2016 Blogging Initiative: Week 3


This week’s post is all about the art of the question.  Now with links!  Gettin’ fancy all up in this blog.

A couple things worth discussing here.  The first is that I keep a little box labeled “Stump the Teacher” in my classroom.  Though I originally made the box as a way to let kids anonymously ask questions during sex ed the year I taught health, I decided to keep it after-the-fact because it provides a fun opportunity to engage with the kids in a different way.  Once a week I collect all the little papers in the box and post responses on a whiteboard that’s exclusively dedicated to these questions.

The kids put lot of interesting things in there.  This week’s submissions were, by coincidence, both animal-related.  One asked, “Can spiders be obese?”  The other included all kinds of statements, such as “some animals can survive space naked” and “penguins have teeth,” and I’m supposed to determine if they are true or false.

I’ve noticed 3 distinct uses for the box.

  1. Questions tangentially-related to the curriculum that we don’t have time to address in class (e.g. “What happens if we compose a trigonometric function within itself an infinite amount of times?” or “Is there an algorithm for rationalizing the numerator/denominator that lets us skip all the icky algebra steps?”).
  2. Genuine attempts to “stump” me with logic puzzles, riddles, or trivia.
  3. General silliness (e.g. “Can I have $20?” or “Would you rather fight one horse-sized duck, or 50 duck-sized horses?”).

So there’s that.  But I also thought this would be a good time to reflect on my “How vs. Why” position.  As a teacher, I’m pretty transparent about my refusal to answer most of my students’ “how?” questions.  I always tell them (and remind them over and over again) that I will have a conversation with them if they can rephrase their question in the form of a “why?”

Here’s my theory.  I may be totally wrong about it, but it’s just been my observation over time that “how?” questions tend to be impatient ones.  “How do I…?”  Insert whatever task they’re struggling with.  “Can’t you just show me how?”  No, no I won’t just show you how.  You already know how.  You might not know that you know how, but you do.  It’s not my job to teach you “how.”  It’s my job to set up the circumstances whereby you teach yourself “how” to do something, through observation, analysis, etc.  I am a facilitator of your own learning.

I really try to make them derive as many of the algorithms on their own as possible.  I know, I know…  This is not an original concept, but stick with me.  My precalc kids are just starting trig.  On Thursday we did an activity using strings and paper plates that I’ve professionally titled, “What the Heck is a Radian?”  They observed that it takes a little more than 6 (2π!) strings the length of the radius to go all the way around the outside edge of the plate.  They drew conclusions about the relationship between revolutions, degrees, and radians, and completed a table with some common angles in all 3 measurement forms.  Then, analyzing the pattern from the table, they developed rules for converting between each type of angle measure.  I did not need to give them the formulas for these, they came up with them on their own.  Now, it took a whole class to get there when I could’ve simply said, “To get from radians to degrees, multiply by 180/π” in a fraction (fraction, ha ha) of the time…  But giving them rules they don’t understand the origin of makes me super sad.  It’s no better than answering their “how?” questions.  Don’t try to understand it, just do it.

So, I like their “why?” questions and I try pretty hard to make them interact with me in that way.  “Why?” questions are patient, and they are rooted in a desire to understand rather than to simply get things over with.  When a student asks “why?” he or she is genuinely trying to make sense out of something.  For example, “Why does the government get the same revenue from a lower tax rate as from a higher tax rate?”  That came up in algebra 2 while studying the Laffer Curve (and watching this clip from Ferris Bueller’s Day Off) in an effort to build some intuition about quadratics.  I drew a couple points on the graph and looking at them, the students said, “Wait, what?  Why???”  Then we had a conversation.

One last thought here.  I’ve been reflecting a lot about how many of my questions to them are in the form of “how?”  “How did you get that?”  “How do you know?”  Etc.  I wonder if there’s a way for me to prompt them to explain their thinking, using more “why?” questions, without sounding accusatory.  “Why did you do that?” sounds a bit… harsh.  I’d like to incorporate more “why?” questions from me to them, but I’m having trouble thinking of good ones.  If you’ve got some ideas or any go-to ones that you like, feel free to share them with me.


2016 Blogging Initiative: Week 2


Look at me!  On time this week!  Barely, but still.  #nailedit

Alright, this week’s challenge is to blog about one of my favorite things.  Of course the “no d’uh” answer is the kids.  However, last week I didn’t really talk about teaching or math at all, so in an effort to direct this back towards the overall teachy-mathy theme at hand, I thought this would be a good time to share my grading policy for tests and quizzes.

I’ve actually been reflecting a lot on that this week, because the kids just took their midterms.  We run on a different schedule and exams happen the last week of the 2nd quarter (the last week of the 4th quarter for final exams), so I don’t get to grade these the same way I would their normal assessments during the rest of the year.  Which is, I must say, kind of a bummer, because I’ve really come to embrace the way I usually grade them.

A lot of teachers do “test corrections.”  Kids get the opportunity after their exams to make corrections and improve their scores.  I do something similar, but with a little twist.  It’s an idea I picked up from my first student teaching mentor.  He called it “rough grading,” so that’s what I call it too.

Kids take their tests.  At the end of the period, I collect them.  That afternoon/evening, I go through all of them and mark their correct work with a little “+” symbol.  If there’s anything incorrect about their work, it just gets left blank.  The next day, they get the beginning of class to look over their rough graded tests/quizzes and make adjustments, fix things, etc.  It gives them the advantage of not losing points for silly mistakes (assuming they can find them), of course.  But they also have the opportunity to at least see the quiz, then go home and study up that night so they don’t completely bomb the whole thing if they’re not adequately prepared.

One of the things I really like about it is that if a kid is just in a bad mental space on that particular day (reminder: I work with kids who have behavioral and emotional difficulties), his/her grade can really improve, simply because of being in a better place the next day.  Another thing is that there’s still a lot of personal responsibility the kids have to take.  They don’t get to do corrections open-book or with a partner; they still have to finish their assessments in testing conditions, on their own, and it happens immediately following the original attempt.  Lastly, some of the best learning I’ve seen from kids takes place when they’re looking for errors in work, rather than trying to solve something from scratch.  They often flounder when I try to give them “find the mistake” problems, but when they’re looking for a mistake in their own work, they’ve seemed much more invested and really proud of themselves when they finally do find it.

Which brings me back to midterms this week.  I really wish the kids had the opportunity to have them rough graded.  I mean, I could, but it wouldn’t go towards their Q2 grade.  And, realistically, they’re not going to have this luxury in college.  But when you see a kid quit halfway through who you know could finish most of the exam, it’s pretty disappointing.  On the bright side, it makes me realize how much I love the rough grading system, and I honestly don’t think I would’ve had the idea on my own.  So all my students have Mr. Denny to thank for that.

Here’s the effect of the rough grade in action.  Kid arrived for the quiz and before even beginning he wrote this sticky note and stuck it on his own forehead.  I took it from him and the next day, after he got to finish (and did so strongly), I added another sticky note to it.  We put it on the wall to remind him why he shouldn’t quit before he’s given things his best effort.  He added the next two sticky notes himself after subsequent quiz.


2016 Blogging Initiative: Week 1


The first week and I’m already behind schedule!  This is one of the things about teaching that I found has made my life hard.  Like, really hard.  There is always more work to be done.  And that work always feels like the priority, so everything else takes a backseat.  But better late than never, I suppose.  Onward & upward.

In keeping with this (actually last) week’s assignment, I thought this would be a good place to recount our girls’ basketball game on Friday.  Even though being an assistant coach means more responsibilities and more drain on my already limited time, it provides such a valuable opportunity to connect with the kids outside of the classroom.  Plus, the two real coaches are men, so having a regular female presence is probably good all-around.  Who else is going to go into the locker room and tell them to hurry up when they’re goofing off instead of getting dressed?

The first thing to know is that the school they played is sort of our unofficial rival.  The second thing is that they’re pretty good.  The third thing is that we only have 5 girls this year.  Total.  That means no subs.  Ever.  And if someone gets hurt or has too many fouls, then we have to automatically forfeit*.  Going into the game we were all understandably nervous, but with our 3-0 record I think our hopes were pretty high that we’d manage to be okay.

Then the other team shows up.  With 12 girls.  The coach tells us, “This is only half our team!”  We tell her back, “Half?!  It looks like an army!”  Our hearts all sink a little bit.

But once the game gets underway, things are going surprising well.  Our team holds their ground in the first quarter and neither team scores.  Then in the second quarter, one of our girls scores and the doors just open up.  Three more successful shots for us, only one for the other team.  The game is 8-2 at the half and we were feeling pretty confident.

Then the reality of having no subs against a team that has 7 subs sets in.  Our girls start getting tired.  They start losing ground.  We put up a couple more, but the other team makes two as well, plus a free throw after a shooting foul.  It’s 12-7 at the end of the third, the lead just slightly narrowed but with things moving in the wrong direction.

The other team makes another basket and halfway through the fourth quarter things stand at 12-9.  Our girls’ nerves start mounting, and with them, a noticeable increase in tension and irritability.  One of our girls has a few physical altercations.  She gets elbowed and pushed over, has her glasses knocked off shortly after, and ends up in a collision with another girl that leaves them both on the ground at the sidelines.  One of our coaches says aloud, “She might not make it through this game.”  We’re all holding our breath.

We make another shot, but then something terrible happens.  The other team has a beautiful 3 pointer.  Respectfully, it’s really just inspired.  What can you do?

14-12 with 8 seconds left on the clock and no time outs for our team.  We have possession and the other team calls a time out.  All we have to do is hold the ball for 8 seconds.  That’s all!  Unfortunately, there is some sort of issue going on with the people running the scoreboard.  They’re not paying attention and the ref is calling out to them, asking if they’re ready to start running the clock.  It’s very distracting.  Meanwhile, the other ref signals our girl on the sidelines to resume play.  This is where things go wrong.  Very wrong.

The girl who should be receiving the ball is also distracted by the other ref yelling at the scoreboard people.  The girl on the sidelines passes her the ball, but she’s looking the other way and it just bounces off her hand.  The other team snatches it up and immediately calls another time out.

So now it’s 14-12 with 5 seconds left on the clock and we’ve lost possession.  They’ve got the ball at about half court.  Our team is pretty confused and understandably, very nervous.  The other team sets up to resume play and, of course, they’re giving it to their best player.  The one who made the 3 pointer.  She can dribble, she’s fast, and she can shoot better than anyone else on the court.  Things are not looking good.

They pass the ball in to her and the clock starts.  She takes it towards the basket, weaving right past all of our defense.  She puts up the shot at the buzzer and…  It somehow hits the back of the rim and miraculously bounces out and away!  It’s over!  We won!!!

There was a lot of jumping, shrieking, high-fiving, and laughing.  In the privacy of the locker room, there was also a fair amount of gloating about how the boys (who are not having a very good season) are gonna be so mad that the girls won another game.  Two years ago there was no girls team.  There was a PE class of all girls that took two “field trips” to play a couple scrimmages.  The boys teased them a fair amount about how they were… uh, not good.  How the tables have turned.

What these girls are doing is amazing.  4-0!  I’m so impressed and proud of how far they’ve come.  Better than that are their attitudes.  They’re so positive and they have so much fun.  It’s a blessing to be around that kind of energy.  No matter how many hours I spent this week writing review packets and midterm exams, the opportunity to share this experience with these girls is something I’m immensely grateful for.

*This may or may not be true.  It’s what the other two coaches told our girls, but maybe that was just to scare them.  Perhaps they can play down a woman, I’m not actually sure.