Undergrads walked into my math pedagogy class at UC Berkeley this evening as emotional as I am about the results of the election. So we talked about it. But first, we graphed it. Using Desmos Activity Builder I asked students to graph time versus their emotions over the past 48 hours. We spent the next 90 minutes analyzing graphs, points of interest, and ended by pushing the tables out of the way, standing in 2 concentric circles with them paired up, talking about everything from how the election affected them, to how it affected students in their teaching placements, to what their role, as future teachers should be in supporting their students to be mathematicians and scientists committed to social justice.

# Fluidity of Expert Status

In a recent post about Great Classroom Action, Dan Meyer mused about how to use the feedback features in Desmos’ Activity Builder to allow students to self-assess while not exacerbating issues of status in the classroom. He is referring to Cathy Yenca’s post on how she uses the teacher screen during card sorts.

Let me first say that since Cathy’s 9/21/16 post, I instantly stole this idea. I had been meaning to blog about it. A whole post just to thank her for refining how I was teaching with Desmos Activity Builder. I appreciate Dan’s musings as now I can post about his thoughts to. First, I LOVED Cathy’s ideas. She is one of my two classroom heroes. Though we have never met and have only an occasional virtual teaching exchange, she, along with Julie Reulbach are two women who I feel most similar to as a teacher. I see myself in them ALL THE TIME. They are my heroes because unlike me, they are still teaching in the classroom. Though I am now an administrator, I glean ideas from their blogs which constantly make my work stronger. And I know, were I to return to the classroom, we’d have a whole lot more to share with one another. And although there are tons of bloggers who influence me, they are the two who I really connect with as teachers. If you teach math, are curious about technology integration, and don’t read their blogs, please do. You’re in for a treat.

Now, onto my thoughts on expert status. As a middle school math teacher (which honestly wasn’t all that long ago, though I often start to feel like it was another lifetime ago), I pulled groups of students who had similar mathematical needs several times a week. I gave exit tickets at least 3 days a week and the following day, I’d pull 1-2 groups of students. Sometimes it was students who made a similar error. Other times it was students who got everything correct and I wanted to push their thinking on a certain concept or better understand how deeply they understood. Sometimes it was students who got the same problem correct, but didn’t show any work and I wanted to hear from them how they approached the problem. These groups were fluid and whomever was pulled was pulled for a specific reason which only corresponded to their work on yesterday’s exit ticket. What amazed me, was how the membership of the groups changed from day to day. It was never the same students pulled day after day. Why? Both because my criteria for how I pulled groups changed constantly based on what I wanted to know from students and because when you pull groups for a very specific reason, different kids fall into that category on different days as the reason is always changing.

However, I often received A LOT OF critique from colleagues in the math department. They said I was exacerbating status in the classroom. Me mentioning that I was pulling groups of students with a similar error made many assume that the same struggling kids were in my group day after day and that gave them a lower status in the classroom. While I completely understood their concerns, I knew that it was different kids every day and felt confident that I was aware of the harm of always pulling the same kids.

Cathy’s idea of having kids see this screen while they are doing a card sort in Desmos Activity Builder made so much sense to me.

Recently, while doing a card sort in a 5th grade class, I too had students strive for expert status. But as Dan mentions, I don’t want this to create status issues and anxieties. There were more subtle things I did while this was happening to have several pathways to “expert” besides having all your cards become green (correct).

* At one point, there was a pair of students who I could see from the screen had no cards correct. However they were very focus, having intense mathematical discussions, and showing each other their conflicting reasoning using scratch paper. I stopped the class (thank you, “Pause Screen”) held up their scratch paper and made a very big deal about how impressed I was that they were having a “Math Fight” (my favorite kind of fighting) and that they were trying to resolve their math fight by using scratch paper to convince the other of their thinking (and yes I did mention the math practices that they were displaying). When the class returned to work, everyone wanted scratch paper. So now, “expert status” was defined by not only getting all green cards, but by convincing your partner with scratch paper (as students were paired up each Chromebook).

* I also am a lover of personalized stickers from Vistaprint. I have about 10 different phrases, all fun like this:

I stole this brilliant idea many moons ago (2012) from Sam Shah. Did you get a sticker because your group was one of the first ones to get all your cards sorted correctly? Nope. Since I already had a reward for those who were faster to get everything accurate, stickers (which are VERY high status) were only given to groups to I saw debating, struggling, and making sense of their misconceptions either within their pair, or by getting help from today’s ‘experts’ who were going around offering help. And somewhere in there I stopped the class to talk about how you earned a sticker and that if you had one, you had done the hardest work of all. Having a sticker with a positive message from me on your hand, as these girls do, becomes a very sought-after status as well.

I think having experts is fine. However like Dan (and Cathy, I’m sure) we have to think about how to have the kids who are experts be defined in multiple ways. Tomorrow’s ‘experts’ on a card sort should be defined in a different way. By constantly changing your definition of ‘expert’ we open up the title as one which can be earned by different kids on different days.

# Math PD for Substitute Teachers

I was asked to lead a math session today for district-wide subs to help them better understand the math they’d find in CCSS classrooms. Thinking about how to craft a PD on mathematics for K-12 substitute teachers who work in any classroom from kindergarten to high school PE and everything in between was a challenge. Like many of you, when faced with a teaching topic on which I am stumped, I head to my friends in the blogosphere

Recently, a UC Berkeley undergrad in my math pedagogy course asked if it would be considered plagiarism to use a lesson his girlfriend had taught in his current teaching placement. My reply was that if it was a great lesson that was appropriate for his students, it wouldn’t be plagiarism at all, and was actually what all great teachers do.

So thank you, Robert Kaplinsky, as I very much stole your work today, though I gave you credit all along the way. I am indebted to you for inspiring my session today which somehow left a room full of subs, with VERY diverse experiences, quite excited to teach math this year.

Between being a teacher in my district for a long while and now having been a parent here for a long while, I was surprised to realize how many of the subs in the room I knew. Several of them had subbed for me and many more had subbed for my colleagues and even my son. That made this a lot more fun for us all.

They started by predicting how 8th graders would respond to the question of:

**There are 125 Sheep and 5 Dogs in a Flock. How Old is the Shepherd?**

They then watched this video which is further discussed in this blog post.

Man did I have a captive audience. My favorite comment was from a woman who admitted that she hates math and would never sub in a math class. She said that had she been asked this question, she would do what many of the kids in the video do, write down the numbers and DO something with them. She would assume that though the question made no sense, that it was she who didn’t understand and she doesn’t trust her math abilities. She went on to say, however, that had this question been posed in an English class, she would have been the first to question the teacher saying that it made absolutely no sense. She challenged the group to pose this question to both a group of middle school math students and again in a middle school English class. She was confident that outside of a math classroom, more students would speak up about how the task makes no sense. I found that hypothesis to be brilliant (while also worrisome that she’s right).

Following this conversation we did Robert’s lesson on questioning strategies which is explained in his blog post. In short, teachers were in groups of 3 where one role played a teacher, one a student and one was an observer who wrote down all the questions asked by the teacher. The teacher was given slip of paper with a math problem and knew the solution that the student had gotten. The student was given a slip of paper with the math problem and a specific misconception. The goal of the teacher was to ask questions to determine the misconception of the student.

For example:

**Student**: You are working on ordering decimals from least to greatest. The problem you are currently working on is ordering the decimals 0.52, 0.714, and 0.3. You correctly place them in the order 0.3, 0.52, 0.714. However, the reason you put them in this order is because you look at the number after the decimal like a whole number (3, 52, 714) and do not understand the significance of place value. You are confident you are correct and don’t realize that you only accidentally got the correct answer.

**Teacher: **Your student is working on ordering decimals 0.52, 0.714, and 0.3 from least to greatest. Determine what understanding the student has by asking questions, especially questions that encourage elaborate responses.

I LOVED this activity and the rich conversations it generated. We easily spent 45 min. role playing 3 scenarios and debriefing each one and these teachers had so much to say. We talked a lot about how developing questioning strategies could help a student unearth misconceptions even when the math the student was working on was too complicated for the sub.

However I realized that for this group of teachers, there were so many who feared math, that they couldn’t focus on the misconceptions and instead, for some, could only focus on explaining to each other HOW TO DO the problem. In hindsight, I think I should have modeled the conversation one could have. I could have role played the student and had the whole room of subs role play the teacher asking questions to me. Only I would know the misconception and the group would ask questions to determine where I was confused. I think had we done that for one scenario, these teachers would have been able to let go of their own fears of making math mistakes a bit easier.

What a neat afternoon for me and for them!

# Next Summer…

Next summer, you say. But why? I haven’t even begin this new school year yet. I just cleaned the lens of my document camera and tested out last year’s white board markers to see which were still keepers. And I did such fabulous PD this past summer that I’m itching to incorporate into this year’s curriculum and pedagogy.

And gee whiz, my husband and I bought a condo in Kauai this summer so why the heck would I do ANYTHING but go here next summer?

Darryl Yong just published a blog post on how he and Bowen Kerins create the morning math sessions at the Park City Math Institute. Read it now, before you read any more of my post. If you haven’t attended PCMI, you should, and Darryl’s blog post leads you to more information about it and how to apply.

Today was my first day of work at my new job, Instructional Technology Coordinator for the Berkeley Unified School District. I’m a teacher. I’ll always be a teacher. So explaining or even stating what my new job is seems to only happen with some contortions as I try to explain that I’m a math teacher, but I guess I’m not a math teacher anymore, but I really am a math teacher. This summer as I have met new people while on various travels, I’ve been asked what I do. I can’t seem to say the title of my new job without a paragraph intro about how I was a middle school math teacher, then had a second child, then wanted more flexibility and became a TSA and then and then…and now I am…blah blah blah.

However, while a lot of experiences have shaped who I am as a teacher and now as an administrator, over the past 17 years, nothing has had as lasting impact as the summer of 2011 when my husband and I packed my then 13 year-old-step daughter, 2 year-old son, Bernese Mountain dog, two mountain bikes and who knows what else into our Subaru Outback, stopped at every McDonalds Playland between Lovelock and Winnemucca, and landed in Park City Utah. Following my participation in PCMI’s 3 week course, I started a blog (yep, you’re reading it now), got connected to a bunch of regular math bloggers from whom I have bounced countless ideas off of, and found myself immersed in the online support world of math teachers. Darryl’s post suggests that PCMI’s curriculum limits the amount of technology which is used. While this is true, without a doubt, I wouldn’t have the job I have today (Instructional Technology Coordinator operating in the body of a middle school math teacher) were it not for Darryl and Bowen introducing me to Geometer’s Sketchpad and how dynamic mathematics software can allow students the opportunity to play around with visual representations of big mathematical ideas and explore open-ended problems which elicit incredibly rich discussions. My use of Sketchpad morphed into GeoGebra which more recently has morphed into Desmos, however the purpose of these tools remain the same.

So Thank You, Darryl, for your post and for reminding me of how I got here. And speaking of gratitudes, Thank You Math For America, Berkeley, for urging me to go and paying my way.

# Pokemon for Breakfast on the First Day of School

I’m tempted to post this without comment. But comment I shall.

Since I’m not in the classroom, I can’t show this on the first day of school. But if I were still teaching 8th grade math, I think I would. Then I’d have them turn and talk, introducing themselves to a partner and discussing whatever the video made them think about. No idea what this video refers to? Your partner will. Or you’ll both lean over and ask the pair alongside you.

Somewhere along the way on that first week we’d do an activity with Desmos. And when Friday rolled around, I’d have them do a quick write and pair-share to compare and contrast playing Pokemon Go to sharing a laptop with a partner when doing math as part of a Desmos Activity. But sadly, I don’t have my own classroom filled with eager 13-year olds to build relationships with or affective filters to lower.

Since I now lead professional development more or less full time, I will instead show this video as part of my opening talk to the 100+ Berkeley K-12 teachers attending my department’s 3-day Instructional technology Institute. Spoiler alert if you are a Berkeley teacher reading this…

And I do hope the Desmos folks forgive me for mentioning Pokemon Go and Desmos in the same sentence.

OH NO…video was taken down today 8/5 for copyright reasons. So sad.

# Do Something

Our country’s values are making me sad. More sad each week as news arrives of yet another black victim in the hands of a police officer.

I have spent much of the day reading social media as I never have before: reading articles, watching videos, and reflecting on the reflections of my friends, colleagues and acquaintances on Facebook. Posting, reposting, reading and writing are all expressions of emotion, but I urge us, especially those of us who are white to make a promise to DO SOMETHING. We have the privilege of choosing whether or not to speak up. DO SOMETHING.

I have compiled the articles I have come across today which have been posted by those whose opinions I greatly admire and respect. While I haven’t yet read all of these articles, I found each through someone who always pushes me to think more deeply. I plan to add to this list in the coming week and will repost this list again. Please share additional links here in the comments, on my Facebook, or Twitter accounts and I will add them to this list and read them myself. This is barely a *something* in the act of “DO SOMETHING” but having these in 1 place will hopefully give me and others a source of reflection and information to share with others. Click here for a beginning of a list on articles being circulated on social media.

If you are white, like me, promise yourself you will do something.

My promises today are:

- Have ongoing conversation with my sons about their role as white boys in being allies for people of color and speaking up for and documenting injustice when they see it.
- Continually donating money to organizations which are supporting social justice and individuals who have suffered from racist acts of violence.
- Get involved in local campaigns to ensure that police oversight and community policing is a priority for our elected officials.
- Get involved in national organizations that are pushing for bringing justice to police officers who have committed racial acts of violence.
- Talk about these issues. In person. Not simply over social media.
- Not remain silent when I hear white people I know making racist assumptions or unknowingly denying their white privilege.
- Think deeply about how to ensure that my work in the public schools is focused on issues of social justice and helping empower students to know how to advocate for themselves and speak up for and document injustices when they occur.

Many today have shared their feelings far more eloquently than I can. Writing my emotions is not something I do well. Speaking and listening is far easier for me. But I need to move on from reading social media and actually take action.

# Why 2:1 Laptops are Gold

Recently, my parents were visiting to celebrate my son’s 7th birthday. They asked what projects I was involved with at work and instead of explaining, I grabbed a laptop and asked them to try out a 5th grade Desmos Activity I had recently written.

In my role as Teacher on Special Assignment for Instructional Technology I find myself immersed in many types of projects, but the one which our district math coach often calls me ‘relentless’ is my work to get all middle school math teachers using Desmos at various times throughout the year. In pursuit of this goal, I taught a lesson using Desmos in 5th grade classrooms at ten of our eleven elementary schools this winter when they were on Engage NY’s Module 6 which is coordinate graphing. The students used Desmos to discuss several topics, however the stickiest and richest conversations occurred when students were trying to write their initials using T-Tables. They’d call me over in a panic explaining that they were trying to make a C but they computer thought they were making an N:

“Huh” was my general response. “I wonder why that happened?”

Some continued to tinker on their own while others would call me over and say that THEIR computer had done the same thing as so-and-so’s computer…thought they were trying to make a different letter than they actually were.

So we’d talk, and eventually kids realized that the computer does just as you instruct it to do, so the order of the points in your T-Table matters.

This led me to write an Activity around this big idea which if you’re interested in trying out, can be found here. I’d love your feedback if you have a moment to try it as because of SBA testing, I haven’t yet been able to try it out with kids, though I plan to do so in the next week.

But there we were, in my kitchen, with my parents (who I am quite sure are reading this post) asking what’s new at work. So I gave them each a laptop and had them try out this Activity. They were lost. Very lost. Both because they hadn’t thought about x’s and y’s since my brother was born and because the format of a self-guided online task was completely new to them. I offered minimal help, with just a quick crash course on how to graph coordinate pairs. However the real help I offered was to tell them to share a single laptop.

The video below doesn’t capture how rich their conversation was once they were sharing a single device. Work which was at their frustration level only moments earlier when they each had their own laptop suddenly was not only fascinating to them, but do-able. Although my dad is the one typing, just moments earlier my mom had figured out a crucial issue that had stumped them. They are going to kill me for posting this, but it’s worth it. When is the last time you saw 2 grandparents productively struggling through a Desmos Activity?