A small math/design experiment I set up this weekend. Please take 30 seconds to cut a line.
Statistics will be posted as soon as they become significant.
A small math/design experiment I set up this weekend. Please take 30 seconds to cut a line.
Statistics will be posted as soon as they become significant.
It’s not like I’m one of those crazy people who are totally against it [Evolution], I’m just not sold on it.
– A precocious, incorrigible teenager in rural Iowa
What’s a teacher to do? I’m not a kool-aid salesman, but I’m also not a it’s-ok-to-deny-something-just-because-you-don’t-like-it guy either. I mean, just because Richard Dawkins is just as intolerable as Chef Ramsay doesn’t mean I hate evolution or cooking (quite the contrary, actually).
Where to begin? I just rewrote this sentence looking for evolution’s analog to “bible-thumping,” but I couldn’t figure it out. Anyways, I can’t just do that, they’ll just repeat me without actually listening.
It’s the same reason that so many people raised in the church end up hating the idea of religion. If your misconceptions aren’t addressed, you’ll just go on assuming everyone else doesn’t get anything either, which leads to all sorts of bizarre psychologies (and inane YouTube comments).
I’ve come to rest pretty heavily on mitochondria and squid. There’s just something about both of those that seem to flesh out the whole concept of evolution for me in a way that doesn’t seem so, well, because-chuckyD-said-so.

Not real, but awesome.
On that note, let me know what you know or have about mitochondria (looking for a plush toy, too)
Second, squid just seem to be so far unrelated to us, yet so, so… smart? I have to bring them up. Each leg has a brain. What a solution!
Finally, there was a super awesome documentary on PBS/NOVA/IDK about cuttlefish that showed their extremely awesome skin and hypnosis patterns. Does anyone have a link? I can’t find it.
OH! P.S> I also want to dissect a squid! Anyone know where to get a few big ( >3′) ones and how to keep it from reeking?
Immediately after class, as the lunch line swells.
Student: Can you show me that cross-product/torque thing again?
Cornally: Sure, what about it?
Student: I just don’t get the math.
Cornally: Do you want me to do another example?
Student: Sure
Cornally creates two random 3-vectors and begins to find their cross product with the determinant of a 3×3 matrix. Student sits on a table and watches. Student listens to Cornally narrate, and corrects Cornally’s inability to keep track of negative signs.
Cornally: There are a few procedural things here, but what we’re trying to do is find a vector that’s ninety degrees to both of the first two, which is why the x-component only does math with the y- and z-components (drones on)
Student doesn’t take notes, just like he did during class. Cornally starts to become annoyed that he’s losing lunch time and Student isn’t even writing this down.
Cornally: …and so this result is ninety to both, and has a magnitude related to how perpendicular they were.
Student takes a picture of work with his high-res camera phone and texts it to the other students in his group. Student then leaves the room.
This kind of remediation is really common. I will often run little clinics during odd liminal times of the day. The students who get left off the Socratic train during class often just need a small piece of direct instruction that they can back-fill under the conceptualization.
I didn’t see the phone coming. I can only imagine how that student’s brain may have engaged differently if he had to copy everything I was writing while listening to me while hoping to go to lunch quickly.
I picked this idea up, like so many things, from Dan Meyer. He claims that it’s one of those games–like chess or mancala–that just has always existed.
My students have become enamored with the game, which we’ve dubbed “Lone Wolfs.” It’s an unintentionally awesome play on words spoken by a student earlier this year (“We’re just two lone wolfs”) The time spent trying to understand whether that was poetry or paltry grammer was longer than you’d expect. Anyhoo…
Here are the rules:
Strategy and tactics abound, but my students keep coming back to the central argument that number of players matters most.
I put together a quick website that sets up games for a random number of players. Give it a play, play it with you students. There’s always a live game, and it starts over immediately. Help us gather statistics!
[FYI: if you put your phone number in to receive text messages, that information is destroyed at the end of the game, I promise.]
Tomorrow morning I’m going to get to do one of the things that makes teaching redeemable from its 37th-circle-of-hell-infinite-time-sink nature, I get to design an independent study course with an individual precocious and motivated student.
Designing such courses are more indulgent for me than the students realize. It’s a way of getting someone else to delve into source materials that I think are face melting while they feed me new analyses I never could have come up with myself. It’s like reverse-parasitism with some symbiosis, and a lot of me responding to questions with questions (but not in a douchey way).
The student I’ll be working with is nominally on the derp-de-derp medical school track (which is a topic we can discuss at length later), so Biology is the name of the game. However, this student is a well established cook and baker, so I think things will head that direction. I’m thinking kind of a Pollan meets Gastronomy meets Supersize Me experience here.
I’m just kind of having an idea monsoon here, so be prepared for a classic ThThTh bulleted list of fury:
In general, I want my student to produce a blog (they blog heavily already) that is readable and full of investigatory information that probably hasn’t been published in the context before. In short, I want my student to be able to produce something from this study that lingers instead of just rots on a hard drive, because, like church, school shouldn’t be about the building.
I’m interested in getting a hold of a mass spectrometer we could use for identifying molecules created during cooking and baking. Anyone have any good ideas? I’ve been searching hackaday for a while now…
If you have anything to add that’s even secantily related (i’ll take tangentially, too) please drop it in the comments!
(I’m back from the semester of hell, btw, let the competitions begin)
It finally happened. The planets aligned, the stars shined with approval in the Western sky as night was chased away by day. We dropped some bags of flour from an airplane in physics today.
The build-up to this has been quite epic. We started planning it in August. We hit road blocks. Our pilot was to finish his coursework and recieve his license, but then the tragedy of delays and red tape struck. We languished in this limbo, jumping for physics problem to physics problem like drifters in box cars.
The goal here is narrative. We started studying acceleration and velocity, which led us to combining the two into the motion of objects as they fall. So often teachers get accolades simply for making things “fun.” I demand a little more than that; lots of things are fun, but I’d rather shoot for perplexing (thanks Dan), engaging–dare I say–riveting. There’s a reason kids play video games and watch movies instead of reading books and doing math problems: Narrative.
So, we call the FAA. We call the department of defense. We get clearance. We look up regulations.
We used Google Earth to find a suitable drop zone:
We calculated how far the object will fall and where it will hit. See below.
We’re ready. The kids and I form a convoy and we drive out into the desolate, pre-winter that is December in Iowa.
The co-pilot and I text message back and forth, and the drops begin:
All-in-all, not the worst way to spend a frigid morning with 40 of my high schoolers.
The co-pilot planned to drop the bag when the plane was directly over the house in the drop zone. This is a great piece of physics, because most people naively believe that an object, once dropped, will fall straight down. When in fact the object will continue along horizontally as fast as it was originally going, while only picking up speed in the downward direction (hooray for gravity).
So, we needed to figure out how long it would take for the object to fall using the model for constantly accelerated motion (again, hooray for unbalanced gravity):
h is height, a is acceleration, and t is time. The plane was 500 ft up, which is roughly 152.4 meters. The acceleration on Earth is 9.81 meters per second per second:
Solving for the time-to-fall yields:
We agreed that the plane would fly at 90 mph (v = 40.23 m/s), so the distance d covered horizontally will be:
However, our bags did not hit at 224 meters, which gives my class a chance to really flesh out a model for drag and its effect on the trajectory of the bag; ho hum, yet another day planned out for me by the natural narrative of figure-stuff-out.
I’m getting ready to give a talk about grades. You never really know where people are at on the continuum that is assessment reform, and it makes me think back about my whirlwind tour of the assessment world during my first four years of teaching.
So, if you will, the first five steps of assessment grieving:
We all have this moment. The formative work we do to help kids “get ready for the test” doesn’t do that at all. Wrestling with this realization is the first step towards changing the culture of your classroom away from adversarial grading to formative assessment and feedback-based assessment.
In what may be the only slide I’ve ever made that matters, which is frustrating because it breaks every rule of presentation design. Sorry:
These five questions should be enough to start any teacher, administrator, or educator down the road to assessment reform. It made me hold my face in my hands, itelluwhat.
We then get down to the nitty-grtitty. Instead of just making it through the material by quizzing and testing it once (ding, done! wrong.) Reassessment starts to creep up on your mind. You fight it. You feel like there’s a demon called “retake” that you’re beginning to bring burnt offerings in secret after school. I knew that this had to happen, but how could I do it without having students stay addicted to the points?

Czernobog, the Slavic god of retakes for points. Pure Evil
So I started letting assessment happen whenever. This felt like the wild west. Seriously. I felt like it was the Gunslinger walking with Clint just hoping that the law will get laid down. Kids showed up at all levels of development. Some had studied and the system recorded their learning. Some were just hoping to get an easier problem and walk away with the points to get their parents of their backs. I had to corral this.
It felt like the experiment was failing, but, as the ineffable Matt Townsley would say, if you’re thinking about assessment and learning at a meta level, you’re doing a better job already.
So, things get wacky. I got to give a TEDx talk right in the middle of my genesis of these ideas. I had to come up with something that would be coherent in 17 minutes. I came up with BlueHarvest.
Let’s get rid of the points and just keep track of what the students do. BlueHarvest is not about me making money, it’s about providing all of us a way to keep track of feedback so that we don’t have to pretend that points and grades are doing that for us. They don’t, and we all know it.
I’m now at the tail end of this experiment.
Now that I’ve spent an entire semester teaching high schoolers, undergraduates, and graduate students without using and numbers at all, I feel like I owe all of you some sort of Results & Discussion.
First of all, it takes a long time to give this much feedback, especially if it’s the only data you’re keeping to justify the inevitable final grade (barf). I’m still pissed about this, but I can’t just start my own hippy commune, not yet anyway (I had a student ask me if he could go to my BlueHarvest school a few days ago, that was heartening)
I’ve seen the forest for the trees. Psychologically, students only care about feedback. We want to pretend that they won’t do anything unless it’s for points, but I’ve lived it. I’ve taught well over 100 students without using a single number, and it looks a lot like people who just care about getting it.
However, efficiency must be considered. Are numbers truly evil, or is it just the way we use them? I’m going to roll out a hybrid system next semester. The students are going to be responsible for putting evidence into BlueHarvest, and I’m going to use numbers and words to communicate to that student my assessment of that work. Parents still love to be able to look at a letter grade, and I know they’re busy, so I owe them a quick-look.
BlueHarvest still emails the parents whenever a piece of feedback or evidence is uploaded. The parents love it, and they feel like they’re a part of how that kid is learning, not just forcing them to learn once things go wrong.
Can you tell I just had some parent-teacher conferences fly by?
I miss you all.
You know, there’s really only one bird that matters. The Gannet is a majestic creature, often found bringing the wreck on fleeing bait fish in the Northern Atlantic. I came across the Gannet while researching my constant obsession with Scottish castles and English feudal relationships. (I’m never not reading The Once and Future King)
I ran across this video and realized that it has about as much #anyqs gusto as anything I’ve ever tried to produce myself.
Here’s what the kiddos came up with:
I had them all draw the free-body diagrams for the birds in dive and under the water. This was awesome, because the underwater part is an inverted projectile motion problem.
The object has positive acceleration but negative initial velocity. This was surprisingly (frighteningly) difficult for my students, and I’m glad we had a chit chat about it.
Each student took on the question they found the most interesting. A lot of time was spent discussing reasonable assumptions about how much force it would take to damage vertebrae. This may seem like a student deflection of concentration, but I disagree completely. So much of the cognitive load is on the teacher to come up with these kinds of numbers for trite little “problems.”
I think that the students are exercising a much atrophied part of their brain when someone says “800N to kill a chicken? No way.”
Another responds, “800N is like the weight of person, do you think you could stand on a chicken and have it survive?”
Macabre? Perhaps.
I love teaching.
I heard an interesting story from one of my college students last night. He had visited a mathematics classroom and witnessed pretty much the most standard classroom that there is:
The teacher collected homework, went over it, taught a new lesson via lecture, then gave new homework that students could work on in class for a few minutes (Yipee! What a benevolent treat!)
We can talk all day about why you may or may not agree with this. Students won’t self start, they won’t be able to apply content in a unique situation, and finally they won’t really care. Any grade or learning that results from this is more a measure of being able to endure boredom and monotony rather than actually learning math.
This is the kind of classroom where any break from the tedium is heralded as fantastic teaching. I once had a teacher come sliding into the room on his belly riding atop his overhead cart. This was talked about for days. As a teacher, a decade later, it blows my mind that this is all I remember from Pre-Calc. What an effing joke, but wait, it gets better.

I've always wondered, should there be apostrophes?
My student observed a weekly ritual. The reclaiming of the potty passes. Students are given two potty passes a week, and, you guessed it, that’s how many times they can go to the bathroom during the week. Here’s the mind numbing part (<= not hyperbole), the students can turn unused passes in for extra credit at the end of the week. This is happening right now. In real schools.
Let’s not throw this teacher under the bus quite yet. Why are potty passes inflating grades? Obviously there’s a hallway issue in this school. Obviously students want to leave their classes. The potty pass is the sticker-chart solution to these issues.
What’s a better, more learning-centered solution? Two things: Lesson design and grading.
The lessons I’ve given that have gotten serious, total buy-in have the following in common:
The grading changes I’ve made that support this type of lesson design and promote student success rather than adverasarial relationships:
Points for potty passes? Really?
This lesson was shamelessly stolen from someone in my modeling workshop this summer. If you’d like your name attached to it, let me know.
Quick Shot for the day.
Get a spring scale used for weighing grain and/or game:

330 lbs. limit, the fun shall never end.
Have each student measure the max pull strength of their biceps. Finding an appropriate way to do this is a fantastic inquiry starter (does the holder exert force and add to the puller’s…)
Give the students a chemistry ring and tie ropes to it. Have them arrange the ropes so that their force vectors cancel out and the ring doesn’t move. Put a glass of water in the ring for added effect. (don’t spill the water)
Have a great Tuesday.
I miss you all very much.