You can teach an old dog new tricks

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Given the title of this post, I write knowing I risk being accused of insulting my colleagues and yet nothing is further from the truth. If anything, this post serves to celebrate the ways we learned to work in a short amount of time when the pandemic hit and our classes went online.  Over the course of a month, we had to move all of our classes to distance learning. Instructors that are ever so comfortable scribbling equations across a chalkboard in a room full of students now faced the reality of teaching online using platforms they might not have yet been aware of and handling student engagement in new ways. There were a lot of growing pains. The college prepared online trainings on various platforms but some were not tech savvy enough to even be able to log onto them. The vast amount of information sent our way during those first few weeks was staggering and some were clearly unable to keep up with it. Despite this many pressed on, learning new ways of teaching, trying out new pedagogies to engage students, sharing information any way they knew how, being flexible, and finding ways to support students.

person working at computer

I was worried about a few of them…very worried. An instructor I sat with in my office also met with a number of our colleagues in an attempt to prepare for distance education. She attended many training sessions before she even realized her computer lacked a built-in camera. Yet here we are weeks later and she is posting videos for her class and running her assessments using a free online software. I wonder how much of what was learned in those first few months has seeped its way into classes even now. Will we make more use of online resources even when we are no longer required to do so? Perhaps we will soon learn the answer to these questions. What we do know now is that for many of us, our new ways of working and living are quite a change from what we were accustomed to and yet weeks later we carry on as best we can, learning new things every day no matter how comfortable we were with the old or how ill-prepared we may have seemed at the start.   

Today I go first

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One of the nice things about Saturdays, at least for me, is that I don’t set an alarm in the mornings. I get up when my body is done sleeping and this is always early enough. I make a cup of coffee, turn on the computer, and get to work checking e-mail messages. I am the first person in my household to get up and get a good 1 – 1.5 hours to myself in the morning on any given Saturday. This is the only time all week that I have completely to myself. Once my family I up, it’s time to make breakfast, help my daughter with school work, juggle the schedules of two working adults and on and on until the last e-mail is returned, the last lesson posted, the last dish is washed, the end of the night hits and it’s time to rest. I have been working on taking better care of myself and yet it didn’t hit me until yesterday that I am giving up the only time I have truly to myself to check my work e-mail. Yes, it is important to keep up with my work, but time to one’s self is beyond precious and checking e-mail messages doesn’t sound to me like the best use of it. So today, I decided to go first.

When I awoke, I pulled out a box of LEGO – a remote controlled car that I was supposed to make with my daughter but that ended up being too difficult for her. We abandoned it months ago. I spent the next 1.5 hours sitting at the dining room table, pieces sprawled out all over, completing it. It was genuinely fun and quite relaxing to sit there piecing it together. I waited to test it out until after my family had woken up. The car zipped around the apartment causing my daughter to squeal with joy when it came close to her. It was both fun to build and fun to drive. A truly rewarding start to the day. Oh, and those e-mail messages, in the end, they got checked anyway. 

Pi Day 2021

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Happy Pi Day!

The mathematical constant Pi represents the relationship between a circle’s circumference and its diameter. Pi is approximated as 3.14 though in actuality the digits after the decimal go on and on without a fixed pattern forever. That makes 3/14 Pi Day.

Pi Day 2021 Image

All sorts of great celebrations happen across the country on Pi day with people holding contests in which they memorize the digits of pi and indulging in round treats including pie.

Following is an activity you (and your children if you have any) can try to celebrate Pi Day and to see how Pi is related to the circumference and diameter of a circle.

Activity – Take some circular objects that you have around the house (coffee cup lids, cups, candles, yogurt containers, jars and so on. Trace around them on paper (one per each sheet of paper) so you get a nice collection of circles. Take each circle and measure its circumference (the distance around the circle) and diameter (the shortest distance from one point on the circle to another through the center) using lentils. Yup, you heard me right, lentils. For the circumference this means gently placing lentils one next to the other all the way around your circle. To measure the diameter, fold the paper in such a way that two halves of the circle fold onto themselves. When you open the paper back up, the crease is your diameter. Line lentils up all along the crease. For each circle note the diameter and the circumference. Then for each pair divide the circumference by the diameter. What do you get?

If you are working with a younger child and the thought of picking up lentils from all over the floor is troubling you or if you are working with a child that does not yet know division, use yarn instead. Cut (maybe you do this part) a few pieces of yarn that are as long as the dimeter. Have your child arrange these pieces around the circumference of the circle to see how many of them are needed. You might want to tape them down when they are in place. Here, a rough estimate is good (a little more than ___ or a little less than ___).

After you try the above, read the next paragraph or spoil the surprise (if indeed it is a surprise) and read it now.

You have discovered the relationship between the circumference and diameter of a circle! The number you get should be a close approximation to pi which is roughly 3.14 or in the case of the yarn you could leave it at “a little more than 3.” Keep in mind that you used lentils which are a non-standard unit of measure (they also aren’t all exactly the same size) and second, you are human and the circle you drew isn’t perfect – neither is the round object you traced it from (perfect circles exist only in our minds). Incredibly if you take the circumference of any circle and divide it by its diameter you will get pi. By the way, what you measure in doesn’t matter. The relationship holds whether you measure in inches, centimeters, lentils or lima beans though your accuracy might change especially when using non-standard units of measure like beans. This works for every single circle. How amazing is that?

To Turn a Star

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In an attempt to keep to my workout routine, I have printed out a blank calendar for the current month and charged my 6 year old daughter with putting a sticker on each day I exercise. She is wonderful when it comes to handing out stickers and takes pride in both choosing the sticker and in affixing it to the page as straight as possible. Today I earned a five pointed star. “I put it on straight,” she said with a smile and then after a brief pause, “but it would be right even if I turned it a bit.” There it was, a perfect opening for a math lesson.

Five Pointed Star Stock Photos And Images - 123RF

I asked her what she meant and she took another star sticker from the pack. “I can put it with this point up but if I turn it and put this point up instead it will still look the same.” My daughter’s statement is akin to a mathematician declaring that the five pointed star has rotational symmetry. I pushed, “How many points are there? Does this always work…will it always look the same when you turn it?” Little by little we talked through how any of the 5 points could be “up” ensuring the sticker would look the same, but that if a point wasn’t up it would be different. She talked about turning it enough or not enough. Mathematically, this has to do with the number of degrees that the star is rotated about its center. As there are 360 degrees in a full turn and we have 5 points which could be pointing up, every time we go 360/5 = 72 degrees we up with the sticker, in my daughter’s words, “looking the same.” In actuality regardless of how the star looks initially rotating 72 degrees as many times as you want will yield an image that looks exactly the same as the one you started with. After my daughter and I talked through the pattern she was observing I told her that mathematicians have noticed this same pattern and called it rotational symmetry. She was delighted by this and started asking if it might work with some of the other stickers she has which gave us an opportunity to play with the concept further. We often think of mathematics as consisting of numbers and equations which, unfortunately, is quite limiting and for many makes the subject feel distant, irrelevant, and even something to be feared. Instead, I urge you to think of mathematics as the study of the patterns that exist all around us. By doing so, a seemingly simple observation by a six-year old pertaining to the way a sticker looks when we turn in it our hands, can become the first step into the elaborate, beautiful, mathematically rich topic of symmetry.

Half an Avocado

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One of the things that sheltering in place has made me very aware of is how much food goes to waste. I am now incredibly aware of the expiration date on every item we own and the goal is to go through all the fresh fruits and vegetables before any of them end up in the trash. Cue the avocado. This little green berry (yup – you read that right) with an awful large seed makes its way into our home rather infrequently. My partner is the only one in our house that likes to eat avocados and never seems to finish a whole one. So I use my fancy avocado cutting/peeling/slicing tool (we love gadgets in this house) to carefully cut, peel and slice half an avocado putting it in a little plate on the dinner table way from the rest of us. The other half of the avocado normally sits in the fridge covered in plastic wrap where after a few days it inevitably ends up in the trash.

This would happen every single time with every single avocado – kind of makes me wonder why I would waste the plastic wrap and not just toss half the avocado in the trash from the start. A week ago I prepared half of an avocado, wrapped the other half in plastic wrap and put it in the fridge. It stared at me every single time I opened the fridge. I could not bring myself to let it go to waste. So after two days I took it back out, chopped it into pieces, threw in some tomato, some mozzarella cheese, a little oil and a little vinegar. When we sat down to dinner that night I was pleased to hear “Wait, is this little salad just for me? Wow…thanks” and just like that the other half was saved!

The Best Thing About Today

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As of last check there were over 41,000 confirmed cases of COVID-19 in New York City. New York is in a state of “pause.” Many businesses are closed and the schools have moved to distance learning as my family and I enter our third week of sheltering in place. It is, at this time, easy for me to think about the things I cannot do. I cannot hug my grandmother on her 99th birthday, hold a gathering of friends and family to celebrate our daughter’s 6th birthday, or continue my tennis lessons. We’ve stopped Sunday visits to parents and grandparents. 

Given all the things we cannot do we thought it important to take the time to reflect upon the good things we could and actually did do each day. Every evening at dinner, we go around the table and each of us shares what, to us, was the best thing about today. Among these best things are coloring, dance parties, sunshine, fresh air on the patio, crafts, streaming yoga classes done together as a family, virtual playdates and long conversations with friends and family. Despite the challenging times we are in, it is surprisingly easy to identify best things each day. Doing so does not make the challenges we face any less. However, it does remind us that even in the most challenging of situations, if we look for them, there are reasons to be grateful.