What is equity? The Danger of a Single Story.

As a Desmos Fellow, we’re asked weekly prompts as a way to get to know one another and dig more deeply into the mathematics we’re doing in our classrooms.  Last week when asked what our goals are for this coming year, I wrote:

“This year I hope to reflect a lot on teacher leadership and how to take what I have learned from 5 years of being an administrator into the classroom. I am deeply committed to equity and want to be better able to define what that means to me as a teacher leader.”

Yes, as I start my 20th year as a (white) urban, public school educator, my goal is to better define what equity means to me.  Over the past 5 years away from the classroom I have coached many teachers on related issues.  Now that I am returning to the classroom, this work becomes even more personal.   If asked what equity means to you as an educator, could you easily define it? I’m always surprised that it’s harder than I think.

Screen Shot 2018-07-26 at 8.36.20 AMMy working definition is that every child gets what they need every day.  I didn’t make this definition up myself, but really liked it when I heard it as part of district-wide coaching for equity work we did with Elena Aguilar’s team last year.  If pushed further I would talk about ending predictability in learning and student achievement by race, class, sexual orientation and other factors.  A more nuanced view of equity for me, also from Elena Aguilar is that equity involves what you see, where you look, who you listen to, and the self-awareness that you develop.

And yet,  I have a deep, deep fear that while we each could craft a public response to the question of what is equity, privately, inside of our minds, our definition is affected not only by our race but by the race of students who struggle at our schools.  This makes sense to some degree.  However, I want to admit some issues which give me pause and challenge us all to consider this notion of the power of a single story and how it might affect our teaching.

Chimamanda Adichie, Nigerian author of Americanah among many others, has an incredible Ted Talk entitled, The Danger of the Single Story.  If you have 20 minutes now, stop reading this blog immediately and go watch it.  If not, carve out time as soon as you can.

“Show a people as one thing, as only one thing, over and over again, and that is what they become… The single story creates stereotypes and the problem with stereotypes is not that they are untrue, but that they are incomplete. They make one story become the only story…The consequence of the single story is that it robs people of dignity.  It emphasizes how we are different instead of how we are similar.”

In my district, there is a huge achievement gap between white students and students of color, however the largest gap is between white and black students.  We talk about why and new programs and job positions are launched constantly to address these inequalities in outcomes.

As a white educator, if pressed, if really, really, really pressed, do I simply believe that equity in my district means getting black students to behave well?  To be on grade level?  I will admit that I have had moments when these thoughts creep into my mind.  I KNOW equity means a whole lot more to me, and yet, these thoughts have existed in my sub-conscious which illuminate the danger of the single story.

To repeat Adichie’s words, “The single story creates stereotypes and the problem with stereotypes is not that they are untrue, but that they are incomplete.”  

For example, when a colleague comes up to ask my advice on a struggling student whom I don’t know, do I immediately have an idea of the race of that student?  Developing the self-awareness, as Elena Aguilar discusses, to consciously NOT do this feels like a critical aspect of avoiding the danger of a single story.

The achievement gap between white and black students in my district is a deeply troubling issue with no one program, recommendation or ‘thing’ that will resolve it.  All of the work we do as a district should be rooted in understanding the complex web of issues at play and finding ways to measure the impact of the numerous programs we put into place to attempt to overcome this.  And yet, my fear is that in doing so, we have created a single story, that black kids struggle in our schools.  And while many do, I fear that it makes us look at black kids differently than white kids before we have ever taken the time to get to know them.  And if we look at them differently, we start to treat them differently because we believe we already know how their story in our schools will end.

I have no definite answers here and would love to explore this further with anyone who wants to.  But as I wrote in my goals to my Desmos Fellows colleagues, “…I am deeply committed to equity and want to be better able to define what that means to me as a teacher leader.”  I hope to be very intentional of what I see, where I look, and who I listen to so that I can continue to develop my own self-awareness and not allow a single story to define students.





TMC18 My Favorites: Making Relationships STICK

Blog revival!   On my honor, I will try, to prioritize my family, my work, my own professional development AND blog with more regularity.

My first TMC is in the books.  Twitter Math Camp, for those who are not yet a part of this fabulous community of math educators.  I hope to write a longer series of posts on how I learned and grew during these 5 days in Cleveland, but let me get this first post published before I start making grandiose plans for future posts.

One of my favorite parts of TMC was the time each day when we shared “My Favorites.”  So often, just hearing 5-10 minutes of a great idea was all the spark I needed to take an idea and run with it.  Mid-way through TMC I realized that I would really enjoy sharing one of my very favorite classroom management strategies…stickers.  It all started in 2012 when I read Sam Shah’s blog post on customized stickers.   WHAT A BRILLIANT IDEA!  I found an online coupon and ordered up stickers, notepads and postcards for positive notes home, stealing many of Sam’s phrases from his stickers.

After I gave my favorite no, many of you asked to have copies of the stickers I use and to hear more about how I use them.  You are welcome to steal any of the phrases, and better yet, make up your own and share them with me as I need to spice up my deck this year.

There are four themes to my stickers: Individual Positive Recognition, Positive Group recognition, Growth Mindset, and Redirection for off-task behavior.  Using these stickers, for me, is an equity strategy.  While there are many facets to my classroom management, a few key core values are represented through how I use these stickers.

  1. I work very, very hard to never say aloud, in front of the whole class, the name of a kid who is off task.  I do a whole lot to support those students to re-engage, and am quite strict with my expectations and consequences.  However I believe that as much as possible, we should say students’ names in front of the class only for positive things.  One aspect of the district-wide equity work we have done is understanding what it means to be a ‘warm demander’ as developed in Dr. Lisa Delpit’s book Multiplication is for White People.  This aspect of how I use stickers is one, of many ways I have interpreted this idea as I continue to understand this notion more deeply.
  2. I know that students need space when they are upset about grades or not doing well on an assignment from class.  I am always there to support and help them, yet recognize that teens are often not ready for this the very minute they receive the bad news.
  3. I try to stay very aware of status issues in my classroom and especially like to use the positive stickers for students who need that positive recognition and may not be getting it publicly or from their peers.  I most often use the positive stickers for students who have struggled and persevered or those who started class irritated at something and turned things around.
  4. As I mentioned when I did My Favorites at TMC, I always hand out these stickers by silently walking over to a student (or a group of students), sticking one on the outside of their hand, and walking away.  It may be followed by a squeeze of the shoulder or making eye contact as I walk away, and I may pull them aside later for a hug, or a private conversation.  However in the moment, whether I am beaming with pride or really frustrated at how off task they are, my demeanor is the same and I simply stick the sticker on their hand.
  5. THEY LOVE THEM!!  THEY COME AFTER CLASS AND BEG FOR MORE.  EVEN SENIORS IN HIGH SCHOOL.  I try to keep them on their toes, never knowing what other phrases I have stashed away.  So I use these sparingly, and NEVER when someone asks to get one.
  6. I made them on VistaPrint and it’s really easy to find coupons online.  If you make-em, share them with me including what you learn by using them.  Screenshots of them all are below.


group work

growth mindsetredirection

notepad and post card


A Tale of 2 Tweets

Earlier this week Eli Luberoff, Founder and CEO of Desmos, Tweeted to inquire how various Tech. Tools are used to support English Language Learners:Screen Shot 2017-12-18 at 8.54.02 PM

Although I’m not working directly with English Language Learners, I spent nearly the first decade of my career as a Spanish bilingual elementary school teacher and try to bring that lens to much of the professional development work I currently do.  While I had a lot I wanted to discuss around technology integration and supporting English Language Learners, I was at work when I read Eli’s post and threw out something quick:

Screen Shot 2017-12-18 at 8.55.23 PM

As soon as I hit Tweet, I regretted it.  Such a stock, somewhat thoughtless answer to someone who I knew was looking for more nuanced reflections.  Yes, both those tools are helpful, but successfully using any tool to scaffold and support the learning of English Language learners is far more complicated than this.


Fast forward a week: Monday, first day of winter break.  I take my 8-year-old son to my favorite homemade doughnut and coffee spot to hang out and play with one of my favorite weekend books: Anna Weltman’s  This is Not A Math Book.   (@annaweltman)

As we always do, I let him peruse the pages until he finds a set of imagery that appeals to him.  He chose this page and we spent the next while doodling.  We started on the same paper, taking turns building a drawing together, almost like a game of dots, but with doodles instead of closing boxes and gathering points.  He then grabbed his own paper, incorporating these mathematical sketches into his own artwork.


And then I had an ah-had moment.  We were doodling from Anna’s book, however THERE IS A DESMOS ACTIVITY which connects these doodles to formal, mathematical language:

Screen Shot 2017-12-18 at 9.35.27 PM

Heck.  There, in the center of Desmos’ introductory icon is the pinwheel my son had so gleefully turned into a flag in the hand of his creature.  It was a reminder of the power of informal before formal.  Language, reasoning, analysis…when first given opportunities for informal use, students are far more able to delve deeper into its formal use.  And while this pedagogical principle is a part of all good mathematical teaching, it’s especially important for English Language Learners and other students who may initially have difficulty accessing the more formal, vocabulary-rich language of mathematics.

So thank-you Anna for mathematical fodder during a lovely morning of doughnuts and coffee and for helping me move beyond my stock response about how Desmos can be a powerful tool for supporting the learning of English Language Learners.

Technology PD for our Subs

Last year around this time I blogged about using Robert Kaplinsky’s Sheep and Dogs in the flock problem as the opener for my session for our district’s substitute teachers on transitions to CCSS math.

District-wide our substitute teachers are invited to a full day of professional development each August.  I absolutely love leading a session as I believe being a sub is among the hardest and least appreciated work within a school district.  I love being able to personally thank them for the work they do as so often they never meet the teachers for whom they work.  Each year I learn of several subs in the group who have subbed for me in the past or who have subbed for my son’s elementary class and it’s always a really fun discovery.

This year I was asked to focus my session on ways teachers are using technology in the classroom and how subs can improve their classroom management when sub plans call for students to be using their Chromebooks.  I co-led the session with my fabulous TSA for Instructional Technology, Mia Gittlen, and we used Pear Deck as the basis for our presentation.  We all had so much fun!


If you aren’t familiar with Pear Deck, it’s an interactive software which allows participants to respond to questions posed during a presentation and their collective thinking is displayed.

Screen Shot 2017-08-26 at 10.01.18 PM.pngAfter some fun warm up questions, we asked them what their level of confidence is with technology.  These responses are from our first group of  teachers. Interestingly, our second group’s level of confidence was far more scared and confused.

screen-shot-2017-08-26-at-10-05-45-pm.pngAmong both groups, when asked how often sub plans expect them to use technology, the vast majority said sometimes and very few said never.  To me, this was the most surprising slide.  As the Instructional Technology Coordinator, it also made me quite happy that our classroom teachers have strong enough systems in place for students’ using Chromebooks that they frequently trust its use when they are out.

I love that students are doing research when they have a sub:


However ultimately, the biggest crowd pleaser was teaching tools one can use for classroom management.  The substitute teachers loved learning about the button that allows them to see all open windows on a students’ Chromebook.  Students occasionally use a keystroke to make their screen appear sideways and use it as an excuse for not being able to do work or to have to share a Chromebook with a friend.  Knowing how to undo this felt really powerful for the subs, especially those who were initially fearful of using technology when subbing.  I loved the feeling in the room as many who were VERY new to technology giggled with one another, trying out their new tools and tricks.

And having a district subscription to Pear Deck which long term subs can use was super exciting for the more techy ones of the bunch.  Pear Deck was obviously completely new to them all and they absolutely loved it and wanted more training on how to use it.  Such a successful session!Screen Shot 2017-08-26 at 10.12.29 PM

Finally, I saw this posted on Twitter this evening...about a Louisiana Senator who substitute teaches during his time off.  It’s worth bearing through the initial advertisement to watch this segment.  Wish more people felt the way he does about the work of teachers…

First Day Plans ->GOALS

What are the first day plans of this second-year administrator?  I am a big fan of writing down what I want to accomplish for the following day before leaving work each day.  So, on my last day of work in June, I wrote down what I needed to get done on my first day back.
Screen Shot 2017-08-06 at 9.55.05 PM

EVERYTHING on this list is an administrative/bureaucratic task.  And while this is actually not at all reflective of how I spend my time in a typical day, it’s a reminder of how easy it could be to fill my days with similar tasks.

Today, however, was my first day of work and I accomplished none of those tasks I placed on my calendar back in June.  Instead, I was at a Management Team retreat with all the administrators and managers in my district.  We reflected on and discussed our leadership styles in addition to district goals and our personal goals.  The highlight, however was this 3 minute video which I urge you to watch before beginning your own school year.

Which brings me to my goals.  I am in my second year of my role as Instructional Technology Coordinator for grades K-8 and my fifth year outside of the classroom.

  • Spend time every day either in a math classroom or doing math.  Working through all of the Desmos Activities which relate to middle school math is something which has helped me deepen my understanding of the connections between and progressions among concepts in these 3 grade levels.  The eight 8th grade math teachers at all 3 of our middle schools have all agreed to teach at least one Desmos Activity per week and I’d like to spend as much time as possible supporting them and teaching/modeling or co-teaching some of those lessons, especially for our new teachers.  Specifically, I want to spend enough time in all 8th grade classrooms to have qualitative and quantitative data around how student engagement and teachers’ ability to differentiate is affected by sustained, regular use of Desmos Activities which are aligned to our 8th grade curriculum.
  • Rethink and rework how I lead our department meetings.  In my district, Instructional Technology and Library and Media Services collaborate very closely as increasingly many of our Librarians and Library Media Specialists integrate teaching digital citizenship and online research ideas into their work with kids. Additionally, we have a strong integration of audio books into our readers’ workshop which is supported by our TSA Teacher-Librarians.  Often, our department meetings are spent reporting out on the work we’re each doing in classrooms and divvying up tasks which need to be completed for upcoming PDs we are leading.  Specifically, I want to begin the year by posting the names of all 3rd-8th grade teachers in our district (as those are the ones who have Chromebooks) and having us put a sticker next to each teacher we’ve provided classroom support for around technology integration.  I modified this idea from  Sara VanDerWerf’s  most recent post about how a school staff did this with their entire student body.
  • Collaboratively rework how my department provides classroom support.  Last year, the 5 of us in my department made nearly 600 classroom visits for observations with debriefs and/or teaching model lessons.  Spending such a large percentage of time in classrooms is rare for an administrator, but after watching the above 7-10 split video, I believe we can have a greater impact on instruction if we focus our efforts.  I’d like each of us to specialize in technology integration around specific student needs (of the 7-10 split): Special Ed. students, English Language Learners, Newcomers, Students needing additional challenges beyond the day-to-day curriculum, etc. etc.  In doing so, we can provide more targeted classroom support for technology integration.
  • Better support teachers to use student achievement data generated by software to differentiate in more powerful ways.  Using tech provides so much data. A single Desmos lesson collects tons of student responses.  Most teachers use a lot of tech tools, but rarely carve out time to use the data generated by those tools.  I want my team to learn to look at and use this data more efficiently to better support teachers to do this during our PD time with them.

I’m curious how others see their 7-10 split and how we can each adjust our teaching to better meet the needs of all of our students.  In the meantime, my 8-year-old LOVES bowling and we’ve learned that nation-wide, kids bowl free, once a week from April through August.  You’ve got 2 more weeks…For real!

Screen Shot 2017-08-11 at 9.55.21 PM

44 Reflects on 17

Recently, as seems to happen about once a year, a conversation or two, probably more, threads the needle of Twitter about online math community aka #mtbos.  I remember it first happening here  and here in 2013.  These conversations are healthy and rich.

Each time this thread reappears, I am overwhelmed with the desire to say thanks.

In the summer of 2011, with generous funding from Math For America, I headed to the Park City Math Institute with my husband, our two mountain bikes, my then 13-year-old step-daughter and 2-year-old son, and our Bernese mountain dog.  Though I enjoyed endlessly fun family time, the real gift was discovering myself as someone who was good at math and welcomed into a community of smart, funny, creative, serious and goofy mathy folks.  At the time I was a middle school math teacher ( I really think I snuck in the back door when I got my single subject credential), it was the first time in two decades that I had studied math.

When I was a kid, I was really good at learning math facts.   In 2nd grade I was literally kicked out of class for being too good at my times tables, forced to memorize my 13s-25s when the teacher ran out of work for me to do.  In 3rd grade I got moved to a 4th grade class and in 5th grade I walked to our local middle school to take pre-algebra with 8th graders.  I took Algebra 1 in 6th grade, BC calculus as a sophomore, followed by MV Calc and Linear Algebra.  Throughout much of this I had the most amazing teacher, John Benson, who used Mathematica in the late 1980s better than most use Desmos in the late-2010s and who never stopped believing in me, even when I had given up on myself.

But give up on myself I did.  Senior year of high school, I promised myself that as soon as I got to college, I would never take another math class.  Sadly, I kept that promise for nearly 20 years.

I had gotten to a point where I could do a whole lot, but understood very little of it.  And I hated, really, truly hated, being seen as a math nerd.  There were maybe 16 of us in my MV Calc class and 4 of us in my Independent Study Linear Algebra class.  My memories (which are probably not entirely accurate) are of me, being the only girl, with a bunch of pimply, nerdy boys who were extremely competitive, quick at math, and uninterested in slowing down for me who needed to carefully draw, model and see every new idea.  I desperately needed Jo Boaler to whisper in my ear when I left for college, but thankfully I found her as an adult.

Although I occasionally get glimpses of this stereotype in my adult life, it’s pretty darn rare.  Starting in Park City and again when I did Math For America and again now within the #mtbos community, I have found my people.  And chances are, like me, you were a nerdy math kid.  But somehow you persisted when I did not and I am so thankful to have found you.  In Park City, among many others, I met Kate and Ashli,  Sam and Tina along with the wise teaching of Bill and Darryl and Cal.  And now, as a Desmos Fellow, I feel so lucky to be surrounded by such creative, silly, brilliant people like Suzanne and Jenn (and so many others!) who do the creative work I wish I had been encouraged to do when I was 17.  THIS is the math I would have loved at 17 and THESE are the people I wish I knew then.  Thankfully, I’ve found them now along with so many more.

Desmos Potluck for Lunch

One of the endless new ideas I have gleaned from being a Desmos Fellow is that of a Mathematical Potluck.  I’ll let Shelly explain…

Screen Shot 2017-04-15 at 3.08.09 PM

Fellows post graphs of a new calculator idea they’re tinkering with and we collaboratively try to recreate it, learn from it, chat about it, etc.  The conversations we have on Slack are pretty amazing and I have been really fascinated at how much math one can learn simply from playing with other people’s creations.

I’m surprised it took me this long, but after 7 months of Desmos Fellow potlucks it finally dawned on me that I should be creating this same learning environment with my own students.  My teaching of students nowadays comes in fits and starts, but one consistent source is a weekly class at UC Berkeley.  It’s a Cal-Teach intro course on math and science pedagogy for undergrad math/science majors who are considering getting their teaching credentials.  The course is just 2 units, meets just once a week, and touches on everything from equity to teaching English Language Learnings to learning to lesson plan to pedagogical content knowledge to integrating instructional technology.  So I share my potluck with the caveat that our time to develop Desmos calculator skills and ideas is a bit fleeting.

However, I found hosting a Desmos potluck to be an incredible way to build mathematical ideas while also building a sense of community among students in my class.  In class we briefly played around with the calculator and I purposefully left their homework very open-ended:

Screen Shot 2017-04-15 at 3.22.44 PM

The next week in class as our warm up, I had them look at all the submissions, choose one which interested them for any reason, play around with it and try to recreate it or use ideas from it to inspire something new.  I encouraged them to walk around the room and speak to the author of the item if it had mathematical features they wanted to know more about or aesthetic features that they hadn’t yet discovered.    Their homework was to continue their potluck contribution:Screen Shot 2017-04-15 at 3.26.25 PM

As mathematically fun as the potluck structure was, what was most exciting to me was seeing their beaming faces and the pleasant surprise of so many students to learn that others had found inspiration in their graphs.  For example, here is Danielle’s original graph:

Danielle’s work inspired multiple potluck contributions including Aubrianne’s contribution: “I was inspired by Danielle’s graph and played with using multiple variable coordinates on a polar graph and with variable shading.”

Meanwhile, Aubrianne’s original contribution was this.

Which also inspired several graphs including Wes who explains, “I was inspired by Aubrianne’s graph. I enjoyed how hypnotizing it was and wanted to create something similar. I tinkered with parametric functions and element lists in desmos. It was basically a lot of trial and error.”

If you’re interested in seeing more, The entire potluck is here.

I am currently helping to teach a 6th grade RTI math class and going to launch a Desmos potluck with them as well.  This notion that students should create something, and later realize that their ideas have inspired new ideas is such a powerful one and I’m looking forward to playing around with how to use this notion to deepen students’ learning of mathematics.