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    • This has been the most unusual, stressful, fatiguing, and challenging semester in the entire careers of every teacher, regardless of whether it was your first year teaching or your 35th.

      Teachers have had to deal with a lack of face-to-face connection with students and other faculty. And daily online teaching caused many teachers to experience “Zoom fatigue.” 

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      COVID-19 has meant teaching without all the answers and improvising with mixed results.

      An After Action Review (AAR) is the military’s version of a self-reflection. It’s an opportunity to share what worked and what didn’t, what could’ve been done instead, and what lessons, ideas and strategies can be effectively implemented going forward.

      I therefore welcome you to an educators’s AAR. A virtual panel of maths teachers from across secondary and university, and from around the globe, sharing their reflections of the good, the bad, and the ugly, how they felt during and about the semester, and any insights they might have to help other teachers in navigating the fall term.

      Panelists: Before sharing your reflection, please let us know what part of the globe you’re from and the grades and subjects you teach. The number of years that you’ve been teaching would be helpful, but feel free to keep that detail private.

    • From Dr. Neil Calkin, professor of mathematics.

      My university is planning on having in person classes in August, with students attending 1/3 of all classes in person (on a rotating basis) and attending online the other 2/3 of classes.  I'm involved in the process of how you allocate the students to A/B/C days so that the numbers work out --- a pretty optimization question in its own right.  I am likely to take the "all my classes are online only for this term" approach, I think.

    • Hi, I am Peter Mattock, an Assistant Headteacher in charge of mathematics at an 11-16 school in England and author of “Visible Maths: Using representations and structure to enhance mathematics teaching in schools”.

      Honestly, I don’t think anything about teaching maths in lockdown is providing an optimum experience for pupils, and I cannot wait until things get back to some semblance of normal and I can work with real learners again. For me, teaching is a hugely tactile and interactive process. Being able to work with a pupil, manipulate some learning tool or just make notes together, getting feedback from what I can see on pupils tables and on their boards are all a big part of my practice. Not being able to do that has got me pretty glum about how my kids are doing without that experience. We are having to rely mainly on videos from an online learning platform, Hegarty Maths. Whilst these are brilliant, and we used to encourage pupils using them independently to support their learning, it isn’t ideal for a learner’s first exposure to mathematical ideas to be without the aid of a teacher that can take cues and adapt accordingly. Unfortunately, we can’t really do that, even through live video lessons, whilst in this position. If this goes on much after the summer holiday, there are going to be a lot of kids whose learning is irreparably damaged, so I think we need to work on making sure every child gets at least some time in front of a teacher, and prioritising developing safe ways for that to happen, even if it can’t be the same full time experience that we are used to.

    • Wow, some great reflections and I expect more to come throughout the extended weekend: Monday is a national holiday in the US.

      Note to panelists: As new reflections are shared, feel free to share your comments on a particular idea that connected with you, a question you have answers to, or a problem for which you can offer a solution.

      One thought shared online with me this week that was most insightful to this discussion. When the pandemic and lockdowns began, teachers had already spent a semester plus in getting to know their students and developing “trust for learning” relationships. However challenging this Zoom semester was, it had the benefit of existing student relationships to get through the unpleasant bits.

      I’m therefore wondering, what strategies would you attempt in order to build positive relationships if the new school year begins online?

    • Great question!

      Panelists, what suggestions do you have for ArtofMathEd?

    • I think another area of concern is the mental health of students during the crisis. Isolation can be debilitating. I was shared this about one student’s breakdown from not being physically in her school.

      But then the conversation stopped. One student began, the green Active Speaker border highlighted around her video image; “I hated my school. I didn’t like going and I didn’t like the routine and the noise and all the bullshit, all day long.” And she started to cry. She wasn’t sobbing. She was crying, openly. She could have left the session or turned her video off or muted her mic. But she didn’t. It was a level of vulnerability I had never experienced. She was enthusiastic at the outset of the session, sharing her achievements and goals and hopes and joy about school and her circles. Was this a mask of bravery she was asking us to believe in? That things really were ok? What inspired this sudden shift?

      She continued, through tears, “I miss people. I miss the jerks in class and in the halls. Cause I know they’re probably struggling just like me. I miss having to report to the office. I miss having to pay attention and speak in class. I miss my teachers and my sports. I miss my friends. I miss people. Mostly, I miss what I took for granted; that everyday stuff I took on that bothered me was just everyday life. God, I miss that. I want it back. I want it all back.”

      Students, a Zoom Session – and Loss

    • We have a two fold strategy:

      1) We are sending lots of rewards for pupils working, and telling all parents that we are. We had an electronic reward system before lock down that would automatically email parents when we assigned a reward to a pupil. We have made sure all parents know that this is continuing, so that parents are expecting to receive notification when their child is working well. We have had lots of positives back from parents who are receiving these, and where parents are not receiving them they know that their children could be doing more.

      2) Every few weeks we are asking staff to report on how pupils are working, through a simple data drop. Our pastoral team is then making phone calls to the homes of pupils that are struggling with work to find out what the issues are and how we can better support those pupils.

    • We have a two fold strategy:

      1) We are sending lots of rewards for pupils working, and telling all parents that we are. We had an electronic reward system before lock down that would automatically email parents when we assigned a reward to a pupil. We have made sure all parents know that this is continuing, so that parents are expecting to receive notification when their child is working well. We have had lots of positives back from parents who are receiving these, and where parents are not receiving them they know that their children could be doing more.

      2) Every few weeks we are asking staff to report on how pupils are working, through a simple data drop. Our pastoral team is then making phone calls to the homes of pupils that are struggling with work to find out what the issues are and how we can better support those pupils.

    • I think there is a big difference here for different staff and pupils. I think it has to be a priority that any pupils new to the school have a chance to put a face to the names of their teachers. I will look to send home a little "about me" to all the Year 7s that start in August if they are not in school and hopefully follow that up with a live video or video message. We will also need to manage things like induction to the online platforms that will be used, as these may well be different to their previous work.

      The members of staff new to the school will have to do something very similar I think but with all pupils. Those of us that have been at our schools for a few years may be able to rely on our reputation to carry some of the weight of that - if kids know that it is me setting work they already know a bit about me and what to expect of me. In fact I have been handling all of the messages going out on our learning platform about the work in general for just that reason, leaving my staff free just to deal with the specifics for classes and individuals.

    • 1/3

      From @Bonnie, High School Math Teacher in Southern California.

      COVID-19 shouldn’t have been a surprise after years of scientists warning the world.  But unfortunately, much of the world ignored them.  Being a science nerd, I always had a feeling this was imminent, but not during my lifetime.  I am saddened by all the deaths and families who are forever affected by this.  For me, being single and no family obligations, this came as a blessing in disguise.

      I was really struggling with my work environment at school.  The only reason I would go to school was for my kids.  I interacted the least amount possible with my co-workers. And when I did, I had to put on a face.  So being quarantined was just what I needed mentally.  I was physically separated from what was causing me so much stress.

      During the past couple of months, I have worked through a variety of different challenges and come to peace with them.  I am the consummate introvert, so being at home is like hitting the jackpot. I am enjoying time working in my garden and spending lots of time with my dogs (although they would probably share that it’s too much time). I really like the flexible schedule.  Although, I am sure that I am unique in this situation.

      My district made the decision that all middle and high school students would receive credit for the semester, no matter the grade they had last.  All work was optional and was not to be graded.  At first, I was shocked and dismayed.  But after further thought, because the vast majority of students come from a highly marginalized and vulnerable background, giving them this was a good decision.  But I am guessing at a couple of the other high schools where families are better off socioeconomically, parents and kids were not so happy. This was a decision in retrospect that I came to agree with.  

      However, this decision came roughly a month into our school closure.  So before that I thought about my students and what was realistic.  I sent kids a survey to see who was interested in improving their grade. And then based on that, I vetted each one to see if they truly were willing to put in the time and work; and were able to.  That worked really well, as then I was able to effectively help about 17 kids.  The rest I gave them work asynchronously and wasn’t stressed if they did it or not.  But calling home multiple times was extremely time consuming and exhausting; not to mention the language barriers. I definitely couldn’t have done this if I were still teaching face to face with one 57 minute prep period each day.

      61 out of 119 students responded to a survey to gauge how effective they felt distance learning was. It was 100% anonymous.  I was pleasantly surprised at how many like the “Attendance/Check In.” Unfortunately, I started that a month into the closure.  But, for next year, I will be starting that right away. That piece of data proves to me that relationships are so important.  Even though I knew every single one of my students inside out, distance learning means I needed to start all over. And it was easy to do, I just posted a “Question” on Google Classroom.  I did this twice each week and gave them about a day to complete.  I was easily able to respond back to all of them. (I type faster than I write, and my writing is really atrocious.) 

      They were questions like:

    • 2/3

      From @Bonnie, High School Math Teacher in Southern California.

      I can’t take credit for this idea.  Lauren Johnson (@mrsjohnsonCA) shared this wonderful idea.

      The wonderful math art challenges (provided by Annie Perkins@anniek_p), the Edpuzzle videos and Delta Math were pretty much a draw.  I wasn’t expecting that at all.  I interpreted this as a need for my students to still continue learning, but have something to help them relax and forget their worries for a little bit.

      Distance learning was a huge transition for all my kids, and most didn’t transition at all or too well.  My kids, as most at my school, come from backgrounds where parents’ philosophy is hands off when it comes to their child’s education.  It is the school’s (teachers) responsibility to educate their child as well as keep them accountable. A vast majority of parents will not voluntarily contact teachers; that is my biggest fear for next year. I don’t think I can call every single parent; especially as most are not fluent in English.  But they need to be more proactive in keeping their kids accountable. It can’t be all on my shoulders.  I am sure that the credit option was only for this past semester, so I hope getting a grade will keep the kids a bit more accountable.  I am not able to change how parents interact with their child, so I am at a loss on how to cope with this next year. I hope my administration and counselors will find ways of helping me and other teachers with this so I can focus on the teaching.  

      For the fall, my priority, our priority, is to figure out how to build relationships with the kids online.  Or at least, the best we can.  Relationships are the foundation to all successful teaching and learning.  If we don’t take the time to do so, then what is our intent? What are we putting above our kids? Our kids need to come first, as they always have.  But I think that needs to be at the forefront even more so.

      We need to get comfortable with the idea that not every single standard will be covered; nor should it.  I hope we take this opportunity to go deeper into the content and help kids explore. But how to do that when we don’t have them face to face is a huge challenge and we may fall back on rote learning and lecture. I hope we look at assessment differently.  I saw so many colleagues on #MtBoS using Desmos as an assessment; something I need to learn how to do.  

      For me, I have taken these past couple of months to be more of a student than a teacher.  I have learned so much about digital learning and all the different tools out there.  I have a better understanding from the kids who worked with me, how to support my new students in the fall.  I still have a long way to go, but with this experience, I think I am better prepared than I could ever hope to be.

    • Teaching, as I do, in a university this past semester meant that half of the time I would spend with my students was shifted to online learning. I have to confess to thinking this would not be terribly challenging as I have taught online courses for years to graduate students with relative success. I set up my office space at home with some Wipebook® sheets taped to the walls, aimed my webcam, got good lighting and a solid microphone ready. I had a lecture on some topic (not even i can recall what it was now) prepped and sequenced...My students logged in, most with their cameras off (this was disturbing but I soldiered on) and off I went lecturing on some introductory idea in inferential statistics.

      A few minutes in, I pause to do a verbal "Check for Understanding" and am struck by just how dumbfoundingly boring I have been when I turn to the video on my screen and the few students whose cameras are on are glassy-eyed, slack jawed, and already visibly wishing they could be anywhere else. I keep going with ginned up enthusiasm...it gets worse, now ⅓ of those whose cameras were on to start have shut them off and audible snoring can be heard (well maybe that was a hallucination on my part but it felt like it). So...I stopped.

      I looked directly into the camera and declared, "This is not working, everyone go back to what you were doing, give me another day or so and we will work something else out." The tension in the Zoom space was shattered and they suddenly started moving around with some excited energy. The relief was real, the renewed hope they expressed was palpable across the fiber optic lines connecting us.

      I would love to say that after this everything was super-stupendous, but that would be a lie or at best wishful thinking. No, not the case, but we all got better. I learned to use the Poll function in Zoom to generate interesting questions that got the students' engaged, then sent them into Breakout rooms to discuss the ideas in the questions. I chose well done YouTube videos of statistical tools I wanted the students to wrestle with and assigned them instead of trying to lecture in the class time.

      My final "exam" is my proudest accomplishment for this semester. I asked the students to either generate, locate, or fabricate a dataset and choose several measurements from the course of the semester and create short videos of themselves using spreadsheets (the aimed for tool of this course) to create these calculations and interpret them. This was my way of eliminating "cheating" as they had to record their voice narrating what was happening on their screen. They all found or used different datasets as well, because they had autonomy over their choices.

      I have been a preacher in the church of student autonomy for years, this crisis shattered large portions of the infrastructure that prevented this from happening more completely. It was revealed to me though, that I tried to fall back on old comfortable (I was going to say reliable but I am convinced that they are not so reliable) methods and move them into new environments. This went down in flames. Out of the ashes though, my students crafted something good.

    • The members of staff new to the school will have to do something very similar I think but with all pupils.

      I’ve worked with at-risk students where the trust relationship was everything: if you had a strong relationship, they would put in the effort even if they hated math. Otherwise, it was a constant battle.

      I can’t imagine trying to establish those relationships via online with at-risk students.

      I was wondering if you or @Bonnie could speak to how NQTs, or teachers new to an at-risk population, can make those connections with school-adverse students should things be online next term.

    • I asked the students to either generate, locate, or fabricate a dataset and choose several measurements from the course of the semester and create short videos of themselves using spreadsheets (the aimed for tool of this course) to create these calculations and interpret them. This was my way of eliminating "cheating" as they had to record their voice narrating what was happening on their screen.

      Can we talk about student cheating for a moment?

      How do you ensure honesty on written exams during the next term if it’s going to be all online?

      And on another topic, how does office hours work as a university professor now?

    • Dee Crescitelli here- I work with teachers and students all over Kentucky as a math coach and professional learning provider. The thing that went the most well here was the recognition that a majority of the children in the Commonwealth are reliant on the schools for two meals every weekday... that without a system in place, children would really go hungry. Districts put plans in place to deliver several days of food via buses at bus stops in spaced out intervals. Teachers took turns helping pack and deliver food, and bags of learning materials (sometimes packets; sometimes explora activities). So, we started with food-which I think was the perfect place to start.

      Access to reliable WiFi for online learning in an issue that has not been fully addressed anywhere, I think, but it is particularly inequitable across Kentucky. There are districts that are 1:1 with devices at school for intermediate grades and up, but that didn’t mean that students had access to WiFi at their homes. We also have teachers without reliable internet service at home here, which makes the expectation to take much of student learning online difficult. There are lots of students who only have access to a smartphone, and are sharing it with a sibling.

      As we start to think about what to take from this COVID-19 emergency teaching and learning experience, my big takeaway is that it laid existing inequities bare for all to see. We cannot allow those to continue going into the next academic year. NOW is the time to make sure that teachers and students have what they need as a basic starting point.

      We also have to look at inequalities beyond infrastructure... we have systems in place for order and compliance that add nothing to educational outcomes... and this was super clear when those systems didn’t and couldn’t reach into homes. Compliance couldn’t record student thinking and understanding... and it never could.

      I don’t have the answers- but I know that the folks making decisions about what school looks like for Fall 2020 need to talk to teachers and students, because those are the people most impacted by these decisions. We cannot go with what might be easiest or cheapest and end up with bad pedagogy and ignore human need.

    • The short answer is that if the test item is something a student can Google, it’s not a good test item. I know that is a little flippant, but I really do mean that multiple-choice regurgitate facts exams need to go. Short essays where students need to make connections... problem sets that relate to each other in a format where students have to explain their thinking help. There is almost no way to make a test “cheat proof” and the few ways there are really seem too big brotherish for me. Professors being able to see everything about a student’s testing location raises all sorts of flags for me. Videos on all the time for Zoom/ Google Meet sessions are bad enough- everyone doesn’t have a nice office room to do their schoolwork. Recording is a whole other layer to this- what happens to the recording?

      So much to think about...

    • In the UK, we are at the point of "strongly encouraging" vulnerable and at-risk pupils to be in school, for exactly this reason. This is a move away from the previous approach which was "be in school if you cannot be at home". They are the least likely to be accessing work from home, and to be in need of the support of a real life person. Unfortunately for some schools this is a significant amount of their school population (particularly those that work in alternative provision) and so that is presenting challenges. However, I think it is essential that we get those pupils into school at least some of the time so that they can establish and maintain those relationships.

      As for NQTs, I think it is going to be even more important to think carefully about the pupils and classes they are assigned. It has always been my practice to bring them into this gently - in some schools they are overloaded with "difficult" classes which are typically categorised with lots of pupils for whom establishing relationships is a big and important step. I think this is a really bad move, for the NQT, the pupils and the school. New teachers need some experience of challenging pupils, but manageably so. The techniques for establishing relationships are out there and well documented, so I don't really want to re-hash those, but needless to say NQTs will find it more difficult to do this if only seeing pupils part time and so they need to have this managed by their line managers to make sure they are not under too much pressure.

    • Can we talk about student cheating for a moment?

      How do you ensure honesty on written exams during the next term if it’s going to be all online?

      A related comment via Twitter from Jim Doherty, Math Educator from the United States:

    • Another contribution to the discussion, a different perspective on concerns over cheating from Dawn Del Vecchio, maths teacher from Los Angeles:

    • From @drewfoster, high school maths teacher from England.

      Hiya, I’m Drew Foster (@drewfoster0 on Twitter) and I have been teaching in the north of England for 25 years. I have taught maths in every phase of the UK educational system from early years (kindergarten) to a postgraduate level. As well as teaching, I have worked in edtech, creating successful maths websites and I also deliver workshops at schools and conferences across the UK. Just recently I have been elected as the Mathematical Association’s (MA) Chair of the Teaching Committee. The MA is England’s oldest teachers' subject association.

      I teach in a High School located in the most deprived Local Authority of the 317 LA’s in England (IMD 2019). When schools were closed at the start of lockdown, we would have ideally liked to have used more digital solutions to provide students with lessons but only a small minority of students that have consistent access to computers with broadband at home. Instead, we set bespoke home study guides, to meet the needs of our students including all the necessary resources as well as in-depth study timetables. We also have a number of digital maths platforms which students can use for distance learning although we know many students will have issues accessing these resources.

      With parents taking on the new role as teachers and even with help from our staff, many parents are finding stay-at-home teaching difficult especially as the weeks turn into months. My greatest concern is that too many of our students don’t have access to the school equipment that is essential to complete their learning. Some students don’t have access to scientific calculators, geometry sets, pencil cases and many of the resources we take for granted.

      My faculty is very concerned that our Year 10 (Grade 9) students will be disadvantaged preparing them for 2021 GCSE exams. I know first-hand that students in more affluent areas have much greater access to technology and some parents have even hired tutors. The sooner our students return to school the greater the chance we can address the developing learning gaps caused by the digital divide.

      We were hoping the Y10 and Y12 students will return to school soon to prepare for the 2021 GCSE’s and A-Levels but are mindful of the health implications. My school has worked so hard to provide an exceptional education to ensure that our students get the life chances they deserve even though they are challenged by a wide range of social, economic and environmental factors which they often have no control over. The coronavirus could undo all this hard work but I know our school will do everything possible to mitigate the challenges ahead of us.

    • Hello!


      My name is Heidi Allum, and I am an Educator in Ontario, Canada. I am currently in a coaching role, specifically my title is an Educational Technology Coach. I support teachers with leveraging digital in meaningful ways. Really, my ultimate goal is for students to create. I teach in the elementary world, so that is what I know, well - I am constantly learning - about.

      Math is a love of mine. Actually, this is a confession: I am actually terrible at Math, and my scope is very limited. What I truly love about math is it opens up conversation and collaboration with students. I love how math puts you in a place where communicating what your thinking, and talking about and exploring how you got there, are paramount.

      I do not have any expertise on COVID-19, and am really just going with the flow as the Ministry of Education and my Board continue to make decisions on moving forward.