Taking Whimsy To The Next Level

So I've done a lot of...unusual things in my classroom.  I honestly should post a lot more about them, but to be fair, I rarely remember enough to make it a cohesive story. Recently, though, I've embarked on something that could either be a gold mine for me, like Standards Based Animals.

I own a small collection of hand puppets.  Yes.  The kind you stick you hand up and make the mouth move.  A long time back, I acquired an ostrich one and used it to mess with my then classroom neighbor Jonathan while he taught, or to randomly bring up while I was doing any direct instruction because why not.  In the years since, my collection has... grown.

Yes, the right one is a unicorn headband.

Still, I felt like I was missing out on how to use them.  My wife, Claire, and I work at the same school in Guatemala, so last week, I idly mentioned that I wanted to use the puppets for something more.

"Why don't you have your Calc kids do a puppet show?"

Dear lord.  How did I miss that?

So that's just what I did.  We had some quick review from previous maths, like parent functions, unit circle trig, etc., but rather than have them just review it on their own, I had them write a puppet show.  The early results were... promising?

The middle kid was quite good at nodding his puppet while listening.

I tried to get them to keep it under 3 minutes, but of course some tried to ad-lib. We discussed strengths and weaknesses in their performances afterwards, like some factual accuracy points, the need for scripting, moving the FREAKING MOUT--sorry.  But, things went quite well for a first time, I think.  I even had them sitting in a circle on the floor in front of the show.

So here's what I'm thinking:  they get used to the idea.  We do periodical 3-minute reviews on a rotating basis by groups.  Bring in some cocoa some days, a Capri-Sun some others, whatever.  But, of course, the big question: why?

I'll tell you that I didn't notice any real nervousness.  One girl couldn't stop giggling as she said the name "Linear Lion".  They played their parts, said their pieces, and did so without a hint of self-consciousness.  It was beautiful for that alone.  The fact that I was filming them ("You're filming this?!" "Well... it's pretty funny." "...Yeah okay") didn't really throw things off.  Rough? Yes. Room for improvement? Loads.

We'll see where this goes.  I may abandon it.  I may invest in a tripod and boom mike.  Who knows?

FOIL = FML and Using Cell Phones on Tests

FOIL = FML

So my Calculus class made a discovery the other day when they tried to reference the distributive property:  I don't like the term FOIL.

The gutteral reaction here is the same as the one that I have to the non-word "guesstimate"*.  The kid was talking and I couldn't help but interrupt with "that's not a thing." After a bit of confusion, I clarified that FOIL is a trick for one specific case of distribution that doesn't apply to anything else, logically, so why do you call it that?  He tried to counter it, but ultimately I tossed up a binomial x trinomial on the board and told him to apply FOIL to it.  It went something like this:

Kids: Okay, so multiply the first ones.

Me: Sure. (draws a line between terms and labels it as "F")

Kids: Then...uh....the middle?

Me: uh-huh... (draws a line between terms and labels it as "M")

Kids: Then last!

Me: (seeing this coming, drawing the line and labeling it "L") and there. Now you know how math feels about FOIL


They had a good laugh and got the point in a very non-PG way, but oh well.


Cell Phones on Tests

I gave my 7th graders a test a few days ago with a slight caveat: I required that they look stuff up to answer questions.  I'm pretty sure I'm going to keep doing this, and here's why:

If I'm promoting realistic thinking skills, why not include the one resource that they'll always have?

The thought is that instead of providing the exact conversion statistic necessary, or rate of whatever, why not put it in their hands to think about what it is that they need?  My question on the test was as simple as:  If a star is 3.412 x 10^7 km away, how long will it take until we know that it has burned out?

Part of taking a test has (hopefully) been knowing what information to use... so why not structure the test so that they need to find the information necessary to solve it?  If we want to promote kids wanting to figure things out outside of class, then why not structure test questions in the same light?

Obviously, this has its drawbacks.  Not every math concept has this kind of possibility attached.  There are lots of resources online to solve straight problems for them.  There are lots of places that have answered questions online that we've all asked, so this isn't totally applicable across the board.  I'm not saying that everything should be like that, but it's an interesting possibility.

I'll have to do some more analysis on the matter and run a few more experimental questions, but so far I'm pleased with the results.

Like a Bandaid. RIGHT OFF

Calculus Blurb:

So I'm about to drop my instructional experiment on Calculus. For years I've been really stuck on a few things that haven't made me happy.  Considering that I'm starting at a school where apparently the AP Calculus results had been less than impressive, I figure this is my chance to experiment.

Here's the breakdown:

1) Early transcendentals.  I know, nothing mind-blowing.  I just have felt kind of gross introducing natural log and e so late that it's well beyond when they actually would have cared. It also makes them seem like something special, which they aren't.  They're about as special as trig, but I don't want to get off on that tangent.  (Sorry)

2) u-notation from the beginning.  I've always hated how stupidly difficult substitution has seemed to kids later.  I figure if we get it flowing at the start, it would help with SO many things (namely derivatives of composite functions).   Again, not mind-blowing, but definitely a step in the right direction.


My thinking is this:  Much like Sam Shah, I have always had a weird problem with Chain Rule.  It's always been just a kooky rule explained with some analogy that has, in my mind, always been classified as a magic trick to teach the kids that robs them of something.  I hate that.  In addition, it's even more of a ridiculous moment when u-substitution rears its head.

"Here, kids, learn a thing that's supposed to make integration of a formerly composite function easier."
"This is hard."
"Hmm... Yeeees....It is."

So u-subs to start sets the stage, introduced under the heading of transformations and their effect on derivatives.  Chain rule becomes "old hat" after a while, and integrating with u's is a footnote as it's just going backwards.  It becomes incredibly simple with natural logs and e's, so there's no need to make a special introduction later.


7th Grade Blurb:

I don't understand Pre-Algebra curriculum layout.  It's the same few skills over and over again, but what drives me nuts is the insistence in so many places to teach the skills in isolation.  Why do you have to learn how to deal with exponents so long before you actually use exponents?  It made way more sense to intro scales of the universe using scientific notation, have that naturally segue to multiplying massive scales by massive scales, and BOOM exponent rules.  Not only that? Exponent rules when coupled with a coefficient.  Turn that 10 into a variable? Same rules.  Yay.

I think my real concern is that I don't feel like there's a sequence to things.  It's just algebraic reasoning explorations coupled with occasional geometry.  I have to be wrong, but I don't know where.  There is so much to be done with more rudimentary skills, like speed in processing order of operations, etc., but I just don't know what my endgame goal is.  Everything else I've taught has had a pretty clear endgame goal.  Algebra is being able to reason with unknowns and interpret various stimuli algebraically.  Algebra 2 is the same but with far more complex relationships.  Pre-Calc is about reasoning with angular movement/forces/observation data.  Calculus is interpreting instantaneous and accumulated changes from various phases of data/functions.

And 7th grade is.....maaaaaaaaaaaaath?  Blargh.

Tests, Stickers, and Unicorns

I finally gave my kids a test as of this week, so it was time for them to see one of the many little secrets still stashed away for their descent into my madness: Animal Stickers.

For those of you already familiar with Jonathan's post regarding the subject, or with the my favorite from TMC14 you can probably skip ahead a bit as I'm going to be a bit more long-winded.

In the Summer of 2012, I made it a point to try and improve my AP Calculus AB classes, specifically by trying my hand at using Standards Based Grading.  I enlisted my friend/coworker Jonathan's help to bounce ideas around with, knowing that getting together on something usually results in the most ridiculous/brilliant ideas ever.  The conversation went something like this:

A: Yeah, this works.  But it's too normal.
J: You know what would be funny?
A: (Ears audibly perk)
J: Animal stickers
A: Good lord... With monkeys as the best?
J: And kitties!

And the mad scientists mathematicians went to work.

1) SBG and Friends!

          If you've ever wondered how funny it would be to hear a high school senior in AP Calculus talk about their grades as having received a "kitty" and two "froggy"s, I suggest that you try this out immediately.  It is very much worth the time and effort. (And, yes, there's always the question about a donkey being a 0)

Upon receiving the returned standards, the grades appear in the form of animal stickers.  Of course, the first hurdle here is that this turns pretty costly very quickly, which is why this alternative arose.

Taking those images, setting them into the appropriate Avery template for address labels, and using a paper cutter.  Works pretty well overall. That brings us to the second development, and inspiration for this post title.


2) The Unicorn Awards

Each of the six-weeks grading periods comes with a cumulative purely context-based exam (think AP Exam Lite) that they cannot retake.  It is also only worth about 10% of their grade. In spite of the low value, this test becomes somewhat of an event in my class for one particular reason: the highest scorer is deemed The Unicorn.  As such, we have the Unicorn Award ceremony.

This usually takes up the majority of the class period post-exam, but it's TOTALLY worth it. We essentially hold an awards ceremony, complete with an official title (ex. "The first tri-annual Unicorn Awards", though I keep up with it every year), sponsors (I set up a slide show with .gif's of stupid meme-ish stuff and products like "Taylor Swift Dandruff Shampoo", which offers to help you "Shake it off"), and, in some cases, actual cue cards and camera operators (poster board with lines for "Mr. M" and "Ugly Kid" as well as a Skype to my laptop from my iPad).  Then we have our three contestants, who have not received their tests yet and don't know their scores, who are asked very pageant-like questions ("If you could be....any person...in the world...what...would you tell their family when they found out that you weren't them?").  

I know. Ridiculous.  Welcome to the madhouse.

Then comes the crowning...

Since the test is such a small percentage anyway, I also do a bit of curving based on the Unicorn, or as I call it, "The Unicorn's Blessing." If there's a tie for top score, MOAR BLESSING.  The Unicorn must wear the headband for the entire class (if there's a tie, I also have a Batman mask because it's the best thing after a Unicorn) and receives a tiny plastic unicorn as a keepsake.

I also make sure that everyone can only be the Unicorn once.  Reason #1: It keeps the same kid from dominating all the time.  Reason #2: I have enough pictures to do this...

The blacked out bars are all of their names.  This goes on a t-shirt that they were surprised with after I secretly got their shirt sizes.



So, why do I do all of this? First and foremost, because it's silly and fun and Calculus is so stuffy in so many places.  So I'm not going to say that I did this with some grand teacher insight in mind, because I didn't.  As I said, Jonathan and I were just looking for a really good laugh.

I'll tell you what came as a result.  The animal stickers took a lot of their heads off of the numerical values.  They started talking about and reacting to the animals more so than what it did to their average.  A kid that everyone told me was a grade-obsessed mess was now going "Huh, a kitty! I can work with that."  (That's verbatim)   The unicorn was an odd point of pride for not just the kid who got it but for the period.  I overheard some kids one-upping each other on how many unicorns their class period had.  Also, by the end, it gave a chance to some of the okay-er performing kids to feel like they were the best.

I would be careful about trying to do something like this, though.  It's very easy to have your alternative scoring system turn into something non-meaningful, thus negating the point of SBG.

So Unicorns will continue.  Animal stickers will continue.    90's Rap/Hiphop Desk cards with playlist randomization and first-person biographies will continue.  Because why the hell not.

Calculus Limit Introduction

One problem I've had in years passed is kids getting a good grasp of what limits are and how to approach them. A few years back, I had a moment of clarity as a particularly confused set of seniors were staring back at me.  In that moment of frustration, I opened up Google and pulled up a map of the school.

I asked them this: If I had never been here before, how would you tell me to get to the school?  Kids jumped on this, giving me the address, the landmarks nearby and how to proceed from them, etc.  One kids went so far as to give me cardinal directions based on nearby freeways (and Houston has enough of those).

I then posed this: pretend that, unbeknownst to you, a bomb blew up underneath the school (please don't tell anyone I said that) and the whole thing flew up into the air and landed about 20 miles that way... were your directions wrong according to your best knowledge?

This sparks some debate.  Yes, because the school isn't there anymore.  No, because you didn't know it blew up.  Yes, because how could you not hear the explosion you live like a mile away.  In the end, they focus on the "to your best knowledge" part and say "No, the directions where right".  Good.

"Why?"

And how quickly they hit this phrase: "Because that's where the school was supposed to be"

From there, it's a quick jump to graphs and values and all that good stuff.

I've since refined that practice.  I start with that stuff now.  I give them a series of addresses/coordinates in the city and ask them to look them up and tell me what's there [f(c)] or what should be there[limit as x approaches c of f(x)].  Some are actually there (continuous) some are construction sites with a "coming soon" (it's a bit hard to find these on google maps unless you remember that something is a new building).  I'll also include two streets that don't connect properly.

"What's on the corner of Wilcrest and Barryknoll?"  "Which one?"  Bam, discussion of one-sided limits and limits failing to exist.   

Conceptually, this hits home pretty quickly.  Number crunching comes later, but by then it's easy since they just know what they're looking for.  The next step is to have them submit screenshots of places they find on maps and refer to them using limit notation.

Example:  Chuy's is located on 9350 Westheimer Rd.

Limit as x approaches 9350 of Westheimer equals Chuy's  (in actual limit notation, with arrow, etc.)

Westheimer(9350) = Chuy's 

Westheimer is continuous

Example:  They tore down a Starbucks on 1655 Voss Rd. Thanks, Obama! (not really, it's still there.)

Limit as x approaches 1655 of Voss Rd. equals Starbucks  (in actual limit notation, with arrow, etc.)

VossRd(1655) = Rubble 

VossRd has a removeable discontinuity at 1655

Thanks, Google.

Two Weeks In

I 've been a little reliant on lots of teacher blogs as of late.  Scratch that.  I've been very reliant. So much so that I've gotten the itch to blog myself in such a way that general forgetfulness cannot scratch.

Teaching in Guatemala is not difficult in the traditional sense.  Classes are small (my largest is 14), administration is very supportive.  The secondary principal loves SBG, in fact, but due to some past issues, he knows what kinds of problems it can spawn with parents. Still he's behind me, and that's awesome.  The director of the school said something to the effect "I invite you to not grade homework" to the faculty.  I couldn't help but grin like an idiot.

What's difficult is this: I'm teaching 7th graders, Algebra 2, and AP Calculus.  Calc is my wheelhouse, I can spin that stuff all day and the kids can dig it.  Algebra 2 is an old trick that I've forgotten how to blend seamlessly.  7th graders... scare me. I mean I have no idea what I'm doing.  

Which brings me back to the first line I typed about fifteen-ish times.  I've been looking at a lot of Fawn stuff and a lot of Sarah Hagan stuff and had so many tabs open from random people that I lost track of all the bookmarks.  I've grabbed a good chunk (read:all) of Jonathan's experimental Algebra 2 stuff since it's something I can definitely get behind and tweak for my room. 

Calculus is going to be an interesting transition back to smaller classes--er, class.  I went from having semi-big classes that got bigger for 7 years, to 6 massive-ish classes last year, and now down to a single class of 12. I know, a great problem to have, but it's still an adjustment.  

7th Grade still scares me. I cannot stress that enough.  I've never taught them, or middle school for that matter, and so I have no idea where they are.

Did I mention that there's an entirely new secondary math department?  I spoke to one 6th grade math teacher who transitioned to science about what they did last year.  Here was the gist:

- Kids grouped homogeneously, Were given packets for self-pacing.  Once the packet was complete, they "tested out" of it and were given a new packet.  Repeat.

The post-year report was something to the effect that some kids were doing quadratics while others were having trouble with order of operations. 

So what do I do?  I find a Problem-Based Learning curriculum.  I try to pre-test a bit and gauge where they are.  I throw some stuff out there and then readjust when the vast variation in ability levels nearly knocks me down.  I get discouraged when some basic pre-algebra (8th grade here is Algebra. Period.) stuff makes an audible slap onto the floor.  I pick it up, dust it off, and stick it in a drawer for maybelaterifIfeellikeitday.  I do all that teacher stuff that I'm supposed to do and only realize it's been two weeks. One week with the kids.

I play videogames to let the back of my brain hammer something out while my conscious efforts out-maneuver an A.I.  I still check random blogs during loading times sometimes--

Which I guess brings me to the purpose of this blog.  The goal is to put out there what I'm doing, what's working, and what plain sucked for me that someone else can chime in on if they like.  

I come back with some good ideas.  And if I don't... [insert reflective statement here]