Sunday, October 25, 2020

Thank You Murphy's Law

We switched to online learning very rapidly in March of 2020. Classes were in person on a Friday and moved online on a Monday. Murphy's Law came into play - it turned out that I was to give one of my exams of the semeter on that Monday. I pushed the exam off by one class day to give me time to get the exam put on Canvas. Unfortuantely, it isn't as easy as it looks. My images did not show within the exam and students still had to do part of their exam on paper and scan and upload it. The exam was in two places and grading became a nightmare. For consistency, I like grading the same question across all student papers at the same time. I can see common errors and score student papers in a similar way for those errors. Canvas does not let me do that, which is a major drawback. Plus, most students uploaded their work in 4 - 6 image files. Grading took about three times as long as it did before and my feedback was limited since I could not type in math formatting.
This fall classes are still being held virtually via Zoom. This and my disasterous issues with assessments in Canvas, led to me to decide to use Desmos Activity Builder for quizzes in my Functions and Derivatives class. It has worked really well and the students adjusted to it quite easily. Several even commented that they liked taking the quizzes in Desmos Activity Builder during a mid-semester check-in survey. Doing quizzes in this way has been so much better that I don't see myself going back to paper quizzes even when we return to face-to-face learning. 

Why would you want to do assessments in Desmos Activity Builder? I can think of four main reasons: they are easy to create, support a variety of student responses, it is easy to manage classes and you have the ability to quickly give students feedback. I'll comment on each of these. 

1) Easy to Create: I can easily embed images within my quiz without having to upload them some place else, link it and check a box to make sure students can see it. I can also design a question that allows for student written input. An example of such a question can be seen in the student work below. Plus, it is very easy to copy one quiz and modify it to create a second version of the quiz.

2) Variety of Student Responses: In Canvas, I can ask a multiple choice question, but would need to ask a separate follow up question to have students explain their choice. In Desmos Activity Builder, that can all be done within the same question. Students also have the ability to type in their answers in math format by clicking on the keyboard. Formatting of math answers is not so easy in Canvas. Here's an example of a question involving rational functions with the math keyboard for students to easily enter their solution.

3) Managing Classes: In September of 2020, Desmos added a "Manage Class" option. This makes it easy to assign activities to classes of students. Why would you do this? If you don't use the "Manage Class" option, it is challenging to see who is taking the assessment and who is not. You might see there are 24 students logged in and you should have 25. Who isn't taking the assessment?  With "Manage Class" all your students names are already listed on the dashboard and you can easily see who has logged in and who has not. Plus, there is easy integration with Google Classroom. For more information about this feature, watch this brief video from Desmos

4) The Ability to Quickly Give Students Feedback:In March 2020, Desmos released its Feedback feature within Activity Builder. This allows teachers to give feedback to their students, including the ablity to type feedback with math formatting. As an added bonus, I can easily grade a single question for every student and then move to the next question! Students can see that they have feedback when they log into As a teacher, you can see if they have read their feedback by looking at the teacher dashboard. The grey triangle means a student has read the feedback and the green triangle means the student has not read the feedback.  
Thinking this might be something you want to try? I have two recommendations. First, if you are new to Desmos Activity Builder, I recommend going to to get started and to see how to create your own activities. Second, start small with just one or two slides of student input. Use Desmos Activity Builder as an exit ticket or warm-up. 

Interested in an activity to getting started?  Here is one of the quizzes I gave a few weeks ago.  If you have an account at, you can copy and edit this quiz on Polynomials, Rational Functions and Limits

Thank you, Murphy's Law, for giving the impetus I needed to broaden my use of Desmos Activity Builder.  If you would like to learn more about Desmos and Desmos Activity Builder, I invite you to join me for my online seminar with BER called Making Best Use of Desmos to Strengthen Your Math Instruction (Grades 6 - 12).  Click on this link to see information about dates and how to register.

Tuesday, September 8, 2020

Learning Math is Social: We Are in This Together

Note: I haven't blogged recently and these thoughts are a culmination of ideas that have been bouncing around in my head over the past few weeks.

When I first saw the rules posted online for a local high school back in July, I shook my head in disbelief. The rules have changed somewhat (masks always required in class), but initially it said something like this:

Students can take off their masks when seated as long as they were facing the front of the room. If they get up to move around the room, they must have their mask on. And teachers were told: Students will not to sit in groups during class in order to maintain social distancing.

What many school administrators, department of education leaders and school board members don't realize is that high school teachers have advanced their teaching methods beyond the 1950's. Classrooms are configured with tables or desks in pods. Learning is social and we want our students to work together. Even after teaching the same content for ten years, my students make new observations or connections and amaze me with what they are able to conclude. This would NOT happen, if students worked by themselves. Or at the very least, only the student that thought of the new idea would benefit from it.

Even within my synchrounous virtual classroom this fall, I use breakout rooms on a daily basis and students work together for 10-15 minutes on course content. They post in a common Google doc or move things on a Google slide or write on a common Google Jamboard. And then we debrief as a class after they return from their breakout rooms. Learning together is really that important for my students. Learning is social and teachers need to be given the tools to help their students learn together while being socially and often physically distanced.

Image from @NeONBRAND

Even as teachers work to modify their lessons, they get new restrictions being thrown at them almost daily. An AP Statistics colleague of mine said he will have 2 days of face-to-face instruction and 2 days of asynchrounous virtual instruction per week. That doesn't sound bad, right? But then he has also been told that new content cannot be taught on the asynchronus days. That could make it a bit challenging to teach the entire curriculum. But it could be done, maybe. But wait...there's more. He will only have half of his students in front of him on the face-to-face instruction days. The other half of his students will be working virtual on those days. This means each day, he needs to prepare 2 different lessons for the same class. And because of social distancing, he will need to create or find new ways to do things that would normally have students do while working beside each other. This is the stuff of teacher nightmares.

Will teachers survive teaching in the pandemic? Maybe some will resign, as happened in a district near Buffalo, leaving nearly 80 virtual teacher vacancies. Those who wish to survive will work with their colleagues. Some will reach out via social media or email or by attending free webinars, like this one offered by The Global Math Department on using Delta Math for Distance Learning:

I recently shared a pacing guide for AP Statistics with a teacher who made a plea for help over an AP Statistics Teacher Facebook group. This led to an email exchange, where I offered the following advice for starting the school year strong.

  1. Be up front with your students - teaching this way will be very different than what you or they are used to.  If something is unclear or is going wrong (I can't tell you how many times I was talking for 15-30 seconds before a student would unmute themselves and tell me I was muted), they need to tell you and you thank them for sharing.
  2. Let your students know, even with 28 years of experience, this is your first time teaching AP Stats.  Tell them to think about something they learned for the first time (like riding a bike or learning to dive) and the fact that it did not go well.  They had friends to help them learn and you have friends to turn to for help with teaching AP Statistics.
  3. Tell them that your goal is for them to succeed, and that you will work along side them, in a physically-distanced sort of way, for this to happen.

Although my students work together in breakout rooms and I can pop in their room to check on them, I miss the collective buzz and energy of math conversations. When I am in the same physical space as my students, I can quickly assess if I need to clarify an idea or if there is a pre-requisite idea that needs to be addressed. I can walk by 8 groups in less than 5 minutes and gather real-time data. I yearn for the day when I can be with my students again.

BONUS NOTE: If you want to experience how I use breakout rooms and teach with Desmos, join me for the virtual PD session offered by BER called, "Making Best Use of Desmos to Strengthen Math Instruction (Grades 6-12)" Depending on which session you choose and the time zone you live in, you might not miss a full day of school. Dates in November, but there will also be virtual sessions in the spring. Feel free to ping me on twitter @mathteacher24, if you need more information.

Wednesday, June 3, 2020

The Writing on the Desk: An Apology for my Silence

Please note: The language I am sharing in this post was used by one of my students over twenty-five years ago. The purpose of this post is to reflect on a personal exprerience from may past and make suggestions for what educators can do moving forward.

 The year was 1995 and I was teaching math at Ames High School in Ames, Iowa.  It was my
first year as a full-time teacher. I didn't make it a habit of checking my desks for student writing.  Perhaps that particular day there was a pencil on the floor or a piece of paper and I went to pick it up near the desk.  I can't recall those details.  However, I do recall seeing something written on the desk and I bent over to read it.  The words I read were burned into my memory.  It said, "Mrs. Nataro is a n***** lover."

I was shocked by the words I saw, naievely thinking my community was safe and free of racism.  It has taken me until now to realize that what I did next contributed to the underlying racism that was in present in my classroom.
Image from

A flood of thoughts raced through my mind, "What do I do? How long had this been written on the desk?  How many students had seen it?  Was it written on other desks?"  I recall quickly walking around the room and checking each desk.  After I saw it was only on the one desk, my thoughts changed to "I can't let other students see this. I need to remove this vandalism from the desk immediately."

I can't recall where I found the products I used to clean the desk, but I do remember scrubbing vigorously and checking several times to make sure the words could no longer be seen.  I had erased the words and thought I had solved the problem.  The desk was clean, but the problem was still there.  I had removed the vandalism, but I did not address what had led to that vandalism.

At the time, I thought I had done the right thing.  I was protecting my black students from being exposed to that vile language and I was preventing those words from being viewed and used by my white students.  I now understand that by not saying anything to administrators or my students, I contributed to the racist undercurrent in the school and my classroom.  And if you were a black student or black teacher at Ames High School in 1995 and you are reading this post, I am sorry that I did not speak up.  I am sorry I did not recognize what my silence meant.

So, what can we do as educators?  I am not an expert on this, but offer a few thoughts.

1) Train educators with what to do and say in response to racism and intolerance.  Train us to listen and train us on the ways we can support marginalized students.  Posting platitudes around the school like "we care for our students" and "your education matters to us" is meaningless without the tools teachers need to promote change and have difficult conversations.

2) Find groups that work to actively support anti-racists practices in education and share your experiences and expertise within those groups.  If you are looking for some ideas, check out the link to the recent statement posted at The Global Math Department.

3) Don't relegate teaching of black history or marginalized groups to one month of the year or a specific week or a single assembly to check off a box. Doing that is like saying, "Look here. We didn't forget about you. Problem solved."  This doesn't come close to doing the hard work that needs to be done.