping me see through the mirage and have given me a clear view of my strengths and weaknesses.

Class Portraits

Take today’s classes in fifth period (Algebra 1) and eighth period (Honors Algebra 2) as portraits of what sometimes goes wrong in my room.

In Algebra 1 we’re making connections between the x– and y-intercepts of the graphs of quadratics and their equations (in factored and expanded form). At least, that’s what we’re trying to do. Today was an absolute train wreck of a lesson. Their attentiveness during yesterday’s lesson (where we reviewed some factoring techniques to prepare for today) was so poor that I decided to transform today’s direct instruction lesson (remember, they’re almost all written that way right now) into a small group activity. I figured if they spent less time listening to me walk through problems and more time thinking their own way through problems that they would have a better chance of making the relevant connections (which are not terribly profound). We eventually got there, but I felt like a slave driver while giving what should have been 30 second “getting started” directions that lasted far, far longer because I couldn’t hold their attention for the life of me. I left class thinking “There must be a better way.” So what is it? Type the directions on a Keynote slide and keep my mouth shut? Type more detailed activity directions out at the top of the handout so they don’t have to wait for me to get started on the activity started? Would they even jump into the lesson right off the bat without any teacher explanation? Is it even possible to train a class to become self starters when they’ve always relied on me as their teacher taking the lead? I expect that it is, but how?

Just to be clear, as I tried to move away from direct instruction today, we couldn’t even get past the directions for their small group task. At the risk of sounding conceited, I feel it’s appropriate to note that outside of this group of students my classroom management is typically stellar and discipline is a non-issue. With that being said, it’s still on me to make things work with this group of kids. It’s just going to take better lessons, better ideas, better systems, etc.

In Honors Algebra 2 I fight another battle. These students are noticeably more interested in the mathematics, and their behavior is mostly excellent. However, they struggle to remain focused, partially because it’s the last period of the day but also (I think) because the pace of our discussion is just right for about one third of the students, too fast for another third, and too slow for another third. I want to break out of direct instruction mode so that students can proceed at their own pace. I expect all of the students would learn at least as much as they do now, and a full half of the class might have an opportunity to learn a great deal more because they aren’t tied to my pacing for the entire lesson. But I don’t know how to make this happen.

More Bad News and a Plea for Help

As you can sense, there’s some more bad news: Even though I’ve identified what I want to change (my teaching style) I don’t know how to get from here (“conversational direct instruction”) to there (something better than what I’m doing now), or really even where “there” is.

So here’s what I need from you. I need some help vision casting (what could my classroom look like). And maybe more importantly, I need some advice on how to get there.

A few things to keep in mind while you’re dishing out the good stuff:

  • I typically teach 4 to 7 different courses, so lesson planning, activity creation, and so forth, is a challenge.
  • I desperately want to design a curriculum where the most challenging thing for students is to think about the interesting, non-trivial tasks they have been given. I do not want to remain mired in a curriculum where the most challenging thing for students is to pay attention when every part of their being is shouting “Boring! Don’t pay attention, it’s boring!”
  • A part of me wants to go all Sam Shah on my students with guided discovery packets like this, but I’m terrified of the monumental task of transforming my direct instruction lessons.
  • I want to include more open-ended problems in all of my courses.
  • I think well designed three act tasks are the bee’s knees, but I’m currently more of a stumbling bumbler than a Dan Meyer when it comes to creating my own.
  • About four years ago I shelved my Algebra 1 and Algebra 2 books and wrote my curriculum from scratch (lessons, homework, and assessments, the whole shebang). The curriculum is heavy on concept and procedure, but light on application (i.e., problems in genuine, engaging contexts).
  • I still use a textbook for Precalculus (Foerster), Calculus (Foerster again), and AP Statistics (Starnes), though I may “escape” from the Precalculus book when we transition to Common Core in 2014-2015.
  • I’m trying to build a Pre Algebra course from scratch, aligned to Common Core standards, but it’s been an uphill battle (and until recently, almost entirely based on direct instruction for new content).

So there you have it. I’m in trouble. And you can help. Get thee to the comments!

(By the way, if you made it this far, you deserve a gold star. Two gold stars for anyone who leaves a comment.)


  1. You have a gold star for having so many preps. That makes life so much harder. Regarding your Good News Bad News section, a small change that I’ve made that seems like it makes a big difference is the grouping of students, and me moving myself physically to the back of the room. I’ll put forth a question, and say they have 1 minute to think with their group and come up with an answer. I’ll walk around, but not “listening” (although I really am listening) and just making sure that a math conversation is happening. Wrong or right, as long as its a related math conversation I don’t stop them. Depending on what I’ve heard of the class consensus, I’ll have the groups share out their answers with the group next to them. A big part of making this stick is if I hear that the class mostly has it, I just move on. I don’t confirm them being right (even though Honors groups want an answer), I just move on. They quickly figure out that the learning burden is on them, not me, and the conversations get serious, real fast. I don’t know how well I’ve described this, but in my 9th year of teaching I’m (finally) really feeling like I’m hitting a sweet spot with group discussion. These are honors Pre-Calc or AB Calc kids who are mature, but often looking for the “right” answer.

  2. Dan, can you share a bit more about how you’ve grouped students in ways that have made a big difference? My students sit at 3 ft by 8 ft tables, typically four per table. I’ve made a big effort to vary student groups, either for an individual activity or for an entire chapter, but about 90% of the time (or more?) I assign the groups randomly just to shuffle the kids and get them collaborating with a fresh group of their peers. Are you more intentional in your grouping? If so, how?

    Great comments about stepping back during group discussion and listening but remaining outside of the conversation. I feel like I do a decent job at that in my higher level classes (by higher I mean age, ability, or both), but I’m struggling massively in my regular Algebra 1 class (with students in grades 8 through 10). I’ll keep trying. I definitely have room to grow in each setting (honors and non-honors).

    Something that may help in that growth: Can you give me a few examples of these “one minute think/discuss” questions that you use in Precalculus and/or AP Calculus?

    Thanks for your comments!

  3. Michael, I remember observing classes all over Los Angeles during my final year of undergrad, and then again all over Fresno (where I live and teach now) during my credentialing. In the last nine years, I think I’ve only visited two or three classrooms off campus, and that was six or seven year ago. I miss the insights gained by peeking into other people’s classrooms.

    So here’s a question that may (or may not) give me a sense of what it’s like in your classroom:

    On a typical day in your classroom, where students are working on new material, what percentage of the time are you…

    (1) At the front of the room
    (2) Meandering through the room observing students, listening to discussions, nudging them along in some way, etc.?
    (3) Standing at the back of the room
    (4) Doing something else (please describe if there is something common I’ve not mentioned above)

    I’m just trying to wrap my head around what it looks like in other classrooms where teachers are using less direct instruction than I have historically used.

  4. Hey Michael,

    Why don’t we swap videos of our classes? I think that would give a more accurate picture of my classroom, warts and all.

    But here’s a description of my classes from yesterday. (We didn’t have school today.) It was a pretty uneventful day on my part, and I wasn’t thrilled with my lessons. I also didn’t work very hard to prepare them, so, whatever. It’s been a long week.

    I’d appreciate any comments those wiser than me have to offer.

    Period 1: Open with this video. I’m at the front of the room. I ask them “What’s going to come out the other side?” I write down their answers. I call on the kid who seems to be shouting something with any semblance of a reason. He explains. While he explains, I move to the side of the room. He finishes. I ask, “Everyone happy with that?” Someone says that they don’t get it. He repeats. He asks if he can come up to show, and I give him the go ahead. Kids are still not getting him, but one kid says “I can explain” and then he goes up to give it a shot. More kids get it now. And now there’s a bit of a debate (this doesn’t happen every day, but it happens not infrequently) and now I drift to the back of the room. When they appear to be getting frustrated and a bit heated, I jump in and try to clarify the arguments. Then I try to take the reigns, and that goes OK for a while and things start to fall apart. I try to use a visual model to explain how to think of fraction division, and MS is NOT feeling that and he’s shouting something like “something about 4 is 4/1.” The kids are getting frustrated, and I’m getting frustrated. Things go on like that until I give them a quiz during the last 10 minutes of class.

    Period 2: I give them a short warm up, which is essentially a kind of mixed review of problems that I think they need practice on. (Solving equations w/ variables on both sides, solving for a variable with a conceptual lead up, solving systems of equations.) This is them working on their own, with me poking my head in to their self-organized group or individual work. There’s a ton of “hey shouldn’t you be doing something just anything and please stop throwing your pen across the classroom” stuff today. I brought them into “whole-group” to go over one of the problems folks were getting stuck on. Then I give them the opening problem set from the CME Project’s unit on inequalities. (I copied it onto a worksheet.) This was me walking around and poking my head into their conversations, and went on for about 10 minutes. That went OK for most of the kids in class, though there was a good deal of goofing off. I’d say that half the class was working hard, a quarter was doing OK work, and a quarter did absolutely nothing. (Which was intensely disappointing.) Then I tried to consolidate their observations and push them toward noticing that there’s a boundary point between the numbers that satisfy a > b and a < b, which just went OK, I'd bet pretty much nobody understood that, but whatever, we're at the beginning of the unit.

    Period 3: This is my loosest class of the day. I give them a very short warm up, with a reflection question and a trig graph to investigate. After setting it up, they work on their own for 5 minutes. Then we go over it, and I set up the rest of the lesson: we're investigating and explaining the properties of graphs, and you're picking the graphs to investigate from a "menu" that I provided. Then we have 15-20 minutes of "you work, I poke around" mode. We've got like 10 minutes left at this point, and in whole-group I ask if anyone investigated cos(-x) (obvs I knew who did and who didn't) and we get everyone to notice, by graphing on the board, that cos(-x) = cos(x). We note that on the board. "We" means "me." Then "we" do that for cos(180-x), sin(180-x), sin(-x), and I frame what I think is cool about this (why is cos(-x) the same, but sin(-x) is flipped?) and I ask for explanations. There's some silent murmuring. A student has an idea, and I walk to the back of the class while he explains. His explanation falls apart in the middle. Someone else goes up. I'm still at the back. He's able to communicate his answer, and then someone else has a "different" explanation (effectively the same one, but in diff words). Then I jump in at the end to mention a fundamentally different perspective, the bell rings, and I hang out for a minute or two explaining my point to some kids after class.

    Phew! Sorry for the word barf.

  5. Hi Michael. I love this, “I’m not a quarter as good as I think I could be.” We all have room for improvement, and it starts with acknowledging that we have much to learn, from colleagues, students, and self reflection.

    One big addition to my class this year are large whiteboards. I did a search on my 180blog and found these posts that show the kids using them (there should be a lot more posts using whiteboards than these, so I must not have tagged them):

    Days that I have the kids use whiteboards are my favorite teaching days because I don’t do any “teaching.” I pose a problem and walk away, well, not walk out of the room or anything :). I walk around, ask more questions of the groups, pose certain questions to the whole class, have one group answer another group’s question, give a hint. These whiteboards are worth their weight in gold.

    And I really do try to implement the Five Practices whenever possible:

  6. Fawn,

    Thanks for reading the post, and for your thoughtful comment. Earlier this year I went to Lowe’s and bought two three-by-five foot whiteboards and had them cut into 12-by-16 inch pieces. They’ve added a lot to my classroom this year in at least a couple of ways. First, when we’re working on smaller problems (I should probably call them “exercises” if I want to stay true to Polya’s definition of a “problem,” which I rather like) the whiteboards provide a wonderfully efficient feedback loop between me and my kids. I used to use TI Navigator (first with 84s, now with Nspire) to get that sort of feedback, but I’m finding the old-school whiteboards are more engaging, more efficient, etc.).

    Second, when students are working individually or in small groups on a challenging problem there is something semi-magical about writing on a big whiteboard with a marker, rather than with standard paper and pencil. I don’t give students opportunities to work on problems like this often enough. It sounds like you do a bit more of it, and I look forward to reading the posts you linked to in more detail soon.

    Thanks for sharing about the Five Practices. The practices make it sound more manageable, which for me is part of the battle. (I have to be able to imagine being successful with a new approach before I’m willing to take the risk of trying it.) Here’s my biggest struggle with implementing the Five Practices more often in my classroom: I need more problems that fit the bill (“Find a math problem that is high-level with multiple strategies”). I guess I’ll find more in time, through my own searching and writing (and blog reading, like this).

    Anyway, thanks again!

  7. A) four to seven preps, goodness. Give yourself a pat on the back just for that.
    And 2) I think that just like its easy to inflate your sense of awesomeness with honors classes, it’s also easy to inflate your sense of awfulness with regular-to-low or remedial classes. I am only a third year teacher, so take my advice for what it’s worth, but I think it’s wonderful that you are reflective and conscious of what direction you want to head. With your schedule, I think baby steps are in order. Think one interesting activity or problem per chapter per course.
    Oh, and the $2 IWB (@fnoschese term, he’s a physics teacher, but amazing) are a cheap easy way to get kids doing practice problems without your leading at the board.

  8. Let me start by saying that you’ve described me rather well. One of the things that prevents a complete mirror with you is I suspect my graph of “perceived awesomeness” jerks up and down, more like a demented sine wave, with reality somewhere in between. I think the fact that you’ve got them sitting at four per table is already a good plan; I’ve bundled my desks into twos, but I’m not there yet.

    As was stated, I think one of the main things is to actually give them time… I have this bad habit of thinking a minute of silence is a problem, but that seems to be the necessary time for them to realize “huh, he’s not going to give hints or answer it, guess I have to do something then”. As a whole, I feel I still do a “direct instruction” style (real world activities almost make me physically uncomfortable) but where I can, I reverse it. Instead of ‘here’s the topic, here’s some examples’, start with the examples. Walk around, see how they tackle them. (I’m not necessarily at the back, but I float a lot more than I used to.) Answer questions individually rather than as a whole. Then present the topic partway through the period, referencing what you saw students do (or having them reference it themselves). This might allow you to transition your lessons to something more open without feeling you need to totally reinvent yourself.

    Sometimes it works. Sometimes students come up with something awesome that takes you on a tangent, so you revise on the fly, and get back to definitions another day. Sometimes they’re off base, but that shows you where the weaknesses are. Sometimes they just don’t want to work on problems, or the topic is so different that you have to fall back on direct instruction. And sometimes you have to do direct instruction anyway, to get through parts of the curriculum so they’re not looking at a boardwide exam going “uh, we didn’t cover this”. Sometimes a song helps too, but that’s me being weird.

    I can’t really speak to group work; one of the main reasons why I don’t think I can just leap into it either is I have terrible observation skills. Also name recollection. I live in fear of putting two sworn enemies in a group together, so mostly they pick themselves. One of many things I need to work on. So I don’t think I’m worthy of any gold stars; a simple “I’m pulling for you, we’re all in this together” a la Red Green will suffice.

  9. Wow, almost everything you said describes where I’m at and where I’d like to head. This is my first year teaching math and I have 5 preps, with two extras on Friday and one extra on Tuesdays… so it gets hard to plan much for them.

    I love how you described your teaching style as “conversational direct instruction.” That describes a lot of what I do too. I don’t stand up there and lecture, but I’m the one leading the conversation rather than the students.

    Most of my classes use a Saxon text book, which I have to use, and have little flexibility for changes. For those ones it’s so fragmented that it’s hard to go in depth into anything. to help with that we start off the day with one more complex problem that can usually be solved in several ways and they have 10 minutes to work on it. they can work together or alone, up to them. Then I invite someone to share their answer and how they got it. sometimes another person will show a different way they solved it, but not usually. I will then have them do some examples from the lesson for the day. if they can do it, great, we move on, if not, I’ll lead a conversation about it and they take notes.

    For 9th grade the curriculum we use is I like most of it. It’s based on tasks and discovery more than on direct instruction… but going straight from Saxon to this is killing some of the kids. Well, more accurately their curiosity/initiative was killed by Saxon and I can’t figure out how to get it back. I have SOOO many disciple problems in this class, but in the rest it’s rare. Many of the 9th graders have NO initiative to try a problem. They want me to tell them how. They want me to tell them if they are right and get frustrated when I just ask them why they think they have the right answer. Knowing what’s coming up in 9th grade I’m getting the lower grades prepared and helping them hang on to the idea that I won’t always give them the answer or they exact steps they need to take, so I hope they will handle the transition out of Saxon math better.

    Take a look at the curriculum we use for 9th grade though, it’s got some good ideas in it.

  10. Thanks for the link to Mathematics Vision Project. I’ll check it out. I’m finding that I would have an easier time making a transition away from direct instruction if I had a catalog of rich tasks to choose from for all of my courses.

    Glad to know I’m not alone in my multitude of preps, my current teaching style, or my hopes for the future.

    Thanks for reading, and for commenting!

  11. What’s a $2 IWB? I assume IWB = interactive whiteboard, but I still don’t know what a $2 IWB is.

    As for baby steps, I am both drawn to and repelled by the idea of changing in small increments. Part of my approach to teaching so many different things is mapping out somewhat meticulously what my sequence of units/lessons/activities will look like. It’s been one of the things that has kept me sane during each school year. Changing one step at a time has the advantage of being much more reasonable in terms of workload during any given year, but it also disrupts my way of thinking about and revising my curriculum (which tends to be in whole-year chunks). As an example, I don’t really make many significant changes to most of my courses each year. Instead, I completely revamp about two each year. Then another two the next year. And so on. So over the course of three years all of my courses get a refresh.

    I feel like I’m drifting from your comments, so I’ll stop and end with this summary of my thoughts:

    What’s a $2 IWB? Baby steps are good (but sometimes even those are hard for me).

  12. Well, not much I can offer that others haven’t contributed. I sometimes feel so confused about what I’m doing that the single thought of constantly reflecting on my practices is enough to make me think I’m doing something constructive. You’ve got the right intentions here. Assessing your work is valuable, reflection is invaluable, reaching out for advice is modesty, and moving forward with optimism is what a quality teacher (now or to be) is made of. You’re on your way!

    Re: “I desperately want to design a curriculum where the most challenging thing for students is to think about the interesting, non-trivial tasks they have been given.”
    I know the feeling, but don’t be too desperate. The more you hang out here on Twitter and the such, you’ll come across some great stuff. You’re writing some meaningful tasks and will continue to improve as you go forward. I firmly believe that no lesson should be taught the same way twice and that goes the same for designing tasks. No task should be designed the same way twice. Continue to evolve. Continue to challenge your students. Continue to do what interested you too when designing tasks. Lastly, when designing tasks, I continue to see that a very successful approach is “less is more”. Keep the tasks simple and let the students take it places. Take notes along the way and pay attention to where they go.

  13. Good words. Thanks for sharing. For what it’s worth, I disagree with the “not much I can offer” opening. 🙂 As for not being too discouraged/desperate, I’ll have to learn how to hang out on Twitter and blogs, envisioning what my classroom could be like, and yet not be unrealistic in my expectations for the present (and also not downplay the strengths that do already exist).

    At any rate, thanks for the comment. Much appreciated.

  14. Awesome. Thanks for the link to Frank’s post. I think I’m heading back to Lowe’s for a size upgrade. 🙂

  15. Whenever I read teachers talking about how their kids just sit there, I always wonder why they expect discussion. I think it’s better to give them something to do, and conversations will start from there. I usually start with modeling linear equations, and it gets the kids doing math right away. It’s not “open-ended”—and, may I just say, math teachers are so totally, woefully wrong about the appeal of open-ended problems, as in students are usually going please god shoot me now–but it gives students the opportunity to start to *do* things, and prove to them that they can do this stuff.

    I also notice that the problems the teachers complaining about “students just sitting there” are always way too difficult for the population.

    I sit my kids in groups by ability, and they mostly stay in the same seats over the year, unless the groups talk too much or one or two of them break away. I think ability seating is essential.

  16. Whoops–hit post too soon.

    “I desperately want to design a curriculum where the most challenging thing for students is to think about the interesting, non-trivial tasks they have been given.”

    THis is soooooo not what students want. You have to give them a sense of genuine success–everyone in the room, not just the best kids–and then, after a while, they will start engaging with small, interesting problems.

    But most math teachers egregiously overestimate the ability of kids who are taking algebra in high school. I know math teachers who present/post these incredibly difficult, open-ended tasks and say “this is what we did in algebra class” and I’ve been to a lot of those algebra classes and most of the kids don’t have a clue what’s going on. I would rather kids get skills that will help them place out of remedial math in college than waste their time on open-ended questions they might, at best, pretend to care about to please the teacher.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s