Using Video To Improve Math Explanations

I work with emerging multi-lingual students every day.  The importance of focusing on content language as well as other language structures are at the forefront of how my lessons are planned and enacted.  One way to challenge students’ learning and improve the use of language having students make math videos explaining their thinking.

It’s a simple idea with powerful advantages.  I’ve found that holding students to a high level of explanation (written and verbal) and use of content language has actually helped students make better arguments and even understand the math more deeply.

The project was simple.  (1) Choose an equation from this list.  (2) Draw the idea using algebra tiles.  (3) Explain your solution mathematically (with algebra tiles, a picture, or with numbers and letters). (4) Write a script and make a video explaining your solution (the script is super important for students new to the English language; different levels of structure and supports can be changed up to support the students with whom you’re working).  Here’s an example of a video from our latest project.

Using Charts to Model Student Progress

Since my first year of teaching, I have thought about the many different ways I could help to demonstrate a growth mindset to my students.  You can read some of my thoughts elsewhere in my blog but wanted to share an example of something new I am trying this semester.

As our school has focused more on formative feedback I’ve made it my goal to give more exit slips.  First, I found that I was doing it just “because”.  I claimed it would help my practice and I would make changes based on the feedback but the reality was that it just didn’t happen.

Then, I tried experimenting with tracking this data.  Below is what I put together this fall.  For each student, I tracked their progress and updated it as I gathered more feedback: exit tickets, classroom conversations, or projects.

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The problem I faced with the spreadsheet was that it was a lot of work on my end (valuable and meaningful data but a lot of work).  However great it seemed I did not share with students and it did not give them ownership of it.

I decided to go another way.

Currently, as you can see below, I am using sticker charts to map the progress and understanding of my students.  It is similar to the spreadsheet except it is more simple and student-facing.  If you’ve shown you understand a standard, you get a sticker.  The students see it every day, and it has been a regular conversation we’ve had in class.

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The picture here shows student understanding after Tuesday, Thursday, and Friday or the same week. The week following this data collection we had a short project before we took a group test and individual test.  The conversations around these charts consist of:

(1) Look at how you’ve grown!  Your hard work has been paying off!

(2) If you have three stickers, you should act with empathy and help others so more students can earn stickers.

(3) You should come in at lunch so we can talk and you can earn stickers by showing me you understand.

Looking forward, I want to reflect more on the student buy-in that this brings and think about even more effective ways for my students to own this information. I want them to actively reflect on how they are doing and what they need to do to continue on the path of understanding, despite struggles.

In the mean time, I will continue and be content with how much kids of any age love earning stickers.

Pay Attention to Patterns of Participation

In 2012, as a new teacher, I still remember my first staff meeting.  I was one of many new staff members, including our new principal.  As a staff, we took a moment to think about the vision of our school.  What should a thriving high school look like? Feel like? Sound like?  I was unafraid and raised my hand.  “Every week should feel like Homecoming week with all the excitement and energy it brings”.  The principal was quick to reply with a smirk, saying “spoken like a true rookie.”

I bring up this story because I believe the way voice and participation patterns exist in adult spaces greatly affects a school and organization.  Creating equitable learning spaces in classrooms begins with an equitable learning space among adults.

Thinking back now about that first staff meeting, I wonder how I had the nerve to raise my hand in front of nearly ninety staff members.  Where did I get the nerve?  Part of it, I would argue, is the fact that I was truly clueless and didn’t know any better.  But more than that, I think a large part of that nerve was because of my identity.  As a white male, society had always told me that my voice carries weight and there would be less judgement toward me if I was wrong.  I did not feel afraid or fear being judged.

That was then, in a staff that was almost completely white.  Now, I find myself working at a school with about half of the staff being people of color.

Staff meetings, both large and small, are noticeably different.  Agendas are carefully crafted with a lens toward equity:

  • all staff members taking turns facilitating meetings
  • creating small groups
  • giving time for each person to write first before sharing with a partner
  • giving each person to a minute to share their thinking, not more
  • providing sentence frames to shape the conversation

Most importantly, each meeting is shaped by the norms of our school, one of them being “step up, step back” and another “pay attention to patterns of participation”.  As a staff, a department, or a working group, we consistently monitor our participation.  It is expected that those of us that could have more status – more experience, more expertise, male, or white – become aware of our participation and do what we can to allow more voices to contribute to conversation.

Second, we process-check each meeting in our closing moves.  We reflect on whether we met all of our norms and values including leaving space for everyone’s voice.  Did anyone talk too much?  Did any specific group talk too much or too little?

There is no perfect answer to creating equitable voice in adult spaces, but I am really proud of the work my school does to move toward more diverse participation.  Next time, you’re in a staff meeting or department meeting pay attention to the different people and groups that are talking.

  • men/ women
  • white/ non-white
  • new/ experienced
  • content area

Create a conversation, establish a set of norms, check yourselves every time.  The process is never done.

Living Your Values

After graduate school, my goal was to teach at a school in which I could learn from and observe amazing leadership.  My advisor connected me with San Francisco International High School.  I knew it was an interesting opportunity because the school was committed to educating recent-immigrant students and had a unique model of distributed leadership.  I had met the principal in one my classes and was impressed.

I just started my second year teaching at SFIHS, and I have to say, I am amazed at how much I learned about myself, about teaching, and about leadership in the past year.  My learning did not come from an amazing curriculum or even an amazing principal; it came from the amazing leadership that emanated from all of the staff.  Everyone was a leader that challenged themselves, each other, and the status quo.  We learned together and supported one another in order to create change in our school and in the lives of our students.

This did not happen by accident.  What I admired most about the school is how deeply it lived its values.  Day 1, we teach the students about the values – what they look like, what they sound like, and what they feel like.  Living the school values isn’t an option, it’s what we do.

Almost more importantly, these are the values by which the staff operate as well.  Each staff meeting we start by drawing attention to a few and end every meeting with a process check to see how well we followed the norms.  Did we honor our time and show up to the meeting on time?  Did we assume positive intent even in those with whom we disagree?

The school values hang in every room and are printed on every agenda.  It’s the common language we all speak, even as students arrive from different countries with little to no English.  We learn together, we act with empathy, we challenge ourselves, and we create change.  These values define us and our students.  They drive us in our work and keep us in check when the workload is large and time is limited.

  1. Learn Together 
    a.) Celebrate success and opportunities for growth.
    b.) Seek resolution.
    c.) Be open to outcome, not attached to outcome.
    d.) Be fully present. Honor our time.

2. Act with Empathy
a.) Assume positive intent.
b.) Communicate honestly about your needs and perspective.
c.) Seek to understand others’ needs and perspective.

3. Challenge Yourself
a.) Take risks and allow yourself and others to grow and learn.
b.) Step up; step back.

4. Create Change

I’m curious what values drive your work or your school?  Do you have a common language and method to keep yourself and your school’s many personalities in check?  Define your values and create a school where everyone leads and grows together.


Teachers Everywhere

The other day as I was helping transport twenty students across San Francisco for a field trip via public transit I sat and watched an experienced driver show a new driver the ropes.  “No need to rush.  Safety is always the most important,” he said as we pulled up to a roundabout.  “Which turn do we take from here?” he asked the new driver.

I smiled, thinking about how this man was a teacher and mentor for this new driver.  He was supportive and patient.  He asked questions and held on to answers only for the moments they were truly needed.  It reminded me a lot about how I traditionally think of teaching and learning within a classroom and the walls of school.  I smiled because I love education and it was a simple reminder that eduction is everywhere.  Everyone is part of the education system because we continuously teach one another and learn from one another in a variety of different ways.

That night, I came home to view some snaps from my girlfriend who challenged herself that day by attending an event put on by her school club: the claybusters.  The claybusters are a high-school club that promotes recreational clay shooting (among other things, I’m sure).  I’m always amazed at how open she is to try new things.  She had never done it before and isn’t really a big fan of shooting in general, but she went because she loves her school, her students, and values being part of the community in as many ways as possible.

At the beginning she did not like it.  She had 30 shots and was ready to give up after ten.  When we talked it sounded like she was holding the gun wrong, not hitting any clays, and the overall experience wasn’t a good one.  Then she told me how the instructors were patient with her, but challenged her to keep going.  They taught her how to hold the gun, how to breathe.  Ten more shots and there wasn’t much improvement.  They supported her after every shot, showing her how to tilt her head, how to follow the clay.  The last ten, she hit eight out of ten, and she even said she would be open to shooting again in the future.

The instructors here modeled something that classroom teachers should always strive for: pushing students past what they think they can handle, consistent and unwavering support, and an understanding that students come with different abilities and desires to learn in the first place.

The final example came today in the grocery store as I passed a chatty two year old (I think?) and his father.  The child was asking questions and the dad was very focused on shopping. “Do we need an apple?” said the child.  “That’s a red bell pepper,” the dad replied.  This simple interaction reminded me of the amazing teaching and learning that occurs by parents and their children.  The dad was not focused on teaching in the moment but was a teacher.  How often and what do you and I and the people around us teach each other?

There are a million examples of teaching outside of schools and even outside of traditional structures devoted to teaching and learning.  If you stop and take a look around at an average day, I’m sure you’ll find them too.  If you feel like teaching me about where you see some of this please comment below and let me know what you’ve found!

FREEZE! Improving group work to be challenging and supportive

If you teach, you’ve seen it.  There are students with high status that tend to dominate group work and feel more confident speaking.  Likewise, there are those students that don’t feel like they have much to offer and often end up with their heads down, off task, or, at best, quietly listening to the conversation.

The goal of group work is an equitable sharing of ideas that allows all students to be challenged and supported.  What I found was missing was an easy way to celebrate students that stepped up to ask a question and admit they were confused or to celebrate students that were empathic and attentive to the needs of struggling students.

The freeze card was an idea stolen from a district PD which was then developed further to aid my specific students.  Below is iteration 3.0.  I began with just FREEZE.  Then, realized that students didn’t know how to have conversations after it had been laid.  Thus, I added some sentence frames to the back of the card.  Bouncing ideas off another colleague we arrive at the current card below.

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It should be noted that this idea was implemented at least six weeks ago and the actual use in class is slow, but consistent framing and celebrations when students lay the card have led to more and more use.  Just today, a student laid the card down and no one in the group stopped to explain.  I took the moment to celebrate the student and said “Nice job!  This student gets 10 points but everyone else in the group loses 2 points because they did not freeze to explain.”  That woke them up and soon they were talking. (it should be noted that points were arbitrary – I had no idea what I meant by that but it got them working!)

What are your thoughts?  What would you change for version 4.0?  What else do you do to encourage equitable conversations and group work?


Substitute? No, I’m a visiting teacher.

Recently, a colleague was out from school, and I decided to check-in on the class during my prep period to make sure everything was running smoothly.  As I walked in I heard a student say, “no mister, when we have a sub our teacher let’s us have our phones out.”  The teacher quickly replied, “I see.  Well I’m not a sub, though, I’m actually visiting teacher today.”  This was one of the wittiest quips I’ve ever heard and loved it.  He had everything more than under control.

After returning the next day, my colleague emailed our team about her new strategy for when she was gone.

“On sub days I have been trying to track student work completion and hold students accountable. I ask that the sub sign their work packets only if students have been working the whole time and not copying from others. For obvious reasons I can’t be 100% sure kids weren’t copying, but overall the sub signature system seems to work. I then make a graph of student completion by class and show it as an opening the next day. I ask students to reflect on how they did; what was successful, what could they improve, how they felt in class, etc.”

Here’s the difference of work completion from the first time she was gone to the second.Screen Shot 2018-03-15 at 8.11.57 PM Screen Shot 2018-03-15 at 8.12.12 PM

I love how this strategy increases accountability as well as the opportunity for students to reflect on why working with a substitute can be valuable.  Whether we end up with an average substitute or a visiting teacher, I think this idea is exciting and worth trying!

What other ideas do you use to motivate students when you are absent?

My favorite growth mindset ideas

I was recently asked by a friend to pass along my favorite growth mindset materials.  His company jumped on the buzzword bandwagon and was spreading the growth mindset message.  He was wondering if I had some other supplemental resources that would be helpful and less focused on the student/ school perspective.

The first to come to mind were these:

1.) Neuroplasticity:

2.) “How Praise Became a Consolation Prize” – A reflection by Dweck about what people have gotten wrong about growth mindset. http://How Praise Became a Consolation Prize

3.) Understanding the Importance of Fixed Mindset – My own thoughts and reflections and anecdote.

4.) This photo

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What other resources should be added to this list?

A day in the life of a teacher

This is a story that answers the question – “How was your day?”  I often answer “it was fine” or “fun day with the kids!” because there a million different details, emotions, triumphs, and failures that occur each and every day.  This day, though, seemed like an extraordinarily normal day.

The day begins with me arriving to school at 7:20, already with a knot in my stomach because I am ten minutes behind my normal routine.  I need to put the final touches on my lessons and figure out what I’m going to do in my advisory class because, at the moment, I had nothing planned (not a good place to be in but something you become skilled at figuring out as a teacher).  


I walk into the school and before I even get to my classroom a coworker says, “Hey Casey, can you come take a look at this?”  He asks about my input on an awesome idea we’ve been developing since a district math PD from a few weeks back.  I give him the my two cents without giving away that I’m internally FREAKING OUT over the work I need to complete before the kids show up.  He doesn’t have a clue about my internal affairs but he’s awesome and the idea is awesome, so I stick around.  


I walk into my class to prepare for the day.  Quick – make the slides, write the objectives on board, and finish the opening question before the students…. “EYYY, MISTERRRRR” (first student enters at 7:39).  Do my best to have a conversation, help kids with homework, as well as finish planning before class starts.

1st Period

In my frantic rush before school, I made groups for the students to prepare for their upcoming test.  Of course, one student says “I’m not working with that group.”  I plead, I beg, I negotiate.  Nothing.  Okay, you win.  I change the groups slightly to make things work.  The groups work really well together!  Next thing I know, one student has ventured to my desk and finds a picture of me with my family.  “How old were you?”  “Is this your dad?” “Is this your brother?” “How old is your brother?” – you know, normal prepare-for-math-test questions.  After a moderately brief interview the students continue to work but decide my family should join them (see pic).  Class finishes up fairly well.  I feel good about the class.

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My family joins group for the math review.

2nd Period

Shit.  I’ve got one period to figure out what I’m doing for advisory.  Growth mindset – it’s my thing.  Let’s go with that.  I tell myself that I can create a lesson that will have to suffice for today, and I can always build on it in the future.  The knot in my stomach is back.  I watch a video and create an activity for kids that speak every level of English.  Magic! (or crap, depending on who you ask).  I run downstairs to print for advisory and find that my planning partner has printed the documents I need for the next day (thank the Lord).  I run back to class, proud that I was able completely avoid a panic attack and produce something of value.

3rd Period

The bell rings.  The phone rings.  “Mr. Casey, I’m just calling to let you know class C (the class about to come to me) might be a little late because they all worked so hard I gave them all Huskies!” Huskies are little statements of accomplishments when kids are caught doing great things.  I’m super excited.  Let’s keep this positive day alive!



I don’t even have all of my kids in my class yet.  Why is the alarm going off between classes?  Did someone pull the alarm?  Is this like Parkland, Florida? Dumb thought.  Is it a dumb thought?  Let’s get all my kids to my room, then go outside.  COME ON KIDS!!!  Okay, everybody outside.  I don’t have my green paper (to hold up when I know all the kids are with me).  Who cares.  Let’s go.  Student crying in the stairwell.  “Are you okay?”  We still need to go outside.  “No, mister”.  “I want to hear you but we need to go outside”.  We go outside.

My students are all scattered at this point and I try my best to wrangle them in.  “Mister, do you think mutations are good for humans or bad?”  “What?”  The student asks again.  “This is not the time to ask me that question”.  Student 1 hits coca-cola out of student 2’s hand and laughs.  We get the go-ahead to head back into the school.

Class C – the class that was just previously ALL awarded Huskies – now resemble that of an unsupervised 3rd grade recess in my classroom.  I decide it’s time for meditation.  “We are going to try to refocus.  You can copy down the opening, you can put your heads down and sleep, but lets be quiet and try to focus.  Let’s take three minutes.”  We take 6 minutes because I’m putting out four different dumpster fires happening all at once.  (I’m actually quite proud of 6 minutes).

We finally start class, kids complain about groups but mostly work pretty well together!  Granted, they didn’t finish nearly as much because so much time was lost to the fire alarm.  Bell rings.  Success!  Then I notice a protractor glued to the table with whiteout. Great.  “Who did this?”

4th period – Advisory

My already rushed, under-prepared advisory lesson began by the two culprits of the whiteout fiasco cleaning up one of the tables.  Although it was rather distracting to start class I felt this small ounce of pride in making students repair the damage they caused.  Advisory continues.  It goes fine.  Not the lesson of the year, but I’ve taught worse lessons.


12:05 I hold one student back because I notice that he has not been getting along with another student who is in his math class and in our advisory.  He gives his side of the story.  I listen and try to give him feedback.  We come up with some positive actions steps which includes me touching base with the other student.

12:12 I get 15 minutes of peace.  Pretty sure I just ate my PB&J quietly and stared at a wall.

12:27 A student walks in that NEVER comes in to lunch.  Actually he is usually absent a handful of times during the week.  He comes in and we chat about life for about 15 minutes.

12: 42  Another student comes in early to class (class starts in 8 minutes).  This student is newer to the school and has very limited English at the moment.  I introduce the students and start to clean up the room and get ready for the next class.  I overhear the first student telling the second how important it is to try hard and that if you want to learn, you will.  If you don’t try, then you’re not going to learn.  My heart swells just writing about it. SO AWESOME

5th period

Bell rings and students show up.  A student shows up and makes a game out of trying to throw oranges into a cardboard box.  Orangeball?  I give him a look, he makes the orange in the box and gives me an I-told-you-so look.  Another student comes running into class dripping sweat and grabs some napkins.  Students get to work quickly!

Another student – usually absent from my 1st period class – shows up in my 5th period class.  He’s kind of distracting but he is being quite respectful just trying to get to know other students.  “What class are you supposed to be in?”  “It doesn’t matter.”  I check the schedule and give his teacher a call.  “He’s supposed to be in the office.”  Ah.  That explains it.  I call the office to let them know.  I pull up a chair and have him work with a group until the AP shows up. “I wasn’t even distracting anyone!”  A part of me is sad because he was engaging well with students but I owe it to his teacher and whoever he was disrespecting that there was follow through.

Class is working so well I change my lesson plans and let them continue to work together and teach each other until the end of class.  I gave out a Huskie to the other teacher in the room and tell everyone to write a Huskie for someone in their group because they worked so hard!

6th Period

Class starts fairly quickly.  I note that when the bell rang there was only one opening out (showing they are ready to start class).  A student leader starts class, another randomly yells nonsense.  Take a minute break, dude.  The other teacher in the class tells me the teacher across the hall is also in the hallway taking a breather – that kind of day.

Mister, I want to take my test.  Mister, I want to check my grades.  Mister, is this right?  I pause the class and tell them how great they are at asking questions and being aware of what they need but terrible at timing.  I get the classes started.  Some work better than others but overall it felt, meh to good-meh.

End of the day

Take attendance, start looking at tomorrow, look at and respond to emails, clean up the classroom.  I try to get out of school early around 4:30 because I have tutoring at 7PM where near where I live, 45 minutes away, and a good chunk of papers to grade waiting for me at home.

How was my day?  It was fine.

Plan, Do, Study, Act to Improve Classroom Routines

Recently, my last period class fell into a habit of struggling to get started each day.  One day, when it took the class ten minutes, I was finally fed up with yelling at students to sit down and get started.  Instead, I asked them “how much time do you need to get started?”  We defined “getting started” as sitting down with the opening out, phones put away, and a student leader starting class.

Student proposals ranged from 3 minutes to 10 minutes and we finally settled on the categories of 3, 5, or 7 minutes.  Three students gave their passionate explanations of why 3 or 5 or 7 were the best for the class (I personally was a fan of the 3 minute speech).  I should have known better than to let the 7-minute delegate talk last but, sure enough, the class voted for 7 minutes.  Fine.  At least it’s better than 10 minutes.

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The first days seemed to go better and they even were able to reach their goal twice.  Then, another bad day set in.  The problem I identified was that the group had set a goal but had not defined any strategies to meet the goal.  What did they need to improve?  Again, after a debate with the class we settled on the following strategies.

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Since that date the time it has taken to start class has continued to decline.  It began to level off at about four minutes this week which I think is a much more reasonable amount of time and similar to the other classes I have throughout the day.  I am now going to start keeping track of how well students follow through with their strategies and maybe we’ll see it decline even more!  Either way, I’m proud of their improvement!