Buying The Groceries

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Coaching is a rough gig. Especially when your successor wins about a million Super Bowls. Image via Yahoo Sports.

Back a million years ago, when dinosaurs roamed the earth and I still talked about sports for a living, the New England Patriots parted ways with their coach, Bill Parcells, after the team made a Super Bowl appearance. He was not super-pleased. In fact, he had a parting shot:

“If they want you to cook the dinner, at least they ought to let you shop for some of the groceries.”

I get what he’s saying: if you are holding me accountable for the performance of 53 guys, I should get to pick which guys they are. Well, teachers don’t get to pick. But in the right place, they get to pick how they teach. In one of my first conversations with my new department chair (now a district-level administrator) when I hired on, I found out that our department was moving in the direction of classroom -level autonomy. The state decides what you have to teach, yeah, but you get to decide how to do it.

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I’m a Stuck-In-The-80s loser. Sue me.

 

Use a textbook? Fine. Ditch the textbook? That’s cool too. All about Three-Act Math and Desmos Activities and WODB? You do you.

We do a lot of planning as content teams. Our main focus during this school year is detracking. Instead of offering three ability-grouped sections, there will be “Honors Algebra II”, and just-plain “Algebra II” next year. Those are the options, kid. So we’re spending a lot of time figuring how to support our struggling learners in a faster-paced environment.


Now, they’re not coming around tomorrow to make a movie. Nobody here is doing anything earth-shattering and disruptive, but it is obviously cool to have the freedom to teach in your own style.  Occasionally, monumentally cool things happen. Sometimes, it’s a smaller victory. In classic “happy accident” style, I may have stumbled across something cool this week, in terms of the order in which material is presented for maximum learning.

We’re in the midst of a (short) trig unit. Right angle trig, sine and cosine graphs, that’s about it. “Coterminal angles” and “Functions of any angle” gets a drive-by. Law of Sines and Law of Cosines get pushed back to Pre-Cal. There’s probably more emphasis on graphing. But: What if the order flip-flopped? Graph first, then tackle coterminal angles and the general definition of the functions?

Maybe with a Desmos activity?

Yeah, let’s do that.

I feel like I’ve got to lay a pretty good foundation with the graphs. Maybe, emphasize that the graph is periodical and hits the same value multiple times. I think the visual will help my students grasp the concept that there is a sine & cosine value for all of those degree measures, then we can go from there.

My 2nd hour wasn’t having it:

 

 

My 5th hour response: marginally better. Then I was out Thursday for an all-day curriculum planning meeting (coincidentally). So we’ll see. If the periodic nature of the sin/cos functions take root, I’ve set the table for Friday beautifully.


 

We quickly recapped the sin/cos graph assignment Friday at the outset of class, pointing out again how the graph of the function repeats. I’m guardedly optimistic. Let’s roll with Desmos, huh? We started with a card sort of definitions – letting the students do some word root detective work.

Desmos Trig 1

They had some mild success at matching words, images, and definitions, and we took a couple of minutes to make sure we were speaking the same language.

 

(H/T to some of my online PLN friends who helped me tweak this activity. Protip: when smart people give you advice, take it.)

After a couple more screens where we pondered the cyclical nature of the graphs, it’s time to get to the meat and potatoes.

Desmos Trig 3

Good news: pretty much everybody could sketch a 135 degree angle. Also good news: most could recall the ratios for sine and cosine. So let’s push the ball upfield. Here’s how to calculate the ratio of any angle. Go.

Desmos Trig 4

We ran out of time before we could dive deep into the idea of positive and negative values for the functions.

Ironically, this activity connected much better with my 2nd hour than with my 5th.

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But what can I say? Friday afternoon, after lunch, sun shining thru my windows….

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Hey, I recognize that guy…

At least some of them let their creativity shine thru as well.


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So, did this little tweak in the order of sections pay off? Not in a fireworks/shooting stars kind of way. I think the visual of the animated unit circle/sine graph was huge. And I think the Desmos activity was an improvement over me standing there and dishing out notes and giving a written assignment.

The bigger story is the freedom to re-arrange things in such a way that it benefits my students. Writ large, my Alg II planning group met last week to ponder some options for next year, including SBG, but we also took a hard look at the course from a power standards standpoint. We front-loaded the course with Alg II standards, pushed the trig section back to the end of the year, and flip-flopped a couple of units to get balance between 3rd and 4th quarter. Standards-Based Grading has some folks curious, and is being strongly encouraged, but individual teachers have the option whether to implement it.

Sounds to me like as seasoned chefs, a lot of us will be buying our own groceries next year. I feel a little bit like Bobby Flay already.

Bobby Flay
Image via Food Network
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College of Arts and Sciences

Growing up, every Tom Cruise character was that super-confident, super-cool guy that could bluff his way through any situation with quick wit and a smile. Who didn’t want to be Joel Goodson or Brian Flanagan or Maverick?

But I definitely also had an appreciation for people who planned every move with military precision. Who could see the downstream consequences to actions that everybody else missed. See: Jane Craig in Broadcast News. So: going by the book, or flying by the seat of our pants? Painting by numbers, or just making some happy little trees?

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Is teaching an art, or a science? If you’ve been around the game for awhile, you’ve probably concluded it’s both.

Joshua Eyler of Rice University turns the question on its head in a 2015 blog post, proposing that “the most effective teaching is that which helps students learn to the greatest extent possible”.

So how might we change the art vs. science question to reflect this positioning of learning?  Though we’ll have to sacrifice the nicely compact nature of the original, a new version of this question might ask whether achieving a deep understanding of how our students learn (both in general and about our fields) is more of an art or a science.

The sorts of collaborations with students that might reveal this knowledge could certainly be called creative and even artistic.  I also think there is something of an art to being attuned to students’ individual approaches to learning (or their Zones of Proximal Development) and adjusting our strategies and techniques accordingly in order to ensure we are helping as many students as possible.

What about science?  I have to admit I’m biased here.  As someone who is writing a book on the science of learning, I lean more heavily in this direction.  Because learning has its basis in the neurobiological mechanisms of the body, I think science has much to teach us about learning.  Learning is also rooted in the social world as well, so the fields of sociology and psychology provide further opportunities for understanding.

Brain science and psychology and making adjustments on the fly for what our students (collectively or individually) need at the moment? Yeah, that sounds exactly like what teaching is. “All Of The Above”.


That was us a couple of weeks ago. I know the look I saw on my kids’ faces after the logs quiz. It’s never a good sign, but that “I don’t get this and math is stupid and I quit” feeling in February makes for a long last 13 weeks for everybody involved.

So I called an audible.

I’m hardly the first to roll out this activity. My favorite instructional coach was doing Barbie Bungee before I was even teaching, long before Twitter and Desmos had even been thought of. The great Fawn Nguyen and Matt Vaudrey have raised it to an art form.

But I gambled that it would be just the antidote for the Math Plague that was threatening to decimate my classroom. Plus, worst-case scenario, I could justify it (at least to myself) by saying that the linear concepts and DOK 3 activity would be ideal for my students in the weeks leading up to ISTEP re-testing season.


 

I leaned heavily on Mr. Vaudrey, who is kind enough to post his materials for anyone to use, and to reflect on his own lessons so that folks downstream might be able to anticipate the stumbling blocks for their students. I teach in the new STEM wing of my school, in what eventually will be a combo computer lab and build/makerspace. So I had some essential ingredients on hand: measuring tools, lots of space, and plenty of surfaces at a variety of heights. What I didn’t have on hand, I sought out: eight bags of #32 rubber bands at WalMart, and 8 WWE wrestling figures from my son’s collection.

Day One I tried to hook them in with an insane missile silo bungee jump, then set them up with a figure, a bundle of ten rubber bands, a data collection sheet, and let them go about the business of jumping.

Perfect world: each group of three or four students would have had about 8-10 data points. Reality: most got 4-5. Several got only 3, and one group managed to record only one distance. Those guys are gonna need some extra support.

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Day Two, time for some estimates backed up by math: How many bungees would be needed to jump off the top of my projector? How far a jump could their figure make with 25 bands?

And in one of those glorious moments of teaching, I had set the hook. Students were madly pouring over their data, trying to use it to give legit estimates to the questions.

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Teamwork, baby. Teamwork.

(It was about this moment that I decided that I would honor their efforts at thinking and reasoning and doing actual math on their own by entering some points for the three-day project as a quiz grade. By department policy quizzes and tests account for 75% of a student’s grade, so a good quiz grade is like finding a hundred-dollar bill on the ground outside your classroom.)

So we dumped data into a Desmos graph, let some groups with few data points share some numbers from other groups (that’s that extra support we talked about), made a trend line, set a horizontal line at 533 cm on their graph, and talked about how many bands they’d need to safely make a jump from the top of our two-story Robot/Quadcopter Arena.

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Letting Desmos do the heavy lifting to free up brain power for thinking.

Quick group huddle to compare numbers, then after a few minutes of table talk I stopped to see each group, ask about how they came up with their number, and (this is key) have them agree on one number, write it down on their page, and circle it.

Day Three, the Tournament Selection Committee has announced the pairings, and the teams are ready to jump.

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Not that I’m craving attention or anything, but yeah, I totally posted the brackets on the window of the arena that faces a heavily traveled hallway.

I pre-assembled strands of ten bands to accelerate the assembly process, then students built their bungees and gathered, two teams at a time, on the second floor. We quickly found out that everyone in my 2nd hour class had seriously miscalculated the number of bands they needed. Fig after fig crashed to the floor. Lacking other options, and wanting to avoid the buzzkill of a six-way tie for last, we finally decided the “less dead” fig would move on.

The afternoon class seemed to have had some better estimates and we had some competetive matchups, as well as some gamesmanship as some teams attempted to scrunch two or three bands together in their hand on the railing to avoid a figurative skull fracture (high school kids, right?). The extra-long bungees in 2nd hour made a great math conversation starter (“what happened, you guys?”). I used Matt Vaudrey’s feedback form, and found out that Barbie Bungee was a near-unanimous hit.

Barbie Bumgee Feedback

Would this three-day activity had made more sense back in September when we were doing linear stuff? Probably. Would I have had the confidence to step back from the curriculum map for a minute when my students needed a breather if I hadn’t been hanging out on the periphery of the #MTBoS with its brilliant minds and fantastic lessons and activities? No way. Would I have tried Barbie Bungee without being able to follow a well-worn path? Not sure. I’m down with taking chances in the classroom, but I’m not sure I’d have been wise enough to add the Desmos piece if Vaudrey hadn’t blogged about it. And that made the whole project. We’d have been dead in the water, guessing a number of rubber bands for the Big Jump without it. Which means we would have missed the math altogether.

What I do know is: my students bought it, real learning happened, we all got the stress relief we needed, and I came out looking like an improv artist taking a prompt and making comedy gold.

Brian Flanagan would have been proud. Jane Craig too.

Art. And Science. It’s a Both/And.

 

10 Pounds of Math In A 5 Pound Sack

School Countdown
You can pay for an actual working countdown clock for your site at countingdownto.com.

Real talk? If you ain’t counting, you lying. Yeah, I know. We’re not supposed to be counting.

But we are supposed to be planning. And adjusting when plans go sideways.

Which is how this happened at our Algebra II (Track 3) Late Start Wednesday Meeting:

Here's The Math

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Low-Grade Panic sets in amongst our ragtag band of Alg II teachers. Image via What A Day For A Daydream.

29 days.

1 day for the final exam, preceded by 5 days of review. That leaves 23 instructional days. For 21 sections across 4 chapters which will account for 32 final exam questions.

Yikes. Something’s got to give.

I’ve got a thought about how to fire up a spaceship on 12 amps. So do my math department colleagues.

But you know who else has a thought? My students. And they might be willing to go along with some changes if they have proposed those changes.

So I asked them.

Here’s what they told me:

  • Skip bellringers
  • Skip the Friday Self-Assessment
  • Shorten up the notes
  • Do the practice assignment (“homework”) in class
  • Quick-hitter quizzes over a couple of day’s worth of skills
  • Rinse, repeat

Good Lord. Why don’t you just tell me to teach the class while standing on my head in a corner? Because that would be an easier change to make.

One of my students heard her classmates making these suggestions about cutting back on notes and not taking “homework” home and said under her breath “Oh God, that’s stressing me out”. Guess what, my dear: it’s stressing me out too. Wayyyy too traditional a classroom for my tastes. And for my students’ needs.

Or is it?

If they are telling me what they need right now, and what has worked well for them in previous years with teachers in my building, it’s worth a listen. Using a solid, ancient negotiating tactic, I came to the table with a mental list of concessions I was willing to make. Then I can can lay it on the table at make-or-break time, like it’s something that it absolutely kills me to give up. I love giving my students a chance to engage deeply with math thru Estimation 180, Which One Doesn’t Belong, 101qs, and Would You Rather?, but right now I’ll make the trade for the time and hope that over the last 7 months we built a culture of curiosity and problem-solving in my class that carries over to “traditional” tasks.

Plus, it’s nice to have a little leverage as the temperatures (inside and outside the classroom) warm up. “Hey you guys, you told me if I did x, you would do y. Time to hold up your end of the bargain.”

Now, it’s time to go try to land a 747 on a two-lane road. In a crosswind.

Wish me luck.