A Message for Every Teacher in 2020

As this year draws to a close, I want to thank each of you for all that you have done in the face of so many challenges.

You have learned to navigate new technology platforms and found ways to adapt your use of them to meet the needs of your students. You have taken every single lesson that you have ever taught and turned it on its head, recreating something that was already fabulous into something totally new and different. You have worked harder than ever at forming relationships with your students and building a community, knowing the loneliness and isolation that they have faced. You have spent countless hours reaching out to students and families to help your students be successful. You have worked tirelessly to make sure that your students have access to devices and broadband, to iron out technical difficulties that they have encountered. You have worked to make sure that your students have materials, creating countless Donors Choose projects to get your students books and manipulatives and all manner of other materials. You have worked to make sure that your students have food and clothing as their families have been hit by job losses. You have checked in on students and families who have become ill. You have been a steady, supportive anchor for kids who have faced such a challenging year.

While doing all of this, you have supported and mentored your colleagues. You have led professional development sessions for national organizations, for the district in which you work, and for your school. You have worked as Department Chairs and Instructional Council leadership to find the best way forward for your school. You have led Professional Learning Communities. You have shared your expertise on Twitter and in Blogs. You have shared lessons that you have created.

You have done all of this while also carrying the burdens that this pandemic has placed upon you and your own family.

Each and every one of you is amazing and I am so grateful to you for all that you have done this year.

My Pandemic Artifacts

A lifetime from now, my grandchildren will ask me or my children about this time.

My daughter who is a Doctor of Physical Therapy will tell them about being furloughed for five months because health care changed so much. She will tell them about the challenges of getting the clinical hours for her residency in orthopedic physical therapy while furloughed. She will tell them about the research that she did with Children’s Hospital of Philadelphia and Arcadia University. She will tell them about presenting her research for the first time virtually at a conference. She will tell them about returning to work and working 70-80 hours a week as she ran a clinic, worked as a research assistant, and graded for the university. She will tell them about not playing soccer for the first time in many, many years in order to stay safe. She will tell them about staying in Philadelphia alone for Thanksgiving and Christmas in order to keep herself, her patients, and her family safe.

My daughter who is a lawyer will tell them about the nurses who came to her because of the unsafe working conditions that they faced. She will tell them of the delivery drivers who came to her because of their working conditions. She will tell them about the trials that she did on Zoom and the hearings over which she presided virtually. She will tell them about the many, many masks that she sewed and sent to all of her Wellesley friends – the friends who are medical students or residents, the friends who are pilots in the Air Force serving around the world, the friends who are scientists and engineers, the friends who are in law school, the friends who are in grad school. She will tell them about the Zoom Happy Hours or teas that she had with her far-flung friends to replace the trips they had hoped to take together. She will tell them about having Zoom Thanksgiving and Christmas with us even though she lives 10 minutes from our house to make sure that there will be future Thanksgivings or Christamases together. She will tell them about the many, many times that she watched Harry Potter because it just felt comforting to go back to a different time.

I will tell them about turning on a dime and learning how to teach math virtually. I will tell them about Jamboards and Desmos and Google Meets and Breakout Rooms with my students. I will tell them about kids who were lonely and families who struggled. I will tell them about staff and students and families who became ill. I will tell them about watching all the Star Wars movies and The Mandalorian so that I could talk to my students about them. I will tell them about watching The Great British Baking Show in it’s entirety multiple times because the worst thing that could happen was that someone’s cake wasn’t quite right. I will tell them about resilience. I will tell them about learning to live in the moment, to not compare themselves or their circumstances to others or to compare what happens in these times to what happened in other times or what might have happened. I will tell them about the power of creating to quiet the mind and the soul. I will tell them about the hours that I spent in the evenings hand-quilting a Christmas quilt, about changing my plans for the quilting design because my eyes were just too tired after a day on-line to do the elaborate design I planned. I will tell them about the weekends that I spent making a cozy flannel quilt in the colors of the sea because comfort and calm was something that everyone needed. I will tell them about starting a bright and sunny pinwheel quilt when the vaccines began to be administered and give glimpses of hope for the spring and summer to come, even as we faced the hard days of winter. Then, I will give them the quilts that I have made, the quilts that tell some of my story during this pandemic, the quilts that are my artifacts of the pandemic and that will become part of their family story.

When the pandemic began, I encouraged my students to write. I told them they will one day want to share the stories of how they lived and how they felt as they lived through this time. I hope they have been doing it. I hope they have been documenting their stories, their histories. I hope that one day they too will share their own artifacts, whatever they may be, from this pandemic.

Classifying Numbers Card Sort COVID-Style

Pre-pandemic, card sorts with actual cards were a regular part of my classroom. I used card sorts to practice properties and to match graphs to stories and to classify numbers and to do all manner of other things. I love that card sorts can be done collaboratively, that kids can have conversations about the choices that they are making and why they are making them. I love that kids can look at choices that other kids are making and question them. I love that kids can debate and revise their thinking and deepen their understanding of ideas. I love card sorts.

Now in the midst of a pandemic, I can obviously no longer do card sorts quite the same way. I have been unwilling to give them up so I have had to adapt. For some of them, I have built them into Desmos lessons/activities. (Desmos has been such a gift this year.). However, I could not figure out how to do Classifying Numbers as the kind of sort that I wanted in Desmos (I know it can be done, I am just not quite advanced enough in building Desmos to do it yet).

Instead, I settled on building the card sort on a Jamboard. I sent students into breakout rooms. There was one Jamboard for each breakout room. The students worked together to sort the numbers into the apppropriate classification. The image below shows one of the Jamboards in progress.

Students collaborated. They had conversations about the choices that they were making and why they were making them. They looked at choices that other kids were making and questioned them. They debated and revised their thinking and deepened their understanding. It was a little bit of perfect in an imperfect world.

Here is a link to the Jamboard for anyone who might want it.


A Slice of Bread

In the end, the day came down to the need for a slice of bread.    It was filled with many other things of import, but that single slice of bread was the heart of the day.

The day was filled with the ups and downs of navigating remote learning.

  • With a little bit of support, almost everyone successfully completed their first assignment.    Each student shared his or her “And I Am a Mathematician” poster .
  • Students  found the video on how to set up their notebook.
  •  Jo Boalar’s video on brain crossing was excellent and set a tone on the importance of making visual and symbolic connections to concepts.  The Jamboards I planned to use for working on visual patterns didn’t work quite as planned but we made it work.  I suspect there will be a certain amount of that as we move through whatever this year looks like.   The kids still looked for the patterns and we still discussed both the patterns they saw and the corresponding expressions.   (And, I spent some time at the end of the day figuring out why they didn’t work as planned so that it doesn’t happen again next week when I am planning to use them for decimal division.
  • The trial run logging into edulastic was  largely successful.   I was able to help troubleshoot any technical issues in advance of the work planned for today so that today’s class time would not be lost.
  • I worked on continuing to build relationships with students., chatting with them before the official start of class.   They told me about their weekend.   Some of what they said made me smile – the student who went kayaking with her family, the student who convinced her mom to go rollerblading with her,    Some of it made me paste a smile on my face even though it worried me – the students who went to a birthday party with a bunch of other kids, the students who had large gatherings with extended family.

In the midst of all this, I got a phone call from my dad.   He had waited until my lunch hour, but there was a problem with his grocery order.   The instacart order that I had placed for his groceries had arrived with several items missing, even though the order showed that they were there.   After much cajoling, I had convinced him to let me order his groceries for him so that he didn’t need to go out in public during this pandemic.   Given his age and the fact that he has cancer, this was a huge win.    As I navigated the incident report, I asked him what was missing.   It was the bread.   Now for most people, it’s just bread.   A bit of an annoyance but you can live without bread.   The thing is, the medicine that my father takes is brutal on his digestive system.   He takes it with a sandwich to soften the blow, so to speak.   Literally anything else could have been missing from the order and it would not have been a big deal, but it was the bread.   He lives in another state, so I couldn’t just run to the store for him to pick it up.  As we talked, I reminded him that he shouldn’t go out and get the bread.   He doesn’t like to ask for help, so I was concerned that he might.   He assured me that he would ask a family friend to pick it up for him.    That slice of bread kept me up at night.

As I think back to that day in the first week of school, to the weight of that single slice of bread, I know I am not alone.   Countless others are also carrying weights that appear to be nothing at all, but which are indeed heavy, heavy burdens.

One Good Thing….

A year ago, none of us would have envisioned that life would look like this now. For each of us, what “this” looks like is a little different but it is strikingly different than what it once was.

As I watched this reality begin to sink in for my students, I decided that it was time to reframe their thinking. One Monday morning, a day where I actually see all of my students instead of just a subset of them, I asked each of my students to tell me “one good thing” from the past week. I got quite an array of responses.

” I don’t have anything. I just stayed home all the time.” That was the answer I could see in some of their faces and I wondered if it would spill out into the open. It did. It needed to be said. It was the fatigue of six months of endless days at home, spilling forth from the mouth of an eleven year old kid. It was an echo of what I had heard from my aging parents who are feeling isolated. It was the echo of my own thoughts as I considered the trips that I didn’t take, the friends I didn’t see, the things I no longer do.

Yet, if this pandemic has taught me anything, it is the importance of taking joy in the small things, the moments that can bring bits of joy. That is what I shared with him that day. I reminded him that “one good thing” doesn’t have to be big, that it can be something small, some little bit of wonder that crossed his path. Kids started to pipe up with all kinds of wonder, big and small. “I got a new puppy” (which we have all now met). “I went to clear a trail in the mountains with my family”. (How cool is that!). “I got to talk to my cousin on the phone” (isn’t that the best? I talked to my parents.) “I made cheese biscuits” (we now regularly discuss her latest culinary experiment). The “one good thing” gave us each a glimpse into the wonders in each other’s lives and gave us the chance to revel in our shared experiences.

Now, every day, I have a question of the day. I open our Google Meet about 10 minutes before class and we just talk for those ten minutes. Mostly, it is just silly stuff, but it brings us together. Here are some of our recent “questions”

  1. Is a hot dog a sandwich? – This was great because everyone had an opinion. Mostly, kids thought only a sandwich was a sandwich. Then, I started asking things like what makes a sandwich? Is a lettuce wrap a sandwich? What about a quesadilla or a taco? What about a calzone? Or an empenada? It gave us the chance to talk about what might be an equivalent to a “sandwich” in a lot of different cultures.
  2. What is the best pizza? – I was expecting things like Chicago Deep Dish, or the folded slices that people eat on the east coast, or something like that. Mostly, kids talked about their favorite toppings. (Surprisingly, not one of them mentioned green chili, which is very much a thing here.).
  3. What is your favorite ice cream? Lots of kids talked about chocolate mint, cookie dough, and the classic vanilla. It also gave us the chance to talk about summer afternoons making hand-cranked ice cream in the back yard.
  4. If you were an animal, what animal would you be (this is not what is your favorite animal) and why? One kid said he would be a chameleon because he could adapt to lots of different situations. Another kid said he would be a shark because he would be at the top of the food chain. The “why” was the best part of the question.
  5. If you were a kind of candy, what kind of candy would you be and why? My favorite response was from a quiet student who said he would be a Reece’s Peanut Butter Cup because the peanut butter cup has a hidden surprise inside that you don’t necessarily know is there at first. He said there are parts of him that most people don’t see until they really get to know him.

Those ten minutes when we aren’t actually supposed to be in class are the most important minutes I have with my students every day. They are the minutes when I learn that someone’s parent is quarantining with COVID 19, that someone’s family had to travel out of state for a parent’s surgery (all non-emergency surgeries have been canceled here because the hospitals are nearing breaking point), that someone has a new baby brother, that a coyote tried to carry off someone’s puppy. They are the minutes that have to carry us forward together until we can be together again. They are the minutes that have to make do for a bunch of 11 year old kids who are all at a new school and who don’t really have friends right now.


On Thursday and Friday, I assigned my students homework for the weekend. Their assigned task was to do something that makes them happy. At home. So that they stay safe. Because my heart will break if something happens to them .

Every week, I have been asking students for “one good thing” that has happened over the course of the last week. I have been encouraging my students to find those small good things that are happening amidst all of the hard things. Sometimes, they are successful at finding those things and sometimes it has been a struggle. My heart ached the day one of them quietly said “there was nothing good this week”.

This week, I decided to shift gears a little bit. As each student arrived in our Google Meet on Thursday or Friday, I asked them to tell me something that makes them happy. It was one more question among the forty-ish questions that I have asked so far this year to help me know them and to tell them that they matter. The answers were poignant, funny, and ordinary. Ice Cream. My family. Hiking in the Jemez. Sports. Watching my little brother. My dog. Spending time with my friends. That feeling I get when I get to really dive into something that interests me. Sleeping.

Tomorrow, I will ask each student as he or she arrives in our Google Meet, what they did this weekend that made them happy. I will listen to their small joys and watch for those that struggle to answer. I will tell them about my small happiness – fixing my sewing machine so that I can sew again.

Next weekend, they will once again have homework. Their homework will be to do something to make someone else happy. At home. So that they stay safe. We will brainstorm things that they can do. Small unexpected gifts of happiness that they can give someone else. A letter to a grandparent for no particular reason. A story read to a younger sibling just because. Cleaning up the dishes after dinner even though it is not their turn. Raking up the leaves that will inevitably come down after our snow this week. Leaving a hopeful chalk message or drawing on the sidewalk for someone to find. A hand-painted rock left on a neighbor’s doorstep. Small unexpected gifts of happiness for others that I hope will also give them happiness.

Living through a pandemic is hard. The lessons that I hope my students will take from it are both big and small. I hope they will learn to see the small moments of wonder in their lives and to not miss them in the mad rush that is life. I hope they will learn to see the importance of finding small amounts of time to do something that makes them happy. I hope they will learn that giving small gifts of happiness to others can also make them happy. I hope they will learn to see not just the sacrifices that they are being told they must make, but also the positive impact they can each have.

A Batch of Cookies

The aroma of freshly baking cookies filled the kitchen. The timer buzzed and I reached into the heat of the oven to pull out a pan of giant chocolate chip cookies. As I placed them on a rack on the counter to cool, I played with patterns – a row of two cookies, a row of three cookies, and another row of two – and I smiled. Like all things, these cookies make me think about math. Earlier in the day, these cookies were my answer to the question “What is division? What does it mean to divide?”.

Every year, I teach my students to model mixed number division. This is a really difficult thing for most people (including adults) to do. It is hard, because, oftentimes people have only a partial understanding of what division is. Here is some of the thinking that my students shared.

In looking at their responses, it is clear that many of them see division as breaking something into a number of equal-sized groups. While that is a good start, it is only part of the story. That is where the cookies come in. It is a tale of two stories, because stories help bring ideas to life.

I made a batch of 2 dozen cookies . I decided to bring them to my student aides as a thank you. I have 4 student aides. How many cookies will each kid get?

This story echoes the student thinking on division. It is the story of dividing something into an equal number of groups and figuring out how big each group is.

It is an important story, but there is another important story as well

I made a batch of 2 dozen cookies. I decided to make bags of 6 cookies that I could use as a thank you for my student aides. How many bags can I make?

This is the forgotten story of division. It is the story of dividing something into a certain size group and figuring out how many groups of that size you can make.

Together, these two stories explain what division is. In order to effectively model division, students must see both stories. It is really, really hard to model something that you don’t understand.

In introducing division models, I utilize both an array model (brownie pan) and a ribbon model. I start with problems in which students know the size of a group and have to find the number of groups. In this problem from Connected Math, students are told that they have nine bars of cheese and the amount of cheese needed to make a single pizza. They then need to determine how many pizzas they can make.

Then, I introduce problems in which students know the number of groups and need to find the group size. In this problem from Connected Math, students are told that they have a certain amount of peanuts that will be shared equally among a certain number of students.

Finally, students have to generalize and determine what kind of a problem it is and model accordingly.

My favorite thing about this lesson yesterday was watching the girl who has been struggling a little big. As my glance danced between her work in Desmos and her face in the Google Meet, I could see that magical look of celebration as she was working on a problem and seeing it fall into place. The model was helping her make sense of the math. It was a “cookie worthy” moment, but the cookies will have to wait for a different time.

Back to the cookies coming out of the oven. They also made me smile because they are from a recipe that one of my student aides gave me last year. I had brought him and my other student aides baked goods from time to time as a thank you for all that they do to help me. He decided to bring me cookies that he made one day. He is a pretty serious foodie and his cookies were the kind that you want to savor. In addition to the cookies, he gave me his recipe. Every time that I make them, I think of that amazing kid and it makes me smile.

You Got This

You Got This. The hand-lettered card proclaimed this in bright pink block letters. The card was attached to a bottle of wine sitting on my porch late this afternoon. A friend left it there for me as a surprise while I was busy teaching my last class of the day. There was no particular reason for her to leave such a thing on my porch. As a retired educator, I think she just knows that every teacher needs a little bit of care and a little bit of encouragement. right now

Every lesson, every day must be created anew. Every standard, every concept has to be re-examined to see how to fit it into a virtual world. Every day is sprinkled with experiments in new ways to do something that was so straightforward before. Every day has small victories and small in-the-moment shifts. Every day, lesson plans must be shifted on the fly, not because plans were not well-formed but rather because this world is filled with un-anticipatable twists and turns – student device and internet problems, teacher internet failures in the middle of a lesson, Beta breakout rooms that work fine when tested with teacher accounts but won’t assign student accounts because they are “outside the organization”, technology platforms that glitch and kick students out and lose their work. Every day, every lesson, every class teachers are digging a little deeper to give students the best experience they can.

In the midst of all of this, I know I am one of the lucky ones. I have experience upon which I can draw. I have colleagues upon whom I can depend to share this journey, I am an engineer and am pretty comfortable with technology. Still, I find myself exhausted. I find myself looking at the 50th or 70th or 100th email of the day and deciding to come back to it tomorrow because it will take more energy/time/work than I can do in that moment. At the staff meeting this morning, they went over the requirements for departments and for professional learning communities and for professional development plans and what we need to do to prepare for Open House in this new virtual world. I have these new things to add to my To Do list but I find that managing the “musts” of meeting my students needs right now are all-consuming. I simply can’t wrap my head around one more thing right now. Yet, I must.

I know I am one of the lucky. ones I wonder how my colleagues who are not so lucky are hanging on, how they are finding their way forward.

You got this. I didn’t need to hear that., I know I will dig deep and deeper and do what it takes to make it the best I can given where we are for my students. Having someone care enough to say it, in this moment in time? That, I absolutely needed that. I think we all do right now.

As I said, I am one of the lucky ones.

This is hard, but….

This is hard.  Everything about this is hard.   It’s hard for kids.  It’s hard for parents.  It’s hard for teachers.    It was always going to be hard, no matter how we ended up dong school this year.   It’s OK to acknowledge that fact.   We would be less than truthful if we didn’t acknowledge that this is hard and that we are all feeling that sometimes.

This  is hard, but the feared “summer slide” didn’t happen.  My students did pretty well on their short cycle assessment at the start of the year.    If anything, my students did a little better this year than they have previously.

This is hard, but we are getting to know each other.   We are talking about kayaking and rollerblading, movies and books, building bunk beds and learning to cook, family heirlooms and the sadness of a friend moving away.   We are smiling during those five minutes before class actually starts while we just chat and we are smiling in those last few moments of class as we wave goodbye.

This is hard, but we are learning how to adapt.    The first platform that we tried to use this year crashed and burned.   Students had trouble reading the questions.   The platform kicked them out partway through an activity and lost all their work.    It was glitchy.  What did the parents do?   They were patient and let their kids take the lead.  What did the students do?   They self-advocated.   They sent me messages, they emailed me.   We found solutions and work arounds.    What did I do?   I gave it a week and tried a couple of different things.   Then, I decided it was too problematic and to move almost exclusively to Desmos.   I used Desmos exclusively in the spring and it worked really well

This is hard, but we are figuring things out.   We needed to be able to use a document camera sometimes.    I brought my document camera home from school so that I could use it.   I discovered my school computer, with the necessary software, doesn’t have a working webcam (it has one, it just doesn’t work)  so I switched to my personal computer.   It doesn’t have the necessary software to drive the document camera.   I set up my ipad and logged into the Google Meet on two separate devices so that I could use the camera function on the ipad as a document camera.   The kids couldn’t really see the writing on the page.   The next period, I switched to something that was printed so that it would have higher contrast.   The kids still couldn’t really see. it.   The next period, I made some changes to the lighting in the room.   The kids still couldn’t really see it.   The next day, I moved to a different room with better lighting.   The kids still couldn’t really see it.   The next day, I put up a whiteboard and focused the iPad camera on the whiteboard.   It worked.   The kids can see it.

This is hard, but we are finding new ways to collaborate and build on each other’s thinking.   We are trying out Jamboards.   We are looking at each other’s thinking in Desmos.   We are asking questions and thinking hard.   We are listening to answers that others give and adding to those answers.   We are asking more questions based on what we are hearing.   We are learning that we are all responsible for each other, that we have to help each other, that we can learn from each other.

This is hard, but we are learning that perfect isn’t always necessary.   We will begin our Hogwarts project next week.  Usually, it starts with each kid getting a letter inviting them to Hogwarts on their school lockers.    This year, there are no school lockers.   Usually, there are little shops set up around the classroom.   This year, there is no classroom.   Instead, this year, our trip to Diagon Alley will be in Desmos.   It will be different, but I think it will still be fun.   I had hoped to go into the computation layer in Desmos to build in a randomizer for each kid’s budget.   I started on it, but did not get far enough to include it this year.   That will be something to work toward for next year.   It’s OK if every kid has the same budget for now.      It will be good enough, even if it isn’t perfect.

This is hard, but we are learning and growing.   We are persevering and learning important life lessons.   We are learning resilience.  We are also learning math and how to do school.    We are doing the work that translates into an education.




“And I Am A Mathematician”

So, let me just say that I hate emojis.    I always have.   I just don’t understand the point of them.

When “bitmojis” came along, I felt much the same way.    I remember my daughter opening a text from my sister and exclaiming, “She made a bitmoji!”   She was clearly impressed that someone my age would even know what a bitmoji was, never mind that she could also make one.   My response was a little bit of “not too sure why she wants one, but ok.”   (My sister has always been much cooler than I am.)

Fast forward a few years and suddenly we are all in a pnademic.   Everyone is under considerable stress.   Experts exclaim that creative activities are good for mental well-being.    Bitmoji classrooms are popping up everywhere.    Summer has arrived.   Normally, I would be madly preparing for the coming year.   This year, I couldn’t though because of all the uncertainty.   I had no idea of what school would look like.   Would it be in person?   Would it be hybrid?   Would it be remote?    How would I teach where kids have to be 6 feet apart and unable to share so much as a piece of paper?    Would kids have 1:1 devices?   The days passed, and I attended webinars and read books and articles.   Still, I had no idea what I was going to do in the fall.   So, I broke down and built a bitmoji classroom.   I thought it would be a good outlet.

My bitmoji classroom  was an exercise in play.    I had no intention of actually doing anything with it.   Then, my brilliant friend , Laura,(who regularly makes me a much better teacher) ,showed me how she was using her bitmoji classroom.

  •  She created a Google Slides presentation to share with her students to introduce  Jo Boalar’s “And I Am A Mathematician” poster activity.   Her example was her bitmoji classroom.   She upped the ante by adding in links to objects in the bitmoji classroom that would tell her students about herself (e.g., if they clicked on her puffin mug, they would see phots of puffins that she has taken).     She also added books to her bookshelf that were various platforms she would be using instructionally (i-Ready, edulastic, desmos, deltamath, etc).   Each book had a link to the specified platform.   Her name had a link to her class website.
  • On her website, she embedded a copy of the slide so that kids would always have easy access to the various educational platforms she will use.

This was something that I could get behind.   So, my bitmoji classroom, which is fairly basic, became an example for my “And I Am a Mathematician” poster and the top of my class website.  Screen Shot 2020-08-16 at 7.54.43 AM

I added a screen shot of Lure of the Labyrinth because I was a Lure of the Labyrinth teacher winner.   In addition to going to MIT to meet the game designers, I got a signed Lure of the Labyrinth poster that usually hangs in my classroom.   I attached a link to the game since we will play it later this year.   I added an Omega because it is the symbol for ohms, a measure of resistance.   It was the best graphic I could think of related to electrical engineering.   I added a link to that that takes the kids on a tour of Cornell University (where I got my graduate degree in engineering).   I added a quilt design to my desk so the kids would see another side of me.   I also added a book case similar to one we have in the classroom that holds all the math games and activities that we regularly play in class.   Finally, I added books on top of the book case with links the students may want as the year progresses.

As I said, my bitmoji classroom is fairly basic.   However, I am so glad that I made it.   The digital “And I Am A Mathematician” posters that my students are creating are a really great way to get to know about my students and for them to get to know each other.