Four Weeks Down

Students finished their fourth week of school yesterday.  Routines are fairly established although there have been interruptions with students quarantining during the past two weeks.  Flashes from last year have been making appearances in classrooms as teacher navigate working with Zooming and in-person students at the same time.  I’m hoping this is temporary but no one has the confidence to say that’s the case.  When students remote into a classroom it changes routines and impacts more that what I can write here.  I’m moving forward and attempting to find lemonade in the situation. Looking back at the last month I’ve found ways to engage students differently this year compared to last school year.  This post highlights two of those instances.

Fortunately, this year my students have been able to work in groups. Words can’t express how big of a game changer this is and what a loss it was last year. Breakout rooms were a poor substitution. I’ve been utilizing whiteboards and math stations throughout the classroom.  While students work on tasks I bounce from one group to another to ask questions and to gain an understand of students’ thinking.  During the last few weeks I’ve been reading through Building Thinking Classrooms have been using some of the strategies found within. Being able to give feedback through questioning at the stations and hearing the students’ responses impacts my next steps as a teacher. I’d like to expand the time at stations a bit more as the year progresses and as social distance policies evolve.

Another strategy that seems to be working this year relates to how students interact during brief math conversations. Students are often given a daily math task or question that’s designed to encourage dialogue. Students take turns discussing the strategy or steps involved in attempting to solve a problem.  While one student is talking the other student is giving non-verbal cues that they’re actively listening.  Students are then brought back to the class as a whole group.  I visibly randomly pick students to share what their partner said during that time.  The student that is picked doesn’t offer their opinion about what the partner stated although the strategy is discussed as a class. I’ve used this at least twice every week since school has started and have noticed that students are listening better in their groups. Another bonus is that students are using the strategies that they hear from their partner/class.

I’m hoping to carry both of these strategies forward as the year progresses.  

Me in Numbers

The first day of school is in the books. Not similar to last year, students were in the classroom and masked today. Most teachers that I know are exhausted after the first day and are look for a short respite before heading back for day two tomorrow. Today I was able to see all of my classes and I tried out a couple different activities. This post will highlight a one of them.

I started off the day with a classroom discussion about our summers. We had a conversation about highlights of the last few months and what we’re looking forward to for the new school year. I then put up a “numbers about me” slide. Students worked in partners (it has been so long since they’ve been able to do this!) for a few minutes to match each number to a statement.

I borrowed this idea from Annie from the recent ICTM mini-conference and used it with a group of third grade students Kids especially had trouble with the numbers that were closer together. After the partners presented their responses I slowly revealed the numbers that matched each statement. Now it was the students turn.

I gave each student this sheet and they came up with three statements. We had a classroom discussion about what is considered a better question than others. They then filled out the numbers. I’m in the process of filling out each student’s sheet so they can grade them tomorrow. : ). Here are a few that I’ve come across so far.

I’m looking forward to seeing the students reactions when they grade my guesses tomorrow. Day two is tomorrow. Here we go!

Considerations for the 21-22 school year

In about three weeks my school starts back up again. I have been told that this upcoming year will be different Last year many school started completely remote and then eased into hybrid as the year progressed. I am assuming there will still be some type of social distancing and masking involved for this year, but it depends on many factors. The next school board meeting along with ISBE guidance will most likely lay the groundwork for what will happen during 21-22.

As I think about August I am tempted to plan out the school year as if it everything is heading back to normal. We are still in a pandemic and our schools should keep that in mind when planning. There are a lot of vocal opinions about masking, vaccines and social distancing that may impact what happens. Instruction last year shifted towards a mostly digital model and my hope is that we do not give up on using instructional components for the new year. Some students experienced success with that model, while others did not. Other students struggled with remote learning and could not wait to get back into the classroom. I would like to believe that schools can and should blend what worked with elearning with the benefits of being back in the classroom. It is not a simple transition and requires additional thinking, but something to consider for August.

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