Discovery

If Shifu can start at Level Zero with his students, so can I.

When we lived in Vegas, I never had the pleasure of coming across an actual, live scorpion. Black widows, however, were everywhere. I saw enough of them to learn quickly to never reach into a dark corner of the garage, or behind the toilet tank, without making sure the space was clear of spiders.

Discovery can be thrilling. Or extremely unpleasant.

We’re in the midst of the Quadratics unit with my Algebra 1B classes – five sections ranging from pure multiple-time repeaters to on-track freshmen. We just finished finding axis of symmetry and vertex algebraically, and are heading towards graphing quadratic functions. Historically I’ve carved out a day for an activity that I honestly can’t remember if it’s stolen from the MTBoS, or just MTBoS-inspired. If it belongs to you and you somehow stumble on this post, let me know. Credit and thanks belongs to you.

Either way, it’s paid off in spades in years gone past.

I’ve got two sets of handouts, asking students to graph the same function, but I give them different x-inputs. One student gets 1, 2, 3, 4, 5. That student’s eventual partner gets -2, -1, 0, 1, 2. Trick is, the axis of symmetry of this function lives at x=2, so neither student gets a complete look at the function, only a sliver. Once they’ve built their table of values and graphed their fishhook, I pair them up and ask them to spend two or three minutes looking at the two tables and two graphs, and discussing what they see.

Docs here:

Axis of Symmetry discovery worksheet part 2

Axis of Symmetry discovery worksheet

I remind them that with our Themed Bellingers (Estimation 180, Which One Doesn’t Belong, 101 Questions, Would You Rather?) that they’ve been noticing and wondering and discussing and predicting and defending answers all semester long.

I’ve grown to love Math Talk. And we’re definitely on a path in my building towards flipping the ratio of teacher talk : student talk in the kids’ favor. We certainly had our moments the last couple of days.

Wait.

Last “couple of days”? I thought this was a one day thing. And it was. Until:

“I don’t get this”.

Not “I don’t understand what you want us to talk about”. Rather: “I don’t know what you want me to do with this list of numbers and strange jumble of letters”.

Oh Crap. I asked my students to evaluate a function for a given value of x and they looked at me like I had two heads.

Image via http://media.tumblr.com/tumblr_lx26rf0SBh1qawn12.gif

Formative Assessment, up close and personal. Time to call an audible. Back to Step One. I ended up taking the better part of a day walking group to group, re-teaching in small groups how to plug in a value for x and simplify. No big deal, I mean, I am a teacher, and it clearly needed to be done anyway before we start trying to graph parabolas.

But still. An unexpected discovery for me. Guess I didn’t teach that as well as I thought.

Persist, you must. Image via http://i.imgur.com/g12KOV8.gif.

Gonna let you in on a little secret. I lecture sometimes. Probably 3 out of 5 lessons, on average. Especially as part of our gradual release model. And it has its place. It’s just that what should be a 15/15 split as far as my minutes vs. student work minutes turns into more like 30/5. They’re just really bad at Sit & Get. Short Attention Span Theatre, here we come. I get frustrated, spend way too much time trying to get people back on task, nobody learns anything, and I get reminded of the words of the great Kate Nowak:

Offload the work to students, as often as possible. The one doing the work does the learning.

Wrote about it last December. Still holds.

Sometimes that reveals some uncomfortable truths. But it’s forced me out of my comfort zone.

Plan what you want them to know. Anticipate the trouble spots. Let them struggle. Get them talking.

And then, every now and then, a magic moment:

“Oooooh, it makes a parabola!”

Pinch me.

I took a minute with a couple of classes to pull back the curtain and talk Standards of Mathematical Practice. The last two days we’ve spent hip-deep in SMP 1, 3, 4, 6 and 8. Not a bad payoff.

“I can…”

 

Of course, the Me that’s on an Endless Teacher Quest wants more. I love the pencil and paper aspect of this activity. Especially considering we’re gonna turn around and graph parabolas on paper. But: am I missing something? Could this be better? Is it a job for Activity Builder?

My first thought is no. To much learning eventually happened today. I don’t want to mess with a good thing.

“Now we will turn this rabbit into a chicken!” Image via http://www.jenn98.com/bugs/images/Hot_Cross_Bunny.jpg

Doesn’t mean I’m not gonna go in there and mess around tho. Because: Children Must Play.

 

 

 

 

Did You Guys Test Today?

The line in the copy room after SATs last week. Image via http://lessonplanspage.com/zombie-based-learning/

How exhausting is it proctoring an exam? All I did was watch kids take the SAT for 5 hours one day last week. And I’m ready to fall out.  Me and about 50 others. Walking dead. A middle school teacher walked in to the copy room, saw a few of us standing there and asked “Did you guys test today?”

I wonder what gave us away?

Image via http://i.imgur.com/wJ7xZZI.gif.

Is it really only April?

And honestly, the ongoing battle of wills in about 3 of my classes with a small but very determined group of students who seem hell-bent on lesson sabotage daily is sapping my mental energy to a dangerously low level.

I must break you. Image via https://49.media.tumblr.com/e52628df98c6ddbb709d340385091570/tumblr_n9olfnBV7B1rxw7iso1_500.gif

And I’m pretty sure my pre-service teacher observers left my room convinced that I suck at teaching.

The Low-Key Countdown is on. And yeah, I know we’re not supposed to Count The Days, we’re supposed to Make The Days Count. I’m down with that strategy. Because really, The. Days. Are. Packed.

Quadratics. Singing. Graphing. More Songs. Testing. Marbleslides. Reviewing. Final Exams.  All in six weeks or so. That’s actually the kind of list that gets me out of bed in the morning. Good times. Seriously good times.

Via https://s-media-cache-ak0.pinimg.com/236x/18/60/00/186000acd3d1870cf4a191631ee2ceff.jpg

I just finished a 100-Day Burpee Challenge with my crazy online running group. Starting on New Year’s Day: One burpee the first day, 2 the second, 3 on the third, on up to 100 burpees on Day 100. Towards the end, our little facebook subgroup was encouraging each other with messages like “Only 10 days left”. Of course, they were the toughest 10 days. No rest. And God Forbid you miss a day and have 95 to make up.

That’s what the end of the year is like in Algebra 1. Like I tell my kids, we take the hardest math they’ll do all year and stick it in May, when all they want to do is leave out for summer vacation.

That’s the big challenge, isn’t it? How to combat the end of the year crash? When students and teachers kind of naturally want to wind down, we need them to run it all the way through to the tape. As with most things regarding this business, aside from, “hit ’em with your most engaging lessons”, I don’t have the answer. I’m open to suggestions.

I’ll have 67 days of summer vacation (Phineas And Ferb were liars!) to catch my breath. And 28 days to Make The Days Count.

Even though they’re testing me. Maybe especially because they’re testing me.

Do You Even FOIL Bro?

It’s Pre-service Teacher Time in my building. I’m hosting 3 students from the nearby regional campus of Purdue University. They’ll be making 8 hours of observations, occasionally helping groups of students work through problem sets, and trying out some textbook tactics for redirecting wayward students.

As we all were, they are well-scrubbed and eager. When they arrived (midway through a class period) earlier this week, I gave them about a 20-second rundown on what we were doing and let ‘er rip. After a class and a half, during my plan period, we spent a little time debriefing.

Pre-service teacher takeaway: “This school… is nothing like ours.”

(Covered “not pretty, but real” here, last fall, with my first round of observers this school year.)

For years I’ve been on a mission to make sure my students aren’t just robotically following a set of steps, but instead working towards real understanding of the math we do. As an example, when multiplying binomials, we talk about using the Distributive Property twice, rather than the shortcut FOIL (first-outside-inside-last) which names the four partial products of the multiplication. The idea is that by using terminology “distributive property” , students will be prepared to multiply any polynomials, not just a pair of binomials. I literally have said “FOIL” zero times this school year.

And no one has asked about it. Until now.

One of my 19-year-old observers, fresh out of calculus class at a suburban high school, asked me: “Have you heard of FOIL?”

Image via http://www.fieldofdreams.it/IMAGES/Moonlight%20Graham%202.jpg

As Shoeless Joe Jackson said, famously, with a shake of the head: “Rookies”.

They meant well. I just let it ride and we continued our quick debrief before they had to head out. I sent them on their way with two assignments: go look up the free e-book “Nix The Tricks” by Tina Cardone, and do a search for the MTBoS.  I figured that would be way more effective than me trying to squeeze in an explanation before they had to take off. (Note To Self: ask them if they did a little googling when they come back around next week). But, Long Story Short: as Cardone says on pg 117:

As students repeat the procedure they will realize that each term in the first polynomial must be multiplied by each term in the second polynomial. This pattern, which you might term “each by each” carries through the more advanced versions of this exercise.

Here’s what that looked like in our class notes:

I foiled your plan.

I used that pattern as a set-up for factoring trinomials of the form ax^2 + bx +c, hoping that it would lead seamlessly into factoring by grouping. I took great pains to remind them they already know how to do the distributive property, and how to factor out a GCF.

I planned this out intentionally, to make learning happen. I think all I really did was confuse them. But on the second day, when we finished the notes and carved out time in class to begin the practice set… a glimmer of understanding.

Kickin’ back. Image via http://www.bdcwire.com/wp-content/uploads/2015/03/bougie.gif

Awwww, Yeah.

We’ve been working hard to create a culture of perseverance in solving problems (SMP 1 baby!), counting on that mindset carrying over to a willingness to struggle with new concepts. It’s an uphill battle, when we’ve trained our kids for 10 years to sit there, be quiet, copy what the teacher writes down, and maybe regurgitate it on a test. It’s a big leap for a student to say “hey, it doesn’t matter if I’m wrong, I’m gonna try to figure this out”. And I’ve actually heard that this year. No lie.

Students gotta have the tools to be able to struggle with a problem tho. The first tool: understanding the math that holds up the new skill we’re learning. I’m happy to play the role of the helpful hardware man.