Launching an activity: Cut to the chase!

Howdy. If you’re reading this and you haven’t read my super long post from last night (technically, it went live early this morning), this post might not have enough context. At any rate, I’m aiming for a better day today in fifth period (Algebra 1) and my game plan is this: When giving directions for a group activity, cut to the chase.

The original activity is here. In the past, I’ve introduced this activity with a minute or so of verbal directions and then cut the kids loose. I fell on my face yesterday using that approach (verbal directions as the means of launching an activity), possibly because I haven’t spent the necessary time clarifying in my own mind both the goal of the activity and the directions for students.

My attempt at more concise directions (in non-verbal form) comes in the form of these slides:

activitylaunching.003 activitylaunching.004

I’ll probably let you know how today goes in another post. I’m hopeful that this new wave of constant reflection will provide my students (at least in the long run) with a better teacher. In the meantime, feel free to comment on what you like/dislike about the activity and the “launching” (key question and directions) of the activity.

Thanks!

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:

Awesomeness

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.)

Triangles

Pre Algebra is on my teaching list this year. The last time I taught it was five or six years ago, and I’ve changed quite a bit as a teacher since then, so I’m building everything again from scratch. (It feels appropriate to note that my philosophy of teaching/learning has shifted more significantly than my actual practice, at least in my other classes.)

For the past week or so we’ve been constructing, measuring, labeling, identifying, and discussing triangles (where the constructing has been mostly with non-digital tools). Given three sides, given three angles, given some combination, similarity, congruence, impossible triangles, etc. Our progress has been frustratingly slow, in large part because my routine of late has consisted of me going into class with an activity and some excitement only to discover that some key element of the activity is seriously flawed. I spend the next evening revising the activity (thereby rekindling my excitement) in order to try it again the next day. I imagine (hope?) our progress won’t be quite as slow next year, but I’m not sure if that’ll be the case.

This is the activity I wrote for today. Since it’s late, I’ll cut to the chase: The conclusions students drew at the end of the activity were on the disappointing side, both in terms of the depth of insight of their observations, as well as their ability to express what they noticed.

This (here and here and here) is what I have planned for tomorrow. I’m hoping that by giving them space to record their measurements (in an organized manner) our debriefing conversation will include more insightful comments from students. We’ll see.

If you’re game, have a look at the handouts and let me know in the comments what you like, what you don’t, and how you’d make it better.

Estimation 180 Rocks

I learned about Andrew Stadel’s Estimation 180 a few weeks ago. I decided this morning it was time to stop watching and time to start playing along. We’re a bit behind the rest of the estimating world, but in first period (Pre Algebra) we worked through Days 1 and 2 and in third period (Honors Algebra 1) we worked through Day 1.

It. Was. Awesome.

I won’t spend a lot of time in this post talking about Estimation 180 in general or how I used it in class today. If you already use it, you’ve probably formed your own opinion and approach by now. If you don’t use it (or have never heard of it), get yourself over there as fast as you can.

What I will say is this: My students were more engaged today, even in those ten short minutes, than they have been in quite a while.

I imagine it had something to do with the accessibility (everyone can make a guess, even if it’s horribly, horribly wrong), the anticipation (“Am I right? Am I right? Am I right?”), and the way these estimation tasks present a natural, un-intimidating opportunity for students to defend their responses by explaining their reasoning. The reasoning—to students, at least—often doesn’t appear very technical or mathematical, but it’s great exercise anyway. And it’s a healthy start to making sure this is a regular part of my students’ experience.

So where to from here? Well, for one thing I’ll continue to use Estimation 180 with these students. But beyond that, I’ll try to incorporate those three elements (accessibility, anticipation, and ready-made opportunities for answer-defending) into other tasks and courses.

I just have one question: When this year’s Pre Algebra students have me again next year in Algebra 1, will there be an Estimation 181-360?

Reason and Wonder

In my third year of teaching I taught AP Calculus AB for the first time. I had 10 students (I teach at a small school; more on that later). All of them passed. In fact, six of them earned 5’s. I felt like the king of the world. In reality, I had no idea what I was doing. (In many ways, I still have no idea what I’m doing; more on that later as well.)

A couple years later, four of my students (out of 18) failed to pass the exam. I had a minor crisis for at least a couple of reasons. One, as I continued investing exorbitant amounts of time and energy into my calculus course, as I thought I was getting better, my students’ results (by one measure) were declining. This was more than a little discouraging. Two, if my goal was to equip students to pass the AP exam in order to earn college credit, then I had failed.

I had to stop and think: Was the year of teaching and learning and struggling a complete waste for these four students (and for me in relation to these four students)? My gut told me no, it was not a waste, not even close. So if it wasn’t a waste, then I must have been deceived when I thought (in no uncertain terms) that the primary (only?) goal of the course was to pass an exam and earn some college credit. So what was the goal?

I sat down on September 17, 2009 and tried to sort out the thoughts in my head by writing in a private journal. After a few passionate, yet meandering paragraphs, I settled on this as the reason I taught calculus:

I teach calculus in order that students may reason more soundly and see the beauty of the created world more clearly.

The reason I share this story now, as the first post in what I hope will be more than a few over the days ahead, is that with some minor revisions it expresses why I teach not just calculus, but anything at all. It also explains why I chose the name for my blog. (Thanks to Justin Lanier and Michael Pershan for encouraging me to finally start blogging, and to consider naming the blog in a way that expresses what I’m most passionate about in teaching.)

So here goes:

I teach mathematics in order that my students may reason more soundly and that they may have the capacity to wonder more deeply and profoundly about the world.

That’s it. That’s why I teach. And while I still wait anxiously for AP results to show up online each July, I no longer count my year as a waste or a success based solely on the numbers that appear in those reports. If I’m helping my students to reason with skill and precision, and if they’re growing in their capacity to wonder about and be amazed by the world, then I think I’m doing alright.