Sunday, September 28, 2014

Value of Visible Random Groupings

I have had students work in groups for my whole teaching career.  I love having students share their thoughts collaboratively, in investigative activities, through practice, to discover and to review ideas.

In my six years of teaching, I have always worked hard to engineer the perfect groups.  I would ask myself questions like:
Who seems like they would make a good pairing?
Who do I want to avoid ever putting together?
Who would have a good learning experience by needing to slow down or speed up with certain people? who are the students who keep a group on task and who are the ones who lead a strong leader in their group?
Do I want the groups to be more homogeneous or heterogeneous this time?

At Twitter Math Camp this summer, Alex Overwijk gave a presentation on Visible Random Groupings.  Although I didn't attend, I did read his post and hear lots of people talking about it.  It got me wondering if all of the effort that I put into grouping students is really helpful.  Students are very perceptive and even when I'm not intending to send a message with my groupings, they often pick up subtle ideas that I didn't even think of consciously.  A student believes that I put them in a certain group because they're the "smart one" or the "off-task one."

Although it needed some time to ferment in my mind, I also read Lani Horn's book, Strength in Numbers, last winter.  She really encourages teachers to get out of the business of grouping students.  I wasn't quite ready for her message yet then.

So, this fall I created my first seating chart by having students get in order of how far they live from the school and counted off by 5s to create groups.  Next, we used the numbers in addresses to get in order.  Then, we got in order by height and counted off.  Tomorrow I'm going to have students jot down their favorite number, get in order and count off.

So far, I've noticed an incredible difference!  The students don't look to me and try to figure out why I placed them in a certain group.  There is absolutely no complaining about groups.  Social barriers seem to break down.  I have way fewer behavior issues (this is a much more well-behaved class overall, but I think it helps).

I think that the visible part is key.  Even if you do it randomly yourself, students won't trust it unless they can see that it's truly random.

Sunday, September 21, 2014

Biking toward perseverance

Three weeks a year we go on Encounter Week.  Most adventures are multi-age (grades 7-12) and range from backpacking to Acadia National Park to knitting.  Students immerse themselves in something out in the world for a week.  Most options include overnights and all students and faculty participate.

Last week, for the fourth year in a row, I led the ninth grade bike trip.  Fifteen ninth graders (the whole grade), an eleventh grade student leader and three faculty members biked around Lake Champlain--206 miles.  We camped out in yards of current and alum families and carried our gear in a support vehicle.  As one of only two single-age Encounter Weeks, it really bonds the class and gives a serious welcome to high school.

I sometimes struggle with having so much less classroom time than my peers in other schools--several years ago when I attended AP institute, I determined that we have 68% of the number of minutes in the classroom as the average in my class.  But I think that the benefits of the program greatly outweigh the trade offs.

We talk a lot about growth mindset and grit and perseverance and collaboration and classroom culture and willingness to take risks.  I find that getting out of the classroom and into a totally different model provides so many students an opportunity to experience these ideas in a new environment.

Each night we asked two prompts for students to share about.  On the last night we asked: "what did you learn about yourself on this trip?" and "what will you take from this trip back to the rest of your life?"  Some of the responses were priceless:

"Staying positive makes things that seem impossible, possible."
"I have a lot more power than I thought."
"If I truly believe I can, I can power through anything."
"Although I thought I always wanted to be with others, its important for me to reflect on my own too."
"Daunting tasks don't need to be scary if I just take them one bit at a time."
"I can do more than I thought if I don't give myself the option to give up."
"A little encouragement can go a long way."
"Being a leader doesn't always mean being in front, it often means hanging back and letting the group figure things out.  It means sacrificing my own needs for the good of the whole."

I look forward to bringing these quotes back to our day to day time in the classroom.

Sunday, September 14, 2014

Giving No Instructions

In addition to teaching at a fantastic little independent school, I also own a tutoring business.  I actually started my company before I entered the classroom.  At this point, I don't do a ton of the actual tutoring--mostly my staff tutors, but I do keep a few students to myself.  Since much of my educational philosophy comes from my one-on-one background, it's important to me to continue working with a handful of clients.  I also get to try out fun ideas with really direct feedback.

One of my tutoring students (I'll call her P) is a freshman who is taking Algebra 1 at the local catholic school.  I started working with her a little over a year ago just before eighth grade.  P doesn't think of herself as a "math person".  Her computation is fast and her procedures are strong, but she rarely has a sense of why she is doing one process and not another.  Number sense is fairly weak (though the long division algorithm or "cross-multiply" are quick) and she often flails when presented with a problem that does not match the last five that she completed.  P is a hard worker and clearly wants to do well; she cheerfully tries again when her results are not successful.

Last year, in addition to helping her with her day to day work, we did a lot of estimation and problems from the Math Forum POW bank.  I wanted to help train her to listen to her common sense and use it to guide her mathematical processes.  P has some strong street smarts and generally a good sense about what something "ought to" be, but often has not trusted that intuition.

This past week in my ninth grade class at school, we tried one of Fawn Nguyen's  Although I've looked at the site many times and heard of others using them, I hadn't presented them to a class yet.  I had my students look at this one:
I asked them to think about what the next pattern would look like and to sketch pattern 28.  Then I had them work on creating a rule for the n-th pattern.  Most of them understood what I meant and others got stuck in knowing what I mean by n-th.  After some think time, they got into groups and shared their work on white boards.  There were some great conversations and it was a fantastic review of algebraic concepts and reinforced the "there are lots of ways to see the same problem".

Now, back to P.  She is not in my class.  Her teachers mostly do not tell her that there are lots of ways to see problems.  I had planned to do something fairly similar to what I had done in my class with her.  But, after I showed her the image and gave her some graph paper, she just started to draw.  I hadn't given her any instructions or direction.  She just started to draw patterns and circle connections between them.  Occasionally she narrated her thoughts, but mostly, she just saw how they interacted.  "The first one fits inside the third one, but not perfectly into the second one."  "The corners stay the same each time."  "The squares inside keep getting bigger by one."  

She also kept counting the squares of the ring rather than working to create a rule for it.  It took a lot of patience, but I held myself back from interacting with her much.  A couple of times I asked her to "tell me more about that".  But otherwise I stayed pretty quiet.  She worked on her own for almost 25 minutes.  With no problem!  She was noticing things, making observations and predictions, and checking to see if she was right.  P did not bring any variables into her figuring.  Toward the end of our time together, I asked her about what the n-th term would be like.  She went right back to proportional reasoning and assumed that it would be a direct variation.  Even with all of her play, once it felt "math-y" again, she lost her intuitive understanding.

I want to find ways to help P, and all of my students, to bridge their intuitive understanding and curiosity to the structure and formalism of our mathematical system.

Sunday, September 7, 2014

First Two Weeks

So, we're two weeks into the school year.  With early year assemblies, grade level hikes, Community Building activities, practice bike rides (I will be biking 200 miles with our ninth grade around Lake Champlain starting a week from tomorrow), Labor Day, and speakers from Amnesty International, I was left with four periods spread over the last two weeks for each of my classes.

I often feel like I need my blog posts to have a theme or a take away message, but I recently realized that I enjoy just getting a glimpse into the flow of other people's classrooms.

Math 9

Visible Random Groupings
Upon entry, I had my 16 students line up in order of how far they live from the school.  There was some debate about whether I meant milage or time, and they quickly settled on time.  I then counted them off by 4's and those were our first groupings for the year.  I told them that in the past I have spent a lot of time trying to engineer good groups, but after making the schedule for the whole school using a random number generator this summer, I see the value in randomness.  Everyone has something to learn from everyone else and working with others is really important.

Cup Stacking
Since our first unit is a review of Linear Models, I did Dan Meyer's Cup Activity.  I held up a Styrofoam cup and asked the students to estimate how many they would need to be my height.  They all recorded their answers.  Then I called on each of them (using cards with their names on them) and got them up on the board.  A couple were super outliers, but most of the rest imagined stacking them end to end rather than nested.  I let that go.

Next, they got into groups and I gave them three cups, a ruler, a huge whiteboard and markers for all.   I teach a in a carpeted hallway, so I let them spread out and lay on the floor.  I'm working on getting more movement into the day this year.  I let them know that I would only be answering group questions.  Whenever a group said they had a question, I would ask a different student than the one who called me over what their question was.  The first question folks asked me was my height.  I told them 170cm.  Then they wanted to know which way we were stacking the cups, and I said that I wasn't going to answer that question.

As groups started to say they were done, I gave them some feedback.  Before giving my thoughts, I talked to each group about what they do when they get feedback in English class or on other writing.  I reminded them of the importance of a reader being able to follow their ideas.  Then, I asked them to just listen and not try to fix or defend anything while I was talking.  I gave them feedback such as: "I'm not sure why this is being divided", "I don't understand why you have two parts here", "I'm not sure what you mean by JH", "I'm having a hard time reading this part".  It was a great way to give some direct instruction on showing work clearly without defensiveness emerging.

The next day we did a gallery walk of the boards.  The instructions were to write an "I notice" and and an "I wonder" statement about each of the boards.  Next, we had a class discussion, but I used Elizabeth Stratmore's "no comment" strategy to encourage listening.  I also didn't give any validation or restating for any thoughts.  After a student finished sharing, they were to call on someone else.

On their reflection papers, a lot of students seemed to get a lot of the take away points:
"we thought better when we listened to each other"
"the group who got the closest showed all of their steps clearly"
"measuring accurately is really important:

Tabletop Twitter
I did Tabletop Twitter with the following prompts:
This class will be incredible if...
A good math teacher...
We study math because...
To do well in math I will...

I'm not sure yet what we're going to do with the work we made.  I'm considering trying to have them capture it all in a google spreadsheet and then try to summarize each one into a couple of tweets and hashtags as the guiding principles of our class.

Interactive Notebooks
Last year I started ISNs during the second semester.  This year, I'm starting from the beginning.  I found Sarah Rubin's ISN Intro Prezi which I showed to my students.  This gave them an idea of what we were going to do.  And so far, they are super bought into the project!  I'm hoping to be more loose with my requirements to allow students more space to take their own notes and keep it organized as works for them.  I'm putting out a few requirements:
-Page numbers
-Titles (not standardized unless it's an all class foldable or notes page)
-Table of Contents for pages we make together (I know we won't all be on the same page, but the important pages will be listed in the ToC)

I'm not a particularly crafty person, so I'm just looking for all of us to be able to find things.  And I think that color and occasional foldables will help us all to remember some key content.

More math this week!
As I've reflected on the first two weeks, I feel like we've done less actual math and more norm-setting than I'm used to.  Hopefully it will all pay off!  I'm looking forward to digging into some algebra review and good linear models work this week.

Talking Points
I tried out Talking Points with my Calculus students on the first day.  We did the Talking about Talking set of points.  They totally loved it!  It was great to deeply listen and to have changing your mind be a part of the activity.  Others have said that their students fly through them; that was not a problem for us.  We seemed to linger over the ideas for quite a long time.

On Friday as they were doing an activity about a the rate of a swinging door opening and closing, the problem asked for an estimate of instantaneous rate of change.  One student said "instantaneous is the same as average rate over a small interval".  I wrote her statement on the board and we did a quick all-class talking point on it.  It was great to have the structure already so we could listen to each other's thoughts quickly like that.

Trig Review
I usually wait until just before we are going to start trig derivatives to do a thorough trig review.  The professor that I'm working with from the University of Vermont does it at the beginning of the course.  I was out for a day on the ninth grade bike ride, so she started some trig with them.  Although they love to think about big ideas and are familiar with unit circle trig, it's not as automatic as I want it to be.  I'm struggling to balance the "you need to know this" with my desire to discourage memorization in favor of true understanding.

Monday, September 1, 2014

Jobs for Classroom Flow

One of my big goals this year is to nag my students less.  To achieve this, I'm working to build better systems for class to flow naturally.  Although I have often asked students to help with materials or cleaning up, but I have never had an organized plan to make this automatic on a daily basis.

Last week, before our second class, I created four jobs to try out:
-Time Keeper
-Materials Manager

I'm working on solidifying the responsibilities for each task, so I thought I'd put it out as a blog.  If you have tasks that you consistently assign to students, what are the jobs?  How does it work for you?  Any other ideas I'm not thinking of?

Time Keeper
-Label times on whiteboard clock--predicted and as needed
-Ring bell as needed--must have eye contact and thumbs up from Jasmine
-Politely offer reminders (to Jasmine & to peers) when we are close to time limits

I bought this great big clock and my boyfriend mounted it on a Whiteboard for me.  When we have a task that I want to be done within a certain time limit (e.g. 5 min to work with your group on this card sort), the time keeper will put an arrow on the clock to symbolize when we plan to be stop.  That way, students can self-monitor their time.  When we reach our time, the Time Keeper will pick up the singing bowl bell, look at me (or tap me on the shoulder if I'm busy) and wait for a thumbs up to ring the bell.  Although times when tasks start can fluctuate depending on how an activity is flowing, I will also put a few times on the board as a guide for when I want to start activities.  It's the timekeepers job to politely check in with me and let me know when we get close to our times.

Materials Manager
-Gather listed materials from Jasmine's office
-Remind peers to clean up thoroughly
-Dismiss, with Jasmine's permission, class when room is tidy

I don't have a classroom, so this student will gather our materials for the day from my office.  I keep most items in a crate.  They will also get the whiteboards and the Interactive Notebook materials boxes and anything else I list on the board.  Although groups are responsible for getting their materials cleaned up and back to my office, the Materials Manager is to remind their peers to clean up and ensure that the room is tidy with chairs pushed in before we are dismissed.

-Photograph boards and other in process tasks to save for next day
-Post photos on-line with captions
-Take at least 2 photos that capture the vibe of our lesson

If we do anything on individual whiteboards or up on the big board that we want to save, the photographer will record it and post it to on-line for our class.  I'm hoping this student will also take a handful of photos for my blog (as I hope to post more often, with pictures!).  Most of my students have Smartphones and I'm fine with this one student using it on that day.

-If period 1, write, using a half sheet of paper: date, Math 9, list students who are not here @ 8:30, put a T next to names if they arrive by 8:35, quietly take to Jill [Note: there are 16 students in this class]
-Collect extra copies of handouts for absent students
-Share notes and update absent students when they return to class

We have class first period two days a week.  This student will run the attendance up to the front desk. They will also be responsible for collecting materials for any absent students and setting them aside.  This student is who I will send students to when they come back from their absence to get caught up (on ISN notes and other activities).

Accountability and Fairness
I've recently been reading The Artist's Way, a book about increasing creativity.  Each chapter offers a bunch of different suggested activities.  The instructions suggest that you do the ones that sound the most fun and also the ones that sound terrible to you.  So, I'm going to ask the students to order the four tasks from most to least desirable for themselves, then I will ask them to do their most and least favorite task at least once this quarter.  I'm going to let students just sign up for the jobs on their own, and ask them to wait for others to have a chance once they have done a job three times in the quarter. I'm going to make a tracking sheet for their Notebooks.

Friday, July 25, 2014

A Blogging Tutor, Please?

It has been only in rare circumstances that I have not been able to sleep in my life.  My mind is so full with new ideas and growth, that I just cannot seem to settle to rest.  I am generally a person who needs 8, maybe 7, hours of sleep each night; I get sick and cranky if I don't get that.  This week, I am struggling to stay asleep for four hours.  It's not that I'm staying up drastically later than I otherwise would, it's that I am so excited about everything and everyone, I wake up with so many thoughts running through my mind.  This is very different from when I can't sleep because I'm anxious or nervous or because I'm sick, this is my passion and joy not having time for rest.  

What will really inspire me to blog?  I participated in the first new blogger challenge after the first TMC (which I didn't attend, but watched with envy feeling like it wasn't for me).  I think I did most of those challenges, but always at the very last minute to get in under the deadline.  Last year I signed up for the Explore the Math Twitter Blog o Sphere Challenge.  I completed a handful of those assignments (and loved the prompts and ideas!).  

In the past, my resistance to writing (which I think is similar to the math resistance and phobia that we see in a lot of our students, and that I'd like to work on unpacking) has taken over and I seem to procrastinate until I have a hard deadline.  When I get up to the deadline, I write like a bat out of hell, and what I write often ends up coming out pretty decent.  I want to find a way to have internal motivation to do this.  Or maybe I just need more consistent (loving) external pressure to get my ideas out there.  I'm a rather extroverted person in general, and I LOVE to connect with people.  So, if I can think of my blogging as an extension of the conversations that I have here at #TMC14, maybe I can find my way in.

I always tell my students that they each have something valuable to contribute, and I truly believe that.  I want to model that belief by taking the risk and sharing of myself.  I want to put myself out there, even when it's uncomfortable or when I don't feel like I have time.  I do interesting things that others are interested in.  I'm part of a collaborative community and by remaining silent on my blog, I do a disservice to everyone.  I know this.  Yet, I want to blog not from a place of shame, but from this well of joy that I feel sprouting within my soul right now.

Yesterday at an informal meeting for geometry teachers, I asked for help with accountability for blogging.  I have a lot of ideas, yet when I look at a list of "things to blog about sometime," I seem to shut down and sink into feeling like a terrible person for not having written about any of them yet. I think many of our students have this same feeling when they look at what they think they "should have" learned in Algebra 1, or in fourth grade or last week.  

In addition to teaching at a rad independent school, I own a tutoring company.  I connect with students who struggle with these issues all the time, and through that coaching connection, through holding space for them to have their experience, through questioning, through love, through patience, through modeled perseverance, through affirmation, through encouragement, through tough love, through structure, through sharing my joy, through allowing space for the frustration, through full attention, many of these students come through the other side of their math phobias and anxieties.  

This is what I would like with my blogging.  I would like a blogging tutor (or collection of them) who help to hold me accountable in the same way that I lovingly hold my tutoring students accountable.  So, who wants to be on my team?