Monday, March 2, 2020

Lesson 12-2: Size Changes Without Coordinates (Day 122)

Today is Dr. Seuss Day, celebrated in many elementary schools. But of course, it's also the day before Super Tuesday.

Today is the big political post that I've planned ahead of Super Tuesday. By the way, if you're hoping to skip over all of this and just get to the candidate, I'll say it write now -- I neither endorse a candidate nor reveal the candidate I cast my vote for. So readers looking for a name might as well stop reading now.

As always, I add the "traditionalists" label to this post. I won't really write about traditionalists per se, but I prefer to confine political discussion to the posts with that label.

Four years ago on the blog, I mentioned that California held its presidential primary in June. This year, California joins the Super Tuesday states. It's well known that our state has a Democratic majority, and so our primary date is set up to help that party out. Indeed, if the current officeholder is a Democrat (as in 2012 and 2016), then the primary is held in June. But if the current President is a Republican (as in 2004, 2008, and 2020), then the election is moved up to Super Tuesday.

In this post, we explore the candidates using the I Side With website, just as I did four years ago. And once again, I'll focus on the education questions on this education blog, filling in dummy answers for just enough questions for the website to process the survey and match me with candidates.

Four years ago, my focus was on the Common Core Standards. There's still a Common Core question in the survey, so I'll answer it. I'll start by giving "yes" as the answer to the Common Core question and rank it as "most important," and then a few extra questions as "least important" in order to isolate the variable that we're really looking for.

Here are my results:

55% Tom Steyer
50% Michael Bloomberg
48% Elizabeth Warren
48% Bernie Sanders
47% Amy Klobuchar

If we change our answer on Common Core to "no," then the following list arises:

63% Joe Biden
50% Michael Bloomberg
48% Donald Trump
42% Pete Buttigieg
28% Tulsi Gabbard

We notice that Bloomberg is 50-50 on both lists. It's easily explained -- Bloomberg doesn't have an answer to the Common Core question. This is despite his being, as mayor of NYC, in charge of a school system with a unique implementation of the standards (EngageNY). If we omit Bloomberg, then we are left with four pro-Core and four anti-Core candidates.

Of course, the correct answer to the Common Core question is the last choice, "This question is no longer relevant and should be removed." This is because Common Core is no longer a hot topic that anyone is currently debating.

Instead, the main education issue in on charter schools. So let's erase the Common Core answer and answer "yes" on the charter question:

86% Joe Biden
73% Tom Steyer
48% Amy Klobuchar
47% Donald Trump
47% Michael Bloomberg
42% Pete Buttigieg
28% Tulsi Gabbard

If I change it to no, we get the following list:

86% Joe Biden
73% Tom Steyer
48% Elizabeth Warren
48% Bernie Sanders

Again, notice that Joe Biden's and Tom Steyer's percentages didn't change, since they actually don't have a response for the charter school question. Apparently, the random answers I filled in just to get the survey to submit are 86% pro-Biden. But we see that Warren and Sanders are the only candidates who moved up when I answered "no," implying that they are the only anti-charter candidates.

One thing I've noticed that is that the political parties are often represented by colors. Democratic states are called "blue" states while Republican states are called "red" states. And swing states are a mix of blue and red -- "purple" states.

The minor parties also have colors, as we see at the following link:

https://ballotpedia.org/Presidential_candidates,_2020

The Green party is named for its color (to represent the environment), while the Libertarian party color is yellow (or gold, to represent the economy). The other minor parties don't have a color.

If we were to color the nominees for the 2016 election, from left-wing to right-wing, they would appear as follows:

green: Jill Stein
blue: Hillary Clinton
purple
red: Donald Trump
yellow: Gary Johnson

And then I realized something -- the colors are (sort of) in the order of the rainbow or the color wheel, except with a branch-cut between yellow and green (instead of purple and red). In fact, this allows us to use a continuum of colors to describe different candidates.

For example, a mainstream Democrat is blue, a moderate Democrat is purple, and a progressive Democrat is between blue and green. If we wish, we can even use Kite's musical colors and call the color between blue and green "bluish" or even "zogu." But in order to avoid confusion, we'll call this in-between color "turquoise" instead.

And on the right-wing, a mainstream Republican is red, a moderate Republican is purple, and a libertarian-leaning Republican is either "reddish," "ruyo," or "orange."

Now let's color the 2020 candidates based on their education stances as given by I Side With. We'll apply the following rules:

left-wing = pro-Common Core
right-wing = anti-Common Core

The charter question is ultimately all about privatization. We can score this question on a continuum from most public to most private:

green = strong public schools
blue = strong charters
red = strong vouchers
yellow = strong private schools (full "separation of school and state")

For example, the blue (mainstream Democrat) position is represented by Barack Obama and his Education Secretary, Arne Duncan, who was strongly pro-charter. On the other hand, the current red (mainstream Republican) position -- Donald Trump and his Education Secretary, Betsy DeVos -- recently favors vouchers over charters:

https://www.forbes.com/sites/frederickhess/2020/02/18/why-charter-schoolers-are-feuding-with-betsy-devos/

OK, so let's start coloring the candidates. The most representative blue (Democratic) candidate ought to be Joe Biden, since he was, after all, the most recent Dem Vice President. But the I Side With survey shows that Biden opposes Common Core -- despite being the VP of the administration that approved the standards in the first place (which is the reason why pro-Core is considered left-wing in the first place)! Instead, the mainstream Democrat is now considered to be Amy Klobuchar, since her I Side With responses favor both Common Core and charters.

The quintessential turquoise candidate is Bernie Sanders. In the Senate, he is an independent member of neither the Democratic nor Green parties, yet holds positions intermediate between them. On I Side With, he favors Common Core and opposes charters, both left-wing positions. The I Side With survey also shows Elizabeth Warren agreeing with Sanders on both education questions, and so she can be considered turquoise as well.

The quintessential purple candidate is Michael Bloomberg. As mayor of NYC, he was a Republican, but now he runs for President as a Democrat. He holds positions immediate between them. But on I Side With, he favors charters but doesn't answer the Common Core question. Instead, we represent purple by Pete Buttigieg, who favors charters and opposes Common Core. (Note: If we're using Kite's colors, we can also use "lavender" or 11-limit instead of "purple.")

Neither Joe Biden nor Tom Steyer answers the charter question. Since Biden opposes Common Core, he's probably purple, but Steyer, who favors the standards, is likely blue.

On the Republican side, Donald Trump, as the incumbent, ought to be colored red. But as a candidate in 2016, he sought to distinguish himself from the GOP establishment, and so perhaps he leans more towards orange. (Trump is often called "orange," but that word is intended to describe the President's hair color, not his politics.)

Then who should be considered red (mainstream Republican)? The last two Presidential nominees -- Mitt Romney and the late John McCain -- as Senators, made controversial votes that diverged from the majority of their party (on impeachment conviction and Obamacare repeal, respectively). So some would consider Trump red and Romney and McCain purple. In the end, it doesn't really matter since as an incumbent, Trump faces only token opposition and is the lone Republican on I Side With.

The quintessential orange politician is one of those token primary candidates, Bill Weld, since he previously ran for Vice President as a Libertarian and holds positions intermediate between them. The Pauls (Ron and his son Rand) can also be colored orange since they hold some Libertarian positions.

So our color chart looks like this:

green: (Green Party nominee)
turquoise: Sanders, Warren
blue: Klobuchar, Steyer
purple/lavender: Biden, Bloomberg, Buttigieg
red: Trump
orange: Paul, Weld
yellow: (Libertarian Party nominee)

Earlier, I claimed that these colors are based on both the color wheel and Kite's musical colors. But those familiar with Kite colors might recall that a "purple 3rd" (neutral 3rd) actually lies between yellow and green, not blue and red. Actually, Kite himself explains the color purple:

"But purple intervals actually come from neighboring intervals: the purple 3rd is both an infrared 2nd and an ultraviolet 4th."

Thus the analogy isn't perfect. (I was considering composing a "presidential song" about the candidates using the intervals represented by their colors, but it doesn't work out well.)

There are a few more things to say about presidential colors. First of all, where exactly should we place Tulsi Gabbard? Like Buttigieg, she favors charters and opposes Common Core (according to I Side With), so it would appear that she's purple. But Gabbard endorsed Sanders in 2016 -- and she also appears to be the most acceptable to Libertarians. So perhaps there's a case for yellow-green -- a color that exists on the wheel at our branch-cut but not in Kite's notation.

Oh, and there's one more color that exists in Kite's world -- white. I suppose if we need to color a (former) presidential candidate white, it would be the late Lyndon Larouche. But this is mainly for musical reasons -- his tuning system is based on C = 256 Hz, A = 432 Hz (Pythagorean intervals), which are white in Kite's notation.

Well, that's all I have to say about Super Tuesday. May the best color win! (And yes, I know that half the candidates mentioned in here have dropped out in the past few days since I voted on Leap Day.)

Lesson 12-2 of the U of Chicago text is called "Size Changes Without Coordinates." In the modern Third Edition of the text, size changes without coordinates don't appear on their own. The first lesson of the new text, Lesson 12-1, corresponds more closely to Lesson 12-3 of the old text. The opening dilation activity of the old Lesson 12-2 is nonetheless squeezed into the new 12-1.

In past years I've called this an "activity," but in reality it isn't. The main lesson is all about how to perform dilations without coordinates, which is exactly what this worksheet does. So don't worry -- I'm not breaking my promise by posting two "activities" on consecutive weekdays, since what I'm posting today is a lesson, not an activity.

This is what I wrote last year about today's lesson (and last Friday's activity):

https://mylifeasmissblog.wordpress.com/2016/01/17/5/

Here's what the author Olivia writes about her activity:

At the beginning of the week, I assigned a dilation project in geometry.  Students were to pick a picture from the internet, draw a grid over top of it, then redraw the picture following the grid on a larger piece of paper.  My district does not have an art program, so many of the students are definitely not comfortable when it comes to art.  I heard a lot of negative comments that day from students saying they sucked at drawing, it was going to turn out horrible, and many pleas of students asking me to “please not hang them up!”  They were especially adamant that they WOULD NOT be putting their names on their pictures.  I told them it would be okay and they would turn out great.  I said that if I could do it, anyone could do it!  Well I gave them 2 full days of class time to work on their posters.  I hung up a couple of the posters after the first day, because two of my students finished theirs by working on it in study hall.  The next day, my other classes were all asking who drew what.  I said, sorry guys this class wanted to remain anonymous.  Well, my geometry class came in later in the day.  I told them all that people kept asking about who drew what but I did not rat anyone out about who drew what.  Then, a very exciting thing happened! Students started saying, “Mine looks so good, I’m definitely putting my name on mine” or “I want everyone to know who drew mine.”  They told me that it wasn’t as terrible as they thought it would be and it was actually fun.  I loved seeing students so excited and proud of their own work. It always makes my day brighter when students realize just what they can accomplish.  Everyone ended up putting their names on their finished products, and I was left as one happy math teacher.

Well, there's nothing stopping us from assigning this activity today. I obtained the pictures simply by performing a Google image search for "cartoon character" -- those just happened to be the ones that came up.

There's one thing about activity -- it works better on a coordinate plane. But note that Lesson 12-2 of the U of Chicago text uses Slope and Distance Formulas just to prove that the mapping from (xy) to (kxky) is a dilation with scale factor k.



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