Then it's up to my new district, and all other districts in the county, to declare a reopening plan. I will continue to monitor my district website and emails for any word on, for example, a board meeting during which such a plan is discussed.
As I mentioned before in my last post, my own opinion on the reopening is mixed, due to my status as a sub. As long as I can get subbing assignments for distance learning, then I'm not in any particular hurry for the schools to reopen. But so far, as you can plainly see, I haven't gotten any calls yet. And I assume, of course, that I'll get calls once the schools reopen. Thus I remain in favor of a reopening.
By the way, as the new school year begins, I've been thinking about the generations again -- in particular, what impact the coronavirus has on each generation. Recall my definition of generations -- the Baby Boom Generation definitely starts in 1946, after World War II. If we then assign eighteen years for each generation, we get the following chart:
Baby Boomers: 1946-1964
Generation X: 1964-1982
Millennials: 1982-2000
Generation Z: 2000-2018
Then each generation graduates high school just as the next one is being born -- for example, the Boomers graduated in 1964-1982, exactly when Gen X was born. The Millennials' name refers to the "millennium" -- they were born in the old millennium and graduated in the new millennium.
There's about two years of leeway in these definitions. Thus even though 1982 is listed as the cusp between Gen X and Millennials, those born in 1980-1984 may be assigned to either generation. This includes yours truly, as I was born in 1980. Thus sometimes we're referred to as the "Xennials," on the cusp between Gen X and Millennials. (Another name for our microgeneration is "Oregon Trail," named after the only game that was available in our school computer labs. And yes, I definitely played "Oregon Trail" as a young elementary student.)
Notice that the generation currently in K-12 is Generation Z, born in the 2000-2018 range. If we cut out two years on either cusp, this leaves 2003-2015 as definitely in Gen Z. Notice that the oldest students in this range are now seniors while the youngest kids are kindergartners. This means that we can equivalently define Gen Z as the generation attending K-12 during the 2020-2021 school year -- a year that's itself defined by the coronavirus. Thus a member of Gen Z is someone whose K-12 education was interrupted by the virus.
Indeed, a new name that's come up for Gen Z is "Zoomers" -- it starts with Z and rhymes with "Boomers," so it sounds like a good name for a generation. And indeed, the name "Zoomers" fits the idea that this is the generation whose education was affected by the virus -- that is, it's the generation that must use websites such as Zoom for its K-12 education.
Current college students are "Zennials," on the cusp between Millennials and Gen Z. Current preschoolers are on the cusp between Gen Z and the next generation.
(Likewise, those in K-12 during the 2002-2003 school year are the Millennials. But there's a tendency to move this up to 2001-2002, as in 9/11 -- the Millennials are those in K-12 during the attacks. The idea is that the tragedies of 9/11 and the virus had a big effect on the education of those generations.)
My eighth graders from the old charter school are now seniors -- in other words, the three cohorts I taught that year are the first three classes that are fully Gen Z.
Apparently, the originators of generation theory are Strauss and Howe. They named generations going all the way back to the fifteenth century, with the Arthurian Generation (1433-1460) and Humanist Generation (1461-1482). Interestingly enough, if we refer to the Arthurians and Humanists as Generation A and B respectively, then X, Y, and Z work out to be the correct generations (although Generation Q according to their list is a short one, 1842-1843).
This is what I wrote last year about today's lesson:
Lesson 0.6 of Michael Serra's Discovering Geometry is called "Knot Designs." Knot theory is a very recent field of topology. Two figures are topologically equivalent if one can be bent, stretched, tied, or untied to form the other.
Of course, knot theory isn't a suitable topic for middle school science. But Lord Kelvin -- of temperature fame -- once believed that atoms were knots in the ether:
"Although his theory was not true, the mathematical study of knots is a very current topic today."
...and so it may ultimately have a link to physics after all. Meanwhile, let's see what Serra has to say about knots. This is Lesson 0.6 in my old Second Edition, while it's Lesson 0.5 in the modern editions, as those editions omit my 0.5.
Serra begins:
"Knots have played very important roles in cultures all over the world. Before the Chinese use ideograms, they recorded events by using a system of knots."
The book depicts a Celtic knot. As Serra explains, the ancient Celts carved various knot designs in stone. He writes:
"Knot designs are geometric designs that appear to weave in or interlace like a knot."
By Serra's definition, the Olympic rings form a knot. Today's worksheet is based on Serra's definition, so there is much emphasis on rings. Of the three questions I selected, one of them has the students draw a knot using a compass (so the shapes will end up being rings). The other two are puzzles involving interlocking rings.
One of the puzzle questions asks students to sketch five rings linked together such that all five can be separated by cutting open one ring. This is easy -- just link four rings to a center ring. The other question is a classic -- the Borromean rings are three rings such that all three are linked, and yet no two of them are linked.
Here is a link to a solution to the Borromean ring puzzle:
http://im-possible.info/english/articles/borromeo/index.html
According to the link above, the Borromean rings are physically impossible -- unless the rings deviate slightly from perfect circularity. Hence the link labels this as an "impossible figure" not unlike the op art from Monday's lesson. Of course, we can draw op art, including perfectly circular Borromean rings, on paper with a compass.
Actually, I found a few interesting links involving Borromean rings. Here is Evelyn Lamb, who writes a math column for Scientific American once or twice per month ("Roots of Unity"):
https://blogs.scientificamerican.com/roots-of-unity/a-few-of-my-favorite-spaces-borromean-rings/
Recall that knots and science are related. Here is a Borromean ring consisting of three atoms:
https://www.livescience.com/9776-strange-physical-theory-proved-40-years.html
And here's a link to Borromean onion rings, courtesy one of my favorite mathematicians, Vi Hart:
https://www.khanacademy.org/math/math-for-fun-and-glory/vi-hart/thanksgiving-math/v/borromean-onion-rings
Actually, Serra mentions the Gordian knot as well, even though I didn't include this question on my worksheet.
The recreational math website Cut the Knot is actually named after the Gordian knot. Here is a link to Alexander (Bogomolny) the Great, who explains why he chose that name:
https://www.cut-the-knot.org/logo.shtml
Knot theory has also recently made the news. A young (Millennial, perhaps approaching Zennial) mathematician, Lisa Piccirillo, recently solved a difficult knot theory problem:
https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-knot-problem-20200519/
Her proof was completed in February. I hope that John Conway, the originator of the problem (a member of the Silent, pre-Boom Generation) was able to read her proof before his passing in April.
Here is the Blaugust prompt for today:
What’s a practice you keep doing year after year? Either something that works great or something that maybe needs examining. Why do you keep doing it?
This is what I wrote about this prompt two years ago -- the last time I posted on August 24th:
Well, I was only in the classroom for one year, so I can't say "year after year." But I can find some practices that I did during that single year. In fact, I found a January 2017 post in which I found both "something that works great" and "something that needs examining."
The thing that works great is the music break. Here I describe a music break during sixth grade math:
In my classes, I often sing songs in order to break-up the monotony of our 80-minute blocks. Today's song is called GCF, since the sixth graders were learning about greatest common factor yesterday:
GCF!
Greatest Common Factor
GCF!
List every factor
GCF!
Circle the ones in common
GCF!
Choose the biggest one
LCM!
Least Common Multiple
LCM!
List some multiples
LCM!
Circle the ones in common
LCM!
Choose the smallest one
I made up the tune as I played it on my guitar. Of course, I couldn't resist the temptation of basing the tune on the actual musical notes G, C, and F.
And the song works because the students enjoy singing along with it -- and the lyrics of the song are the steps to finding the GCF or LCM. On the other hand, something that doesn't work is -- you guessed it -- the way I teach eighth grade science:
But first, let me provide some explanation. My small charter school has no middle school science teacher -- instead, I, as the math teacher, must include some science into the lesson. Notice that some STEM projects, like the ones I gave sixth and seventh, already contain some science. But I want to be sure that the eighth graders receive sufficient science content since this is a tested subject here in California.
And so I go to our online software that we use for science, and download a worksheet based on questions that they may see on the state test. The hope is that next week, they can go to the online program itself and answer the questions correctly. The lesson is on the environment, because there is an upcoming science unit that will begin next month. It is called Green Team, and the students will be learning about energy and water conservation.
But then one girl -- the top student in math -- begins to complain. She argues that at the very least, science should be project-based, and so she wants to have some project rather than a worksheet. I assume that she had her hopes up all week when she saw that we'd be doing science, only to be disappointed when she sees the worksheet today. She says that she enjoys the science projects that she performed at her old school, before she transferred to our school over a month ago.
There are several issues at play here. In sixth and seventh grades we have the Illinois State "STEM" projects in math, but "STEM" projects are not actually science projects. At our charter school, there is neither a science teacher nor a specially designated time for science. But at our sister charter, there is an actual science period, even though there's no separate science teacher there either. At our last meeting, the math/science teacher at the other school tells me that there are separate texts published by Illinois State for actual science projects, distinct from the STEM projects. She says that her students enjoy the real science projects more than the STEM projects.
My top student wants to do actual science projects. She isn't satisfied by the STEM projects -- which isn't surprising, since the students at the sister charter feel the same way.
As I reflect on this discussion (and the student mentioned here is the "special cousin," by the way), I can easily point out one big mistake I made there. I shouldn't have downloaded the worksheet from the Study Island website. Instead, I should have had the students do the assignment online. It wasn't until I saw the Edgenuity website last summer that I realized that this is the age we now live in -- entire assignments can be given online. Even though the special cousin was hoping for a project, she probably would have liked answering the questions online better than on the printed copy.
The most recent Blaugust post is from Beth Ferguson, aka Algebra's Friend:
http://algebrasfriend.blogspot.com/2020/08/just-for-fun-brain-teasers.html
Awesome Shelli asked early today if anyone has a slide show of brain teasers that could be used as an "away" screen on Google Meet.
Her ask resonated with me ... felt like a challenge that I wanted to tackle today.
So ... I pulled together a few brain teasers today that might be interesting to a wide range of students.
So ... I pulled together a few brain teasers today that might be interesting to a wide range of students.
Just like so many other Blaugust participants, Ferguson here takes something from her pre-virus classroom (in this case some brainteasers) and finds away to adapt it to distance learning.
Another blogger is Sue Jones, who works at a community college in Illinois:
https://resourceroomblog.wordpress.com/2020/08/24/school-has-started/
If today’s any indicator, I’ll be *plenty* busy.
Somebody asked when I let them know they’re getting rid of our department: what will the students do?
I don’t know. These students, today, went from overwhelm to under control, relatively speaking.
And once again, Jones converts a pre-virus task to distance learning. In this case, it's a multiplication task for Geogebra.
Meanwhile, I'd like to link to one more blogger, for honorary reasons. I recently found out that New York teacher Wendy Menard has recently passed away:
https://hermathness.com/
She hadn't blogged since September 2018, but she was active during the year that I taught at the old charter school (and I linked to her blog often that year).
In one of her final posts, she wrote:
I am not any kind of an expert. I am a middle-aged, [...] woman with health issues, who, recognizing that it was not my job to ‘save’ my students but rather to educate them as best I could, has taken upon a course of self-study in order to honestly see myself and the system in which I operate.
And those health issues got the best of her, taking her away while only middle-aged.
Her penultimate post (and final post with an August date) was about the traditionalist debate. She challenged traditionalist Barbara Oakley, who wrote that widely-discussed New York Times article.
And her final post was titled "The Binary." It's about politics, Black Lives Matter, and related issues, nearly two years before the passing of George Floyd. Since this is considered a school-year post, I won't say any more about it -- just go directly to her blog to read more.
Rest in peace, Wendy Menard. I'm sure your students miss you the most.
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