My First Flipgrid

I have been wanting to try to use Flipgrid for a long time. With distance learning the number of tools available can be a bit overwhelming. I decided Flipgrid would be worth my time because it would give me the chance to hear my students voice and possibly see their face. I had already had some success getting students to screencast themselves solving a Desmos Marbleslides challenge. Very few students are comfortable turning on their video when on Google Meet office hours or live sessions although a few more are comfortable using audio since it can be quicker than typing.

I was inspired by my fellow Open Up Resources community coach, Tashima Price, who delivered a PLC on the topic. I had also heard frustrations with the lack of participation from some students. So I reached out on Twitter for good prompts, and got some nice responses. I used one of the suggestions by Howie Hua:

As you can see the prompt lead to student participation as well as teachers getting a nice link in their inbox of a student describing their favorite lesson. I wanted to look at how students responded, and did some tallying to find out that 32 students used video, and of those 32 12 either hid their face with an emoji or used a blurring filter. 8 students used audio only. 19 students did text only. That’s a total of 59 responses, out of 130 students registered on Google Classroom. This sounds like a bad percentage since it’s under 50%, and I think part of it is due to there being less than a month left in the school year. We have to remember students are burned out in person at this time of year, so why would it be any different when they’re overloaded with screen time?

I had some major takeaways on what makes a lesson memorable. Some lessons were mentioned more than once:

  • 7th grade history unit on Warlords of Japan
  • Socratic seminar discussions in English class
  • learning to play music better
  • Desmos Marbleslides (recency bias maybe?)
  • online learning

Students really liked the simulation of Japan. They liked the competitive nature they said. Also, students liked Socratic seminars because they said more people participated and you had to build off of what others said so it involved a lot of listening. (How can we do this more intentionally in math class?) Desmos Marbleslides is no surprise and the students liked the game like feel. Surprisingly many mentioned online learning because it was something they had never done before and it was very unique. I wish they had elaborated a little more.

One student mentioned a life lesson I taught him. He said, “Mr Joyce said if you’re having a bad day, it’ll stay a bad day unless you make it good.” He summarized a life lesson my grandpa taught me, and the way I originally said it was, “You don’t have a good day, you MAKE it a good day.” The moral of the lesson still got across, because if you just let life happen to you, not many good things will happen. But if we take charge and do our best to make it good, it will be good. As many of you know, I’m a glass half full type of person, so I tend to try to stay optimistic.

I won’t share any examples with student’s faces, but I have to share this one students who made an animation. I don’t know how they did it, but it’s pretty cool:

I also loved a student sharing that they learned the importance of giving to those that were less fortunate through their youth group leader at their religious organization. I loved that.

Anyway, next steps? I want to do an academic version of Flipgrid where we record our screen of correcting one of Mr. Stadel’s exponent mistakes. I did a quick google search and found this Desmos activity. I will either use Screencastify or test out Flipgrid’s screen recording feature. I like how Flipgrids are all there for students to view each other’s.

According to the stats there were 69 responses and over 1500 views and 9 hours of shared learning. I also used the moderating feature so that I could approve it before making it public. Only one student needed this because they uploaded a meme that had nothing to do with the assignment. If you had trouble figuring out how to make a Flipgrid active when moderating it, click on “My Activity” at the top of the toolbar.

Oh yes. And we are not supposed to do any academic lessons the last week of school, so each day I am going to introduce a new Flipgrid prompt from one of the suggestions on that Twitter thread I posted above and share some stories with my students and listen to their stories!

Desmos Marbleslides Screencast Hyperdoc

As one of the community coaches for Open Up Resources, we have been shifting our focus from unit overview PLC’s to distance learning PLC’s and compiled some resources. On April 2nd, Morgan Stipe presented on HyperDocs and afterwards I went over the basics of how to use Screencastify [request access to view PLC recording], a screen recording solution. During her presentation, little did I know, that I was going to combine her ideas with mine to create a project for my 8th graders.

That’s what I’m sharing with all of you today. I am proud of it and want you to help me make it better by using it with your students before the school year is over. Personally we have 6 weeks left, and I know New York and other east coast schools started after Labor Day so they have even more time.

Our school jumped into distance learning by doing daily lessons. After spring break, we had some PD days and re-launched with Math and Science coursing having 3 lessons a week, Monday, Wednesday, and Friday. One of those days was expected to be live, and my colleague Bob and I picked Wednesday. By the way, on Tuesdays and Thursdays we do 1 hour of office hours instead of 2 separate 1 hour chunks. Our administration and district is showing grace to myself, students, and parents to not be overwhelmed as they may be otherwise.

Anyways, enough with the logistics. Well, more logistics actually. I posted this morning in my Google Classroom:

Today is a live lesson. I will be explaining a project that will be due Friday May 22nd. For today, wednesday April 29th, here is the schedule for the Google Meet:

9 – 9:45 am 1* and 6*
10 – 10:45 am 4* and 5*
1 – 1:45 pm 3* and anyone who missed their first time slot

Here is the google Meet link. . My expectation is that you are in the Google Meet as well as the Desmos activity which is at this link: . That’s the best way to get live written feedback on Mondays and Fridays also.

Attached is the HyperDoc instruction sheet that I will go over with all the links necessary.

Here is the link to make a copy of the HyperDoc.

I usually wait 3 to 5 minutes after the hour to start and also restrict students to screen 1, which is a starter screen you can add by turning on Desmos labs and making a copy of Desmos Marbleslides to copy and paste this slide into your set. I loved finding out students were learning the guitar, getting to level 35 in Pokemon Go, cooking a lot, etc.


For screen 3 the students had to adjust y=1/2x+1 to have a different y-intercept, so I asked in that what they did to fix it and how they knew it would work, but set my timer for 1 minute for them to type it in the chat box and not enter it until I said so. This is a great tip I learned from Ashli.

what the most important equation of 8th grade was (y=mx+b) and we talked about how m, the number before x was the slope and b was the y-intercept. When you type y=mx+b on that screen it defaults to m=1 and b=1 so I asked students what this new red line had in common with the blue line and they said they both have a y-intercept of 1 but the red line has a slope that’s steeper since 1 is greater than 1/2.

I then restricted their screens to the next few fix it screens for about 3 minutes, paused, asked some questions in the chat, then unpaused for 8 minutes while they examined each part of the equation y=-0.14x+3{x<5} with prediction screens then a verify screen to see if their prediction was correct.

With about 5 minutes left in the 45 minute session, I shared my screen and went to the HyperDocs link to go over the project. The goal is for students to record themselves solving a challenge screen start to finish while explaining what the parts of their equations mean.

Today was easily my best day of distance learning yet. I got to check in with my students. I got to see them engage in math because I went back to my Desmos class code and saw out of 140 students, 79 logged in to the activity. I could see that some students solved more than one of the challenge screens and about 12 students already turned in their screencast according to my Padlet wall. It is a JOY to hear their voice. It's optional to embed the video of your face and I made sure to mention, especially for one particular student (selectively mute), that they could write a written description instead of talking on the video.


One student had trouble installing the extension so on Google Meet I had them share their screen and I walked through the process. Basically it involves signing up at and signing in with Google and enabling and selecting your microphone and webcam. Another aspect I addressed on my screen cast on the HyperDoc

is when you finish recording the screencast you can copy a shareable link to the video because it automatically saves to your Google Drive. They then copy that link to a Padlet wall I created.

Please let me know if you use the activity with your students, I promise you and your class will not regret it! I want to share an example from a student and I am waiting on them to give me permission since it has their name on it.

Slopes Aren’t Always Positive

Unit 3 lesson 9 today (11/9/19) in grade 8 was overall a success. The cool down was a bit brutal with students making slope triangles without lattice points and drawing a line through a point with a slope of -2 but not making horizontal correct, overall it was a success.

It starts out with one of my favorite WODB prompts which allowed me to dust off my sentence frame anchor chart ( I believe in seasonal charts so when we are using that routine it comes out of storage).

I’ve actually used this exact prompt at Back to School night at the beginning of the year with parents and at the end of the year’s Open House to model one of our routines. They talk about steepness and some remember slope. The most unique answers I’ve seen is s is the shortest segment.

At this point in the unit, according to the Course Guide, students are expected to be producing the language of slope by lesson 5. So, it is possible they may say line V has a negative, decreasing, downwards slope. According to the lesson narrative, they are not expected yet to say positive or negative slope.

The launch to the first activity is awesome. It provides the context of fare cards on a subway. My students were able to relate to this because I said, “raise your hand if you’ve ever ridden on BART?” So, students were able to offer how you buy a fare card and then when you put it into the machine it takes off money. I made sure they knew that in this problem it was a flat fee per ride, unlike BART and other systems where they take off more per ride based on how far you travel.

In the activity, students find out how much money is left on the card after 0, 1, 2, and x rides, graph the results, and answer how many rides Noah can go on before his card runs out and where do you see this on the graph.

In the synthesis, you ask students, “why does it make sense the slope of your graph is -2.5 rather than 2.5?” After discussing that the amount on the card decreases by $2.50 every ride, and the points are decreasing on the graph, you ask where we see when the card runs out. This brings up 16 rides. “What do we call that point on the graph?” Many students will remember “x-intercept.” Also in the synthesis, you bring back the graphic from the warm-up showing that two lines have a slope triangle with a vertical of 1 and a horizontal of 3, but they are not the same slope. One is negative 1/3 and the other is positive 1/3.

Since many students struggled with the expression with the variable, I made a point of asking students exactly how they calculated 1 ride, and wrote 40-2.50*1 and 40-2.50*2 to emphasize the structure of the x being the number of rides being multiplied by the price per ride. It’s important to increase access to this abstract thinking for all students to see this pattern and be able to reason about x rides being 40-2.5x as seen below:

We also got side tracked a little bit about mental math when students were getting 40-2.50 incorrect. I think some may have got 38.5, so I talked about how you can subtract 40-3 to get 37, and since 3 is .50 away from 2.50, you can add the .50 back on.

In the next activity, students are asked to notice and wonder about this graph:

Screen Shot 2020-03-03 at 10.00.41 PM

Then students describe what is happening with the graph, ensuring that the x axis is no longer number of rides but days passed. They also plot and label 3 points, write an equation, and write down what makes sense for the slope of the line.

Some students see that all the coordinates share a y coordinate of 20, so the equation is y=20. Many students did not see this. I encouraged students to make sense of the structure of the first equation, y=40-2.5x, and how it could relate to this new graph.

And this is where a very proud moment happened. A student of mine that is frequently tardy, disinterested, uses the restroom every day, gives little effort, and tests my patience a lot came up with equation below: y=20-0x with no help from myself or their peers. I was so proud that I wrote the person’s name on the board. I also took the chance to call their family with a positive phone call home to show that they showed me that when they give forth their best effort that they showed they can achieve.

Students realized that the slope must be zero because it’s not increasing or decreasing, so it could be y=20+0x also or even y=20 since anything times zero is zero.

There is an optional activity after this, and then a really awesome lesson synthesis. The instructions are “Ask students to pretend that their partner has been absent from class for a few days. Their job is to explain, verbally or in writing, how someone would figure out the slope of one of the graphed lines. Then, switch roles and listen to their partner explain how to figure out the slope of the other line.” This is really awesome to listen to. It’s amazing formative assessment to see students talk about what they learned using a graphic that’s not in the book, so no one has a head start on it. One line has a slope of 3/4 and the other is -1/2, so as the teacher we are able to walk around and eavesdrop during the synthesis to call on people to share with the class. Finally, the cool-down is calculating 2 slopes, interpreting what a slope of zero could mean, and drawing a slope of -2 through a given point. This last question was quite difficult for students.

This is one of my favorite lessons, and a memorable day in my classroom, way back in Unit 3. I like this lesson because the context is culturally relevant. Students can relate to it. A fare card, money, thinking when the money will run out, etc. Also, writing equations is a really important skill that they’ve worked on in 6th and 7th grade and will continue to do in 8th grade and beyond.

Revisiting Co-Crafted Norms 2019-2020

I have blogged previously about co-crafting norms with student input within the first month of school.

I noticed last year that the same students who participate in class discussions were of not surprisingly the same students who were sharing their ideas on norms. I felt that my norms weren’t getting input from the students who didn’t share much or at all and whose ideas I needed the most to make it a better environment.

I mentioned this idea below during my recent presentation on anchor charts. If you’ve developed norms with students, you’ve already done the most important anchor chart of the year!

So, my idea to increase participation was giving all students a post it note to write what they didn’t like people saying or doing in math class. Then when I said go they all came up and emphatically stuck it onto the blank chart paper. I also said no names to get more honest opinions.

Then, one by one, I read them out. If someone said something just to be funny I did not read those. We then sorted them into categories of similarities to consolidate our norms into summary sentences. If you look closely at this cluster, you’ll see a common theme that permeates through every class period and I’m sure yours too:

As you can see, that common theme is how peers react to wrong answers. Calling people dumb, telling them they’re wrong, laughing at them. This reinforces the need to be hyper aware of how we as the teacher and the rest of the class reacts to a wrong answer. I definitely address particular people or the whole class if it’s more than one person. It usually involves me complimenting the student who got the wrong answer because they showed courage to share. So, the ones not raising their hand have no right to judge.

So, at the midpoint of the school year, I felt many classes were forgetting about the norms and rules, so it was time for a rules refresher and a norms refresher. I also had a pair of students transfer to another teacher because they stopped working for me, one student who transferred to a different period based on what a kid said to them, and another kid transferring to another teacher because of a conflict with a classmate. Also, some of my students felt they were getting picked on for talking while I was talking or being off topic and said they weren’t the only one doing it. Which may be true, and I think the students that are the most frequent and loudest get my attention more, unfortunately.

This is what a student that transferred out of my class didn’t like people saying or doing in math class.
And what they liked. Clearly this student doesn’t understand the importance of learning the math and showing the work to arrive at the answers. Interesting that they like people being nice when they themselves would loudly complain about being randomly assigned a seat near someone they weren’t friends with. I do respect them telling the truth about their motives to talk with friends during class discussions. Is this just a maturity level thing?

So, I recently posted this tweet:

I got some great responses, which lead to me to borrow the book Teaching with Love and Logic to have a little refresher on classroom management. I haven’t started reading it yet, but plan on highlighting, taking notes, to write a blog post book review at some point before the end of the school year.

I wondered how I could do a rules and norms refresher that was an effective use of class time. It had to be time well spent because I wouldn’t be teaching a full lesson that day (in fact I got a decent lesson in, not so good synthesis).

I decided to take the norms for each period and type them to make them more legible. Here they are:


  1. Laugh or tease others when they are wrong (it’s discouraging).
  2. One voice at a time.
  3. Others are not included.
  4. Bragging about test scores.
  5. Someone says “this is easy.”
  6. When the teacher yells.

  1. Be nice. Encourage others with “good job” or “nice try.”
  2. People help others without giving answers.
  3. Participate by trying your best and “doing  the work” and not goofing off.
  4. Respect personal space.

  1. When people laugh at a mistake or idea.
  2. Called on when not raising your hand.
  3. Saying “that’s easy” or “I thought you were smart.”
  4. Shouting out when not supposed to.
  5. Name calling or yelling.
  6. Trying to get attention for off-task behavior.

  1. When people offer help.
  2. Like humor, just not all the time.
  3. When people encourage each other with nice things such as “keep it up, nice try, or good job.”
  4. Have the courage to ask for help.
  5. We work alone before talking to our partner.
  6. Everyone participates.

  1. People are talking during quiet, independent think time.
  2. Bragging about test scores.
  3. Call out people that are tardy.
  4. The sample people raise their hands.
  5. Saying “That’s so easy,” or “How do you not know that?”
  6. Criticizing a wrong answer.
  7. Give an answer while we are still trying to figure it out.
  8. Gossip or tell rumors.

  1. People explain their ideas.
  2. When people actually try.
  3. When we compliment and encourage each other like saying, “You can do it!”
  4. Ask for and offer help.

  1. Talking while one person is sharing to the class.
  2. When it’s too hot or cold in here.
  3. When people say “How do you not know how to do it?” or this is “too easy.”
  4. When people don’t talk about the math.
  5. Classmates not trying.
  6. Classmates that aren’t listening.

  1. Talk about the math and classmates support them when necessary.
  2. Have the courage to ask questions.
  3. Don’t just give answers and work hard.
  4. Listen to each other.
  5. When more people participate.
  6. Trust each other.
  7. Be positive and respectful.

  1. Laughing when we make a mistake.
  2. Throwing stuff.
  3. My partner doesn’t talk to me.
  4. Being mean or name calling.
  5. Saying “How do you not know that? It’s easy.”
  6. Copying work instead of trying to learn it.

  1. When the teacher gives fair warnings and does not yell.
  2. Pay attention to your classmates instead of ignoring them.
  3. People are patient.
  4. Classmates are nice, friendly, and make new friends.
  5. Giving effort and being productive.
  6. Offering help.
  7. Giving positive feedback like “nice job, good work!”
  8. Asking for help instead of copying.
  9. One voice in class discussion.
  10. Courteous mathematical arguments.

My idea was to read the things students didn’t like first. Then I asked which of these norms do we need to improve on the most? In many periods students immediately shouted out, “all of them.” I agreed that that may be true and that’s why these norms were developed. A close to perfect classroom would follow all of the norms all of the time.

I had students vote by putting their top choice as the number of fingers they were holding up. Or students spoke freely. Once we narrowed it down to one or two I made those bold. Then I asked what they think they were doing well with. I then put a (+) next to those. Then I repeated the procedure for the things they did like people saying or doing. We concluded by myself writing a goal that summarized what we need to work on improving at and what we need to continue to do well. It offers some insights into commonalities as well as unique situations in class periods which I will reflect on here.

Things I don’t like people saying or doing: Things I do like people saying or doing:
    1. Laugh or tease others when they are wrong (it’s discouraging).
    2. One voice at a time
    3. Others are not included.
    4. Bragging about test scores.
    5. Someone says “this is easy.”
    6. When the teacher yells. (+)

  1. Respect personal space. (+)
  2. Be nice. Encourage others with “good job” or “nice try.”
  3. People help others without giving answers.
  4. Participate by trying your best and “doing  the work” and not goofing off.

1* GOAL:

We want to be nicer to each other, encourage each other, and have more people participate by raising their hand and people giving forth their best effort. We want classmates to help others when asking for help.

First period is always a challenging class I feel every year. Students are still half asleep and may not have gone to bed at a reasonable time. I also experience students that understand the math but resist sharing. This affects their participation grade. Clearly students feel like some people are not being included, so cooperation in think pair share needs to be more explicit and reinforced by myself. It also looks like I am not yelling so that’s good. (I even had a former student visit me this week and commented how I calmed down in the middle of last year. I attribute that to giving a Teacher Report card (new one to follow in a future blog post) and piloting SEL curriculum that made me pause and reflect on my values before making a decision, like yelling, and therefore usually deciding not to. We also have some students that get off topic or off task because they’re not persevering and not engaging in the process.

Things I don’t like people saying or doing: (3*) Things I do like people saying or doing:
    1. When people laugh at a mistake or idea.
    2. Called on when not raising your hand.
    3. Saying “that’s easy” or “I thought you were smart.” (+)
    4. Shouting out when not supposed to.
    5. Name calling or yelling.
    6. Trying to get attention for off-task behavior. (-)
    1. When people offer help. (+)
    2. Like humor, just not all the time.
    3. When people encourage each other with nice things such as “keep it up, nice try, or good job.”
    4. Have the courage to ask for help. (+)
    5. We work alone before talking to our partner.
    6. Everyone participates.

3* Goal: We are going to continue to not say “that’s easy” but we are going to improve on not trying to get attention for off-task behavior. We are going to continue to offer help, but will try to work on working alone before talking to our partner and having more people participate.

This class has a mix of many students who have challenging behaviors. Many also struggle academically and give up easily. It looks like students are being respectful in how they talk to each other, but need to continue to work on making mature decisions that have their learning as the main goal. It also looks like they also agree that they don’t like the same people always participating, and that they sometimes move to collaboration before individual think time is over. It also sounds like people are afraid to ask for help and want people to offer help more. Although the class thinks they’re getting more courageous in asking for help.

Things I don’t like people saying or doing: (4*) Things I do like people saying or doing:

  1. People are talking during quiet, independent think time. (-)
  2. Bragging about test scores. (+)
  3. Call out people that are tardy.
  4. The same people raise their hands.
  5. Saying “That’s so easy,” or “How do you not know that?”
  6. Criticizing a wrong answer. (+)
  7. Give an answer while we are still trying to figure it out.
  8. Gossip or tell rumors. (+)
    1. People explain their ideas. (+)
    2. When people actually try.
    3. When we compliment and encourage each other like saying, “You can do it!”
    4. Ask for and offer help.

Today’s 4th period goal set January 28th, 2020 is: we are going to work on being quiet during independent think time, and we are going to continue to not brag about test scores, say “that’s so easy” and to avoid gossiping or telling rumors. We are also going to work on asking for and offering help in class and actually trying our best. We are going to continue to explain our ideas.

This class has gotten better at following the think pair share procedure since revisiting the norms. I’m actually working on pinpointing who is disrupting myself or others when addressing the class. That’s another reasoning I’m reading Teaching with Love and Logic because making threats without consequences or lecturing about it is not effective. It also looks like the class thinks that people are not giving forth their best effort. There truly is such a thing as positive peer pressure and it’s a great thing when there’s visible evidence of it in class.

Things I don’t like people saying or doing: (5*) Things I do like people saying or doing:
    1. Talking while one person is sharing to the class.
    2. When it’s too hot or cold in here.
    3.  When people say “How do you not know how to do it?” or this is “too easy.”
    4. When people don’t talk about the math.
    5. Classmates not trying. (+)
    6. Classmates that aren’t listening.
    1. When people offer help.
    2. Talk about the math and classmates support them when necessary.
    3. Have the courage to ask questions.
    4. Don’t just give answers and work hard.
    5. Listen to each other. (+)
    6. When more people participate. (+)
    7. Trust each other.
    8. Be positive and respectful.

5th period Math 1/28/2020: We are going to work on talking about the math and not saying this is “too easy” or saying “how do you not know that?” We are going to continue to try our best. We are going to work hard, offer help, and not just give answers. We will continue to listen to each other and have more people participate.

This class after lunch has made a big improvement lately. They seem to be learning a lot more and pressuring each other in a positive way to create a culture of learning. There is a student who works ahead and barely missed the accelerated track and the negative talk of belittling is not appreciated by classmates who don’t understand something as well. There are also some people that are good friends outside of class which leads to more frequent off-topic discussions. The class feels more people are participating but people are still giving answers and not explaining as much.

Things I don’t like people saying or doing: (6*) Things I do like people saying or doing:
    1. Being mean or name calling.
    2. Saying “How do you not know that? It’s easy.”
    3. Copying work instead of trying to learn it.
    4. Laughing when we make a mistake. (+)
    5. Throwing stuff.
    6. My partner doesn’t talk to me.

  1. People are patient.(+)
  2. Classmates are nice, friendly, and make new friends. (+)
  3. Giving effort and being productive.
  4. Offering help.
  5. Giving positive feedback like “nice job, good work!”
  6. Asking for help instead of copying.
  7. One voice in class discussion.
  8. Courteous mathematical arguments.
  9. When the teacher gives fair warnings and does not yell.
  10. Pay attention to your classmates instead of ignoring them.

6* Goal for 1/28/2020: In 6th period we are going to work on not throwing stuff and actually talking to our partner. We are going to continue to not laugh when people make mistakes. We are going to work on paying attention, staying on task, and not ignoring our partner. We will continue to be patient and friendly.

This is my last class of the day. Again, there is a constant battle to develop math identities, boost confidence, to diversify and increase participation. I mentioned to this class that they are the only class that mentioned throwing stuff. I said that’s not something to be proud of because that’s clearly only an issue in this class. So, there’s a couple people that find it funny and once again trying to distract from their own learning. It also looks like there’s a lot of fear to participate in partner talks. It came up on the right side of the norms in classmates ignoring each other. I mentioned that if you are talking to another table or to someone across the room, it’s pretty disrespectful to the people at your table. Once again, there are some students that feel they are getting picked on for their off task behavior which is another example of why I’m reading Teaching with Love & Logic.

Anyways, I hope this blog post was helpful to read. It was basically a way for me to talk about how I co-develop norms, and how I tried to re-engage students with those norms after winter break when I felt at this mid point of the year I have to make sure they are not giving up and still encouraged to do their best.

The next 2 blog posts I write are on the teacher report card I gave this year and the ideas I want to implement from the book Teaching with Love & Logic.

VIDEO: Opening Up Grade 8 Unit 4 Lesson 11

I made a screencast reflecting on a lesson (link). The main points are:

  • For a Notice & Wonder routine, copy and paste the image into a Google doc, create a 2 column table for I notice… and I wonder… to type student ideas below the image rather than writing it on the whiteboard. I also write the students name in parentheses to increase their math identity. This also works really well for me because I can type faster than I write and it’s much more legible
  • I didn’t show it, but I mention that I project students group seating in groups of 4 via Flippity. It also makes it easy to switch to groups of 3 if we are going to stand up at the Wipebook whiteboard stations to do some problem solving
  • I show how you can access the free Google Slides from the lesson plan link called “Community Resources”
  • If a lesson involves graphing with precision, I print out student task statements and project it under the document camera so what I write on is exactly what it looks like in their workbook to make sure all students have a chance to correctly write and understand an activity
  • I finished reading 5 Practices in Practice, which I will blog about soon, and it emphasizes that discussing “partially developed ideas sends important messages about taking risks” and how “there can be important benefits to discussing errors and false starts.”
    • I show the development of students thinking in creating a correct graph of y=-2x+15 by asking students what’s right and what’s wrong about: y=2x, y=2x+5, y=-2x+20, and so on (Desmos link)
  • Remind students and yourself that not all students will be done with a problem when you start synthesizing and that the discussion is super important to be involved in to learn from.
  • Know that the Lesson Synthesis can and most times will be direct instruction. You have to make sure to make the learning goals explicit from the lesson.

Since I have the free version of Screencastify, the screencast is broken up into 2 10 minute chunks. Please leave me a comment on the blog or tweet me any questions or comments.

Part 1:

Part 2:

CMC South 2019 Recap

It must have been a good omen for the start of the weekend, because my flight out of SFO included Jay from Desmos and Kathy a Desmos fellow. We hung out before take off and got to know each other better. I am going to review my written notes in this blog post to synthesize big ideas and reference this post later on, rather than my notes.

Building Math Residue with Lessons that StickGraham Fletcher

I have seen Graham present on a video recording, but never in person. I had the chance to see him, and I am so glad the K-5 label it had didn’t scare me away. Experienced presenters can use humor that’s  planned and not improvised, and I love this quote from him, “What was the last word problem you gave your students? … Can’t remember? … Neither can you your students.”

This lead to his main idea that if we launch a unit with a juicy task, it will constantly be referenced throughout the unit, especially if we tap into students curiosity with notice and wonder to co-craft questions that can be explored later on.

One salient point was not saying “simplifying” fractions but “renaming.” Also, to read 1/4 as “one one fourth” rather than “one fourth,” emphasizing it as a unit fraction. Saying 3/4 as “three one fourths.”

What I learned was that he is intentional with his language. We also looked at comparing fractions by:

  1. Common denominator
  2. Missing Parts
  3. Benchmark Fractions
  4. Common Numerator

For example, 8/11 is greater than 4/7 because both have 34 parts missing, but the 3/11 is a smaller part than the 3/7 missing from the second fraction.

Graham suggested students using blue pen before scaffolding, and a red pen after scaffolding to see students growth. He also referenced Pam Harris’ graphic organizer about Counting leading to additive, to multiplicative, and then to Proportional. It’s a great reminder to see how my students thinking has developed over their history.

To emphasize how context helps, he asked us to think of things that are white… (stuck, can’t think). Then think of things that are white in your fridge. (then we can say more: milk, eggs, cheese, etc.) Context helps.

I believe we finished with an Open Middle problem after watching some cool 3 act task launches he just created with one of his daughters. Great session and start to the conference.

Supporting Equity: What we are learning at IM – Bill McCallum & Dionne Aminita Samb

I think it’s obvious why I went to this session. Bill is one of the writers of common core as well as the curriculum I use, Open Up Resources 6-8 Math by IM. I also watched Dionne’s Shadowcon talk and participated in the follow-up email PD.

In this graphic you can see the path IM has taken. I remember being frustrated with teaching 2 way frequency tables and finding amazing tasks for it on the IM web site many years ago, and many of those tasks found their way into their curriculum.

I believe they are testing their new K-5 curriculum in the Council of Great City Schools, which in 2010 represented 8 million students, 71% of which are on free and reduced lunch.

The cited statistics from “The Opportunity Myth” to conclude that it’s not who can do the math, but who gets to do the math. Too many students are not getting access to high quality rigorous curriculum aligned to current grade level standards.

This slide talks a bit about what a problem-based curriculum is as well as the supports IM offers.
Then we got to dig into some math from Grade 3 where we located 1 and 3/4 on different number lines. It provided some great discussion.

Dionne leads the 3-5 curriculum. She cited Culturally Responsive Teaching, a book I really need to read. She looked at two categories of learning: collectivism and individualism. Students of color are more collectivist culture than individualist.

We then noticed and wondered at this data where a high score was more a more individualist country. We noticed lots more Spanish speaking countries being collectivist and Western society being more individualist.

We then took a look at a task from Grade 5 and similar to Mr. Stadel, did a brave too low, too high, and about right for the number of number cubes in the image. I said 45, 63, and 180 respectively. The answer was 90. Great table conversations about layers and one person mentioned your estimate must be a multiple of 9, especially if it’s not hollow.

Then she mentioned how instructional routines support equity because they engage student curiosity and offers daily opportunities for discourse and students to explain their thinking. They can “unleash higher learning in ethnically diverse students.”

Dionne showed how the IM lesson structure is similar to the one suggested for a Culturally Responsive Lesson. As you can see the descriptions in the slide, you first ignite, chunk, chew, then review the lesson.

Ask yourself two questions each day:

  1. Who participated in math class today?
  2. Who got to do math today in class?

Use Anchors to Make Math More Accessible – My session

Here’s the bad selfie I took right before we got started.

I am going to present this same session in a 60 minute format rather than 90 at CMC North this Saturday so I won’t go into too many details. I will write another blog post with the slides and the feedback I got from attendees. For the 60 minute I will do a stand and talk rather than a complete Successive Pair Share as shown below with the graphic organizer.

I’m really proud of the rough drafts attendees came up with. The goal was to plan a particular anchor chart about a big concept coming up in your classroom and how you would organize it and use #purposefulcolor.

This partnership was talking about 7th grade y=kx proportional relationships.
Another 7th grade group was thinking about visuals to go along with two step distributive property equations.

I am also really proud of 3 different people coming up to the document camera to show their work to the whole group.

Devin Rossiter talking about visualizing division.

MLR’s: Building Discourse Communities Vanessa Cerrahoglu (@mymathsoul) & Craig Schneider

I had to go to this session because last year Vanessa presented in the same time slot as me so I missed her. She’s a coach for IM and so is Craig. We looked at the routine Co-craft questions with a 9th grade Unit 1 Alg 1 Statistics task. Basically the questions provide lead ins to help answer questions you want to ask the students anyway. It also provides a natural extension for those that are done.

Similarly to the first IM training I went to, we reflected on how Vanessa launched the routine. For co-craft questions, I noticed she asked us to have our books (packets) closed, individual think time, pair share, then write the questions up near the visual. My wonder with the routine was what do you do if students can’t come up with a question without giving an example and reducing the cognitive demand. A person at my table also thoughtfully said that there is less pressure to get a question then to get an answer.

We analyzed some student video of the routine, and we could see that students were working on calculations and solving without being told to solve anything and to only come up with questions. So, it shows that our students are trained to solve solve solve, even when we’re not asking them to. The positive side effect is that in the time they were coming up with questions they were exchanging great ideas that lead to questions.

We then did the same procedure with MLR 1. I like their example of a graphic organizer that had the instructions in English and Spanish, since the class that they were using the routine with had 3 newcomers from a Spanish speaking country. The quality of their output greatly improved with each share and had a mix of Spanish and English written. One takeaway is in the pre-write, it’s OK students aren’t done with their first draft. That worried me the first time I used the routine, and now I am less worried with this advice given.

That night was the Ignite. I live tweeted again this year, and it was a great event. I didn’t take any pictures because I was too busy listening and then live tweeting Dr Kristopher Childs.

That night was the pizza meetup which was a lot of fun. I got to meet new people and connect with friends I’d already met. I was so exhausted that my eyes were closing on me so I walked home to my hotel room at around 8 or 9 PM.

Day 2:

Teacher Confessions About Meaningless Ways to Teach Math – Andrew Stadel

Surprisingly this is another person who I’ve never seen present in person. Andrew main theme was “gimmicks die, mathematical reasoning lives.” He challenged us to think about “what math rule are we going to better understand” and how we were going to teach it without using gimmicks. He also encouraged us to write a mission statement to guide our work and focus. I also noticed that he’s pretty good at using pre-planned humor and stating norms for a session.

He played an excerpt from his podcast where he interviewed Hedge about “slip, slide, and divide” I way to factor quadratics with an “a” value greater than 1. It lead us to looking at ways to factor with physical algebra tiles, virtual ones, as well as the generic rectangle.

We wrote down gimmicks we are guilty of using and shared with people from other grade levels. I shared that I had used “keep, switch, flip” for dividing fractions and asked 6th graders to memorize the perimeter formula P = 2L + 2W.

During work time I tried working on how to scaffold a problem where two friends live 7 miles apart and travel towards each other at different speeds. I wondered how I could scaffold it and also wondered why you get the same solution if one is y=0.15x and y=7-0.2x or one they’re flip flopped and one is y=7-0.15x and y=0.2x and asked some people in my next session.

Beauty of Movement: Increasing Discourse in Math Classrooms Sara VanDerWerf & Chris Luzniak

OK, so I have been looking forward to meeting Sara in person for a very long time. She is the originator of the first 5 days name tents and has written a ton of amazing and impactful blog posts. The fact that she teamed up with Chris, who I saw at last year’s CMC North Asilomar for his Debate Math session was a good omen. And before I continue it was easily the best session of the whole conference.

First of all, the atmosphere upon entering was high energy. There was a great soundtrack playing, which I have already borrowed a few songs off. Here’s the tweet with the Spotify playlist:


Let’s just say I plan to play Gloria Estefan’s “Get On Your Feet” at some point this year in my classroom. Maybe on Into the Groove by Madonna and I wanna dance with somebody by Whitney Houston.

Had to get a selfie!

We started with a stand and talk with the prompt “what is the same? What is different?”

Standing increases discourse. Sara observed for turn and talk students only talked when the teacher walked by. She mentioned @alirubinf incorporates movement daily. We need our students to move every 20 minutes. That’s at least twice a period. Big goal.

Just like her sticker says, Sara firmly believes:

  • Students will see it before I show them, and say it before I tell them.

I have already downloaded the podcast of her Global Math Department talk on Stand and Talks I just haven’t listened to the whole thing yet.

A great tip for stand and talks is if it’s a notice and wonder, to ask students to take turns sharing at least 15 things you notice and wonder. She said not to ask for mathy, it will come. This honors the culture of feeling safe to share what students think, and yes that’s going to involve some humor sometimes.

There were 3 goals for the session:

  1. Intro to Movement activities
  2. Look at the Rationale and Research
  3. How to adapt to your classroom
I just realized this is probably a clip from Hamilton

Peter Lilljedal got a shout-out for his VNPS work (kids standing at whiteboards) and a quote from John Medina was shared, we are “designed to solve problems… in near constant motion.” Movement improves cognition.

Before you give instructions for the prompt, firmly announce, “Everybody: stand up.” And repeat it to those not or moving slow and make eye contact. It’s also a good idea to get students in the routine of tucking their chairs in after standing to allow safe pairing up.

We did two activities from a link that is a collection of a bunch of them ( Balance Points and Rumors.

Balance Points is basically a pair of students working on a problem and when they have a solution that number is the number of contact points they have with the ground. You must be in contact with your partner at the same time. It gets students in the habit of using gestures. Sara picked my partner and I as one of the models to demonstrate how we showed “5.”

From the slides, 7 tips for success were shared:

  1. No opt-out, no negativity.
  2. Infuse excitement in voice and movement.
  3. Move with your students.
  4. Cross-lateral movement helps memory.
  5. Move 10 school days in a row.
  6. Pick 1-2 movement activities to start with.
  7. Accountability partner.
And Sara offered some of her amazing stickers.

Then we did the activity Rumors. On an index card you write 3 ideas to share. When you partner up you share your 3 ideas, hear 3 ideas from your partner, then exchange cards and share your partner’s ideas with a new partner. They suggested to say “take _____ steps to find new partner.” I think you then do 1 more exchange after that.

Brain imaging showing the research

2 of my ideas I wrote were to bring back the function / algebra walk into my school year and use balance points to review 1 step then 2 step equations.

My goal for 2020 is to bring back the Algebra Walk, do more stand and talks with Flippity for random partnering, try balance points, and get my students up working on the Wipebook whiteboards I invested in. Another tip is she advised us to set a calendar alert for Sunday night to remind you of your goals for the week.

This was a powerful quote of an anticipated response for a teacher not ready to try this.

Like I said, the best session!

Fawn was at my table so I had to bother her for a selfie!


Ran into Jessica Borah in the hallway, a member of our #openupmath PLC!

After lunch it was Mike Flynn or Ed Campos and I opted to check out how Ed integrates computer science into Algebra concepts through Bootstrap.

Bootstrap Algebra Ed Campos

Ed ran his session through PearDeck which was a really cool way to make it interactive. Basically Bootstrap Algebra has modules that allow students to learn algebra concepts through a programming language. We practiced writing expressions as a “circle of evaluation” which is a cool visual that helps write the code. It helps students understand the order of operations and the syntax of a programming language.

One of Ed’s students created a game where a dog shoots knives out of it’s mouth to stop ice cream and collect biscuits. The student made all the graphics in Adobe Illustrator themselves.

There is a lot to explore with the interface and it’s all executed on the web site He also talked about how we can use #purposefulcolor to help students see the connections between the multiple representations of code in an expression and the circle of evaluation. You can also draw shapes like (ellipse 50 100 “outline” “red”) and students can figure out if 50 is the height or width by switching the numbers, changing outline to solid, red to a different color, etc. I like how you could then put that whole command inside (scale 3 (triangle 40 “solid” “purple”) to make your shape bigger or smaller.

What do I say now? Responsive Facilitation of Small Groups Geetha Lakshminaryan & Alissa Fong

Geetha has done some coaching work at my school when partnering with my district’s math coordinator so I wanted to spend some time learning from her and her colleague Alissa. They work at Stanford’s Center to Support Excellence in Teaching (CSET) and remotely coach new teachers. They referenced a book I must request my district to get, In the Moment: Conferring in the Elementary Classroom by Munson. The session was about adaptive expertise for in the moment classroom decisions. One quote they showed was, “The first question is easy – it’s the follow-up question that is hard to learn.”

We thought about 5 ways an interaction could move a group forward:

  1. Collaboration
  2. Conceptual Understanding
  3. Strategy Development
  4. Representation / Connection
  5. Communicate Thinking

Alissa mentioned that as teachers we need to avoid always jumping to 3 and trying to help students develop a strategy. For interaction 1, the group may not be sharing their ideas and need assistance doing so. For interaction 2, the students may or may not understand the problem hindering conceptual understanding. For interaction 3, we have to be careful not to just give the students OUR strategy, therefore robbing them of doing their own thinking and lowering the cognitive demand the task may provide. For interaction 4 we might be asking questions that lead students to see a connection to a different representation. And finally, we know that sometimes we want students to communicate their thinking more clearly verbally and written so that other groups and the teacher can understand their ideas better.

Their recommendation is that 75% of time spent conferring should be eliciting student thinking only. Really understanding what they do and do not know.

The session focused on nudging. It’s a cycle where we elicit student understanding, attend to what they say, interpret what they know, decide what to do, and then execute a nudge that is a question or suggestion that will advance the group’s progress and allow us to elicit from other groups.

They talked about a cycle of how they work on nudging as a core practice.

  1. Introduction and learning about the core practice
  2. Prepare for and rehearse what you will do
  3. Use it with students
  4. Analyze and reflect

One of the video clips we analyzed was Dan Meyer’s 3 act task about the Super Bear which was cool because I was familiar with the context.

Geetha’s session ended early so I got to see the last 10 minutes of Bill McCallum’s number line progression session. It was cool because he gave out a packet on the progression from K through 12.

It provided me with some cool stuff to dig into on the plane ride home. For example:

In second grade students are figuring out intervals, and then labeling exact points between the intervals. This is from the alpha materials of their upcoming K-5 curriculum.

When I got to the session he was talking about addition and subtraction of integers on the number line. I am very familiar with teaching it so I was discussing it with some participants from earlier grade levels that were unfamiliar.

And of course I got to remind myself of the 2 major instances the number line is used in grade 8:

Zooming in on a repeating decimal, 2/11
Using a coordinate graph and a circle to approximate the square root of 2.


Of course I had to ask someone who wrote the Common core standards and is the president of IM for a selfie!
Special thanks to Ed Campos for being my mentor and zoom chatting with me to help review my presentation outline with me. He also let me stay with him and is a class act person and a friend.


If you made it this far, great, thanks for reading. CMC South continues to be the premier math conference to go to with speakers coming to the west coast nationwide. It’s awesome they reimburse for office supplies so that some lucky participants went home with sharpie flip chart markers to create their own anchor charts. I’m looking forward to reviewing these notes to implement some ideas and take on a whole new set of ideas this weekend at CMC North Asilomar.


So my County Office of Education (San Mateo) offers a lending library in their STEM center now. I have used it before to read Strength in Numbers by Ilana Horn, which I also wrote a blog post about. Now their library selection is available online and I saw a book I’ve heard many people speak about: The Impact of Identity in K-8 Mathematics by Julia Aguirre, Karen Mayfield-Ingram, and Danny Martin.

Since I have to return the book, I am going to write a blog post covering some of the main points that I can reference later.

In Chapter 1 they offer a comprehensive definition of equity:

“All students…must have the opportunity and support to learn rich mathematics that fosters meaning making, empowers decision making, and critiques, challenges, and transforms in equities and injustices. Equity doesn’t mean that every student should receive identical instruction. Instead, equity demands that responsive accommodations be made as needed to promote equitable access, attainment, and advancement in mathematics education for each student.”

This definition requires us as teachers to really learn about our students as learners and identify and recognize their strengths to further their learning.

At the end of the chapter, one of the discussion questions asks, “What strategies have you used to learn about the school and life experiences of students in your classroom?” Every year I have continued to use the “Mathography” prompt from CPM to have students write me a letter describing themselves and their relationship with math. I am able to find out about what unique interests they have that I can tap into and ask further questions about, as well as their mindset around math. I find out about their family situation at home as well as how they may not see much uniqueness about themselves, which I then try to uncover throughout the year. Many students unfortunately recall competition and punishment regarding math facts. They also talk about how math got a lot harder in 5th and 6th grade. I feel this is due to division of fractions and more ratio thinking. Another strategy is using name tents the first 5 days of school ( that allows me to have a back and forth written conversation with students which is super helpful for the shy and non-verbal people.

Chapter 2 discusses vignettes of students describing their mathematical identities. Agency is the ability to participate and perform effectively in mathematical contexts. Gresalfi introduces two different types of mathematical agency: disciplinary and conceptual. Disciplinary being the ability to recall facts and execute procedures to get a correct or incorrect answer. Conceptual agency is students being positioned to take initiative in constructing meaning and understanding methods and concepts.

A goal for all teachers is to creative opportunities for disenfranchised students to engage in productive forms of agency. A new term I hadn’t heard was “collective mathematical agency when teachers and their students act together to solve problems, working from the shared belief that viable strategies can be developed and solutions can be found.” This definition totally reminds me of the 5 Practices, with the teacher positioning students to share their ideas as the teacher selects and sequences their work to make connections between them and to the learning goal. Reading it was a great affirmation that I am constantly trying to make students see themselves as capable problem solvers.

In Chapter 2 it also mentions the five intertwined strands students can show mathematical proficiency according to Adding it Up: Helping Children Learn Mathematics by the National Research Council:

  1. conceptual understanding
  2. procedural fluency
  3. strategic competence (formulate, represent, & solve problems)
  4. adaptive reasoning (logical thought, explanation, & justification)
  5. productive disposition (“inclination to see math as sensible, useful, & worthwhile, coupled with a belief in diligence and one own’s efficacy”)

Relevant to my student population, the book points to resisting “model minority” myths comparing Asian and East Indians to African American, Latinx, or Native American. Scholars have challenged this idea by pointing out the educational struggles of various Asian American subgroups like Laotian, Hmong, Mien, and Cambodian students. It also overlooks poor and working class Chinese and Vietnamese students. I must reflect and understand Asian American students are varied and diverse in their identities and backgrounds.

We can also empower our EL students by considering them as “multilingual language brokers” rather than “limited English.” I need to value how mathematical concepts in English are said in students home languages, and research how to say some of these words myself. I recall earlier this year talking about how to get from a center of dilation to a point to dilate by describing “how many up and over.” I honored Spanish phrases by saying “tres a la izquierda” (3 to the left) and a student who often isn’t in class or engaged contributed “cuatro debajo” (4 down).

The authors say a focus on learning rather than labeling is critical. Rather than seeing students as “at-risk” we need to see them as a more positive trait: resilient. I know in my class I try to raise the status of students that who may have been labeled and show that they have valuable ideas to contribute. It’s up to us to listen closely and catch those moments and celebrate them.

In chapter 3 math teachers are examined in vignettes sharing their identities as math learners growing up. This clearly has shaped how they shape the decision we make in our classrooms. Some teachers will go on to try to replicate their own experience for their students, or offer students a different, more positive experience than theirs.

Society values math as a high-status subject that often acts as a gatekeeper. Luckily over time quantitative literacy has become a critical competency, essential for making sense of the data, information, and technology that are part of our daily lives.

My own mathematics learning autobiography would have to include acceleration in middle school and then some struggles towards the end of high school when I found out my foundation wasn’t as strong as I thought it was. It also showed in college when I felt I was not ready for pre-calculus or calculus after struggling in pre-calculus my senior year. I left San Diego State after a year, after making poor decision academically and socially, and found a renewed focus in community college. There I took a math class where I listened to the lecture and it was time for group work. My group turned to me and said, “did you understand anything he just said?” I said, “Yeah, this is what I think we need to do…” and proceeded to explain it and see that my peers understood me. That was my light bulb moment that I wanted to be a teacher. After transferring to Sacramento State, I still didn’t know I wanted to teach math all day so I got a K-6 liberal studies focus and went on to another college to get a multiple subject credential. I started teaching 6th grade math and ended up studying hard and taking the CSET single subject math subtests 1 and 2 to be authorized to teach up to 9th grade math. I also took a Calculus course a few years into my teaching career and excelled at it with a better foundation in Algebra. I feel that my experience allows me to relate to students that feel they are ready for more and also those that feel frustrated of feeling a lack of background knowledge.

Part 2 of the book highlights 5 equity-based math teaching practices:

  1. Going deep with mathematics.
  2. Leveraging multiple mathematical competencies.
  3. Affirming mathematical learners’ identities.
  4. Challenging spaces of marginality.
  5. Drawing on multiple resources of knowledge.

One of the first vignettes describes Mr. C exploring a student claim that a student was “suspended for being Mexican.” He organized lessons that allowed students to explore real suspension data from the school along with racial and ethnic group statistics.

He also posted 5 amazing promises publicly to his students:

  1. I will work with you until you understand.
  2. I will not waste your time, every activity is tied to a learning standard.
  3. I will ensure that our classroom functions as a positive learning community.
  4. I am open to suggestions.
  5. I will learn along with you.

He also positioned himself as a social justice advocate by telling his students that he did not want to work at a “racist school.” His lessons encouraged mathematical analysis and agency.

Chapter 5 profiles a student “Curry Green” who gets in trouble in his math class that is a lot of independent work. When he is transferred to a new class, he is amazed by the Think-Pair-Share routine, of being allowed to share ideas with a partner after a short amount of think time. He also enjoys that when sharing ideas or coming to the board, they present as partners so one partner can pick up where the other leaves off, building confidence. His teacher Ms. Davis leverages multiple math competencies by having students work in stations to see multiplication in different contexts. One of those stations was a visual representation which was one of Curry’s strengths.

Chapter 6 is titled “Mathematics Assessment Within Equity-Based Practices.” One big theme is giving students feedback on what they did that was worthy of praise and which ideas need further development, advancing their thinking through specific questions. The authors acknowledge how time-intensive it is, but how productive it can be.

It reminds me of a tweak I made to how I gave feedback on cool-down exit tickets. I moved to C, PC, and NY instead of checkmark, caret (^) and an X.


I also added comments on what productive mathematical decisions they made as well as questions that hopefully made them consider other important ideas. I started doing the same on unit tests instead of writing “-2” or minus 1 for certain problems. I also omitted a final score so students would not brag or compare with others or more importantly feel embarrassed or shame. This allowed students to really dig into why they may have gotten a PC instead of a C, or a NY instead of either of the other codes.

In part 3 of the book the authors talk about engaging families and communities. There are examples of teachers using newsletters and calendars to communicate what’s being learned in class and what activities families can engage in at home related to the material.

I’ve hosted a Family Math Night, and read this passage after I had presented our 2nd annual one at my school. I definitely touched on the first few bullet points but not the last few. I did suggest

And I absolutely LOVE this resource below!:

I totally want to start a template like this for each of my students so that when it is time to meet with the parents, or to make a positive phone call home, I have specific qualitative data about strengths, weaknesses, and a plan to move forward.

This was a great book and I only touched on some of the ideas, of course not all. Since I have to return the book, I will look back on this post to work on implementing some of these practices. I feel the piece that is missing from my teaching is really learning more about my students’ identities and using that to motivate them to develop their own agency and motivation.

P.S. I searched for Danny Martin on twitter but found a link to his NCTM keynote called “Taking a Knee in Math Education” which I will definitely view in full later.