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:
Curriculum partner and I sensed that 10th graders and students who had seen more simplifying with Algebra Tiles were getting restless, so we split the kiddos into homogenous groupings. We always try to frame this as letting students challenge themselves with students who need similar challenges.
FASCINATING to watch some of our newer students who frequently hide in the shadows start to step it up (and also to see 10th graders using tiles and expressions in a more meaningful way).
Photo: “We don’t speak any English!” said one newbie (in Spanish). But that didn’t stop them from a) using the tiles and b) saying the names of the tiles in English.
Spent about 45 minutes after school with the Littlest Advisee, revising a quiz. It’s a slow process that (currently) involves me reviewing the problems they missed and then them showing me they can do the problem (with help). If they can do the problem, I’ll give them half credit (up from 0, in this case). If they can do a different version of the same problem, on a different day, I’ll bump their score up as if they had just taken the test.
Spent another few minutes helping one of last year’s kiddos with his homework. Compound interest. What is that even? #PleaseHelpCantMath
Bowtie Tuesday. Because yes:
I keep forgetting (or just denying) that Afternoon Me is the Worst Me (as the cool kids say).
We did a reading guide, which went slowly in some classes, just right in some classes/groups, and was a struggle in others. Now wishing I had been harsher and a bit more vocal with the participation quiz aspect.
Student work (from the afternoon, but still some solid work)
At any rate, I liked the opening. We showed them a bunch of windows and asked them how many there were. Almost every kiddo was talking or writing:
Teacher confession: after 1 class, a colleague pointed out that there were different numbers of small windows in each cluster, so my initial calculation of 900 was far greater than what many students calculated as about 768 windows.
Also, we cleaned almost all of the papers (except notes) out of the math section of our binders. Maybe this is the organized year. (Dinna hold yer breath.)
The last time we taught this course, Curriculum Partner and I realized that there was power in making the kiddos explain problems to each other. So we gave them the steps to different problems, have them solve them and have them explain to each other. Quite a bit of English spoken and kiddos mostly seem excited to be talking to each other.
We also had them do an explanation quiz where they draw figures based off of Figure X and vice versa. The kiddos work in groups, complete a problem, then call the teacher. I quiz a kiddo at random. If the kiddo can explain correctly, they move on. If not, they get a chance to revise and retry. First explanation quiz of the year, so a bit rough, but a good start.
Photo: Kiddos explain parts of Figure X to each other. I’m not sure where the sandwich thingy came from.
So, we’ve been making the kiddos draw patterns for a bit. Last time we taught this course, we decided we wanted to make the kiddos create their own patterns. And we wanted to do it with stations. Fond memories of this lesson (though in hindsight, many of them went the “Figure One has 1 square, Figure 2 has 2 squares” route. While it does help them make the connection, it’s super boring. Ya heard that, kiddos? Booooring).
Photo: One group knocking it out of the park. You can’t see it, but Black Fingernails is basically teaching 2 total newcomers how to speak English and how to make patterns at the same time.
Context: The Mathematics Twitter Blog-o-Sphere – a group of mathematics teachers who share their practice on the internet – is dedicating the month of August to writing a blog aday. It’s spearheaded by DruinOK. If you’re looking for ideas (and who isn’t?), prompts are here.
The beginning of the year is always a new start, but it’s a big start. Bigger than I remember at the end of the year. While some of our kiddos from last year (especially the ones who arrived at the tail end) are showing tremendous growth in English and leadership, going through all of our structures, which will soon be familiar enough, always takes longer than I expect.
Today, Curriculum Partner and I introduced reading guides. The reading guide is a structure that we use a lot, but for many of our kiddos who have never seen it (or saw it briefly without perhaps fully internalizing it), this is a big step. The kiddos are supposed to take turns reading sentences and then work on related mathematics problems together. Today’s reading guide focused on patterns and extending them.
Photo: Typical work sample from today. What do you notice? What do you wonder?
We did our first community circle in advisory. Circles look a little different this year as a result of a training I went to this summer. Kiddos actually go around in a circle, which makes when they’re speaking easier to predict. We also talked a lot more about norms, so kiddos were a bit more respectful than usual.
Photo #2: Things that make kiddos feel safe and successful. What do you notice? What do you wonder?
Context: The Mathematics Twitter Blog-o-Sphere – a group of mathematics teachers who share their practice on the internet – is dedicating the month of August to writing a blog a day. It’s spearheaded by DruinOK. If you’re looking for ideas (and who isn’t?), prompts are here.
If yesterday was the first day of actual content, today was the first day of actual relevant content. (And groupwork absolutely counts as content, it’s just not as much in the content standards. Perhaps “timely” is a better word than “relevant”).
Our first unit uses pile patterns to look at linear relationships (side note: “patterns” is confusing enough for emerging bilinguals, so I’m dropping the “pile” and just saying “patterns”). It’s pretty visual and therefore accessible, which makes it a great starting unit. We also did our first participation quiz today. Kiddos work together on a group task while I monitor and try to highlight group behaviors that help move them forward (like pointing at specific parts of the pattern, working with their group in the middle of the table, leaning in so they can work together, etc). (Similar to Class Dojo, but on paper and thus subject to me getting distracted)
We’re off to a decent start, though I wish I had done some more explicit modeling on how to show patterns. Kiddos seem to be able to find the pattern relatively quickly, but showing their thinking around the pattern is tricky. Counting the number of squares in each part feels helpful.
Photo: Our opening and some patterns. What do you notice? What do you wonder?
Objectives and opening:
I didn’t take photos of my participation quiz notes, but we’re doing it again tomorrow! (So wait until then?)
First day of actual content. We plan a groupworthy task (I always have trouble with this word, for reasons I don’t quite understand) with the idea being that the kiddos will have an authentic need to work together and speak English. We select the string challenge (kiddos have to make 2D and 3D shapes out of string; everyone must touch the string at the same time). Many kiddos claim that we did this last year, which is entirely possible (though I swear the last time we did this was 2 years ago and I’m pretty sure our lesson plans will back this up).
There are some pretty cool moments that come up. It does actually prove to be challenging enough that kiddos struggle with it and need all of their group members (or, um, more, which is challenging since we’re still underenrolled) and the groups that tend to do best are the ones that speak the most English, or at least talk together.
Photo: Kiddos make a star (the only 2 dimensional shape on the list).
What do you notice? What do you wonder?
Openings and objectives:
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.
This photo is from the middle of the Packaging Project. Kiddos found the volume for 6 everyday objects (pencils, tape, gluesticks or erasers) and then had to design a package to fit them. One part consists of drawing 3 nets (2d versions of a 3d shape) and finding the surface area and volume.
Around this point, my coach told me to stop intervening so early and to wait for a group to call me over with a group question. Interestingly (and probably obviously to everyone but me), when I don’t intervene, students work it out.
The two kiddos who were working on this paper did a good job. At some point, we did go back and correct the misconception of 2d versus 3d. But it was pretty cool to see them talk it out and work so hard while they did it.