"Food manufacturers are seeking to use genetic techniques to manipulate genes in various produce to enhance shelf life, size, taste, and resistance to pests. The altering of genetic codes can now be done in a minute fraction of the time it has taken the process of natural selection to take place."
This is the final page of the genetic engineering section in Pappas. Here she is clearly writing about genetically modified organisms (GMO's) as food. GMO's are controversial to this day, and there are any number of websites discussing the pros and cons of GMO's as food. She concludes:
"[Genetic engineers] are experimenting with life as it has evolved over millions of years!"
As we read these science pages in Pappas, I've been writing about how I should have taught these lessons to my students last year. I doubt I would have taught the about the GMO controversy in any class last year. But there's one thing in science that's on my mind today -- and I'm sure it's on many of your minds as well.
Of course, I'm talking about the solar eclipse. (California isn't in the path of totality, but only in the penumbra, so we have only a partial eclipse.)
Last year, I did teach a little astronomy to students in all three grades. The whole idea was to use the Rosh Hashanah holiday to explain how the earth, moon, and sun work, as well as why there would be no school on that day.
I believe there was one question in that lesson on eclipses -- draw the earth, sun, and moon in order to represent a solar eclipse. The right answer is that the moon should be between the earth and sun. And indeed, today, August 21st, 2017, the moon is between the earth and sun -- so that's why there's a solar eclipse today.
It's awkward to think about how I would have taught my students about eclipses last year. A much more interesting question is, had I not left my old school, how would I have used today's eclipse to teach them about astronomy?
Well, I must point out that since I left, my school has made a few changes. First of all, both my school and our sister charter have moved to new locations. The charters are no longer co-located with district schools, but instead they own their own buildings.
This means that the school calendar is no longer dependent on the LAUSD calendar. In particular, the school year started later at the charters in order to give more time to move everyone's belongings to the new sites. The first day at LAUSD was last Tuesday, but the first day at the charters is today.
It would be one thing for the day of the eclipse to fall during the second week of school, or even later during the first week of school. But instead, the eclipse occurs on the absolute first day of school. So this makes a huge difference regarding how I'd set up an eclipse activity, since it would suddenly have to double as an opening activity for the first day of school.
For example, I might want to purchase eclipse glasses so that my students could see the eclipse. I'd try to buy enough of them for all the students in whichever class meets at 10:21 (Pacific Time, the darkest moment of the conjunction).
The problem is that I can't be sure of the class size, so I wouldn't know how many glasses to buy. As teachers, we know that even if we receive rosters before the first day of school, there's no telling how many students will actually show up the first day. Some students who lived right across the street from the old school might not attend the new site -- over a mile away -- while the new location may attract students who live closer to it. And I wouldn't have met the new class of sixth graders starting middle school until just minutes before the eclipse begins.
If I don't buy enough glasses, then the students without glasses would try to look directly at the eclipse anyway. And then some of them might go blind -- a risk clearly not worth taking. There's just no way to know how many kids there'll be in the 10:21 class.
And that leads to the other confounding factor -- the schedule. Recall that I had to teach science because our school lacked a science teacher. There's a strong possibility that this year, a science teacher would have been hired. If there's a science teacher, then there would have been no need for me to teach science and thus no need to have an eclipse lesson. But I still like the idea of having an eclipse activity at 10:21 -- after all, the students in my class at 10:21 wouldn't be in the science class at that time. So it might be nice for all teachers to talk about the eclipse with whichever class they have at that time.
For today's speculative post about how I'd have taught about the eclipse, let's assume that my schedule would have been the same as last year's. On Mondays, I began with seventh grade, then eighth grade (with 10:21 about halfway through the class), and then sixth grade. Oh -- the new school starts 45 minutes earlier than the old school (so there's a possibility that the first class would leave before the eclipse begins), but we'll ignore this for today's speculative post. (For this post, I assume that there is no coding Monday today. Last year the coding teacher didn't arrive until the third week of school.)
So let's say that my day begins with seventh grade, and that this class lasts at least until after the eclipse begins. I'd have this class construct "pinhole projectors" -- the classic method of viewing an eclipse before they came up with eclipse glasses. The only problem would be whether I can round up enough shoe boxes to make the projectors. (Actually, I've heard of cereal boxes being used for this purpose as well.) I hope that there is some time left for the students to view the beginning of the eclipse before this class ends. It's also possible to have some students create an "eclipse banner" made up of black moons covering up yellow suns. They could even use the die cut machine, if there's a circle shape. (Recall that one problem I had at my old school was my failure to employ the die cut machine for Illinois State projects.)
Now eighth grade arrives during the darkest part of the eclipse. This is the class that I'd want to purchase glasses for -- but would this class be too large? Last year, eighth grade was my smallest class, but notice that this year's eighth graders would be last year's seventh graders -- and seventh grade was a larger class. I was told that the reason eighth grade was small last year was that the previous year, the seventh grade troublemakers were counselled out of enrolling for eighth grade. So if we assume the same happens this year, the resulting eighth grade class would be small enough for me to purchase glasses for all of them. I've seen some eclipse glasses on sale at 7-Eleven, and so maybe I'd only have to buy seven to eleven (or slightly more) pairs for this class. Then they can view the eclipse at its maximum coverage (almost 70% here in Southern California).
Sixth grade comes to my class as the eclipse is almost over. I let them view the last part of the celestial event through the pinhole projectors. Once it is over, I begin a project from the Illinois State science text -- a flashlight represents the sun, and balls represent the earth and moon. The intent of the project is to demonstrate the phases of the moon. But the new moon phase can be modified slightly to represent the solar eclipse position.
But alas, none of this happened today because I wasn't in a classroom. Maybe I'll be teaching in a classroom on the day of the next total solar eclipse visible from North America -- April 8th, 2024. I point out that meanwhile, the last great American eclipse was in 1979, just before I was born -- but I do remember a partial annular eclipse occurring in May 2012.
Hold on a minute, you might ask. How do I know when the next eclipse will be? That's easy -- the following website lists all of the eclipses up until the year 3000:
http://moonblink.info/Eclipse/lists/solcat
Okay, then -- now you ask, how does the owners of this website know when and where exactly all the eclipses will be? Did someone build a time machine and travel all the way to the year 3000 to find out when the eclipses are? (Or maybe Bender from Futurama sent back all the eclipse info all the way from 3000?) Actually, the simple answer is -- mathematics.
Most likely, spherical trigonometry can be used to find the location of an eclipse. Much to my surprise, there is no mention of solar eclipses in Glen Van Brummelen's Heavenly Mathematics. (That book mentions only lunar eclipses, twice in Chapter 1.)
But we can use some ideas from spherical trig to predict eclipses. According to Van Brummelen, the sun always travels along the ecliptic. (Get it -- eclipse, ecliptic?) So an eclipse can only occur when the moon crosses the ecliptic. This crossing happens approximately twice a year -- creating two "eclipse seasons," with each containing one solar and one lunar eclipse. The above link also explains when the eclipse seasons are:
http://moonblink.info/Eclipse/stats
Solar eclipses only occur during new moons, but the lunations don't line up with eclipse seasons. It turns out that a cycle containing approximately both a whole number of lunations and a whole number of eclipse seasons is called a "Saros cycle," about 18 years long. (This isn't the same as a "Metonic cycle," which is 19 years long and used to determine Easter. A Metonic cycle contains a whole number of lunations and solar years, not eclipse seasons.)
So 18 years and one month from today is September 2035. According to the link, there will indeed be a total solar eclipse that month (labeled as "Saros 145"), but it will be visible only in Asia.
But this is how I can tie eclipse to a possible math (as opposed to science class -- the fact that math can be used to predict eclipses. I've already written about what my ideal first day of school would have been like -- but what about the music break? The plan for my second year of teaching would be that I'd repeat the songs from my first year on their corresponding days. And so I'd repeat my first day of school song -- the Dren Song. But I'd make a change to one line from last year:
The Dren Song -- by Mr. Walker
I don't know why I take math.
I'm all caught up in its wrath.
I'd rather just be a dren.
I would be so happy then.
Tell me what would happen when,
I'm no longer just a dren.
What if I were great at math?
What would be my future path?
Customers won't think it's strange,
When I figure out their change.
Algebra and calculus,
Get me in a cool college.
Once I finish my degree,
Future employers will see,
Of my strong background in STEM.
I know that will impress them.
I won't just be a zero!
I'll be great, or it may seem,
That this all is just a dream,
'Cause my math skills are so bad.
I can't subtract! I can't add!
I can't multiply by ten.
I will always be a dren.
Now I know why I take math.
Help me find a better path!
I would be so happy then.
But I'm just a dren.
Thus I make the connection between math and the eclipse -- math is used to predict eclipses.
Another song that might fit today is "Earth, Moon, and Sun." I said that I want to sing last year's songs on the corresponding days this year -- and last year I sang that song the day after the Rosh Hashanah school closure. But the charter school, no longer co-located with LAUSD, is hence no longer bound to observe district school closures. If the school is open on Rosh Hashanah (which falls in one month at the next new moon, September 21st), then it might make more sense to sing the song today -- with extra lines to describe eclipses, of course:
EARTH, MOON, AND SUN - by Mr. Walker
I know of how the earth goes,
It revolves around the sun every year.
I know of how the earth goes,
It revolves around the sun every year.
The earth's tilt is the reason,
That we have four seasons.
Winter, spring, summer, and fall,
That is all.
In the north, remember,
Winter's in December.
Tilts toward the sun in June,
It'll be summer soon.
I know of how the earth goes,
I know of how the earth goes,
I know of how the earth goes,
It revolves around the sun every year.
I know of how the moon goes,
It revolves around the earth every month.
I know of how the earth goes,
It revolves around the sun every year.
That's why every 30 days,
We can see every phase.
New moon, waxing crescent,
Half moon, waxing gibbous.
That's why every 30 days,
We can see every phase,
Full moon, waning gibbous,
Half moon, waning crescent.
Moon between the earth and sun,
That's a solar eclipse.
Earth between the moon and sun,
That's a lunar eclipse.I know of how the moon goes,
I know of how the moon goes,
I know of how the moon goes,
It revolves around the earth every month.
Professional songs referring to eclipses are Bonnie Tyler's "Total Eclipse of the Heart" and Carly Simon's "You're So Vain" -- but my own songs should be sufficient for the lesson. Oh, and even though I usually give out candy as a reward for A's (see my November 17th post for more info), today would be an exception as I could give out Milky Way bars, Starburst candies -- and of course, Eclipse gum.
Even though Van Brummelen doesn't write anything about solar eclipses, another book I bought at the same time -- last spring's Barnes and Noble teacher day -- was Ian Stewart's Calculating the Cosmos, and Stewart does mention solar eclipses. (Actually, all month Barnes and Noble is having more teacher discount days, and yesterday I bought a Dover text on the cheap, C. Stanley Ogilvy's Excursions in Number Theory. I may or may not write about this book on the blog, but for today let's stick to Stewart and eclipses.)
Solar eclipses appear in the prologue and first chapter of Stewart's book. Let's look at the prologue:
"Conversely, astronomical phenomena have influenced the development of mathematics for over three millennia, inspiring everything from Babylonian predictions of eclipses to calculus, chaos, and the curvature of spacetime."
So now we see who the first eclipse predictors were -- ancient Babylonian mathematicians. Let's look at Stewart's next mention of eclipses:
"Einstein saw his theories verified by two of his own predictions: known, but puzzling, changes to the orbit of Mercury, and the bending of light by the Sun, observed during a solar eclipse in 1919."
I remember watching this in an episode of Genius, the series whose first season was on Einstein. He actually tried to send a colleague to observe an eclipse five years earlier, in 1914. The path of totality passed through Russia, but World War I derailed Einstein's plans. The colleague was arrested by the Russians as a possible spy!
Stewart continues writing about eclipse predictions in Chapter 1, "Attraction at a Distance":
"People calculated aspects of the cosmos, such as eclipses, for millennia before anyone realized that gravity existed. But once gravity's role was revealed, our ability to calculate the cosmos became far more powerful."
As the first chapter title implies, this chapter is all about gravity and the scientist who first came up with the theory of gravitation, Isaac Newton.
Here is Stewart's final mention of eclipse prediction:
"So exquisitely accurate are those rules that astronomers can predict eclipses of the Sun and Moon to the second, and predict within a few kilometers whereabouts on the planet they will occur, hundreds of years into the future. These 'predictions' can also be run backwards in time to pin down exactly when and where historically recorded eclipses occurred."
Hence the website I linked to above is made possible. Not only does it predict eclipses up to the year 3000, but it also goes all the way back to 2000 BC. Here Stewart is writing about mathematical modeling -- a key Common Core Standard -- and the error terms associated with such modeling.
Okay, I can go on and on all day about the Great American Solar Eclipse. But we need to get on with the Geometry lesson.
Lesson 0.4 of Michael Serra's Discovering Geometry is called "Op Art." Serra explains what this is:
"Op art (optical art) is a form of abstract art that uses straight lines or geometric patterns to create a special visual effect."
Optical art is closely related to the concept of optical illusions. I don't even want to attempt to draw some of the more complex optical illusions by hand, so I just use a Google search instead. On the other hand, the impossible objects page comes directly from this site:
http://brainden.com/impossible-objects.htm
Unfortunately, only the Penrose triangle printed properly. It is named for Sir Roger Penrose, whom Serra describes as a British mathematician and avid puzzle enthusiast. (He is in fact still alive -- he just turned 86 this month.) So I actually had to draw in one of the impossible drawings -- "Three prongs from two?" (called "the devil's fork" by Brainden). Well, I suppose if I can draw it, then so can our students.
Well, that's it for today. I'll see you on April 8th, 2024 -- the day of the next American eclipse. It's a Monday, so it should be a school day. (Don't worry about Easter that year -- solar eclipses occur at new moons while Easter falls at the full moon. But at schools that take the week after Easter off, eclipse day will be the very first day back to school -- just like at my school this year.)
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