Oh travel. How you mess up any attempt I make at routine.
Quick post as things are busy! I’ve been trying to learn more about elementary math as it feels like a gaping hole in my knowledge. I only learned the words partitive and quotitive about a year ago and now there is this thing called subitizing and with the number of niblings now in my life I have a compelling interest in elementary math ed beyond pure intellectual curiosity.
To that end, my recommended reading of the day is Nicora Placa over at Bridging the Gap. She posted about number bonds today, which is a topic that’s come up a few times in the last month for me so it was pleasing to further my understanding.
Back to work with me. I’m resting my head in 5 different places over the next two weeks and have PD to finish prepping :]
I’m reading 5 Practices for Orchestrating Productive Mathematical Discussion and ran across the term foothold. Now, I watch a fair amount of sci-fi so this typically means alien possession within an organization to me so I did have a moment of confusion. That’s definitely not how it’s meant here.
While laying out the case for good task selection as a way to promote equity in the classroom, on p19 Smith & Stein note that
“Once a student has a foothold on solving the task, the teacher is then positioned to ask questions to assess what the student understands about the relationship in the task and to advance students beyond the starting point.”
I really like the term foothold used this way. “Will this task allow all my students to gain a foothold?” Isn’t that a nice question to ask as you plan out tasks for your kids?
There was a lot of artwork in my classroom. Origami everywhere, as you might expect, but also a large poster by Alex Ross of the Justice League, decals of transformers (including a 3 foot Optimus Prime behind my desk), video game posters, photos from my backpacking trips, space posters by Greg Martin, Escher prints.
My challenge to those still working on #MTBoS30 (and everyone with a blog, really), is to post some of your favorite classroom decorations that you either have or want to have.
These posters from Zen Pencils are on my want list 🙂
Hung-Hsi Wu wrote a nice 10 pages on “Order of operations” and other oddities in school mathematics back in 2004. It has some good food for thought and I recommend taking a look if you’ve not seen it before.
It’s possibly I use cleaning to avoid other work, but we’re not going to get into that right now. This is about information flow.
On a whim I pulled open my spam folder in gmail today and found a bunch of emails that shouldn’t be there. Nothing critical, but still. I also found some subscriptions I had forgotten about (and clearly didn’t miss), so I unsubscribed from several of them. Anything after this paragraph is me rambling. The takeaway for this post should be: check your spam folders regularly for things you might not want to miss.
Information is a curious thing. There is so much out there and it’s easy to get sucked into reading thing after thing after thing until you’re 20 clicks deep in wikipedia trying to understand the history of miners and worker’s rights in Turkey.
And everything has a bias. It’s the sensational stuff that makes the top headlines. I’ve been reading too many things lately that just break my heart from Syria refugees to kidnappings to rampant privilege and sexism. When I worked with students every day, these stories didn’t hit me as hard because each day I was confronted with evidence the world has good people in it who want to do well and make things better. Working from home that is not as much true.
But I still get to read blogs from you all who are doing cool things and working to help your students become the people they want to be. So thank you to all the bloggers out there for helping me stay optimistic. The little paintings of your worlds mean a lot to this stranger.
post-edit: bonus! Today’s xkcd sums up nicely how I feel about all the information sliding across my screen this past week.
Ever want to give each kid in a class a piece of patty paper and have them measure out a line of length l somewhere on it and then tell them that’s the hypotenuse of a right triangle and then ask them to drawn in that right triangle (but it has to fit on the paper they have)? Then take all the papers and line up all the l‘s?
Because I do. Though I’d probably also throw in that isosceles right triangles are boring and that I expect more interesting angles from them.
These are the semi-random musings that interrupt my reading. Bonus points for anyone that has a class do this and send me pictures [:
I find that the ability to remember names of things is not a forte of mine. I’m reading an article from Mathematics Teacher on The Circle Approach to Trigonometry and got to a section where they kept using the word ‘subtended’ and for the life of me I was not picking up what that meant in context (“an angle measure of 1 radian implies that the angle is subtended by an arc 1/(2pi) of a circle’s circumference.”) and I couldn’t pull up a definition from the ol’ memory banks. My brain is a bit slow after a day of reading all the things, so thank goodness for wikipedia and it’s graphics.
The other fun term in this article I think I’ve seen before but never really dug into was covariational relationships. Google search popped up a study from 2002 that defines covariational reasoning as “the cognitive activities involved in coordinating two varying quantities while attending to the ways in which they change in relation to each other.” (p354, Carson, M., et al, Applying Covariational Reasoning, Journal for Research in Mathematics Education, 2002). I like this term a lot as I think it describes the type of reasoning that is very challenging for mathematics students as they are confronted with more and more types of functions.
Carl went and put together a little survey for #MTBoS30. I would love it if you went and filled it out so I could get some recommended reading 🙂
The survey reminded me of a forum that I like to visit and read hosted by Sybilla Beckmann. The Mathematics Teaching Community is a nice place to post and respond to a whole menagerie of math teaching queries. Nice people, good topics. I recommend.
Mathy McMatherson’s most recent post reminded me of a student I hadn’t thought of in a while.
This student made one of my classes a bit of hell for me. And using the words ‘a bit’ is a massive understatement. To the point that I would feel sick to my stomach before the class would start from nerves. I didn’t know how to work with her most days. She swore at me, other students, life. Frequently late and disruptive when she did show. Some days would be all rainbows and sunshine–focus, niceness, working on assignments and with others. But always that lightning storm right in the corner of my eye remained and as the tallest thing in the room my nerves never went away that class.
I don’t deal well with highly emotional situations and I avoid drama as much as possible. If you’re the type of person that thinks yelling arguments are an acceptable for of communication, we’re probably not going to get along. But this was my student. I couldn’t avoid her and I couldn’t understand the choices she was making. I could barely see past my own heart palpitations when she would walk in and my nerves over what could happen the next 50 minutes.
If I am better now at dealing with highly-emotional situations in the classroom, then this student is a big reason for it. Teaching kinda forces you into dealing with others yelling at you and taking out their anger on you and that is exactly what she was doing. It wasn’t me. It wasn’t her classmates. Over time I learned more about her. About what she was dealing with at home. About the stress in her life. Was she responding to the stress well? No. Of course not. She was a kid. One that had had a lot of adults bail on her.
I wouldn’t let myself be one of them.
My nerves never quite settled over the course of the semester, but they got better. When the school year ended and that class finished I exhaled fully for the first time in a long while. I suspect my blood pressure also dropped back to normal levels.
The next year I would see her in the halls and she would stop by my classroom in the mornings or after school once in a while. She would say hi and be all smiles. Sometimes she’d ask a math question and get homework help. I was left completely confused the first few times. In one semester she did more to push me toward being the teachers I want to be than any other student in the past. At the time I didn’t see it being too busy just trying to not break down in reaction to her rage at the world.
I miss her. I hope she’s doing well.
[This whole thing is a ramble, but it’s an oddly accurate representation of what my brain does as I try and assimilate new information and ideas into the current structure. You’ve been warned.]
I mentioned a few posts back (and yes, I’m still thinking about elevator questions–trying to finish a book first that’s helping me thinking about them) that I’m reading The Art of Explanation by Lee Lefever. Throughout the book so far he’s been making use of the following diagram as a way to plan explanations:
p78. I’m reading an ebook so it may not match up.
One analogy he uses that I like is that if someone needs to change a tire, they probably already have the big idea down and are over on the right side of the chart needed an explanation of how. On the other end of the spectrum I think about the students I’ve had in my class. How many times did I start with “how” before establishing why? And I’m good at “how”! I can lay out steps like a pro with three examples and then practice time but if that kids is still over at the start of the alphabet, then I suspect that “how” is just going to cause them to tune out or teach them how to mimic.
The “why” bit means a lot of things to me that I’m still poking at. Why this method? Why this problem? Why should I care? How do I, as a teacher, present problems in such a way that those “whys” are answered? Off the cuff, I think different tasks are going to do this in different ways. Some will, to borrow Dan‘s phrase, perplex the kids. Others will be topics with human interest (“real world” applications). Whatever we choose, we need to get an answer to “why” that a student will follow down the alphabet into the weeds of “how” and that’s where all sorts of mathematical fun can be had.
So I’m still processing, but I’m liking the image as a way to think about where students will start before designing lessons around specific problems. Yes I’m recognizing that it’s like a fancy way to say the kids need to buy into what you are doing, but I like thinking about ‘givens’ from new frame works and the why/how understanding spectrum depicted in the picture is new for me.
Lastly, I’ve worked with a lot of struggling kids who had a hard time getting to “how to be an active, engaged math student” because they were stuck on why they would want to be one and why they would want to worry about doing well in a math class when there were other things going on in their lives. I can’t address every why my kids come in the door with, but hopefully I can not add to their list and give them a place where more understanding can happen and give them something to be proud of.