The One with the Linear Representations Scaffold

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One thing I’m finding, 3 weeks (to the day) into summer school, is that when in doubt, lean on your routines (I’m fairly certain I read this in Carl Oliver’s blog, to give credit where credit is due). We have about 5 weeks with 50 minute classes, so there is not much time to teach or to plan (let alone condense everything into a cohesive, project-based unit that may or may not sync with the biology class next door).

It’s taken me a while to remember this, and to get back into it.

I do recall that one of the structures that was most successful from our linear functions unit is the multiple representations paper (It says “Different Representations” on the actual paper and that is how the kiddos largely refer to it. Change it? Leave it? The eternal dilemma…)

For some reason, the kiddos love this one. There’s enough to talk about, there are different sections, and (added benefit of teaching summer school to some awesome multilinguals, many of whom I taught some portion of the year to) enough kiddos know something about the things that we’re seeing that most kiddos have some access to the content but still need to practice what goes where in the table or why we don’t just put the y-numbers from the table on the y-axis.

I’m also fairly certain that only our school talks about “Figure X” as I had to stop class and review it every time. It’s sometimes a bit too complicated for my tastes, anyway (but makes a nice stretch point).

Photo: Different Representations Paper

2017-06-21 15.35.24What do you notice? What do you wonder?

What I’m Reading

This week’s post for the Exploring the Math(ematics)TwitterBlogosphere blogging initiative is about a post or posts that you appreciate.

I find myself going back to Dan Goldner’s post on fault tolerant mathematics programs frequently (fun story: I forgot to bookmark his post initially and spent about 6 months googling and searching for it. It’s now bookmarked in my browser). Dan discusses how his department thinks about their mathematics program in ways that support students who come in below grade level or are repeating a course or have minimal information about their prior mathematics knowledge. As I watch our department struggle with many of the same issues, it’s always comforting to know that other schools are thinking through the same things and facing similar issues. (This is also an embarrassing reminder to myself that I need to actually go back and watch Uri Treisman’s speech, which inspired that post)

As an advisor, I also find myself rereading Chris Lehmann’s post on Making Advisory Work (not technically mathematics, but we teach kiddos mathematics, so…). Our school has an advisory program and it is relatively supported (we delegate certain days to certain topics and probably more importantly, have other advisors with whom we can plan and brainstorm), but there’s still so much to do. And this post covers a lot of it. I find the points about “There’s nothing about the typical teacher preparation program that [prepares teachers to be good advisors]” and “I was good at the one-to-one with kids, but I don’t think I maximized the time we spent together.” (except I’d say I’m a solid to low so-so with the kiddos).

So those are the posts I go back to.

In terms of blogs, I will read anything Fawn Nguyen has to say any day.

Y un gran saludo a Heather Kohn and Mathy McMatherson (Daniel Schneider) for so many #MathandELLs posts that I am trying to be more diligent about reading these days.

And to Sarah DiMaria, Kaitie O’Bryan, and Sheila Orr. I try to read your blogs for the awesomeness and in hopes that I’ll have something smart to say about them when I see you at conferences.

My Favorite: Group Roles

It’s always hard for me to think of something that’s my favorite that a) feels like it’s something I feel I’ve used enough to call it “mine” and b) is related to mathematics.

I’m rather fond of the 4 group roles we’re currently using in mathematics class (9th and 10th grade algebra and geometry). It’s hard to trace where the roles started from, but I’m fairly certain they’re from CPM and have been used frequently by folks from Grad Skool and in the Complex Instruction schools in our district. We’ve put our own emerging multilingual spin on them. Most of the credit here goes to my awesome Curriculum Partner and our Teaching Coach.

Here’s how it goes:

I seat kiddos in groups of 4 (or 5, if we’re getting stuffed to the gills, which, surprise, we are, right now). Each kiddo is given a role:

Task Manager: Responsible for getting the group started. Asks “What do we do?”

Group Manager: Responsible for making sure everyone understands. Asks “Do you understand?” (I lean on this one heavily; there have been disputes over whether such a closed question is useful, but I find it easy to ask and understand)

Communications Manager: Was responsible for making sure people are writing. I think I’m going to rewrite this one to make people put things in the middle of the table or helps with translation. Currently asks “What do we write/say?”

Resource Manager: Calls the teacher for group questions (if no one in the group knows and all resources have been exhausted). Says “Excuse me, we have a question.”

(Side note: I love the use of “excuse me”. So polite and makes it ok to ask other people things even if they look busy. Also the use of “we” rather than “I”.)

Evolution of How I Use Roles

I used group roles when student teaching and tried implementing them unsuccessfully for about 2 years.

The gamechanger was actually taking away structure. I used to assign each manager a role and them make them sit in a specific seat. Somewhere during Year 2 or 3, I gave up on assigning roles and just told all the kiddos in one corner of the table that they were Task Managers and went from there. I also taped the roles down on the table and one of my super awesome coaches taped the sentences on them.

It’s been a game changer. Mostly because I’m able to name and call different managers. Even if the kiddos don’t remember their roles (they often don’t), they are visible enough on the table that some of the more on-point kiddos can remind them.

How We Made the Roles

At some random District planning day, Curriculum Partner, Coach and I randomly decided to pick apart the roles. We knew about them and had tried to use them, but weren’t entirely sure about them. We decided that there needed to be a tension between someone who pushes the group ahead (Task Manager) and someone who slows the group down so everyone has access (Group Manager). We’ve always needed a Communications Manager and a Resource Manager, so those roles stayed.

(I teach mathematics at a high school entirely for emergent multilinguals who are recent immigrants. Groupwork is heavily encouraged in all classes.)Laminated group roles

The One Where the Kiddos Teach Algebra Tiles

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One of the tricky things about having kiddos for 2 years and constantly taking on new kiddos (emerging multilingual/recent immigrant school) is that many of the kiddos have seen or already learned things that are important to know (like, say, algebra tiles) and half the kiddos have never seen it (or the mathematics leading up to it. Or a class in English. But, I digress…).

Curriculum Partner and I were both excited at various points about a lesson we did last year where kiddos who had been in school longer taught their group members about the algebra tiles and had them do practice problems.

We did it again today and it was about as awesome as we remember it. For all the worries that creating status and rocky starts to the year bring about, kiddos generally did really good at teaching each other and helping each other. In groups where there were multiple kiddos who had seen the algebra tiles, they often (somewhat) naturally co-taught or translated or otherwise differentiated their support. I tried to videotape one group, but they promptly stopped talking.

This photo taken shortly after trying to talk one kiddo down about phone calls home and shortly before the video caused them all to awkwardly stop talking:

2017-01-06-11-12-56-3What do you notice? What do you wonder?

(Context the first: This is from a mathematics class for students who are all emerging multilinguals.

Context the second: This blog is part of the #MTBoSblogsplosion, spearheaded by Carl Oliver (Thanks, Carl!). The Mathematics-Twitter-Blog-o-Sphere is a collective of mathematics educators on the internet who commit to blogging a certain number of times throughout January.

I’ve said I’m going to post a photo of student work every day for #teach180 (Thanks Sarah Carter!) and one post every weekend on more reflective things.)

 

The One With Balance

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First day back from vacation. New unit on balance. Wish I’d put more of an emphasis on the word “equals” and given kiddos the names of the shapes on the paper. I think the most thinking and talking when I let the kiddos draw on the paper. Also, there were about 10 new kiddos spread across my 4 classes. Which is not a lot, but is enough to complicate things (especially when all the kiddos are emerging multilinguals). Dem’s the breaks at a school of emerging multilinguals, I suppose.

(Also, I am largely back on the bandwagon due to Carl Oliver’s #MTBoSBlogsplosion. Check it out and join in!)2017-01-03-17-23-23

What do you notice? What do you wonder?