August 27, 2015

Math Practice Standard Portfolios

At our standards based grading implementation meeting the teacher working with us from the charter school asked about how we wanted to include the CCSSM Standards of Mathematical Practice. At the time we weren't sure but I've done some more thinking:

Last year I asked PreCalc kids to journal sometimes on which one they'd used that day. They referred to posters I have in the back of the room to choose one. I never asked Algebra 1 kids to do the same, but they're fully capable of it.

While I want to assess them, because they're important, I don't want to require every kid to use the same practice on a single assignment (because that's not the point). However, assessing students on whatever standard(s) they do use sounds like a logistical nightmare, especially since we aren't due to get an SBG friendly online grading system until second semester at the earliest.

Instead, what if I made the kids keep track? Basically, a portfolio! Kids would get the sheet below early on in the year and I'd tell them that they will need to find four good examples in their work of how they used the mathematical practices each quarter. That makes sixteen examples, two per standard. I could check their binders mid-quarter and near the end of quarter (providing enough time for revisions before report cards) and give them one SMP score based on the quality of their examples and explanations.



Reviewing my student friendly phrases, I feel like the modeling standard should include something about interpreting in context. Do the rest seem sufficiently clear?

I wanted to make this fit on a single sheet front and back but I also want them to write a decent explanation. Maybe we should do one example of each per semester? It would still be four per quarter but that way I could give them one sheet for each semester which means more room to write. And that way they can't leave all the seeing structure examples until fourth quarter when they may not have two good examples of it. A possible alternate handout:



Have you done this with your students? How did it work? I'm still not entirely clear on what the evidence should look like. How would you make the reflection meaningful? Can you edit the following invented student responses to make them better? I'm definitely going to need some quality examples make this a valuable venture.

"You can see I persevered in this problem because I tried three different equations before finding one that worked. I highlighted all three trials and boxed my final answer. My final equation is the one that makes sense because ____."

"In this problem I made a table and a graph. I found the pattern in the table which helped me to identify the slope of my line. I labeled the y-distances in green and the x-distances in blue on the table and the graph. In the original problem that slope means ____."

August 21, 2015

Algebra, the first month

Our first unit in Algebra 1 is focusing on the priority standards of Number Sense and Evaluating Functions. Four of the seven of us who will be teaching the course had the opportunity to work together this summer to map out the unit. That's five math teachers and two special ed teachers - our double block classes changed this year from co-taught every day to co-taught every other day and the math teacher with a smaller group (a subset of the co-taught Algebra 1 class so kids will have the same teacher both days) on the opposite day for a support class. Our goal with the support class is to do some pre-teaching and work on foundational skills that we'll need for the full class. In the map below that's the grayed out B Days. To recap- some kids will have class 90 minutes every other day, they'll do the white rows. Some kids will have class 90 minutes every day, they'll do all the rows.

It was fun to work with the team to find resources because we had plenty of time to share our ideas and search for new ones - they know about the MTBoS but none of them have jumped in (yet?). All the materials for the unit are in a dropbox folder. I'm sure we'll stray from this map by the end of the first week, but I'm so excited to have something available to refer to!

Unit 1 MAP


Vocab:
Mad Minute: It's not a race to do the whole sheet in a minute, it's a promise we'll only do this rote practice for two minutes, and it's as close as I ever get to pre-testing.

Exit Ticket: We don't know how we're going to have to grade the support class, we think it will be pass/fail. If so, the exit ticket will be a problem or two related to what we worked on that class and will be something in the online gradebook to appease admin :)

Flapper: An index card summary: definitions/generalizations go on the front of the card, an example goes on the back. They're taped to cardstock so they flap.

TIP chart: Three column vocab organizer. Term, Information, Picture.

August 20, 2015

Summer Reading

J, my rising eighth grader, has a summer reading assignment, as most kids do. I have a few stories to share about our summer reading experience. There's a tmwyk story* at the end, don't miss it just because you're not excited to read about reading!

At the beginning of the summer J had no interest in reading, it's hard for her and she just wanted to be on summer break. I offered her some choices for our daily reading time including: finding fun articles/blog posts, What If (from the creator of xkcd) and Charlotte's Web. She chose me reading her Charlotte's Web (yay! She wants to spend time with me!). I made the novice mistake of introducing it as a kids book which then made her question if she could use it for summer reading. Hey Tina, you know better than to tell your ninth graders that the worksheet is from a third grade math site, what matters is that it's interesting and appropriate. This applies to all things, even at home. Anyway, we recovered from that. As we read I was thrilled to find Charlotte using great vocabulary and Wilbur modeling excellent questioning techniques to understand. It had me wondering if there's a mathematical equivalent to a story with one character advanced and another character trying to learn. The EDC does great model conversations in their books, but what if we showed students an example of a new math technique and had them ask questions. Is this just another way to use notice and wonder?

We eventually finished Charlotte's Web and J picked out a graphic novel to read next (from the Lunch Ladies series). The summer assignment, by the way, was to read two books and submit reviews online. Any type of book they want! The reading specialist even said that research shows independent reading books should be a bit below the child's current reading level - the goal is to practice with something that is comfortable. J picked a book that was definitely easy for her, but I learned! I didn't say anything about it being a kids book, instead I was thrilled she'd picked out a book herself. She read it independently and was even willing to read before our usual scheduled reading time. While she read her book, I read my own. I was confused about what was happening in my book and J scolded me for interrupting her. She finished the whole book and was so proud of herself!

*TMWYK paragraph here
J wondered aloud how many pages the book she had just finished (in such a short time!) was. But the book didn't have any page numbers. I asked her to take a guess and she didn't have any idea. There was a 100 page book on the table so I told her, "This book is 100 pages, how long do you think yours is?" She decided to use the book as a ruler! She held them up next to each other, then matched them up spine to spine and determined that her book was over 100 pages. I asked, "A lot longer? A little? One and a half times as long?" She decided on one and a quarter. So I asked what a quarter of 100 was. "Hey! No, you always trick me into talking about math." I laugh silently and think: we've been talking about math kiddo, and I'm not trying to trick you, but, yes, we are talking about math. I smile broadly and say, "You can do that... What a quarter?" She says twenty-five cents. "So what's a quarter of a hundred?" Twenty-five. Great. I was done with the conversation and was going to continue reading my book when I saw her pick up her hundred page 'ruler' again. I watched her line up the books, mark the spot with her finger, open the book to her measured out 100 pages, and start counting aloud. She wanted to know if she was right! I watched, impressed that she counted pages (I was thinking about how many sheets of paper, but that's not how you number the pages of a book) and when she got 22 as her result I was seriously impressed! 

Since then she read the other book (in that series) we'd gotten from the library without prompting. And then she asked to go to the library (wonderful surprise! Of course we'll go!). When we got there she grabbed all the other books in the series without hesitation. As we headed out of the library with our piles of books she was able to verbalize that she likes these books because she likes reading short stories. I think I have a Shel Silverstein book from my childhood, that might be my next suggestion...

August 15, 2015

I Did That?

About a year ago, the EDC ran a training for eCMI table leaders. These individuals would be returning home and attending online PD with their departments throughout the school year. The PD is problem sets provided by EDC, but since these are remote sites, the table leaders would manage the participants and report back to whoever was running the session from Boston. Since I've been a table leader at PCMI (the live, in person, 3 week intensive version of eCMI) they invited me to model for the group. This was a fascinating experience. We spent some time working some problems together and engaging in discussion. They were an easy group to manage. When we finished the demo I was asked to explain what I did - this was shockingly hard to do. I could spout back some tenets of the program (don't give answers, you don't need to know any formulas to solve the problems so don't teach) but had no idea what else to say. People started asking questions and my answers surprised me. Someone from the EDC asked how I dealt with one of the quieter participants. My first reaction was "like everyone else" but that obviously wasn't true. I realized that I'd made a choice to let her work independently. Then at some point I'd made a choice to check in. Then I prompted a conversation with her neighbors who had a different perspective. After sharing that (and a few reasons why plus an anecdote about a particularly independent table member I'd had previously) the participant in question responded. She shared that I'd managed her very well, especially because she does not usually enjoy group work, and she hadn't even noticed what I'd done until I explained it.

It was this interaction in particular that struck me, and that continues to strike me (I've discussed this day with several people this summer so apparently it's really stuck with me). When teacher as facilitator works, it seems effortless for both the student and the teacher. Neither of us noticed that we were doing a particularly good job working together until someone else asked. (It might've been Bowen who facilitated this realization.) I've heard the claim that the only people who make more decisions per minute than teachers are air traffic controllers, but I've never considered how many of those decisions are subconscious. Or maybe more accurately, conscious but not noteworthy? Reflecting back on twenty minutes of teaching, I couldn't identify my best teacher moves. I can sometimes identify my worst ones, those moments where the class or the interaction is suddenly derailed. But most days I attribute successful classes to a good lesson plan, or students having a particularly good day. I never celebrate something I did during the time I was teaching. Do we even have the language to describe such things?

I am curious how I can have more of these realizations. How can I reflect on this aspect of my teaching? And I'm also concerned. If I never consciously think about where I give my attention, how can I eliminate bias in my teaching? Short of demanding Bowen observe my classes and ask insightful questions, what can I do?

Two possibilities come to mind:

  • Someone makes a list of things to be aware of, I pick one to focus on for the day or for the week. This could make an awesome blogging series if others joined in.
  • I record video and convince people to ask me questions. I don't think I can post it publicly though. And how would I know which chunk to share so that there's something interesting? Maybe that's exactly the point - I choose the most boring ten minutes I can and then others convince me I was still doing something worthwhile (or should've been).
This whole thing has me curious about teacher prep. Is this why people say that teacher prep is useless and you either can teach or you can't? It takes a trained eye to recognize key decisions, how do we train more eyes?

Now What?

I spent one afternoon at TMC listening to Peg Cagle and Levi Patrick talk about ways to grow as teachers without leaving the classroom. As I mentioned before, TMC brought to the forefront that I'm entering a new stage of my career, and I don't know what that means. Peg and Levi pointed out that there aren't pathways for growth in the US if you're a teacher. This isn't the case everywhere though. In China there are levels to achieve and (diverging) pathways to take as you grow as a teacher. They gave some examples - mentor, research, write a book, spend part of your schedule training pre-service teachers, other things I don't recall. At least in my district, there's no support to do anything beyond my regular teaching schedule. And the teacher leaders are the ones who sign up for committees - which I hate doing because they're typically run during school and remove me from my class. Because I don't want to stop teaching. I love teaching. But it no longer requires 100% of my energy and I want to do more.



So what are my options? I sign up each year to mentor new teachers, because sadly our department turnover is so high that we hire at least one math teacher every year. But this year we lucked out and hired only experienced teachers! They'll certainly need some support learning about our school, but they're much more established than teachers I've mentored in the past.

I never had any intention of writing a book, but that happened. I spoke at several conferences last year but working the conference circuit holds no appeal to me. I don't like to travel far just to spend a day somewhere. As appreciative as I am that so many people want to learn more, presenting to large groups isn't engaging in the way that teaching a class is. Finally, I hate missing school (if you're reading this you don't need me to tell you why).

I see Michael and Dylan digging into topics to explore them from multiple perspectives. This doesn't appeal to me, though I do enjoy scanning their writing to glean new information. I participated in a teacher cabinet advising the mayor last year, but I didn't find that we did anything impactful. So what's left?

This summer I've had the opportunity to do some curriculum work (Paid time! Not taking away from class time! Amazing!) with other teachers in my department. One day our leader from the charter school pointed out how wonderful it was to be doing this work with people who all know the content. That day I was working with our department head (another leadership position I don't really want because right now it's all bureaucracy, with only two teaching blocks) and another teacher who has taught five sections of Algebra 1 for each of the past three years. The same thing happened this past week, there were four of us in the room and with four years of Algebra 1 classes, I might have been the one with the least experience with the course. I also don't want to do curriculum work all the time, but these sessions made me appreciate the expertise of my co-workers. It's so much easier to work with people when I can say, "We need a lesson for the scientific notation part of this standard" and everyone 1) knows what's reasonable to ask our students, 2) has an idea from what they've done in the past, 3) can quickly assess other resources we discover, 4) can take my half sentence and turn it into a lovely handout doing exactly what I want (well, that may have more to do with us getting along that I didn't need to finish my sentence), 5) checks for common misconceptions and discusses how to address them. This is the benefit of having teachers stay in the classroom: we mapped out a month of classes (including a new Algebra support block), made student friendly handouts for all those lessons and chose assessment questions for each of the skills in the unit, in twelve hours. Two half days and a full day and we have photocopy ready plans for a month. There are some parts of class that aren't mapped out (we'll probably all do different openers and closers) and every pacing guide is meant to be broken, but what a huge accomplishment! (Right now all the files are in different places, including the school network, but once they're organized I promise to share.) These occasions make me see how important it is to have ways to keep these teachers in the district, in the classroom, with the students who deserve a teacher who knows what they're doing.

I still haven't answered the question of now what? Soon the answer will be "teach" because despite a decade of doing this, I still have a terrible time learning names. I never remember to make extra copies of the syllabus for Meet the Teacher Night. I always want to try something new, or have to try something new, because every group of students is different. There is one more thing that I want to consider, but I'm going to make it a separate post because it raises many important questions, beyond those of teacher professional paths. Stay tuned...