A few weeks ago, I brought up negative numbers in my 4th Grade class. I framed this in terms of “giving kids permission” to bring up negatives in class.
Yesterday a couple of 4th Graders asked, “Wait can you multiply by a negative?”
Any guesses as to what prompted this question?
Kids had been working on a multiplication puzzle and (accidentally) gotten themselves into a position where they needed to solve ___ x 20 = 10. If positive numbers make multiplication bigger, then shouldn’t negative multiplication make things smaller?
This is very smart and interesting, and that’s all I have to say about that.
On a totally different note, there’s a dead pigeon right outside the window of my 9th Grade class. It’s becoming a distraction. (“Someone should really call animal control.”)
I was trying to talk about congruence and stuff and kids started getting fascinated and freaked out by the dead bird. So I climbed up on the window sill (there’s no draw string) to pull the shade down. And then the whole curtain contraption got ripped off the wall and missed a few kids’ head by an inch.
I get reminded about this daily. And I still haven’t called anyone about the bird.
I made a commitment this year to work on the relational side of teaching. To an extent, I am, but I’m realizing that it’s been entirely haphazard. Is there a way to be more systematic about this?
Another question: working on curriculum and learning can be serious intellectual work. Can working on relationships be serious intellectual work? How?
I was going to work on fractions in 4th Grade yesterday, but the multiplication practice that my kids dug into swallowed them up for the whole period. They loved it! (It was from these books.)
Multiplication practice can be fun for kids.
Then again, I’ve been trying to get one of my Geometry classes to work on flowchart proofs and that is a slog. I’d love for them to get great at this, but it looks like we’re going to move on without having everyone on board.
Sometimes skills practice sucks, and sometimes it doesn’t.
Teaching With Problems 
It gets worse!
If the height of Everest is 27,000 feet and the height of K2 is 25,000 feet what is the height of both mountains? (don’t need negatives for this one)
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What is a flowchart proof?
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It’s like a two-column proof, but with arrows showing logical dependence.
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1. Ok, so on your note about dead birds.
When I was teaching high school a bird died in the courtyard outside my window, and I had one of my students put gloves on, go get it, and move it RIGHT outside the window. Then we outlined it in a masking tape square. Then we took a picture of it every day as it decomposed. East Texas means serious ants, so it only took two or three days before it was just visible bones and fluff. I’m pretty sure that’s in the standards somewhere.
2. second, on making relational work systematic. Something I did rather haphazardly this year was to write a sincere, and specific, observational-type email to students (pre-service teachers) saying things like, “I noticed that you were really demonstrating some awesome discourse practices today, like when I heard you ask _____ to explain her thinking about her strategy, or asking ____ to explain some similarities between __ and __’s strategies….. What a great way to orient students to one anothers’ ideas!….”
The two somewhat random times I did this, the response was genuine gratitude for giving them feedback that helped them know how and whether they were growing. I noticed it also changed the dynamic in the classroom between me and those students, and also seemed to changed how they viewed their own sense of competence and identity in class activities and discussions.
It made me realize that in my post-class debriefs with the TA, and/or in my thoughts on the way home, these “man, he/she did really well today” thoughts occur to me, but 93% of the time I don’t do anything with that info. But when I have, it proves really generative. I recognize that this isn’t the same as building relationships for relationships’ sake. But when dealing with elementary school teachers specifically, I’ve noticed how negative many of their own mathematical self-concepts can be. A goal of mine for next semester is to be more systematic with this “hey I noticed” email process.
What does your ‘relational’ work usually look like?
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1. I can’t believe you left high school teaching. You were the perfect high school teacher.
2. I’ve been doing this “hey I noticed” email with my 8th and 9th graders. It’s nice, though most don’t respond or acknowledge the email. Definitely is a huge thing for some. There are definitely a few tough cases that I’m chasing down.
Right now I have two moves that I can employ self-consciously to improve the relationships between me and the kids. The first is that email thing. The second is that relentlessly chasing down a kid who I don’t have a great relationship with to find some one-on-one time to build trust.
I tend to get along pretty well with my 3rd and 4th Graders, but neither of these moves work particularly well in those contexts.
I dunno, I find all of this confusing. I don’t have a framework for thinking about it.
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1. sometimes teaching 20 year olds, it’s hard to remember that I left high school. today was kind of rough.
2. it’s interesting, isn’t it? relationships we build with students are super different from relationships with other people.
They’re forced by institutions, like colleagues. But they aren’t peers.
They’re in lower authority status than us, like employees. But we’re the ones working for them.
They’re children and we are adults. But they aren’t family.
We spends lots of time getting to know them, rooting for them, supporting them. But because of all that other stuff ^^ they’re not friends.
So as odd as it feels to want a ‘framework’ for relationships with small humans, it does indeed feel necessary. Because these aren’t relationships that there are normal scripts for. Especially in a profession which has historically tried to ignore the fact that big/little, authority/no, institutionally organized/stakeholders, we’re all humans stuck in a room trying to figure stuff out.
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I like how you drew out the paradoxes in teachers’ relationships with pupils. Regarding frameworks, although I/we teach our student teachers about this with things like Leary’s circumplex, the 5 axioms of Watzlawick, the four-sides model of communication, teacher behavior that acknowledegs/ignores/rejects messages or persons, and teacher controlling/structuring/autonomy supportive behavior from Deci & Ryan’s SDT, the process of relating to pupils remains hard to frame I think, because it’s such a personal thing – although I really appreciate how you drew out how these relationships are embedded within some form of institutionalized context. Maybe this article about the basic but complicated nature of teacher-student contact helps to provide some form of framework for you: http://dx.doi.org/10.1016/j.tate.2014.01.006
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I think your Hey I noticed approach is quite well grounded in evidence. See: https://www.researchgate.net/publication/263737664_A_strength-based_approach_to_teacher_professional_development
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Responding the question about the “relational” side of teaching. I’ve been working on this, too. As a born introvert, I can do OK with the “on stage” part of teaching, but building the one-on-one relationships within the limited classroom time window always feels a bit like the old saying: If you can fake sincerity, you’ve got it made. To me, relationships are built in conferences, tutorial sessions and other moments where the kid can finally see you as a person, not a room manager.
Anyway, something that’s been working well with an honors group I teach is having students write daily reflections via an online Google Docs journal. The class is very open-ended, so the reflections can be about anything — life, school, sports, what they ate for dinner. The rules are the same as the “accountable talk” rules in the classroom: say what you mean, mean what you say. You can make it private to the teacher, but I should have the right to comment back (or report behavior that might put a student in harm’s way). I generally get a chance to check in once a week and use the comment feature in the sidebar to offer feedback, suggestions or compliments.
I started doing this two years ago and found that reading and commenting on students’ journals was the highlight of my work week. I took that as its own strong signal and doubled-down on the practice with the next group. This year, I’m forcing it on my remedial algebra students. The buy-in hasn’t been as strong. I’ve had to work through the tech challenges (limited computer access, how to get back to the same Google-Doc each time, etc.) but the writing has been good (much better than expected, I must say). I’ve been getting very strong “intel” on how the students see math and how they see their own personal place in math.
I’m debugging it on the fly, so I’ll have better info on the algebra side of this experiment in a few month’s time. For the moment, I see online journaling as fast becoming a non-negotiable in all my classes.
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Nice to hear from you Sam, and this is a thoughtful and interesting approach! I’d love to hear more about how this goes with your remedial class. You’ll give us an update later in the year to let us know how it’s going?
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