One of the many changes we’re making to our curriculum is thinking about how to represent negative numbers. We’ve used CPM‘s Algebra Tiles a lot, but this is the first year that we’ll really explore negative tiles, but also the idea of opposite.
Side note: last time we taught this unit, we used the Interactive Math Program’s hot and cold cubes (hot cubes cause an increase, cold cubes cause a decrease). Which I think was a neat idea, except that CPM’s negative tiles are red, which confused students when we talked about hot cubes causing an increase. This was not helped by a school-wide evacuation in the middle of one of our lessons. We had planned a summative project entitled “Mystery Soup” (how many hot and cold cubes are there? Maybe?) but with all the confusion and our eventual movement away from hot and cold cubes, we all seem to have forgotten what “Mystery Soup” refers to.
At any rate, watching the kiddos think about and represent negatives and opposites has been interesting. This group thought of different ways to show an expression with negatives using tiles. Any time we can get kiddos to talk together, but show their own way of thinking is pretty cool:
Largely for Hedge, who’s asking for pictures of math(s) teachers’ classrooms.
This is from the beginning of the year, so it’s probably changed a little bit. Also, my camera can’t actually take a full 360, so you can’t see the main board. Go figure.
What’s your classroom look like?
Friday was our last day of professional development before the kiddos arrived. During team meeting (around 10am), I said, out loud (oops), “Yeah, I think I’m just going to leave at 3:30 and be done with it.” The rest of my team was, um, flabbergasted (I can’t ever get myself to leave at a decent hour.”
It’s tradition that seniors come to school on Friday for their orientation. It’s crazy to see this class, since they are the first class that I taught as freshmen. My first advisees are seniors (it’s a bit mind-blowing to me, and I tell them as such on a pretty much daily basis).
By 6:30, most of my team had (rightfully) left and I was just starting to round the bend on Things That Needed To Be Done Before Monday (namely, seating charts). I gave up and decided to come in on Sunday.
A while ago, there was an offer at our school to get more bookshelves. I asked for one. Mostly so I could stand on it to change my seating charts (out of the range of kiddos, though an advisee last year tried to jump in order to switch seats, so…).
Our district does a fair amount of collaborative work with mathematics, which is really cool. I still find that I’m meeting teachers I didn’t know and teachers who are new to the district. And much as I’m frequently a crankypants about “this wouldn’t work in my context”, it’s really neat to see teachers in different contexts thinking their way through and around the same issues.
Anyway, we always start off district sessions by doing mathematics together. What do you notice? What do you wonder?
Also, professional development was held at a friend’s school, which I had never been to before. Here is a photo from the school:
I asked if he went to Target every day. He said he did not. I am flabbergasted.
Every day of Professional Development week starts to get a little more real. And I think yesterday (Wednesday) was the actual day where everything felt real. We started talking heavily in our teams about concrete things like leadership and advisory. We have pretty accurate class lists (as accurate as they get before the first week in an urban school) and a master schedule. My to-do list has actively pending things that feel real and important (“share information about last year’s students” versus “dream big about reading through Smarter Balanced claims”.)
We did some writing about ourselves as leaders and how we feel about advisory. What do you notice? What do you wonder?
*I know, I know, “The Real Day and Me.”
Curriculum partner and I are starting to talk curriculum amongst the orientation and team building of professional development. It’s our 4th year teaching together and our 2nd year teaching this particular course. So we have the basics down. Spent part of yesterday watching Rick Barlow’s Ignite talk about classroom culture and then spent a bit of time thinking through how the groupwork norms we set up in class (which we’ve used quite a bit) tie back to our classroom values.
What do you notice? What do you wonder?
We are back. And it is everything you’d think it is and all the feelings you thought it would be. So good to see old colleagues (many of whom I still haven’t quite had the time to talk to. Because: summer and school and theory and room setup and…) and meet new colleagues. We are counting down until the first day of school (next Monday) and there is much to do.
Some of what we do in professional development is thinking big picture stuff about our teaching practices.
Some of what we do is more practical, like plan for our first week and set up rooms (which seems to be never quite done).
What do you notice? What do you wonder?
We are back to school-based professional development today (pretty much as soon as I send in this blog, actually).
Context: As part of MTBoSBlaugust, mathematics teachers from the Mathematics Twitter Blog-o-Sphere are posting one blog a day for the month of August. It’s not too late to join in.
Our school uses a cohort-based model. Especially for 9th and 10th graders, it fosters a greater sense of community and is a huge support for some of our kiddos who have less schooling and are still adjusting to the idea of being in a United States school for the first time (and for a few each year, being in a school of any sort at all). As such, we put a bit of thought into who goes into which cohort. Most of the schools in our network use a heterogeneous class model – no tracking and students of all abilities are in the same class. (We apparently tried tracking one year and our school is so small that it threw off the culture of the school).
We recently sat down to look at cohorts from next year and shuffle students around as needed. This is something that I helped with last year.
Things I try to look for when thinking about cohorts:
- Levels of English, Academics and School Skills: Is there a mix of English, Academics, and School Skills? Which is to say, a general range of these skills throughout the cohort with at least a few students who have more of these skills in each class. We try to think intentionally about status and are looking for ways to talk about students’ abilities without resorting to a “high”/”low” dichotomy (especially since there are very valid reasons for so many of the range of abilities that we see).
- Mix of languages: If the goal is to have kiddos speak English, a mix of languages help. We had a decent mix last year (60% Spanish, 25% Cantonese or Mandarin and a few others thrown in). 2 years ago, I frequently had 23 Spanish speakers and 2 non-Spanish speakers in a class. I had more trouble getting those kiddos to speak English (though many of them made huge gains this year with more languages). Recently, I’m also trying to look for languages that the District doesn’t tell us about. We have students who come from Spanish-speaking countries but speak indigenous languages. I’m thinking about how we can place those students together (which is hard since we often don’t realize they speak another language until after they’ve been placed).
- Mix of Personalities: It’s high school. Some kiddos are super supportive to each other. Some kiddos drive each other crazy (especially after a day being in the same cohort). We try and take this into account.
- Other Factors: We look at a couple other factors too. Does a student have interrupted education (and thus will likely need more support)? Does a student have an Individualized Education Plan (and will probably need more support)? IEPs are rare at our school as the District won’t test students when they first arrive (in a well-meaning, yet sometimes frustrating effort to keep students from unnecessarily being placed in special education when they don’t need it). For my own interest, I try and figure out which cities and countries students are from. Too many students from one country (or city, even) can throw off the character of a cohort. And knowing what town a student is from can help give insights into what other languages they might speak and what their schooling experience was like.
Aight, back to work. We who are about to professionally develop salute you.
My new favorite thing is to hear more experienced teachers talk about their practice (though I hope this was always true). In the middle of figuring out many ways to represent a line during CPM training today, I realized that (much like the balloon toss problem), this problem could probably anchor part of our upcoming unit. What do you notice? What do you wonder?
The District says they’ll have a training on CPM, a mathematics curriculum. Our district curriculum pulls from it and we talked about it in grad skool, so I’ve seen it. But I jump at the chance to hear from people who use it frequently and know it better than I do.
We basically spend the whole day doing mathematics. At one point, another participant remarks that our work (which I am explaining on the document camera because: mathematics teaching) looks like a flag, to which I can only respond: “Yes, for the country of Squarelandia.” To which my teammate, who drew the diagram says, “I’d totally live there.”
What do you notice? What do you wonder?