Summer Thoughts and Takeaways

This summer has been different compared to other years. Certainly different than last year when everything was shut down. I think the hectic pace of this past school year has many educators taking a break from school related work. Instead, they are focusing on other activities. Being outside, reading, cooking, gardening and other tasks have taken the place of planning for the new school year. I think this is a good thing. It is unfortunate but not shocking that many teachers left the profession last year. Teacher burnout is real and educators need time to decompress after the 20-21 year.

This summer I have taken a step back from working on creating /editing my Desmos decks and planning school tasks. I have not touched google slides and my school backpack remains closed – at least for now. I am taking a stats class this summer and learning something brand new. Feeling the struggle of learning something new is refreshing in a way and a good reminder of what students go through when new content is introduced. Even with the stats class on my plate, I am able to prioritize taking time for other activities. I have been able to read for enjoyment and work in the yard more this summer than I have in the past. My book list includes American Dirt by Jeanine Cummins (highly recommend this book!), A Promised Land by Barack Obama, and am taking recipes out of The All-purpose Baker’s Companion. I have not learned how to make sourdough like many of my colleagues, but my skills are improving.

The last few weeks have been refreshing. I have limited the amount of time on social media and have focused more on less tech-related activities. I still check-in, but am enjoying the outdoors when the weather cooperates. The last three weeks have me thinking about how teachers should have a work/life balance for the 21-22 school year. I don’t think happened last year. I feel like educators are more productive emotionally and physically when they are able to manage and balance their responsibilities.

Although it will be much different, there may be certain aspects of the 21-22 school year that will continue from last year. I am assuming that this upcoming school year will minimally resemble last year. We are still awaiting guidance from the state on social distancing requirements and masks. Will there be remote classes? Will social distancing still be required? What about sharing materials or the new variant? So many questions and not enough answers. It is still not going to be a typical school year, but that is okay. It is all about balance.

Let us grab a few self-care takeaways from the summer and use them when school starts back up in the fall.

New Learnings and Insights for Next Year

Back in May I decided to register for a college level statistics course. I decided this for a couple reasons: 1.) The credits could be used to receive a teaching math credential that will be useful in the future 2) I have always enjoyed analyzing school/student data as it relates to different types of assessments. I did not take the class in high school or college. A few of my graduate school classes required me to analyze data and set goals based on certain criteria but nothing was formally titled education statistics. I would characterize myself as a rookie in the stats knowledge department. With that being said I do not remember that last time that I took a non-education college level class. Near the end of May I confirmed my registration, purchased a textbook and found a used TI-83 calculator on marketplace.

The class is from a nearby community college but I opted for the “anytime” class as it work better with my summer schedule. The class started at the beginning of June and ends close to August. It is the first time experimenting with an “anytime” class so I was not sure what to expect. I was pleasantly surprised to see that the class was in Canvas (that’s what we used in school!) so I already knew my way around the platform.

The class opened up last week and I took a gander and what was inside the modules. The class has 11 multiple choice quizzes that you can retake up to three times. I am a fan of retakes, but you have to retake the entire quiz and not just the questions that you had incorrect. I am planning on giving feedback on this after the course has finished. There are lecture notes and power point slides for each chapter. Besides the quizzes, there are also Excel and TI calculator assignments, a mid-term and final exam. Old school are the two words that came to mind after reading the syllabus.

The assignments open and close on certain dates so you can only go ahead so far. This is not a self-paced course. Last week I read chapter one and completed the quiz. Many concepts were new to me and I had to retake the first quiz. Before the second attempt I took out the highlighter, reviewed the concepts online and found a few Desmos AP stats decks that were about the chapter. The second time was better but not by much. I decided to move on and not dwell on the need to chase a perfect score. As the class continued I took an additional quiz and performed better but still did not feel like I was was thriving in this “anytime” class. I am learning new concepts and feel like I grasp certain skills better than others. I think part of this is due to the format of the course and most classes that I have taken are more structured with some type of in-person requirement.

After reading through another chapter today I decided to reach out to coach at the college. The college offers help through Zoom. I clicked on a Zoom link and was paired up with a tutor to help talk through some of the problems. We discussed the skills that I had questions about and some of the concepts started to make more sense. In more than a few cases I had a conceptual understanding of what the problem was asking and was able to estimate correctly, but I was not using the the formulas correctly. Go figure. It is usually the other way around in the classroom! I felt much better after the session and things started to click much easier. It was time well spent.

After the Zoom session I started to think of a few takeaways that might be applicable for next school year:

1.) Sometimes you need to talk with others to grasp a concept. Digital resources are pretty awesome for learning new things, but some topics that are much better in-person. In this class you get zero feedback with passive digital resources. For the quizzes I received a correct or incorrect. I had to debate with myself whether it was worth it to retake the quiz not knowing what was incorrect the first time around. With a human you can receive feedback and take action based on the communication. What is your retake policy?

2.) It can be frustrating when you do not understanding something after reviewing it multiple times. I wonder how our students feel in this same situation and what feedback/re-teaching opportunities exist?

3.) What type of support is given to students that have questions outside of class time? This happened quite a bit during remote learning.

4.) How do we normalize the struggle that occurs when a student does not show that they understand a concept after multiple attempts. Please do not say growth mindset.

5.) How comfortable are students when asking for help?

6.) How do students know what to expect when it comes to assignments and quizzes? What formats are you using? Communicating the format and showing students an example can help ease anxiety.

I am learning new skills and am finding the small wins during this journey eye opening. It has been a while since I felt the struggle of trying to learn something new that is not in my wheelhouse. I am looking forward to the journey telling my students about the process next school year.

Studying Women Mathematicians and Scientists

Rosalind Franklin and the two-strand model of DNA

This year my students have been learning about mathematicians and scientists. This exploration started back during Women’s history month in March. My 3rd-5th grade classes highlighted a different woman mathematician every week. We studied Ingrid Daubechies, Florence Nightingale, Ada Lovelace and Marie Curie during the month of March. Not surprising, the study of women mathematicians was new to most students in the classroom. That dynamic changed when I asked the students to explore Mathigon’s site on the history of math.

Students were tasked to review the different mathematicians on the timeline and their contributions to society. I also asked to students to review the posters on a class bulletin board.

By the beginning of April I felt like students were feeling confident with the four women mathematicians and students started to show interest in wanting to learning more. I decided to assign a women in mathematics (could have been titled women in STEM) project at the beginning of May. Students were asked to study a female mathematician from a list

The list was mainly created from the Mathigon site and the Women in STEM site. A google form was used for students to pick their mathematician. I used a Form add-on that eliminated a choice once a person was picked to ensure different mathematicians were chosen. I also asked students to email me if they would like to study another female mathematician that was not on the list. That is how Trachette Jackson and Shakuntala Devi were added.

Students were then asked to make a copy of a Google Slide presentation template. That template was used to help students organize their thinking about what a particular slide should contain. A rubric was also created in the process.

After that the students used a Nearpod collaboration board to brainstorm what a great presentation looks like. I gave the students time to write whatever came to mind. The document was saved and then shared with the students to keep them thinking about what might help improve their presentation moving forward.

Students were then given about 2-3 weeks to periodically work on the presentation. They used time in and outside of class. They used this resource site to gather information about the mathematician. I found early on that more resources were needed and that is why I eventually turned it into a Google Sheet. Feel free to make a copy if you would like to use a similar project in your classroom

After about two weeks students were asked to share what they have put together so far. Most had 3-4 slides completed. They shared via Zoom screen share (since there are elearners and in-person students in the same class) with a partner and gave constructive feedback. Students used the opinions shares to polish up their presentations.

After finalizing their projects in Slides students screen recorded the presentation. Students used iMove to add effects and some even added a voice over element to narrate the presentation.

I am proud of what the students created given the circumstances this year and am encouraged to see students learn more about women mathematicians. I am looking forward to next week when all of the projects will be shared.

Silver Linings

It is hard to believe that this school year closes out in three weeks and it is challenging to describe this year in a brief statement. While the school year end is near it has also been a good time to reflect on a few positive changes that have happened.  Before turning our backs on this year it might be beneficial to see if there is a silver lining.  That potential silver lining has nuggets that will help with planning for a more usual 21-22 school year.

Here are a few ideas to ponder:

  • I am still planning on using digital platforms like Desmos and Nearpod to engage learners in review and math exploration.  Although screen time will be minimized compared to this year, I have found that teacher-paced digital decks have potential and the data that is collected in the process pays dividends for planning.  On multiple occasions I have found myself taking screenshots of student work or quickly writing a note in the chat about a certain element of a student’s response. 
  • Every year I find myself thinking about how to curate a more organized library of resources.  This year has encouraged me to be more critical in how I organize my Desmos decks.  I have been using mainly Sheets for this and am hoping to be able to quickly retrieve this resource for certain skill next school year.
  • Along with the curation of materials, I believe local assessment practices have improved this year.  Since all assignments are online many resources moved from paper-based to digital.  A large chuck of time has been dedicated to that this school year.  My math unit tests have decreased in overall length which I think is a good thing and are more constructive in evaluating students’ understanding of the material.  Questions that were not clearly aligned to a particular standard were eliminated in favor of tasks that were more robust. I cannot remember the last time the tests were re-evaluated and I am glad that my team analyzed them with a more critical eye before digitizing them.
  • I have said this before and I continue to see the importance of having a brief “meet and greet” time as part of the daily schedule.  Checking in with students and allowing them an opportunity to discuss what is important in their lives helps create a better learning environment.  This year most classes have started with morning meetings or something like that to offer a listening ear to students as they traversed this long school year.  This has become even more important as students came back to school for in-person learning
  • One of the highlights his year was being able to meet with students’ parents over Zoom.  The limited time on video has increased the effectiveness of these meetings and has also provided an opportunity to meet where transportation/timing was not ideal.  I am hoping this is still offered next year along with professional development opportunities.

As I write this, boxes are sitting in my room ready to be filled up as I am moving classrooms again. I have to decide if items are worth putting in a box for reuse.  While doing this I should keep in mind that there are a few silver linings that I would like to keep for next fall.

Graphing with Context

This week one of my classes has been studying coordinate grids and graphing. They’ve learned about coordinates, using a table, identifying rules and created ordered pairs during the last part of March. On Monday the class reviewed line graphs and change over time. At this point in time the class is identifying the informal slope (without a formulas) of a graph and describe events that are taking place by analyzing the relationship between the x and y-axis. Earlier this week my students worked through Kurt’s Retro Desmos solving systems by graphing task.

I selected specific slides to complete as the class hasn’t been introduced to the y-intercept yet. The class spent a good chunk of time on slide four – a class favorite. Students tried out different strategies to see what happens as the lines cross or increase in steepness. This led to a class discussion about the slope of the line and what the x and y-axis means in context. A number of students experimented with what happens when you make multiple lines on the graph. This slide caused students to think about the context first and then how the lines look second. Near the end of the class students mentioned that they’d be interested in the process of finding the rate or speed of each character as time progresses.

During the next class I used Kurt’s slides and idea to create an assignment. I added a few criteria pieces related to the 100 meter dash. Some of ideas were taken straight out of the original activity. Click here for the Desmos assignment slide.

Criteria: Mario starts 30 meters ahead, Sonic and Mario are tied at 4 seconds, Sonic takes a 3 second break, and Sonic wins at 9 seconds.

Students worked on this assignment in class and checked their work by pressing play. I was impressed with how students made multiple attempts in trying to meet the criteria. The video playback of the race was used as a self-checking mechanism.

Students then answered a question related to Sonic’s line.

Tomorrow the class will review the graphs in more detail. I’m looking forward to diving into more graphing fun tomorrow.

Changing Models

Arrows indicating direction of student traffic flow

For most of the year my school has been following a hybrid AM/PM model.  Half of my classes attend in the morning and the other half in the afternoon. Some student are in-person and others (about 25%) are elearners, but all attend the same class Zoom session together. In the morning I have three math classes that are about 40 minutes each and then I repeat the process with a new group in the afternoon.  My largest class is about 14 students since it’s split in half.  While not ideal, this model has led to some positive outcomes and I’m glad that district moved in that direction. A few observations:

Since there are less students in the sessions I find it much easier to discuss topics as an entire class.  Guided group discussions take on more meaning as students have more opportunities to ask/answer impromptu questions. Students are able to social distance at an optimal levels because there are less students in the school. There isn’t a lunch period so families and staff feel safer regarding virus transmission opportunities.  

I’ve also noticed that the class has had a community element, but is not the actual entire class.  Since half is in the morning and the other half in the afternoon, students aren’t able to get to know their classmates as well as before the pandemic  Some of their friends that they saw last year aren’t in their session.  Also, math time is limited to 40 minutes, which means something has to unfortunately be cut. This year that cut is taking the form of students working together in groups

Starting tomorrow the model will shift. Boom. Instead of having an AM/PM class, I’ll see my entire class for a full 60 minutes – that’s 20 additional bonus minutes. Approximately 25% of my students are still elearners so they’ll join-in along with the rest of the class in Zoom.  You heard it right, all of my classes and students will be in Zoom.  I’ll be modifying the model from earlier in the year. I’m planning on incorporating more student group work with that present of time. I feel that component has been one of many important elements that have been missing with the hybrid model.  Along with the extra students comes a re-emphasis on social distancing and routines as students will be in school for the entire day.  This is a significant change as lunch, recess and hallway congestion all become more of an issue. The thing that will be immediately noticeable for students is the increase in the number of desks in the classroom and probably the amount of tables/desks needed to eat lunch with social distancing.

New protocols related to recess, social distancing, shared materials, and lunch will need to be communicated to students. Technology and chargers will need to be brought to class and students will have music, art, and PE in-person in the classroom and outside if weather permits. Just writing the last few sentences brought a slight smile to my face.

Even though the last few days have been used for planning, I’m finding that there’s a sense of anxiety that’s permeating the air. Usually that’s reserved for the first day of school. In a certain context it’s like teachers are starting a new school year.  Norms and community building will be forefront as students start getting used being in-person again, although a change in expectations may be needed as school is much different compared to what we left last March.

I’m looking forward to this seven week adventure. After that we can close out the infamous 2020-21 school year.

Solving Equations – Progressions

For the past few weeks my students have been exploring equations. The current unit of study introduces equations by showing different visual models end eventually ending with an inverse operations strategy. Students initially see equations through solving for ? or x by using trial-and-error. Up to this point in time that’s how they’ve solved equations. There hasn’t really been a formal procedure until this particular unit. As the unit progresses the class uses bar models, pan-balances, hanger models and inverse operations. This post is designed to review the different models that are introduced.

Bar-Model

Using a bar model is fairly new for most of the students that I teach. Students separate a box with a line. The left side of the equation goes on the top and the right on the bottom . Students use logical and spatial reasoning to solve for x. This was a jump in challenge for students. The spatial piece of being able to visualize how much space the variable will take has the potential to be confusing. My class ended up spending about two sessions reviewing this strategy.

Hanger Model

Students have already been introduced to Solve Me mobiles so this wasn’t as much of a stretch as a bar model strategy. This was the first time that students started to “balance” terms with a hanger. Another two lessons were spent here. Students enjoyed working on this although it was quite challenging when students reached the mastery level on the solve me mobiles site

Pan-balances

The next strategy involved pan-balances. This model involves more operations and steps. Students tended to thrive with this and it was great to use in breakout rooms. Students took items away from both sides of the equations and strategy played a role. As students discussed their strategy they found not all methods to solve them were efficient.

Inverse operations

Near the end the unit students were introduced to the inverse operations strategy. This is generally what students come to class knowing, but they’re unsure of why it works. Up to this point students have relied on visual models and are continuing to make sense of equations. They also reviewed how to combine like terms and integers during this process.

The progressions of how students see equations starts to really shine through between the pan-balances and inverse operations strategy. After reviewing all of the different strategies I surveyed my students and most are now more favorable to using the inverse operations strategy. I even had a few students comment that the strategy actually depends on the equation. Bingo!

I’m looking forward to reviewing the solving equations unit after spring break.

Here are a number of Desmos activities that I used throughout and to review the solving equation strategies:

Reviewing all the strategies

Combining like terms

Solving one-step equations

Kindness Calendar

One my school’s themes during the past few years has revolved around acts of kindness. There has been an intentional effort to reinforce what kindness looks like and sounds like in elementary classrooms. It is part of the community culture and I believe the school even purchased a banner or two that students see as they enter the school.

It was much easier to reinforce the idea of kindness when students were all in-person. Quick acts could be mentioned in the moment and then used as reference points throughout the year. Fast forward to today and the instructional setting has dramatically changed. Many schools now have at least a certain amount of their population online and some are present in a socially distant classroom. This has made it more challenging this year and I am finding the new emphasis on social/emotional needs ties nicely with the kindness theme.

Earlier in the year I came across a tweet from Megan about an optional kindness calendar. I have seen similar calendar but I was digging the idea that her students came up with daily acts of kindness.

I took Megan’s idea and had my students come up with a list of how they could be kind for the next month. They had a number of ideas and many were built from the original calendar that was shared. I was able to collect around 60 different responses.

The ideas were then put into a calendar for the next month. Students online and in-person were able to view it as a Google Slide and it was part of my agenda presentation. Each day the class briefly reviewed the ways in which they could be kind. I made sure to indicate that this was optional and just an idea to consider for the day. As the weeks went on students expected to see the daily kindness act of the day as part of our routine.

This week I tried something different to see the calendar’s relevancy and if it was something that I would like to keep for the remainder of the year. I used Desmos and asked students how they were kind for that week.

Students reviewed the past week and picked one day. I did not want to guilt anyone into having to pick one so I added the did not participate option. Here are the results for students in grades 3-5.

The results were fun to look at but the real gem was in the open response sections. It was great to see the different acts of kindness and how deliberate people were in completing them.

Based on the responses I will most likely keep the calendar for the last couple months of the school year. Feel free to use the Desmos template by clicking here.

Math Breakout Rooms

I was introduced to Zoom breakout rooms last March when my district went remote. Breakout rooms were novel and many teachers started to use them during the last couple months of school. It was one way to get students into smaller groups where they felt more comfortable sharing. They were awkward at first for students and staff but most were able to get their breakout room sea legs by May.

Fast forward to the 20-21 school year. Like many around the nation, my school started the year off completely remote. Having a head start in March helped most teachers get into a routine quickly. Most teachers started to use breakout rooms immediately and were able to see the benefits. The social interaction that usually occurs in-person can’t be exactly replicated, but a form of it can in a breakout room. I’ve been part of some amazing student math discussions in breakout rooms this year. I’ve also been in other rooms that were full radio silence. Some this year have had detailed agendas that students follow while others are more student-directed.

Most of my elementary math breakout rooms consist of 2-5 students. Since we are using a hybrid model I try to match students in-person with those at home. I found early on that partnering up kids in the classroom over Zoom causes major audio issues. Less students participate in the breakout room when there are more than five participants. Generally, students in the breakout room have a specific task or activity. Sometimes the assignment comes from their consumable journal and other times it might be a prompt. Students are usually in the their breakout rooms for 5-15 minutes. We have a 45 minutes block for math. While students are working I pop in and out of the rooms with my camera and sound off. I observe the conversation and ask questions if needed. Most of the time, I visit a room and listen to what’s happening, add something in the chat for that room and then move to the next room. After the breakout rooms close the class has a debrief sessions and I try to have each team discuss their solutions. This strategy has worked out well this year, but I’ve had inconsistent success.

I still have questions.

  • What makes a good breakout room?
  • What’s the ideal room size and time?
  • Does camera on/off matter?
  • How do you manage breakout rooms while teaching in-person and elearners at the same time?
  • Should students share their iPad screen?
  • Do you find annotation through Zoom helpful?

I don’t believe there’s a perfect formula for a breakout room, but there are better practices. Feel free to let me know what has worked in your classroom.

Math Schedule and Hybrid Routines

I’ve been teaching in a hybrid model setting for most of the school year. My school started remotely and proceeded with an in-person staggered start. The classes are divided so I have half of the students in the morning and the other have in the afternoon. I appreciate that the school has made social distancing a priority and is limiting the amount of kids in a physical classroom at one time. The overall schedule has also changed and my math block has decreased to 40 minutes instead of 60.

Long story short, I teach kids at home and in the classroom at the same time. My instruction is mostly digital. I do that for a number of different reasons. While the digital model hasn’t been ideal, it allows everyone to participate and I can gauge engagement by looking at a teacher dashboard. My agenda and routines for each class have changed over time. Currently this is how I’ve been managing my quick 40 minute block.

11:00 – 11:05


Students come into the classroom and login to Zoom. Students at home do the same. Once everyone is logged in we start the meet and greet session. Usually there’s a prompt that students answer. This is whole group and students talk to each other about the responses. This time is dedicated to help build classroom community and connect with students. You can find many of the pictures for the meet and greet here.

11:05 – 11:10

Students log on to Nearpod for a brief review of past concepts. I use Nearpod for this time slot around three days a week or so. It’s a quick 2-3 slide presentation. Sometimes I’ll replace the Nearpod with a Quizzes or Desmos task. This time is purposefully used for students to review past concepts and I can see if additional practice is needed for specific skills.

11:10 – 11:25

Students take a look at the agenda slide and then review the goal for the day. The class completes a consumable journal page under the document camera. This is generally the time that is used to introduce new concepts/skills. Questions are asked the most during this slot. This time slot can be a challenge to manage as far as engagement is concerned. Still tweaking.

11:25 – 11:40

During this time students are either working in breakout rooms, on a set of problems from the consumable journal or independently working through a teacher-paced Desmos task. During this time I’m working in Zoom breakout rooms with students or sending feedback through the Zoom chat. I’ll often turn off my mic and video so I can hear the students and so the conversation doesn’t slow when I enter a breakout room. At times I might ask a question or two to check for understanding. The class then comes back together before the end of the session to review the group work/Desmos task results. There’s a quick closure statement about what we explored that day. I then say goodbye and a new group of students start populating the Zoom waiting room.

This routine will probably change, but it has been working so far. Ask me in a week and I might have a different answer.

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