Day 118 and the Hypocrisy

I’ll never forget Day 118.   **I don’t know how to add footnotes on a blog, but I can assure you that I consulted an expert, my 1st grade son, to tell me what day of school today was.**

I had perfect attendance. Let that sink in for a moment. I teach 112 students and not only did I have perfect attendance today, I rarely have more than 1-2 students absent on any given day. As students logged on, class began with a song, chosen by one of my students, they then reflected on why we celebrate Black History Month, we did a formative assessment in preparation for Thursday’s quiz, students did quick sketches of something from their weekends in order to learn new tech tools just released on a graphing calculator software we use, they collaborated in breakout rooms to deepen their knowledge of y=mx+b and the mathematics behind parallel lines, then did a deep reflection about how their breakout rooms collaborate today and whether or not their team was read for the upcoming quiz. Recently they used their knowledge of linear equations to write 1-word New Year’s Resolutions. 

Today is day 118 of full distance learning. Perfect attendance, about 80% cameras on and deep reflective conversations on social justice topics and mathematics. So much of what is working well is my school staff’s commitment to this work: we have been deeply reflective and collaborative about how to best support kids and families during the pandemic since last spring. Day 118 wouldn’t have been memorable except that KQED published an article using video feed of our teachers’ union president taking his 2-year-old daughter to preschool. And that article got picked up by national news, so now we are ground zero for parents’ cries of hypocrisy.

According to the Oxford English dictionary, hypocrisy is “a behavior that does not meet the moral standards or match the opinions that somebody claims to have.”

I am filled with questions which maybe by writing and sharing and reflecting with you I can get answers to.

What exactly is the hypocrisy? I’m honestly not sure.

  • Is the hypocrisy that some teachers have found private child care for their young children so that they can do their jobs while working tirelessly to figure out the incredibly complex issue surrounding school’s opening in person?
  • Is the hypocrisy that it most certainly is safer to have kids in a tiny, private pre-school where the student:teacher ratio is 1:4 than in my public middle school where I see 112 students per day and some teachers see up to 150 students per day in class sizes that range from 26-30 students?
  • Is the hypocrisy that nearly EVERY parent I know whose voices are the loudest on school reopening has also broken quarantine to go skiing, travel to airbnbs with friends, visited Hawaii, etc etc?
  • Is the hypocrisy that most parents whose voices are the loudest on school reopening do not know anyone in their immediate family who has died from COVID and has not asked the opinion on school reopening from those who do?
  • Is the hypocrisy that there is a small, minority of parents who have used their privilege and power to create a public narrative which claims to speak for us all, but actually doesn’t?
  • Is the hypocrisy that a “Guerilla Momz” who took the video of a dad walking his 2-year-old to preschool refuses to identify herself because she fears repercussions but yet goes to the press with a video which KQED publishes knowing quite well that those same repercussions could now fall onto this Berkeley father?
  • Is the hypocrisy that the public narrative is to reopen schools, when actually schools never closed?

I am a BUSD parent, teacher, and a proud member of the Executive Board of the Berkeley Federation of Teachers. I am and always have been 100% focused on coming back to school in person. Teachers in Berkeley have the same goals as parents. Keep our families and ourselves safe while upholding ourselves to the highest possible standards of educating the youth of Berkeley. If you’re here with us to figure that out, I’m all in.

Pure Bliss (Is that even possible nowadays?)

When I look back to this year, I’ll need to take some very large deep breaths to allow myself to remember the emotional toll that it took. But I’m hoping that I’ll never forget the incredibly deep gratitude I have for so many of you who have gone through this year with me. I don’t know that I have EVER felt as deeply connected to other educators as I do right now. And these connections have fostered some of the richest collaboration I could ever imagine.

I think of the great jazz musicians, or other pure improvisational bands like Phish, and how their artistic craft riffs off one another. BECAUSE teachers have had to reinvent our craft and BECAUSE we are in this together, there has been some true improvisational bliss that has gone down.

I teach 8th grade math in Berkeley, CA and our entire district uses Desmos’ math curriculum which is based on Illustrative Mathematics’ lessons. I love Desmos. I am a Desmos Fellow and a Desmos Certified Presenter and having an entire year’s worth of curriculum in Desmos is pretty much a dream come true for me. HOWEVER…it wasn’t written with distance learning in mind and as fabulous as it is, I sometimes find it very hard to have authentic student-student discourse and collaboration over Zoom, particularly in breakout rooms because in Desmos there is no way for multiple students to be working on the same screen simultaneously. Google Slides and Jamboard allow this, but frankly, I am so in love with the Desmos curriculum and pedagogical tools, I had no interest in modifying it to use with another tech tool.

This graphic comes from a recent EdWeek article on remote learning. I have some critiques of the article which are outside the scope of this blog post, but this graphic stuck with me. My desire to have structured student-student discourse has been keeping me up at night, and one of my colleagues, Lara Collins at King Middle School has been making these really wonderful Google Slide shows for activities to use in breakout rooms. The improvisational jazz riffing is that I used Lara’s slide show, plus a perfect post-breakout room reflection tool from Marlo Warburton at Longfellow Middle School, plus ideas from this SUPER practical webinar by Theresa Willis and suggestions from Rose who is also doing incredible things with Desmos and Google Slides.

Students had just learned about y=mx+b and needed time to practice graphing lines.

  1. Go into breakout rooms for 4 minutes and figure out your birthday order and write your names in the boxes of job roles in order. Your breakout room # is the same as your slide #. Breakout rooms in my classroom are stable. They have been the same for 3 months now so everyone knows their room #. Each has 3-4 students. There are 5 jobs here, so some students had more than 1 job. **SIDENOTE** I have a rotation breakout room job which is the AAA: Anti-Awkward-Analyst. They choose who will do that job but their role is to make jokes, encourage cameras on, tell a story, and encourage everyone to participate. I get feedback from the AAA after breakout room days.

2. Back in main room, I modeled each job. The slope person writes the slope of the line in the box. The y-intercept person writes the y-intercept and moves the blue dot to the y-intercept’s value. Then the points person drags all the points onto the graph, using the slope and y-intercept. Finally the line tool person drags the line and connects the points. Finally, the status checker decides if it’s all correct and if they believe it is, they change the yellow text box to green.

3. I am sitting alone in the main room watching all the slides, using “Grid View’ as needed. When I see the status box turn green, I look at the slide and see if it’s correct. If it is, I turn their status box back to yellow, delete their equation and paste in a new one from this list. I purposefully made each a different color so they would see that a new one had been pasted and so I could quickly eyeball which # they are on. If there are errors on their graph, I turn the status box to red When I first do that, I don’t provide any feedback. However if a few minutes have then passed and that slide isn’t corrected and turned back to green, I paste a brightly colored text box on their slide with 1-2 questions or feedback to push their thinking.

4. Once they have a new equation, the student whose job is the ‘undoer’ drags the points and line away to prepare for the new equation.

Students spent about 15 minutes doing this and while each worked at their own pace, every group got enough done to become proficient at graphing these equations. I use the Cool Downs in Desmos’ curriculum as my formative assessments.

5. Finally, I turn off the public chat and make it so students can only chat privately with me. That’s when they give me their feedback using these sentence starters.

As I receive their private chats, I read aloud the ones where a specific student is shouted out.

The very next time we do breakout rooms, I choose a few refections from the previous day for them to read and challenge them to do an even better job collaborating than last time.

This year has been an endless journey. But I am so thankful to be going through it with so many of you who inspire and challenge me daily to figure out what’s possible. I’m now super curious to think about ways to use Google Slides (or Jamboard) in conjunction with Desmos. I’d love to see ways you’ve connected the two or simply how you’re structuring your online group-work in Desmos to create more sustained and genuine student-student conversations.

Community Building From A Distance: Desmos Art

I teach 8th grade math in Berkeley, CA and we are 100% distance learning and will be for the foreseeable future. Like so many of you in the same situation, community building has become more important than ever since we are teaching students whom we have never met in person. One tiny slice of this complex work has been doing art projects in Desmos to give students the opportunity to be creative and teach one another the techniques they discover. I have always had students writing their name in Desmos on the first week of school. It is such a great way for them to express themselves creatively and run around the room learning tips and tricks from students who create something that they want to emulate. I found the prospect of teaching art on Desmos over the first week of school in distance learning VERY DAUNTING. But I decided to go for it.

It is MUCH HARDER to teach art via distance learning than in person because kids can’t run around the room to see what others are working on. Finding efficient ways for kids to help other kids is far harder on Zoom. But I’m so glad I stuck with it as there was so much joy in my classes as students celebrated the gorgeous fonts they had created. Below are some examples. These 4 names are from this year, distance learning, using only tables and connecting coordinate pairs with lines.

This next group of 4 names are the project I am doing just after winter break where they write their names with horizontal and vertical line segments. These are some examples from last year.

For anyone looking for a project to build community right after winter break, this one could be ideal. At CMC-SOUTH and CMC-NORTH this year I presented on how I scaffold my art projects. Below are the handouts which include links to each of the 3 projects I do during the year, student work samples and rubrics. I’m sharing my hour-long presentation if hearing me explain the scaffolding step-by-step would help you know how to get started.

Over the year I have 3 projects:

  1. Writing your name in Desmos using only tables to connect coordinate pairs to review graphing in 4 quadrants. I do this the first week of school or just after a long break to build community as kids love writing their names and seeing each other’s artwork. You can also do this whenever you need to teach/review 4 quadrant graphing.
  2. Writing your name in Desmos using horizontal and vertical line segments. I do this as we begin our unit on linear equations in 8th grade We do this in January and students write a 1-word New Year’s Resolution. You can see examples here and here. I teach them how to do restrictions for this project.
  3. Designing and creating a Pet House. I teach this project in the middle of our unit on linear equations when students are comfortable graphing equations of lines. They already know restrictions from project #2. I have also taught this project to 7th graders who don’t know equations of lines and they simply design their pet houses using only tables and polygons.

I hope these resources are useful and I and so many others are available to help you in your Desmos learning journey.

Here is my presentation from CMC-SOUTH on how I scaffold each of these projects which also includes some instruction on using the Desmos graphing calculator for art.

Humanizing the 2020 Election

I have been a math teacher for 22 years. And during that time, far too many times, I haven’t paused our regularly scheduled pacing guide to have deep conversations with my students about the world they are living in. Today I made sure to carve out that space.

Actually, I made the decision to carve out space on September 30. It started with Jess Lifshitz’s Tweet. Thank you Jess, for sharing such powerful books and pushing me to constantly think about humanizing my teaching.

Though I teach 8th grade and Jess teaches elementary school, I have purchased so many books that Jess has recommended from her classroom as kids are never too old to be reading and discussing themes from children’s’ books. When my copy arrived, I eagerly read and discussed it with my two (white) sons and was fascinated how it resonated with both my 6 and 11 year olds. I already felt so much uncertainty and fear around the election and knew that whoever won, a whole lot of uncertainty and fear would remain in my students’ lives. I decided then to read it the day after the election. I’ve been holding onto it for today.

In my class we have been talking for weeks about the importance of getting everyone they know to vote. How it doesn’t matter who you vote for, but we all deserve to be heard and all our voices matter. We did math earlier this week to understand the power of the electoral college system and why swing states ultimately decide the election. And we looked at various data visualizations to build understanding of the US population and how it impacts how states vote:

But today we needed no numbers, just our humanity.

Let me take a quick thematic detour here to say that this is the first read-aloud I have done this year. OMG, the neck craning one has to do on Zoom to be able to read a book aloud while holding it close enough to the camera for students’ to see the pictures is NO JOKE. K-5 Teachers doing 100% distance learning, my heart goes out to you. It is TOTALLY not as easy as these authors make it seem.

As I introduced the book I said that I had been saving it all year to read today, the day after the election. Long before we’d know who would win (and ironically even now we don’t know), I knew that the election season would bring up a lot of hatred and fear and that all of us would feel some anxiety about what comes next, especially as we’re living through this pandemic. I shared that a huge reason why I teach is because youth give me so much hope and I love that year after year I can build a trusting, caring space that doesn’t only revolve around doing mathematics together, knowing that when the year ends each and every student will go into the world shining bright. I shared that I hoped that through talking about our uncertainty from the election we’d all feel a bit closer to one another and I was confident that this closeness would also allow us to better support one another when doing math.

After reading the story aloud, I explained that we’d spend the next 10 minutes doing 3 things:

  1. Everyone would write in the chat what this story makes you think about.
  2. Everyone would spend time quietly reading other students’ comments in the chat, scrolling back to read at whatever pace they wanted.
  3. Everyone would respond to at least 2 other students’ comments using the @ symbol and addressing them by name.

What they wrote was endless, powerful, brilliant, and wise. Their words, their humanity and their care for one another is so apparent. I’m only sharing bits and pieces, a mash-up of all my classes, to protect all my students’ privacy.

  • I’m not a threat, I’m a child with a life.
  • Yeah, me too, it’s like when I go to synagogue and there’s security guards with guns.
  • I am so sorry! That is awful.
  • I think about that all the time, that if EVERYONE did little things to make the world a better place there could be so much change
  • I want to know more things I can do so that everyone feels safe wherever they go.
  • Climate Change is really scary for me and I don’t feel that enough adults are doing anything about it.
  • I hate being scared of existing in society. I’m upset that I have to be afraid.
  • I’m thinking a lot about racism.
  • Yes! You are entirely right. It is super messed up that people are killed and treated unfairly for who they are.
  • I’m glad my whole family voted.
  • I hate being scared of going out in public because I’m Black.

We will know the results of the election in the coming day or two. No matter who wins, our students are desperate for these conversations. May we always work to create the space and truly listen.

Distance Learning Tips from Berkeley’s Middle School Math Team

Several years ago I was named Berkeley’s Instructional Technology Coordinator.  As part of my work as a new administrator, I wanted to get to know teachers and teaching styles in my district as well as I could.  That first year, along with my DigiTech team of 3 others, we made over 700 classroom visits.  My biggest takeaway: there are SO MANY incredible teachers doing SO MANY incredibly varied things in their classrooms and we should showcase and learn from them as often as possible.  From then on, I was committed to the idea of encouraging teacher-leadership and teacher-led PD.  I have many mentors and collaborators within my district for this and am honored to work with each of them.  Two years ago, when I decided to return to the classroom, I made a promise to myself to continue this theme of supporting teacher-leadership and teacher-led professional development.

Screen Shot 2020-08-09 at 2.17.42 PMMy gratitude for The Berkeley Public School Fund runs deeper than words could ever express.  You can read about their extensive work on their web site, but I want to especially thank them for being such a powerful supporter of teacher-led initiatives and professional development.  For the past 2 summers, King Middle School teacher Geeta Makhija and I have received large grants to run middle school math summer institutes.  At both, our idea was to develop teacher leadership and strengthen our middle school math team’s collaboration.  Although our original grant was for an in-person summer institute to focus on middle school math intervention, we pivoted to organize a virtual institute focused on sharing & reflecting from distance learning in the spring and improving it for the fall.  We have 3 middle schools and around 25 middle school math teachers.  We offered everyone the opportunity to be paid to learn something new over the summer to improve distance learning and then present on it to our entire team.  Eleven teachers said yes and the presentations were incredible.  Our institute spanned 4 days and each day had presentations plus small group collaboration time to dig deeper into any one of the topics we had learned about that day.

I know I don’t have the time to carefully write up summaries of each of the presentations, so instead will share bullets of what I want to remember.  I don’t have permission to share each presenter’s slide show, so I removed the links, but here are the presenters and their topics.  I’m so incredibly proud of our team, the unique and powerful topics that each teacher took on for their summer learning.

    • Have a slide show template.  Students build a slide to show their work and record a Screencast explaining their thinking.  Cap the time they are allowed to record so that you are not listening to them for too too long.
    • Give students leveled choices using choice-boards for asynchronous work and a rubric for how you’ll evaluate that work.
  • DESMOS: Escape rooms are an incredibly fun way to do team-building activities.
  • HONORING BIPOC MATHEMATICIANS: I blogged about it here.
  • IXL:
    • Explicitly teach students how to learn from an example so that when they get something wrong and an explanation pops up, they have learned what to do with that.
    • If you use the diagnostic, don’t give it all at once.  Spread it out over several days and teach students how to find and click “I don’t know this yet” when they honestly have no idea how to do a problem.
    • Explicitly teach students how to go back and forth between their Zoom screen and their Pear Deck screen.
    • Use for Quick Writes & journal responses.
    • You can run a lesson synchronously one day, then create a new link to have it available asynchronously for students who were absent.
    • Use different types of mood meters to address how students are feeling, socially/emotionally on different days.
  • 3-ACT TASKS:
    • When showing an image and you want students to think of a story to describe what may have happened, have them use the chat.  Call out students names and highlight stories as they go.
    • Have students use the @ button to reply to comment on others’ stories in the chat.
  • ZOOM:
    • Use a sand timer when putting students into breakout rooms.  Show them the timer and say you’ll flip it when you click to have them zapped into breakout rooms and will call them back when the sand runs out.  Use the sand timer for short ‘turn and talk’ type situations.
    • Connecting a document camera means you can have a permanent writing surface without having to rely on Apple Pencil/iPad.
    • If you can get physical white boards into kids’ homes, they can show work and hold it up to camera.  Very easy to see it.  Trying to see kids’ written work on paper over the camera is nearly impossible.
    • Berkeley Everett’s web site Math Visuals  is a great one for Zoom-led number talks.
    • Kids on Chromebooks cannot rename themselves, so be ready to do this as the teacher/host when a kid’s Zoom name isn’t their real name (as often happens when signing in on a family member’s device).  Host can change a students’ screen name by going to participants->More
    • All students (and teacher) can add pronouns to their name by going into Zoom settings and editing their Profile.  Your pronouns will then permanently show up on any Zoom session alongside your name.
    • “Leave Computer Audio” turns off all Zoom audio.  Great to use when you are giving quiet work time to kids while they are on Zoom.  A kid can turn that on when they want quiet work time and off when they want to come back onto audio to ask teacher a question.  But that way, others won’t have to listen to the questions.  It’s found by clicking the arrow next to the microphone/audio button.
    • In breakout room settings you can set it to have a countdown timer broadcast into the screen in breakout rooms so participants always know how much time is left.

I hope these tips are as helpful to you as they were to me.  I wish I had time to write up a full summary of all 11 presentations, but this is the best I can do for now.  Our math institute was far more powerful than a list of bullet points.  There were several times when teachers were brought to tears by the incredible depth of diverse knowledge and strengths among our team.  We learn SO MUCH from one another and have such profound respect for one another.  Our teaching styles and strengths differ from one another, yet we also have so much in common.

And a huge thanks to Geeta Makhija, who wrote this year’s grant and didn’t let me walk away at times this spring when I wasn’t sure I could hang on to the work any longer.  Her unrelenting confidence in our ability to make this dream a reality in the midst of all the uncertainty about this coming school year (and us both having very young kids at home) is something I will always be grateful for.   The Berkeley Unified School District’s Middle School Math team is truly remarkable.








Celebrating Blackness and Mathematicians of Color

Before I share how and why I celebrate Blackness and the Achievement BIPOC Mathematicians in my classroom, take a few minutes to watch this video of Alexis Scott, an electrical engineer.

After watching this video, think about your reaction to the clip or what Professor Scott’s have to do with us as math teachers.  When I asked the middle school math teachers in my district to share their reactions (in the chat on Zoom since that’s where we live for professional development nowadays), they wrote things like:

  • I wonder if staff members at my school feel like this?
  • I am angry.
  • I worry this is how families of my students feel when they come to my school.
  • This makes me so profoundly sad.
  • Do I perpetuate this feeling in my classroom?

I shared this video to help explain how my commitment to celebrating BIPOC mathematicians has evolved over the past few years.

I first started thinking about this after reading high school math teacher Annie Perkins’s blog post and resources around mathematicians are not just white dudes.  Soon thereafter I discovered Math-Teacher Educator Dr. Kristopher Childs’ slides on Black Mathematicians and Latinex in Stem and the website Mathematically Gifted and Black.

Screen Shot 2020-08-07 at 11.00.22 PMIn February, for Black History Month, I would use the last 5 minutes of class twice a week to feature a Black Mathematician on a slide.  As a class we’d read the information, then I’d ask students what fascinated them about this person and/or what questions they had.  We’d use our final minutes to Google the answers to their questions.  At the end of February I made a bulletin board with the printed copies of those slides.

However, over the past year, my thinking on WHY it’s important to feature BIPOC mathematicians in my classroom has evolved.  It’s not just my BIPOC students who need to see themselves reflected in the successes of professionals in STEAM fields.  My white students need to know of their incredible accomplishments as well.  As Professor Scott so poignantly reminds us in her Ted Talk,  BIPOC mathematicians are constantly made to feel invisible by people not believing they have accomplished all that they have.  And I want to do everything in my power to ensure that this eraser does not get perpetuated in my classroom.  My hope (which my students know well) is that they never make assumptions of who can or cannot be successful in their math and science classes and that my job as their teacher is to make each and every one of them believe that they belong, not just in my math class, but any math class.

So now I do the work of celebrating the accomplishments of BIPOC in STEAM fields all year long,  I aim for once a week during the last 5-7 minutes of class.

Here are a few examples of how this can be done.

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Take a moment and think to yourself: what you notice and wonder about this photograph.

When I asked our middle school math team (again in the chat on Zoom), their responses included:

  • I wonder if her earrings have great significance to her.  They are striking and beautiful
  • Her posture shows her pride.
  • She is wearing a lab coat from Harvard Medical School.
  • She looks like she knows something we don’t.
  • Her eyes tell 1000 words.

I then gave teachers 3 minutes to read this article about Lash Nolan, the first Black President of Harvard Law School.  I let everyone know ahead of time that 3 minutes wouldn’t be long enough to read the entire article, so not to worry.  The goal was just to learn a bit more about her.  Afterwards, I again asked them to use the chat, this tine writing something they would remember about Ms. Nolan.

As a final example, I showed teachers this video of Mimi Aung, a Burmese-American engineer at NASA’s jet propulsion laboratory.

Again using the Zoom chat, I asked teachers to share what interested them about Ms. Aung’s work or what questions they have about her work.

Several teachers asked factual questions which we were quickly able to answer through a Google search.  However the majority of comments focused on a central theme: what microagressions does she endure working with what appears to be exclusively men and nearly exclusively white men?

You could share any of these photos, articles or videos similarly to this.  And the conversation you have with students can be as brief or extended as you have time for on any given day.  Now that I have these conversations weekly, I know that some weeks we will go deeper into issues that arise and other weeks we won’t have time.  But over the course of the year, these conversations becomes an integral part of my math classroom and are used explore how ALL my students define a mathematician or someone working in STEAM.

I am happy to share my resource list of texts and videos with one request: that you will email or send me a Tweet as you discover more resources I can add.  This list allows me to do this work over the course of a school year, but honestly barely scratches the surface of the incredible work in STEAM fields happening by the BIPOC community.  I treasure your feedback.   The resource list is below:

Celebrating BIPOC and Women professionals in STEAM



Compliance vs. Actual Communication


Know Better. Do Better.

I have read this in various forms on Twitter threads and it’s a notion often shared by my district’s PD Coordinator whom I greatly admire.

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In his talk, How to Overcome Microwave Equity in the Leading Equity Summit’s Virtual Conference, Cornelius Minor adds a nuanced lens to this idea.  When asked what he wishes he had known when he began his career as an educator, he replies, “Instead of what I wish I’d known, I think about what I wish I’d listened to.”

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How often have we felt that we needed to hear a new idea several times before it actually sinks in or before we actually believe it? I know at times I have felt this sentiment.  I feel challenged now, more than ever, to check myself.  Am I actually listening?  Especially when what am being told pushes or challenges my own beliefs or ways of seeing the world.

But he didn’t stop there.  What REALLY sticks with me is his challenge to educators to broaden what forms of communication we listen to.

“Everything that a child does is a form of communication.  Our first missteps are that we assume that all of those messages are going to come verbally or in a written form.”

As a teacher, I feel I always listen when kids come to talk to me about something.  And I often begin class with some quiet writing time where I’ve asked questions to check in with how they are doing, or to reflect on some aspect of my class.  Check.  Done.

But what if we open our eyes to this notion that every aspect of a student’s’ behavior is a form of communication with us.  What happens when we deeply listen there too?

“The way a child walks into the room; the way that a child wear’s their hoodie; the way they respond to my requests.  All of those things are forms of communication.  And if I am not paying attention to those things, I am missing the message…A student’s behavior is a form of communication.”

What if instead of being frustrated that kid #1 takes off his hood before entering class and kid #2 always wears it and then refuses to take it off when I ask him to, I instead spent time reflecting on what each of those students is communicating with me and built my relationship with each kid around learning more about that?

We are challenged to constantly ask ourselves,

“What is the difference between compliance and actual communication?” 

He explains that we have to intentionally work towards decentralizing power because,

“No kid is going to tell me their truth if I am holding all the power.”

Finally, a call to action to each of us:

“What messages do we communicate to students through our affective responses to them?  Often we articulate words that say we value kids, but then engage in behaviors that do the opposite.  WE must work to ensure that our words are in alignment with our actions.”

This notion that often, unknowingly, our words our not in alignment with our actions reminds me of the notion of “discretionary spaces” which Deborah Lowenberg Ball and Amber T Willis discussed at CMC-North this year in their talk, “(How) Can Mathematics Teaching Disrupt Racism and Oppression.”

Though a detailed analysis of student/teacher/class interactions, they show how any of our common “best” practices as teacher, whole class discussions, calling on students to show their thinking at the board, etc., will can reproduce patterns of racism and marginalization unless we are constantly and consistently reflecting on the impact of our words and affective responses to students-not just the one who is speaking, but everyone else as well.  In this whole class discussion there were 59 student/student/teacher interactions in just over 2 minutes.

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As educators are we thinking constantly and intentionally about status, student agency, and the spoken and unspoken messages students are communicating with us (and to each other) in each of these countless discretionary spaces?

As I return to the classroom for the first time in 2020, I enter with a new definition of what it means to deeply listen to my students.  This quote, engraved in the National Museum of African-American History and Culture in Washington DC, applies to changes large and small that I hope to make this year as an educator.  I hope you will each question and challenge me and hold me accountable as this new year marches on.

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Fa-La-La: Pre-Winter Break Math

The week leading up to winter break for a middle school teacher is a unique mix of giddy, feisty, whining, forgetful, happy, flirtatious and most of all exhausted teens.  Oh yeah, and lots of absent ones who left early for holiday travels or trips back home to see family in other countries.  Every year I seem to make different choices about how much to embrace this perfect storm of challenging teaching and how much to ignore the reality and just carry on.  This year I decided I wanted our last two days of school to feel as joyful as possible so that everyone would leave simply loving the beauty of math.

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But how to achieve that elusive goal?  I tried my luck at a Twitter post.

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I owe a huge thank you to everyone who responded.  If you are looking for art projects suitable for both 8th Grade Math and Math 1, click here to see the incredible ideas gathered from my post.  And most certainly click if you are looking for art projects for yourself or your family for winter break.  Since posting my request, I have done nearly every one of the recommended projects at home with my kids and have a few more we’ll try over winter break.

I chose to do Susan Russo’s (@Dsrussosusan) Kaleidoscope Project because it was the one which literally made me squeal in delight when she shared it with me.

Since I wasn’t sure all my students would know what a Kaleidoscope was, I started with this video from inside the world’s largest, located on a resort in upstate NY.  I showed 10-15 seconds, then paused it and asked students what they noticed and wondered.  They talked about repeating shapes, wondered how it was made, or if mirrors are involved, and how the video was taken from inside it.  We played and paused a few times, to see it through various iterations.  After the video I mentioned a few fun facts from this travel web site.

Building a model in GeoGebra requires both a general understanding of reflection and also what y=x and y=-x looks like.  We haven’t yet studied linear equations, so wanted to do a brief introduction.  Using this graph in Desmos,  I asked table groups to come up with as many points as they could which would be graphed by each equation.  After graphing their coordinate pairs, I had them predict what the graph would look like.  I then turned each graph on.

We were then ready for GeoGebra. My students had used GeoGebra a few times during our transformation unit, so they were already comfortable with how to create rigid motions.  Creating a Kaleidoscope is surprisingly simple.  Using both axis plus y=x and y=-x, you add a single point, then reflect it 7 times over both ends of each lines.  Once you have 8 points, they all move in unison since they were created as reflections from point A.  To create the drawing effect, you highlight all 8 points and turn on the trace tool (through settings)

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Some students were satisfied with a single color (which is easy to change by highlighting  points and changing their color).  However helping them understanding dynamic colors became quite thrilling.

The idea of dynamic colors is that the color changes depending on how far the points are from (0,0).  To do this, you add (0,0) to your graph, then add a segment between point A and (0,0).  Once again, select all the points, then right click and open settings.  Choose the advanced tab and play around with values for red, green and blue using multiples of your segment length (called h in my graph).

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Students played around for a LONG TIME with both colors and drawing and redrawing designs in their kaleidoscopes.  I simply let them explore and run around the room checking out each other’s designs.  Eventually, I asked that they choose a design they wanted to use for a permanent display.  I had them take a series of screenshots of their design as it morphed and grew.  They used to create gifs with their screenshots.  ***I learned that having students make their own accounts in gify is a nightmare so I eventually just signed everyone into my account which was far easier as now I have all their work in 1 place.  I also (thankfully) learned that lots of people can be logged into a single gify account at once, all creating and saving gifs. ***


They’re each so proud of their gifs and I cycled them together into a slide show which will play on the monitor in our school’s hallway when we return from break.  And with that, I’m good and ready for vacation!

13 Seconds of Mathematical Bliss

Got 13 seconds?   Good.  Watch this.

I used this silent video today for a stand and talk as part of 8th grade rigid motions.  I asked if anyone knew what the sum of the angles of a triangle are.  Maybe 1/4 of the class raised their hands and knew it’s 180 degrees.  I said that there are a lot of things we know in math, but often we don’t ask why.  I asked if anyone knew why the angles add to 180.  Crickets.

Before we had any conversation, I showed the above video 3 times in a row.  Students ooed and awed.  Some busily started talking to a neighbor, bouncing up and down with, “I get it, I get it.”

Then we broke it down into a whole series of pair-shares.

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“What do you assume is true here?

They concluded that L1 and L2 are meant to be parallel.  I threw a few extra points on the image, at each intersection point, telling them that these points would help them describe what they saw with more mathematical precision.

Screen Shot 2019-09-30 at 8.53.05 PMI then paused here and pairs described everything they had seen.  Students talked about corresponding angles, congruent angles, translating an angle along a vector.


We repeated the process pausing here and again here:

The rich mathematical language this 13 seconds of video evoked was so exciting to witness.  It felt like nearly everything they had learned over the past two weeks of rigid motions was giddily talked about.

Are you a math coach?  A technology TOSA?  Or someone who loves having students talk about visualizations?  If so, I so want more of these gems.  For the second year in a row, I am teaching a new grade level, so I don’t have a whole lot of time to seek them out as I can barely keep up with tomorrow’s content, so I am selfishly blogging in hopes that some of you will send me more of these resources connected to my course (8th grade math) or any course before mine.



Informal to Formal: Building Confidence

I teach a math support class (called Math Studio in my school) which is a second period of math for a small group of students.  For me, there is a magic one can create in this class.  With just the right amount of preview and scaffolding in math support, students arrive in regular math class later in the day ready to shine.  And many have never felt that shine in math class before, so it’s incredibly rewarding for me to watch and for them to experience.

Next week we begin our 8th grade unit on transformational geometry and today in Math Studio we developed an informal understanding of various transformations, going especially deeper on translations.

First, students did Shifting Shapes, a relatively new Desmos activity which provides a visual and conceptual look into rigid and non rigid motion.  They are given a square with draggable vertices and asked to make their own shape.  In subsequent slides their shape undergoes various transformations which they are asked to describe in words.

Here is an example of one student’s shape (original in grey).

I so love both the informal and formal language they used to describe it:

“It went woop and to the side”

“It did a backflip”

“My shape rotated”

“It was turned sideways.”

Here is a second transformation (from a subsequent slide–again grey is original and red is after the transformations)

Students descriptions are again quite elegant:

“It went smaller then to the left”

“It got small then ran away”

“The shape got smaller then moved to the side”

I have to admit, I LOVED the idea that a translation is when a shape runs away from itself.  I ended up naming this idea after the student who said it and for the rest of the period, when we talked about translations, we talked about it being a slide, but also it running away from itself.  I’m smiling thinking about this idea as I type this.

While Shifting Shapes was a great, quick way to get some informal language out about transformations, I then went deeper into the mechanics of translations.  Again, I wanted to spend time looking at them informally first.

Using GeoGebra, I drew a polygon and a vector. Screen Shot 2019-08-29 at 10.55.17 AM Students then talked about what they saw and made predictions of what the arrow on the vector meant.  I explained that a translation was the same as the shape ‘running away” and the vector showed the direction and distance that it would ‘run’ (or slide).

Screen Shot 2019-08-29 at 3.51.29 PMWith this drawing on my LCD, I gave students 2-3 minutes to go to a vertical white board, draw the original shape, then draw their prediction of where the translated image would be.

They then came back to their seats where I showed in GeoGebra what the translated figure landed, and we discussed their drawings.  At first, their drawings had the translated image in the right general area, but they were considering only the direction of the vector, not distance.  I had them predict where the end of the vector would be if I moved the beginning of it to A.  I modeled this on several vertices as we discussed, like this:

We did this back and forth between vertical white boards and watching GeoGebra about 5 times with different figures and vectors.  By the end, maybe 15 minutes later, nearly every student could accurately draw the translation, label its vertices with A’, B’, etc, and explain whether the translated figure would overlap the original one or not.

I am hoping this deep conceptual dive, rich with visual models and lots of time to both practice and refine ideas will provide the scaffolding my Math Studio students need to feel confident and skilled when we cover this concepts in 8th Grade math beginning on Tuesday.  By no means will I eliminate the visual models in my regular math classes, but the reality is that we’ll move to the informal a bit more quickly and with a few less examples.  This blend of GeoGebra and Desmos within a single lesson felt seamless to me as the 8th grade Common Core transitional geometry work blends so well with the strengths of each of these tech tools.