Today I subbed in a sophomore World History class. It's in my LA County district. Yes, I know that it's a Monday, and so it's all online learning. Being called to such a class is rare -- since the regular teacher could just teach from home -- but not impossible. Apparently this teacher is too sick to teach at all today, even from home.
Moreover, this is my third visit to this classroom. I still remember being called to this class in both October 2017 and 2018 -- both on the day after Mole Day (the science holiday on October 23rd). In these two cases, I asked some of the students whether they did anything special for Mole Day in their science classes. But today is much different -- yesterday wasn't Mole Day, and there's a pandemic, and the classroom is empty, and everyone is on Zoom.
The students are learning about Josef Stalin, the Russian dictator. The assignment is on Common Lit -- a website I've previously seen used for English classes, but not history until today. There's no need to do "A Day in the Life" today.
As it's been a while since the last time I performed it, today I sing "Mousetrap Car Song."
It's tricky to see whether the online students are achieving excellence on Common Lit since I don't have the passwords to that website. In this district, the schedule states that students can officially leave the Zoom meet after 30 minutes (that is, only a half hour of attendance is required). If I were to enforce this resolution, I'd say that they can't leave unless they have a good score on their Common Lit -- but since I can't see their Common Lit scores, I can't enforce it.
This is what I wrote two years ago about today's lesson:
Lesson 14-3 of the U of Chicago text is called "The Tangent Ratio." In the modern Third Edition of the text, the tangent ratio appears in Lesson 13-5. (By the way, Lesson 13-4 of the new edition is all about the Golden Ratio. This lesson doesn't appear in the old edition, but we did mention it back on January 6th, Phi Day.)
Normally, I don't post Desmos activities on Mondays. But on Twitter today, I see the following Desmos trig activity, created and posted by Paige Sheehan:
https://teacher.desmos.com/activitybuilder/custom/6071fe226636900d2a39f828
In Sheehan's Geometry class, her first post-spring break lesson is an intro to trig. In my Geometry class on the blog, my first post-spring break lesson is an intro to trig. And on Sheehan's Desmos activity, the first question is, "Tell me one thing that brought you joy over break" -- as in spring break.
Thus this lesson is so perfectly timed -- an intro to trig just after the Easter holidays -- that I just can't resist posting it to the blog. And so I'm replace the exercises from two years ago with the activity. No, she isn't using the U of Chicago text -- instead, she's using Eureka, which we recall to be the Common Core curriculum developed in the state of New York.
Also, notice that in this Desmos activity, the word "tangent" is never used. Instead, she sticks to the terms "opposite," "adjacent," and "ratio." In fact, in the Twitter thread, there was a link to a webpage by James Tanton:
https://gdaymath.com/lessons/gmp/7-7-topic-the-story-of-trigonometry/
Tanton tells us that he prefers to think of the trig functions as circular functions first and foremost, before thinking of them as trig functions -- in fact, he calls it "circle-ometry" instead of trigonometry.
This idea also came up last summer on my blog, during my Shapelore posts. In deciding what to call the cosine and sine functions in Shapelore, we thought of names like "ringex" and "ringwye" (or "wheelex" and "wheelwye") -- that is, looking at them as circular rather than trig functions. I admit it's tricky though -- the trig functions appear in Geometry while circular functions don't appear until Algebra II at the earliest, so we'd have to rethink how to teach this concept in both courses.
Tanton tells us that the word "sine" is Latin for bosom, and so if we were to calque this word from Latin, we ought to call it the "bosom" function, since "bosom" is an Old English/Anglish word. (Yes, that's an attention-grabber.) The reason for this name, he explains, is confusion between the words in Sanskrit, Arabic, and Latin. (Oh, and speaking of Arabic, I wish a blessed Ramadan to all readers who celebrate it.)
As for what to call the tangent function in Shapelore, I'm still undecided. I was considering a name that starts with "tan" -- otherwise we'd have to explain why it's called "tan" on the calculator. Hmm -- perhaps we can call it the Tanton function, after the teacher who's introducing a new way to teach it. (I point out that proper names are allowed in Anglish and hence Shapelore.)
Let's post the first worksheet from two years ago, to be paired with Sheehan's Desmos lesson.
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