A Musical Revisit
Introduction
This is my first summer post, after a successful year of teaching high school math. But I'm still deciding what exactly I wish to write about this summer.
Last year, I wrote about some of Eugenia Cheng's books (including her first children's book about a girl named Molly). And we read Laura Lemay's book about Java, just in case I wasn't hired to teach and needed to switch to a career in coding. Keep in mind that with my pink slip becoming official, this may the start of another uncertain summer -- so perhaps returning to Lemay may be in order here.
But I'm not sure whether I want to make lengthy blogposts this summer. Blogging is a dying art, and since I can't be sure how many people are even reading my blog these days, long posts may be a waste of time. I can still learn about Java from Lemay's book, but I'll no longer be blogging about it.
And even Twitter is turning out to be unsuccessful. It's not that no one's reading tweets these days -- it's that no one is reading my tweets. I'm not writing in a way that draws readers, likes, or responses.
There are two ways to be popular on the MTBoS. One is to be a good conversationalist -- for example, a teacher who writes about and shows pictures of her classroom, and responds well to other teachers who write about and show their classes. But as I know, I'm lousy at having conversations -- whether it's online or in person, whether it's with students or my fellow teachers.
The other way is to make new content. The rock stars of the MTBoS -- Sarah Carter, Sara Vanderwerf, Dan Meyer, and so on -- don't need to be great at conversations with us mortals. They blog about a new activity and tweet a picture of it with a link to the blogpost, and we all follow them.
Believe it or not, since I'm so terrible at conversations, the easiest way for me to gain traction in the MTBoS is to post original content. And there's one thing that I hope I'm good at that's original -- namely the math songs that I post.
Music, unfortunately, turned out to be a failure this year. Very early in the year, one parent complained that I was spending too much time playing the guitar and not enough time teaching -- and as I'd shown that I was new to teaching Stats, the parent even questioned my qualifications for the job. That turned me off from singing songs for almost the entire year.
And so I was considering revisiting the year that just ended, and writing about the songs that I would have performed had there not been a parent complaint. I can already think of some songs that would have fit -- "Measures of Center" (a parody of "Row Row Row Your Boat"), "Rudolph the Statistician" (another obvious parody), Square One TV's "Ghost of a Chance" (for probability). In Trig class some songs from Square One TV might fit basic Chapter 1 material ("Angle Dance," "Triangle Song"), and even Calculus might take some Square One TV songs about infinity. These would be in addition to any original songs that I might have composed.
But in this post, I'm going to take a different approach. After all, I don't always sing for Grades 11-12 since older students don't appreciate my songs as younger students up to Grade 10 do. Instead, I wish to return to the old charter middle school. Yes, this was the year that I did sing songs in class -- but I didn't teach the curriculum properly. Instead, I wish to post the songs I'd had performed had I taught it right.
What about the Rapoport Calendar?
Today on her Daily Epsilon of Math 2022, Rebecca Rapoport writes:
Find the area of a parallelogram with side lengths 5 and 4 and angle 30 degrees.
Last year, I regularly posted Rapoport questions on my old Geometry blog -- questions that are related to that particular branch of math. This now is a Stats blog -- but Stats questions are very rare on the Rapoport calendar. Even Calculus appears more often than Stats. In fact, on May 24th and 26th, she wrote Calc problems both days -- and I used these as Exit Passes that week (the last week before senior grades were due).
Well, I can justify posting this one today since it can also serve as a Trig question. Indeed, the area of this pgram is the the product of the sides and the sine of the angle between them:
A = (5)(4)(sin 30) = 10
Therefore the desired area is ten square units -- and of course, today's date is the tenth.
Anyway, I might continue to post some Rapoport questions on the blog, but the main focus of the blog will now be on music.
New First Day of School Lyrics
We will now revisit the my year at the old charter school (2016-17) from a musical perspective. On the old blog, I've discussed over and over again how I should have taught that class -- especially, how I should have fit science into that class. In my last post, I also mentioned interactive notebooks -- and yes, I also should have implemented INB's that year. I could have declared one side of the notebooks to be for math and the other for science -- and that would have forced me to spend equal time on both.
But we're going to start with the first day of school, and the song I performed that day. In that song, I used a certain word that I made up to describe students who are lazy in math class -- and even though it was an invented word, it still drew some parent complaints. Two years ago when I started the long-term assignment, I used the word again, and there were more complaints, enough to convince me never to use that word again (not even here on the blog, so I won't post what the word is here). Last year's complaints weren't related my the use of that word or that song -- instead, it was the fact that I was singing and playing music at all.
And so my goal here is to restore that song, albeit with some new lyrics. First of all, I'll drop that troublesome word and replace it with "zero." The emphasis here is that I'm not calling any lazy students a "zero" -- instead, I'm giving lazy students a zero as their grade. And second, the new song will contain many formulas -- the ones that they'll learn throughout the upcoming year. The idea is for the students to tell their parents that their new math teacher is singing math formulas in class, rather than playing the guitar in class.
Indeed, I will only sing this new first day of school song, rather than play it on a guitar. All of the songs that I perform in August will be vocal only -- no guitars until September. By this point I should have established that the songs are for teaching math content and are thus part of the lesson. Most of the August vocal songs will be from Square One TV, on the importance of learning math. This includes "Count on It" (which I really did perform at the old charter school), as well as "That's Math" and "Wanna Be" (which I didn't find on YouTube until after my charter year).
But the first day of school song will be my own original song. It will have new verses based on which level of math I'm teaching. This summer, the focus will be on the eighth grade class (only because I know the most about the eighth grade science curriculum, and so I can write about how I'd perform for both science and math):
Heroes and Zeroes -- by Mr. Walker
I don't know why I take math.
I'm all caught up in its wrath.
I'll just get a zero grade.
I won't pass math, I'm afraid.
Tell me what would happen when,
I will study now and then.
What if I were great at math?
What would be my future path?
Once I pass it in grade eight,
Math class I'll no longer hate.
When I graph lines, now I'll see,
Y equals mx plus b.
And each sphere has its volume,
Which is four-thirds pi r cubed.
Also a squared plus b squared,
Right triangles, that's c squared.
Reach the moon, be a hero!
I won't just get 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'll just score zero again.
Now I know why I take math.
Help me find a better path!
I will be a math hero,
If I beat zero.
New First Day of School Tune
In these musical posts, I will post a tune that goes with the song. This is one of the first songs whose lyrics I posted on my old blog, and I've performed the tune, yet I've never posted the tune.
First of all, this tune has nothing to do with any of those Mocha EDL scales from the old blog. This is because I wrote it before I discovered Mocha. (Later on, I might write some songs in those scales, even though it's unrealistic to believe I'd have performed them in my charter year. My discovery of Mocha wasn't until after I left the school.)
Instead, I wrote the song in the key of C# minor, using the following notes:
0 = B#, 1 = C#, 2 = D#, 3 = E, 4 = F#, 5 = G#, 6 = A
Notice that C# (harmonic) minor is the only common scale that includes the note B#. (While C# major can be written as Db major, C# minor -- the relative minor of E major -- can't be so rewritten.)
The other thing I did with this tune is compose it as a Mobius strip. (The "mathemusician" Vi Hart has a Mobius strip tune in one of the videos.) This means that the second half of the tune is just like the first half, but with the notes reversed. Where the first half has Sound 0 (B#), the second half has Sound 6 (A), Sound 1 (C#) in the first half corresponds to Sound 5 (G#) in the second half, and so on.
This means that, although it's not based on Mocha scales, we can write it in Mocha by taking advantage of its Mobius property. We are using the standard 12-note scale, so we can use the PLAY command:
https://www.haplessgenius.com/mocha/
As usual, click on Sound before you RUN the program.
There are a few more things I must say about this code. First of all, the opening lines establish Sound 0 as the note C instead of B#. This is because neither B# nor Cb (rendered as C-) can be used in Mocha (even though E# and F- are allowed -- this is likely because B/C straddles the octave boundary).
The first 12 lines are the original tune, while the next 12 lines are the reversed Mobius tune. This adds up to 24 lines -- yet the song as written above has 28 lines. I repeat the first four lines as the last four lines of the tune -- just RUN the program again, and press the Esc key (Break) after the fourth line.
Sometimes I sing the entire song a second time, modulating up to D minor. On the guitar, I'd play the song in E minor, an easy minor scale to play on the guitar. (In standard tuning EADGBE, four of the open strings are part of the E minor chord.) But of course, this will now become one of the August songs that I'll no longer play on the guitar, so I'll just stick to C#/D.
Conclusion
There are still many summer topics that I haven't decided whether to extend yet. I'll probably stop doing side-along reading books, for the simple reason that most teachers don't read them. I often like to read recreational math books that I can find at library book sales for $1.
But on the other hand, the books that are popular on the MTBoS are usually about the pedagogy of teaching math. For example, we have Geoff Krall's Necessary Conditions (foreword by Fawn Nguyen), or Tracy Zager's Becoming the Math Teacher You Wish You'd Had. But I've never read either of these books -- I don't think I've ever seen either at the bookstore even at full price (much less for $1).
If I ever get either those books someday, maybe I'll blog about them. Otherwise, I won't blog about any more books -- not even Eugenia Cheng's books. I hear she's writing another book soon, but I won't devote blog posts to her latest book.
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