1. Introduction
2. Accommodations
3. Barry Garelick
4. Music Class
5. Spring Break Mocha Music
6. New Xenharmonic Wiki
7. Coding Kite Colors in Mocha
8. Operation Varsity Blues
9. Bruce William Smith
10. Conclusion
Introduction
Today's second spring break post will consist of a hodgepodge of recent topics that I started to discuss in old posts but I never had time to return to until now. It also involves a reference to one topic that I intentionally saved until spring break.
The title of this post, "Twenty Years a Bruin," refers to the fact that today is the 20th anniversary of the day I received my fat envelope in the mail informing me that I'd been admitted to UCLA.
Accommodations
I try to avoid writing on the blog about the accommodations granted to special ed students. Many of these accommodations are of a personal or sensitive nature, and these students and their families wouldn't want me posting their accommodations on a blog.
But there is one recent accommodation that I want to discuss today, only because it reveals a flaw in my classroom management style. So of course, I want to post as little identifying information about this accommodation as possible.
Here are the only details that I wish to reveal on the blog:
- The accommodation was granted at some point during this calendar year. I waited until spring break to post it to make it more difficult to trace.
- The accommodation was granted at one of the two districts I where I sub. It might be the district that's already on spring break, or it might be the one that's still in "Big March" mode.
- I don't reveal the gender of the student receiving the accommodation. I'd rather use the ungrammatical singular "they" than give away the gender.
- The student themself isn't aware that they're receiving the accommodation. (Yes, "themself" is even less grammatical than singular "they.")
- I don't reveal what the accommodation is. All that matters for this post is that the student must be in their assigned seat in order to receive the accommodation.
And on the day that I subbed in that classroom, I was able to grant the accommodation to the student without incident. So why am I blogging about it at all? Consider the following imaginary scenario.
I enter a classroom and am supposed to grant an accommodation to a student. The student must be in their assigned seat in order to receive the accommodation. But when the student enters the classroom, they go to a seat other than their assigned seat, preventing me from granting the accommodation.
I tell the student to go to their correct seat. But then one of their friends say, "How juvenile! Only kindergarten teachers make their students sit in assigned seats. All our other middle/high school teachers let us sit wherever we want, just like college professors."
I tell the student to go to their correct seat again. This time, the student themself asks, "Why do I have to sit over there?"
"So I can give you the accommodation" I reply truthfully.
"You're not supposed to talk about our accommodations openly!" the student complains.
And that's not what I want to have happen, yet this is what I fear if this scenario were to occur if I'm the regular teacher.
To seasoned teachers, it's obvious what I should have done in this fictional situation. The only correct answer to the question "Why do I have to sit over there?" is "Because I said so." And if the student refuses to sit in the assigned seat, then I punish them for defiance -- not for avoiding accommodation.
This scenario never happened at my old charter school, but of course it could have. Back then, it never occurred to me to answer "Because I said so" -- I hated that phrase when I was a young student, and so I never wanted to give that phrase as an answer.
But as I know now, there are many times when it's better for the students not to know the reason behind an unpopular rule. In this case, seating charts allow the teacher to conceal accommodations -- always from the other students, sometimes even from the accommodated student themself.
Even though this never happened to me at the old charter school, something similar to this scenario really did happen to me as a student teacher. (This was back before I started blogging, and the student at the time was a junior/senior and is now an adult, so I see no harm in blogging the accommodation.)
In this case, my master teacher was telling me about accommodations. One girl needed to sit near the front of the room so she can hear the lessons better. My master teacher told me to have this girl switch seats with another student -- she insisted that I be the one to tell both of them to move, so that I could practice giving my students directions.
But the two students refused to move. I then told the other student that I needed to accommodate an unspecified student -- but the original girl easily figured out that I was referring to her. That was when she complained about my talking about her accommodation.
Of course, many students talked loudly in my student teaching class all the time. There were these two guys who, according to my master teacher, needed to be separated. (This has nothing to do with any accommodations -- it was just to keep them quiet.) But every time she separated them, one would ask me to let him sit next to the other for the day. Since he asked for permission, I would allow him to move, thus undermining the master teacher's efforts to keep them apart.
Now imagine all of this from the perspective of the accommodated girl. She was probably wondering why it was so important for her to be quiet and sit in another seat when these two boys could move and talk whenever they wanted. She might even had suspected it was because I was sexist.
In order for me to fulfill accommodations effectively, I need to be a strong classroom manager, so that accommodation can fit smoothly into a classroom where students generally listen to, obey, and respect the teacher. "Because I said so!" needs to be my answer to any question regarding why the students need to obey me, since the truth might be that my directions are to give accommodations that I should not reveal.
Barry Garelick
This post is labeled as traditionalists, because Barry Garelick is back to posting. His blog entry dated Thursday is mostly a link to an article he writes for another site, so I'll just link directly to his article:
https://truthinamericaneducation.com/education-reform/various-narratives-growth-mindsets-and-an-intro-to-one-of-my-parole-officers/
Notice that Truth in American Education is mostly an anti-Common Core website, so it's logical that Garelick would write articles for them. OK, let's proceed:
If you are reading this, you either have never heard of me and are curious, or you have heard of me and have pretty much bought into my “narrative” of math education.
You wish, Barry! I've heard of you, but I haven't bought into your narrative at all. I do agree with some of what Garelick and the other traditionalists write, but obviously not everything.
I’m currently teaching seventh and eighth grade math at a K-8 Catholic school in a small town in California. Prior to that, I taught seventh andeighth grade math for two years at a K-8 public school in another small town in California, which is where I will start this particular narrative.
So far this "narrative" is interesting. I knew that Garelick is a California middle school math teacher, but I didn't know that it's at a Catholic school. I do recall some of what he wrote about his prior student teaching, which is what this narrative is all about.
But now he muses about why he had to leave his old district:
Specifically teachers like me who choose to teach using explicit instruction; who use Mary Dolciani’s 1962 algebra textbook in lieu of the official one; who believe that understanding does not always have to be achieved before learning a procedure; who post the names of students achieving the top three test scores;
Posting the top three test scores reminds me of the data wall I had at the old charter school. But I'm not quite sure what exactly that has to do with traditionalism, since our old Illinois State text is as far from traditional as you can get.
who answer students’ questions rather playing “read my mind” type of games in the attempt to get them to discover the answer themselves, and attain “deep understanding”.
This is a tricky one. What exactly does Garelick mean by "answer students' questions"? For example, suppose a student asks "What's the answer to Question #30?" Simply telling the student the answer doesn't lead to increased student learning -- it's just bailing out a lazy student. Therefore when I'm asked this question, sometimes I do try to get students to discover or work out the answer themselves.
This also reminds me of another traditionalist complaint -- when we make students explain their answers or show all their work. Sometimes this is the only way we can tell that a student isn't cheating on the test. Thus Garelick forgets that there are students who are lazy, cheating, or looking for ways to get credit without knowing any math.
For example, I once told my latest eighth grade algebra class that my classroom is one place where they won’t hear the words “growth mindset”—to which the class reacted with loud applause. The current educationist narrative interprets “growth mindset” (wrongly, in my opinion) as building confidence in oneself which then leads to engagement which breeds motivation and ultimately success.
And here we go again with "growth mindset." It's surprising that traditionalists would find a "growth mindset" to be so objectionable. The opposite of a "growth mindset" is a "fixed mindset" -- the idea that mathematical intelligence is fixed. It's the idea that some people are good at math and others are bad at math, and that nothing will make a bad math student into a good math student -- not even do traditional p-sets. Indeed, students who believe in a "fixed mindset" are very likely to leave most traditional p-sets blank. It's only because of a "growth mindset" that students can do anything at all to grow from being bad at math to being good at math -- whether that something is traditional or not.
Notice that Garelick does say that "growth mindset" has been interpreted wrongly. Presumably he believes that there is a correct interpretation of "growth mindset" -- one that at least allows students to grow from "bad at math" to "good at math" by doing traditional p-sets.
Garelick now describes a conversation between himself and his master teacher (or more precisely, his "induction mentor"):
“Students should do math not only in the classroom, but outside; give examples of real world problems. Many students dislike math because they find it irrelevant.” As a final proof to this statement she added that it is common for adults to say:”What on earth did I learn algebra for?”
Anyway, here's Garelick's punchline, when someone tells him the following:
“You must know this. Your students love you. They tell me that they really learned a lot about math and that you were the best math teacher they ever had.”
Once again, since Garelick is describing living, breathing students, I must take him at his word. I have indeed seen evidence that while a majority of students don't necessarily enjoy traditional math, they aren't quite as enthusiastic about reform math as the reformers.
I notice that once again, Garelick has posted an article dated March 31st -- yet I can see it on my computer today, March 30th. I'll try to get in the habit of waiting to comment on such "post-dated" (or Greenwich-dated) posts until after that reaching that date in the Pacific time zone. This gives more time for him to receive additional comments, which I can then mention in my post.)
Spring Break Music
It is spring break in my old district whose calendar is observed on the blog. But in my new district from which I get the lion's share of subbing assignments, it is not spring break. In fact, I subbed in four classrooms this week, from Tuesday to Friday.
The first class was a eighth grade math class. I was almost guaranteed to sub in a math class on Tuesday, since that was the day the Math Performance Tasks were graded. So the one day I knew I'd be in a math class in one district just had to fall during spring break in the other district, making it into a non-posting day. I'll write a little about the class today, but not "A Day in the Life."
(Last year, I wrote that I might make a "spring break" post when I subbed for math in the other district, but this year I didn't post it. I wanted to make that special post about the Easter date and didn't want to post again so soon.)
Three of the classes were Common Core 8 and the other two were Algebra I. Fortunately, you already know what these classes are learning from last week's post -- angles and parallel lines in Math 8 and factoring in Algebra I.
Oh, and by the way, in the two Algebra I classes, one student in each class was a seventh grader. I asked the two guys what math class they'll take next year. Actually, they're not quite sure -- one of them said he might take Geometry at the district office while the other might take it online.
The next two days were both science at the same middle school. Many of the same students in Tuesday's math class were also in this science class. Once again, I was reminded about my science failures at the old charter school -- especially since this district, just like my old charter, uses only an online textbook. So these classes show me what my own science lessons could have looked like if I had taught them correctly.
In these classes, seventh graders are currently learning about photosynthesis and cellular respiration while eighth graders are studying evolution. The seventh graders in one of the classes even got to watch some videos by Bill Nye the Science Guy.
Oh, and sorry Garelick -- one of the science teachers told me not to answer student questions directly, but to get them to figure out the answers themselves. (You should be glad it wasn't the math teacher!)
Yesterday, my final class of the week, was in a high school music class. You know what that means -- this is now going to be a Mocha music post as I try to convert some of the songs I heard yesterday into computer format.
I know -- I often post music during vacation posts anyway. Eight days ago I mentioned music only to discuss the Johann Sebastian Bach Google Doodle. This time, it's back to Mocha. But first, let me describe the classes.
Second period was Guitar, while the remaining classes were all vocalists. The guitarists prepared for a test next week. I've decided to convert the guitar music into Mocha today.
In two of the vocal music classes, the students will be going on a trip to New York in two weeks to perform at on the most famous musical stage in the country -- Carnegie Hall. But as we all know from the riddle, the only way to get to Carnegie Hall is to practice. And that's exactly what the singers in third and sixth do. In New York, they'll perform is Spiritual Potpourri -- as the name implies, it's actually a combination of four songs, "Do Lord," "Walk Together Children," "A City Called Heaven," and "Old Time Religion." They practiced the first two of these songs yesterday.
As we learned last week with the Bach doodle, music is typically divided into four parts -- soprano, alto, tenor, and bass. But actually, one of the classes -- third period -- was only for girls, and thus there were only the soprano and alto parts. In sixth period, all four parts were present. The singers divided into parts, with each part practicing in a different room.
In both classes, the sopranos were the ones to remain in the choir room with me. As we also found out with the Bach doodle, the soprano section typically contains the melody of the song (the part that a soloist would sing). The highest note that these sopranos sang was a" (or A5), which is the second A above middle C. This note -- also the highest playable note on the Bach doodle -- is Degree 48 (Sound 213) in Mocha.
Fourth and fifth periods didn't have a performance to prepare for. Instead, these students get to have a "talent show" day -- some of them come up to the front of the room and sing their own song. Like third period, fifth period consisted of all girls, while fourth period was co-educational.
The first duo to perform was two guys who sang an original tune. The topic of the song was their Biology class -- "Punnett Squares" This of course reminded me of the songs I sang at the old charter during music break -- and this inspired me to sing those songs that day in class. I didn't bring my music book to the classroom, but I rushed to my car to grab the book before fifth period began.
One girl in fourth period also performed two songs. Both of them come from The Lion Guard -- a spin-off series based on Disney's The Lion King. One of the songs has a title in Swahili -- "Zuka Zama," which means "pop up and dive in." As I mentioned on the blog last year in another post, Swahili is the language spoken in the movie Lion King -- many catchphrases ("Hakuna Matata") and even character names (Simba, "lion") come from that language.
When fifth period began, I had my book of songs ready. This class was smaller than fourth period and these girls were less willing to perform. Thus I gave them an incentive -- each time a girl performed, I'd perform a tune from my book. Just as I did at the old charter school, I played the songs on a guitar, since there are so many guitars in the classroom.
Here are the songs I played yesterday:
It's possible to use the basic 10EDL/20EDL framework for "Peace Like a River." Instead of a perfect fifth, we use the wide fifth 20/13. Like the sixth, the fifth only appears as eighth notes. But these eighth notes are consecutive, so it's easier to hear the defect here than with the neutral sixth above. I thus recommend that we use 12EDL for both songs. (And 13 for the fifth is completely unacceptable for "Scotland," which needs the fifth in the higher octave.)
Let's code the songs now. First is "Peace Like a River."
Don't forget to click on the "Sound" button. The song repeats thrice as there are three verses:
First Verse:
I've got peace like a river,
I've got peace like a river,
I've got peace like a river in my soul;
I've got peace like a river,
I've got peace like a river,
I've got peace like a river in my soul.
Second Verse:
I've got joy like a fountain...
Third Verse:
I've got love like an ocean...
And here is "Scotland's Burning." Of course, Mocha doesn't play it as a round:
Lyrics:
Scotland's burning,
Scotland's burning!
Look out!
Look out!
Fire! Fire!
Fire! Fire!
Pour on water,
Pour on water.
Once again, these songs play in the key of white D major pentatonic. The closest we can get to the key of A is to change line 70 to N=11 (key of lu A below white A) or N=21 (key of red A).
New Xenharmonic Wiki
Last year, I wrote that the Xenharmonic Wiki would no longer exist. Well, as it turns out, the Xenharmonic Wiki is back:
https://en.xen.wiki/
Even though I've linked to this site in the past, recall that most of the links at this site are EDO's, or equal divisions of the octave. But Mocha music is based on EDL's, or equal divisions of length. But there are a few pages on this wiki that are relevant to Mocha music.
First of all, it's possible to approximate some of the EDO's in Mocha EDL. This is mainly true for the macrotonal EDO's -- the ones where each step is larger than the usual standard (12EDO) steps. Here are the best approximations to the macrotonal EDO's in Mocha EDL:
7EDO: Degrees 156, 141, 128, 116, 105, 95, 86, 78
8EDO: Degrees 202, 185, 170, 156, 143, 131, 120, 110, 101
9EDO: Degrees 132, 122, 113, 105, 97, 90, 83, 77, 71, 66
10EDO: Degrees 256, 239, 223, 208, 194, 181, 169, 158, 147, 137, 128
11EDO: Degrees 162, 152, 143, 134, 126, 118, 111, 104, 98, 92, 86, 81
Subtract 261 from each of these Degrees to obtain the corresponding Sounds.
Extending this to the microtonal EDO's -- the ones where each step is smaller than the usual 12EDO steps -- is less accurate and is not generally recommended. But then again, last year I wrote an Easter song in 28EDO and played it on Mocha. To understand why I did so, you must know what I was thinking when I created that song.
I was fascinated by the fact that the Easter date, while seemingly random, followed patterns. For example, the next three Easters fall on April 21st, 12th, 4th. The first two dates are nine days apart and the last two are eight days apart. There are other sequences of three consecutive years that follow this same pattern:
1995-1996-1997: April 16th, April 7th, March 30th
2063-2064-2065: April 15th, April 6th, March 29th
I was hoping to take advantage of these patterns to make a tune based on the Easter dates -- for example, nine days could be a major third and eight days a minor third. Then all three of these patterns correspond to triads -- either major or minor, depending on how I decided to convert dates into notes.
At the time, I'd never heard of alternate scales (other than 12EDO, of course). But a simple correspondence didn't work out.
Then when I read a book written by Theoni Pappas, I learned about EDO scales. I was researching these scales and realized that 28EDO best preserves the patterns found in the Easter dates.
It was afterward when I discovered the Mocha emulator of my old computer. I remembered the Sound command and was curious about how the computer could play microtonal music. After a few tries, I learned that Mocha used EDL's, not EDO's. Still, it was the only way I knew to play music in anything other than 12EDO, and so I composed the 28EDO Easter song in it. It's not quite as accurate as a real 28EDO instrument, of course.
Since I wrote my 28EDO song in Mocha EDL, I suppose it's reasonable to estimate all microtonal scales between 12EDO and 28EDO in Mocha. But no higher EDO beyond 28EDO is recommended.
As a microtonal scale, 28EDO isn't one of the more common scales. It is notable for having a very accurate 5/4 major third at the ninth step of 28EDO. (Thus all those nine-day intervals between Easters map to major thirds.) But unfortunately, 28EDO lacks an accurate 3/2 perfect fifth. As we saw when trying to convert the guitar songs into EDL's above, I keep using 18EDL (with a just perfect fifth on the root note) over 20EDL (with a just major third over the root instead). This is especially true because the usual 12EDO scale has such an accurate perfect fifth, so our ears demand more accurate fifths compared to accurate thirds.
Is it possible to write the Easter song in an EDL scale instead of an EDO? For example, what if we were to map March 22nd-31st to Degrees 22-31 and April 1st-25th to Degrees 32-56? The resulting song would be considered 56EDL. Notice that 56EDL and 28EDO have the same number of steps in an octave, namely 28.
But unfortunately, EDL's hide the patterns we find in the Easter dates. For example, let's revisit the pattern I mentioned above:
1995-1996-1997: April 16th, April 7th, March 30th
2019-2020-2021: April 21st, April 12th, April 4th
Converting these to 56EDL, the first triad is 47:38:30 while the second is 52:43:35. These are not the same triad. For example, 47/38 is about 368 cents while 52/43 is about 329 cents. Neither one of these is equivalent to the major third of 28EDO (386 cents) -- and indeed, both of these would be the same triad in 28EDO while they are distinctly sounding triads in 56EDL.
Then again, EDL scales contain just major thirds, even more accurate than 28EDO. We might at least wish to modify the Mocha approximation of 28EDO (which, as I wrote above, isn't accurate) to include as many just 5/4 intervals as possible.
Here is Mocha's best approximation of 28EDO:
28EDO: Degrees 210, 205, 200, 195, 190, 186, 181, 177, 172, 168, 164, 160, 156, 152, 148, 145, 141, 138, 134, 131, 128, 125, 122, 119, 116, 113, 110, 108, 105
And here is our modified version:
28EDO: Degrees 210, 205, 200, 195, 190, 185, 180, 176, 172, 168, 164, 160, 156, 152, 148, 144, 141, 138, 135, 132, 129, 126, 123, 120, 117, 114, 111, 108, 105
Here we start with multiples of five from Degree 210 to 180 and then switch to multiples of four from Degree 180 to 144. This allows several 5/4 major thirds to appear: 210/168, 205/164, 200/160, 195/156, 190/152, 185/148, and 180/144 are all just major thirds. After 144 I switched to multiples of three instead. This results in several 4/3 perfect fourths appearing as well: 180/135, 176/132, 172/129, 168/126, 164/123, 160/120, 156/117, 152/114, 148/111, and 144/108 are all just fourths. In fact, this is an improvement over pure 28EDO, which lacks just fourths (and fifths).
The modified version of 28EDO can be coded in Mocha. We either use three For loops -- one loop each for five-, four-, and three-degree steps -- or include the whole list in Data lines.
Here is the link to 28EDO on the new Xenharmonic Wiki:
https://en.xen.wiki/w/28edo
And before we leave the Xenharmonic website, let me link to Kite's color notation, which I still use to describe EDL scales as well:
https://en.xen.wiki/w/Color_notation
This link includes the new version of Kite's color notation (including the use of "azure" or "zo" to mean "blue," and "lavender" to mean 11-limit).
Notice that Mocha EDL's are utonal. This means that only the colors that contain "u" in their symbols (plus white) are needed for Mocha:
Limit Color
3 white (wa)
5 green (gu)
7 red (ru)
11 lavender (lu)
13 thu
Coding Kite Colors in Mocha
It's possible to write a simple program in Mocha where we enter a Sound from 1-255. The program converts this to a Degree (by subtracting it from 261) and then naming it using Kite colors.
Here's how the program works. After the Sound is converted to a Degree (D), Mocha starts finding the factors of D. Here C$ (the color) starts out as blank space (Line 30), and if it remains as a blank space (Line 110) then the color must be "white" (the syllable "wa"). Lines 40-90 contain syllables for the primes 2 through 13, including a null string "" for primes 2 and 3.
Line 100 assumes that any factor left after sieving out primes 2 through 13 must be prime (since the smallest possible composite would be 17^2 = 289, but the highest Degree in Mocha is 260). The syllable for these primes is the prime followed by "u" (17u, 19u, 23u, and so on).
The subroutine starts at Line 200. Here we keep track of both the letter name in L and the keyspan (which determines sharp of flat) in K. The flats are printed as "-" in Mocha because this is what the Play command also uses for flats.
Lines 240 and 250 use a 12EDO framework to determine the name of the note. Here Degree 11 ends up as Bb and Degree 13 becomes G#. Even Kite himself admits that the names for 11 or 13 can go either way (lu B or lu Bb for 11, thu G or thu G# for 13). I myself tend to use B and G for 11 and 13, but the 12EDO framework requires Bb and G# (since 11/8 is closer to an augmented 4th than a perfect 4th, and 13/8 to a minor 6th than a major 6th in 12EDO). Kite would write "ilo 4th=P4, tho 6th=M6) for my method and "ilo 4th=A4, tho 6th=m6" for Mocha's.
After returning from the subroutine, L and K are used to determine the note name. Here L=0 denotes the note G, L=1 is F, and L=2 is E, and so on. (The note names are backwards because EDL's are utonal/undertones.) And K=0 is also G, but K=1 is F#, K=2 is F, K=3 is E, and so on. (Line 30 starts at N=2, K=3 because the fundamental corresponding to Degree 1 is E.) Line 120 uses .4 for the rounding instead of .5 only because .5 happens to place a 12EDO note between B and C instead of between A and B as is proper for (American) 12EDO. (Germans like Bach actually would put an extra note between B and C, called H! But we don't want Mocha to follow the German convention.)
Line 170 prints the color and note name, Line 180 plays the Sound, and Line 190 ends the program.
Here are the names determined by Mocha for all the Sounds in the 200's (Degrees 6-61):
Sound Degree Note
255 6 wa A
254 7 ru F#
253 8 wa E
252 9 wa D
251 10 gu C
250 11 lu Bb
249 12 wa A
248 13 thu G#
247 14 ru F#
246 15 gu F
245 16 wa E
244 17 17u D#
243 18 wa D
242 19 19u C#
241 20 gu C
240 21 ru B
239 22 lu Bb
238 23 23u A#
237 24 wa A
236 25 gugu Ab
235 26 thu G#
234 27 wa G
233 28 ru F#
232 29 29u F#
231 30 gu F
230 31 31u E#
229 32 wa E
228 33 lu Eb
227 34 17u D#
226 35 rugu D
225 36 wa D
224 37 37u Db
223 38 19u C#
222 39 thu C#
221 40 gu C
220 41 41u B#
219 42 ru B
218 43 43u B
217 44 lu Bb
216 45 gu Bb
215 46 23u A#
214 47 47u A
213 48 wa A
212 49 ruru G#
211 50 gugu Ab
210 51 17u G#
209 52 thu G#
208 53 53u G
207 54 wa G
206 55 lugu Gb
205 56 ru F#
204 57 19u F#
203 58 29u F#
202 59 59u F#
201 60 gu F
200 61 61u E#
Notice that I use the syllables ("gu," "ru") rather than the full colors ("green," "red"). This is so that Mocha can combine the syllables if needed ("gugu," "rugu"). I could have used "white" in Line 110 since this is never combined with another color, but I used "wa" for consistency.
Operation Varsity Blues
I did say earlier that I'd write about the recent college admissions scandal. Yes, on the anniversary of the day I got into UCLA, I'm discussing how others got into UCLA, USC, and other schools. As it turns out, this scandal has a name, "Operation Varsity Blues." It's named for a movie that came out 20 years ago -- just two and half months before I received my UCLA admissions letter.
Operation Varsity Blues is causing everyone to rethink about what students need to do to gain admissions to selective college. We all agree that students who pretend to play sports that they don't actually play is an illegitimate way to get into selective colleges.
But some people are starting to wonder whether colleges admissions offices are too reliant on SAT, ACT, and AP exams. Just this month, I've written extensively about how my new district, unlike many others, offer AP English Language to sophomores and AP English Literature to juniors.
Again, I wonder whether these early AP's are intended to help students get into colleges. After all, the AP's I personally took in my senior year didn't help me get into UCLA, since I didn't get the scores of those AP's until about four or five months after I received my fat envelope from UCLA. The only AP scores that helped me get into UCLA are the ones I took as a junior -- and in general, only AP's taken no later than 11th grade are seen by admission decision makers. By taking the AP exams a year early, this allows an extra score to be seen by decision makers before fat envelopes are sent out.
So far, I haven't seen as much for early AP math classes -- but then again, AP Calculus is much more difficult than AP English Lit. I did write earlier about the two seventh graders in Algebra I -- those two students might be headed for junior year Calculus.
I often consider the tweeter CCSSIMath to be a traditionalist. This user has retweeted several articles this month pertaining to the Operation Varsity Blues scandal:
https://twitter.com/CCSSIMath
But unlike the other traditionalists, CCSSIMath doesn't agree completely with the push to place everyone in Algebra I in seventh or eighth grade. The user links to the following article:
https://www.chicagotribune.com/suburbs/deerfield/news/ct-dfr-district-109-math-curriculum-concerns-tl-0321-story.html
Some said they’re starting to see negative results with the district’s decision to cut the “regular” math course for seventh graders this year, leaving them with the options of taking an accelerated or advanced class.
Here the accelerated class leads to completing Algebra I in eighth grade, while the advanced class is itself seventh grade Algebra I. What I'm wondering is, is the reason to dropping regular Common Core Math 7 related to making students more competitive for college.
I'm not quite sure whether there is a simple solution to this problem. I recall reading about how college admissions are different from most other businesses. For example, successful eateries such as McDonalds used to brag about how many customers they had -- "99 billion served." But Ivy League colleges do the opposite -- they brag about how few students get into their schools, not how many.
But the only way to make colleges more like fast food is if the most successful colleges -- say the Ivy League trio of Harvard, Princeton, and Yale -- educated the most people. Imagine if almost every college -- even community colleges -- were run by Harvard, Princeton, and Yale. Then many more people could earn diplomas from those schools, and so Operation Varsity Blues would disappear.
Of course, I can't see how that could work in reality. So far, I don't know a solution to the college admissions scandal.
Bruce William Smith
It's been a while since the traditionalist Bruce William Smith has posted. He used to be active at Edsource, but not lately. Recall that Smith's zeal for earlier advanced math goes one step further even than SteveH. SteveH promotes eighth grade Algebra I and senior year Calculus, but Smith prefers seventh grade Algebra I and junior year Calculus!
Yes, this means that the schools in Deerfield, Illinois (CCSSIMath link above) are placing all students into either accelerated (SteveH-level) or advanced (Smith-level) classes. And I subbed in two eighth grade Algebra I classes (SteveH-level), and in each class there was one seventh grader (Smith-level).
Anyway, Smith has now been posting at the Joanne Jacobs site -- a site I often go to in order to find certain other traditionalists. So let's find out what he's been up to:
https://www.joannejacobs.com/2019/03/why-kids-need-to-learn-standard-english/
This post is a who's who among traditionalists. Not only does Smith make his first comment in response to this post, but also among the commenters are Bill (a regular at the Jacobs site) and Ze'ev Wurman (who occasionally comments here). Moreover, Jacobs even links to a blog (co-)authored by another traditionalist I haven't seen in some time -- Katharine Beals!
But the post that has drawn so many traditionalists has nothing to do with math. The topic of this post is English -- standard English, to be exact. And unfortunately, this post is racial, since it's all about black students and whether they should speak Standard American English or the dialect known as African-American Vernacular English.
So far, I've seen Smith mainly write about math in his traditionalism comments. But Bill, Wurman, and Beals have all discussed traditional English instruction as well. On the other hand, we already know that race (specifically tracking) is a fairly common talking point among traditionalists.
Since this is a racial discussion, that's why I had to delay writing about this grand traditionalists' reunion until spring break. I try to bury controversial racial discussions at the bottom of vacation posts (though this was impossible when reading Eugenia Cheng's latest book).
Let's start with the original Jacobs post, which as usual contains a link of its own:
Now here are our traditionalists. Let's start with Smith, whose return first drew me to this post:
brucewilliamsmith:
Standardization in English (and other languages) is more applicable to its written than its spoken form; AAVE is distinguished from standard English in its grammar as well as its vocabulary, to a point, in extreme versions (such as Gullah), where it may be argued to be a separate dialect rather than a mere variety of English.
Next up is Bill:
Bill:
As a Californian, I'll inform readers that yes, it was indeed Oakland. The third traditionalist to comment is Wurman:
Wurman:
Here "Henry Higgins" is a character from the My Fair Lady clip that Jacobs includes in her post. I assume that "she" refers to Lane, the author of the blog at the first link.
I won't quote Katharine (or Catherine) here on this blog, but it's significant to note that the post at the link is all about diagramming sentences -- something that traditionalists (of English class) wish that students still do nowadays.
Yesterday I subbed in a music class. The students were singing spiritual songs to prepare for their trip to Carnegie Hall. Many spirituals have their roots in the black church, and so some of their lyrics are written in AAVE. I heard the sopranos (none of whom are black, by the way) sing about going to the "promis' lan'," and I believe the word "nevah" appeared in the song as well.
So let me conclude the racial portion of this post with my own opinion on this issue. We might wonder why black students speak AAVE and have trouble learning Standard English. Well, the answer is that from ages 0-5, all the young black students hear nothing but AAVE from the parents, and old habits are hard to break once they reach school age. So now we wonder do the parents speak AAVE and have trouble learning Standard English. Well, the answer is that from ages 0-5, all the parents heard nothing but AAVE from the grandparents, and old habits are hard to break once they reach school age. So now we wonder do the grandparents speak AAVE and have trouble learning Standard English. Well, the answer is that from ages 0-5, all the parents heard nothing but AAVE from the great-grandparents...and so on.
And after we go back sufficiently many generations, we reach one where during ages 0-5, the language they spoke wasn't any English dialect, but an African language that they were speaking on the continent of Africa. This language probably wouldn't have been Swahili (which I mentioned earlier in this post). For example, Kunta Kinte in Alex Haley's Roots spoke Mandinka. As the Africans began to learn English, their speech was influenced by their native languages, and hence AAVE was born.
Thus in order to break the AAVE cycle, we'd need a generation that hears nothing but Standard English for the first sixty months of their lives. Then this generation can grow up and teach Standard English to their children. But once again, I don't know how achievable this is.
Jasmine Lane (the author of the link above) tells us that black students must make a choice between their native dialect that they naturally want to speak (AAVE) and the dialect that leads to success in the real world (Standard English). On the other hand, whites don't have to make such a choice, since their native dialect is the same as the dialect that leads to success. This is the source of the debate -- blacks must make a choice that whites don't have to make.
Unlike Lane, I am not an English teacher, and so much of the AAVE debate isn't relevant to me. But there is one part of AAVE that is relevant to me as a math teacher -- student names.
It's well-documented that certain names are the equivalent to AAVE -- they are strongly associated with being black. And ceteris paribus, job candidates with resumes containing the AAVE names are less likely to be called for interviews than those containing SAE names. (Notice that some of these names actually are Swahili, such as Imani -- named for the last principle of Kwanzaa and is equivalent to the name Faith in SAE.) And no matter how much black students change their dialect from AAVE to SAE, they can't as easily change their name.
When I was at the old charter school two years ago, recall that almost all of the eighth graders there were black. At the start of the year, one girl was clearly at the top of her class. I won't reveal her name here, but I will say that her name contains an apostrophe. Names with apostrophes (unless they are Irish names beginning with "O'-") are strongly associated with being black. (This is the "neutral girl" from my January 6th post.)
And even this week, I notice that one of the two seventh graders in the Algebra I class was black. He has a common Biblical name, except that one of the letters is replaced with a "z."
These two students are clearly strong math students and might even apply for high-paying STEM jobs in the future. But I fear that the apostrophe or "z" in their names might lead to their resumes being rejected.
At the old charter school, I was considering telling the girl that when she sends a resume to a company someday, she should spell her name without an apostrophe. (Save the apostrophe for after she's hired and she's filling out her W-4 forms.) But she moved away from the school after a month and I never got to say this to her.
And of course I didn't give this sort of advice to the Algebra I seventh grader, since I only knew him for two days. (He was also in one of the science classes I subbed for later in the week.) Indeed, this is the sort of thing I'd only tell a student at the end of the year, after the student has attended my class for an entire year and learned to trust me.
Conclusion
Notice that race isn't the only controversial topic I wrote about in this spring break post. Somehow, religion has quietly dominated the two spring break posts, from calculation of the date of the religious holiday Easter to the lyrics of spiritual songs to students with Biblical names.
Just as I ordinarily don't post "A Day in the Life" when one of my districts is on spring break, I normally wouldn't post a worksheet from such a day. But I can't help but post the following worksheet today because it fits my most recent U of Chicago lesson like a glove.
On the day I subbed for Algebra I, the teacher assigned an extra credit worksheet. One side of the worksheet was a Pizzazz worksheet on simplifying radicals. But the other side just happened to be a logic problem about college roommates.
Of course I have to post the logic problem today, since it fits perfectly with Lesson 13-6 and the logic problem I posted last week. And it's all about college roommates, which also goes well with today's UCLA anniversary post.
As for our next lesson, spring break ends and I'll cover Lesson 13-7 in my next post, scheduled for Monday, April 1st. For those who have completed spring break, I hope you enjoyed it. For those who are just starting spring break, I hope you'll have fun. And those of you for whom spring break is still a week or more away, just sing the Big March song and hopefully you'll get through this tough time.
To seasoned teachers, it's obvious what I should have done in this fictional situation. The only correct answer to the question "Why do I have to sit over there?" is "Because I said so." And if the student refuses to sit in the assigned seat, then I punish them for defiance -- not for avoiding accommodation.
This scenario never happened at my old charter school, but of course it could have. Back then, it never occurred to me to answer "Because I said so" -- I hated that phrase when I was a young student, and so I never wanted to give that phrase as an answer.
But as I know now, there are many times when it's better for the students not to know the reason behind an unpopular rule. In this case, seating charts allow the teacher to conceal accommodations -- always from the other students, sometimes even from the accommodated student themself.
Even though this never happened to me at the old charter school, something similar to this scenario really did happen to me as a student teacher. (This was back before I started blogging, and the student at the time was a junior/senior and is now an adult, so I see no harm in blogging the accommodation.)
In this case, my master teacher was telling me about accommodations. One girl needed to sit near the front of the room so she can hear the lessons better. My master teacher told me to have this girl switch seats with another student -- she insisted that I be the one to tell both of them to move, so that I could practice giving my students directions.
But the two students refused to move. I then told the other student that I needed to accommodate an unspecified student -- but the original girl easily figured out that I was referring to her. That was when she complained about my talking about her accommodation.
Of course, many students talked loudly in my student teaching class all the time. There were these two guys who, according to my master teacher, needed to be separated. (This has nothing to do with any accommodations -- it was just to keep them quiet.) But every time she separated them, one would ask me to let him sit next to the other for the day. Since he asked for permission, I would allow him to move, thus undermining the master teacher's efforts to keep them apart.
Now imagine all of this from the perspective of the accommodated girl. She was probably wondering why it was so important for her to be quiet and sit in another seat when these two boys could move and talk whenever they wanted. She might even had suspected it was because I was sexist.
In order for me to fulfill accommodations effectively, I need to be a strong classroom manager, so that accommodation can fit smoothly into a classroom where students generally listen to, obey, and respect the teacher. "Because I said so!" needs to be my answer to any question regarding why the students need to obey me, since the truth might be that my directions are to give accommodations that I should not reveal.
Barry Garelick
This post is labeled as traditionalists, because Barry Garelick is back to posting. His blog entry dated Thursday is mostly a link to an article he writes for another site, so I'll just link directly to his article:
https://truthinamericaneducation.com/education-reform/various-narratives-growth-mindsets-and-an-intro-to-one-of-my-parole-officers/
Notice that Truth in American Education is mostly an anti-Common Core website, so it's logical that Garelick would write articles for them. OK, let's proceed:
If you are reading this, you either have never heard of me and are curious, or you have heard of me and have pretty much bought into my “narrative” of math education.
You wish, Barry! I've heard of you, but I haven't bought into your narrative at all. I do agree with some of what Garelick and the other traditionalists write, but obviously not everything.
I’m currently teaching seventh and eighth grade math at a K-8 Catholic school in a small town in California. Prior to that, I taught seventh and
So far this "narrative" is interesting. I knew that Garelick is a California middle school math teacher, but I didn't know that it's at a Catholic school. I do recall some of what he wrote about his prior student teaching, which is what this narrative is all about.
But now he muses about why he had to leave his old district:
Specifically teachers like me who choose to teach using explicit instruction; who use Mary Dolciani’s 1962 algebra textbook in lieu of the official one; who believe that understanding does not always have to be achieved before learning a procedure; who post the names of students achieving the top three test scores;
Posting the top three test scores reminds me of the data wall I had at the old charter school. But I'm not quite sure what exactly that has to do with traditionalism, since our old Illinois State text is as far from traditional as you can get.
who answer students’ questions rather playing “read my mind” type of games in the attempt to get them to discover the answer themselves, and attain “deep understanding”.
This is a tricky one. What exactly does Garelick mean by "answer students' questions"? For example, suppose a student asks "What's the answer to Question #30?" Simply telling the student the answer doesn't lead to increased student learning -- it's just bailing out a lazy student. Therefore when I'm asked this question, sometimes I do try to get students to discover or work out the answer themselves.
This also reminds me of another traditionalist complaint -- when we make students explain their answers or show all their work. Sometimes this is the only way we can tell that a student isn't cheating on the test. Thus Garelick forgets that there are students who are lazy, cheating, or looking for ways to get credit without knowing any math.
For example, I once told my latest eighth grade algebra class that my classroom is one place where they won’t hear the words “growth mindset”—to which the class reacted with loud applause. The current educationist narrative interprets “growth mindset” (wrongly, in my opinion) as building confidence in oneself which then leads to engagement which breeds motivation and ultimately success.
And here we go again with "growth mindset." It's surprising that traditionalists would find a "growth mindset" to be so objectionable. The opposite of a "growth mindset" is a "fixed mindset" -- the idea that mathematical intelligence is fixed. It's the idea that some people are good at math and others are bad at math, and that nothing will make a bad math student into a good math student -- not even do traditional p-sets. Indeed, students who believe in a "fixed mindset" are very likely to leave most traditional p-sets blank. It's only because of a "growth mindset" that students can do anything at all to grow from being bad at math to being good at math -- whether that something is traditional or not.
Notice that Garelick does say that "growth mindset" has been interpreted wrongly. Presumably he believes that there is a correct interpretation of "growth mindset" -- one that at least allows students to grow from "bad at math" to "good at math" by doing traditional p-sets.
Garelick now describes a conversation between himself and his master teacher (or more precisely, his "induction mentor"):
“Students should do math not only in the classroom, but outside; give examples of real world problems. Many students dislike math because they find it irrelevant.” As a final proof to this statement she added that it is common for adults to say:”What on earth did I learn algebra for?”
Anyway, here's Garelick's punchline, when someone tells him the following:
“You must know this. Your students love you. They tell me that they really learned a lot about math and that you were the best math teacher they ever had.”
Once again, since Garelick is describing living, breathing students, I must take him at his word. I have indeed seen evidence that while a majority of students don't necessarily enjoy traditional math, they aren't quite as enthusiastic about reform math as the reformers.
I notice that once again, Garelick has posted an article dated March 31st -- yet I can see it on my computer today, March 30th. I'll try to get in the habit of waiting to comment on such "post-dated" (or Greenwich-dated) posts until after that reaching that date in the Pacific time zone. This gives more time for him to receive additional comments, which I can then mention in my post.)
Spring Break Music
It is spring break in my old district whose calendar is observed on the blog. But in my new district from which I get the lion's share of subbing assignments, it is not spring break. In fact, I subbed in four classrooms this week, from Tuesday to Friday.
The first class was a eighth grade math class. I was almost guaranteed to sub in a math class on Tuesday, since that was the day the Math Performance Tasks were graded. So the one day I knew I'd be in a math class in one district just had to fall during spring break in the other district, making it into a non-posting day. I'll write a little about the class today, but not "A Day in the Life."
(Last year, I wrote that I might make a "spring break" post when I subbed for math in the other district, but this year I didn't post it. I wanted to make that special post about the Easter date and didn't want to post again so soon.)
Three of the classes were Common Core 8 and the other two were Algebra I. Fortunately, you already know what these classes are learning from last week's post -- angles and parallel lines in Math 8 and factoring in Algebra I.
Oh, and by the way, in the two Algebra I classes, one student in each class was a seventh grader. I asked the two guys what math class they'll take next year. Actually, they're not quite sure -- one of them said he might take Geometry at the district office while the other might take it online.
The next two days were both science at the same middle school. Many of the same students in Tuesday's math class were also in this science class. Once again, I was reminded about my science failures at the old charter school -- especially since this district, just like my old charter, uses only an online textbook. So these classes show me what my own science lessons could have looked like if I had taught them correctly.
In these classes, seventh graders are currently learning about photosynthesis and cellular respiration while eighth graders are studying evolution. The seventh graders in one of the classes even got to watch some videos by Bill Nye the Science Guy.
Oh, and sorry Garelick -- one of the science teachers told me not to answer student questions directly, but to get them to figure out the answers themselves. (You should be glad it wasn't the math teacher!)
Yesterday, my final class of the week, was in a high school music class. You know what that means -- this is now going to be a Mocha music post as I try to convert some of the songs I heard yesterday into computer format.
I know -- I often post music during vacation posts anyway. Eight days ago I mentioned music only to discuss the Johann Sebastian Bach Google Doodle. This time, it's back to Mocha. But first, let me describe the classes.
Second period was Guitar, while the remaining classes were all vocalists. The guitarists prepared for a test next week. I've decided to convert the guitar music into Mocha today.
In two of the vocal music classes, the students will be going on a trip to New York in two weeks to perform at on the most famous musical stage in the country -- Carnegie Hall. But as we all know from the riddle, the only way to get to Carnegie Hall is to practice. And that's exactly what the singers in third and sixth do. In New York, they'll perform is Spiritual Potpourri -- as the name implies, it's actually a combination of four songs, "Do Lord," "Walk Together Children," "A City Called Heaven," and "Old Time Religion." They practiced the first two of these songs yesterday.
As we learned last week with the Bach doodle, music is typically divided into four parts -- soprano, alto, tenor, and bass. But actually, one of the classes -- third period -- was only for girls, and thus there were only the soprano and alto parts. In sixth period, all four parts were present. The singers divided into parts, with each part practicing in a different room.
In both classes, the sopranos were the ones to remain in the choir room with me. As we also found out with the Bach doodle, the soprano section typically contains the melody of the song (the part that a soloist would sing). The highest note that these sopranos sang was a" (or A5), which is the second A above middle C. This note -- also the highest playable note on the Bach doodle -- is Degree 48 (Sound 213) in Mocha.
Fourth and fifth periods didn't have a performance to prepare for. Instead, these students get to have a "talent show" day -- some of them come up to the front of the room and sing their own song. Like third period, fifth period consisted of all girls, while fourth period was co-educational.
The first duo to perform was two guys who sang an original tune. The topic of the song was their Biology class -- "Punnett Squares" This of course reminded me of the songs I sang at the old charter during music break -- and this inspired me to sing those songs that day in class. I didn't bring my music book to the classroom, but I rushed to my car to grab the book before fifth period began.
One girl in fourth period also performed two songs. Both of them come from The Lion Guard -- a spin-off series based on Disney's The Lion King. One of the songs has a title in Swahili -- "Zuka Zama," which means "pop up and dive in." As I mentioned on the blog last year in another post, Swahili is the language spoken in the movie Lion King -- many catchphrases ("Hakuna Matata") and even character names (Simba, "lion") come from that language.
When fifth period began, I had my book of songs ready. This class was smaller than fourth period and these girls were less willing to perform. Thus I gave them an incentive -- each time a girl performed, I'd perform a tune from my book. Just as I did at the old charter school, I played the songs on a guitar, since there are so many guitars in the classroom.
Here are the songs I played yesterday:
- U-N-I-T Rate (parody of UCLA fight song)
- Ghost of a Chance (Square One TV parody of Michael Jackson's "Thriller")
- Measures of Center Song (parody of "Row Row Row Your Boat")
- No Drens (parody of TLC's "No Scrubs")
- All About That Base and Height (parody of Meghan Trainor's "All About That Bass")
- Big March (parody of "The Ants Go Marching")
Of course I had to sing the UCLA fight song parody yesterday, since today is the anniversary of the day I became a Bruin.
Notice that all of these songs are parodies. I assumed that my most popular songs are versions of tunes that they already know, and so I intentionally chose these songs as an incentive. This includes the Measures of Center Song (an extra tune I played while waiting for a girl to perform) and the Big March Song (which I played since in this district, we are indeed still in the Big March).
Notice that all of these songs are parodies. I assumed that my most popular songs are versions of tunes that they already know, and so I intentionally chose these songs as an incentive. This includes the Measures of Center Song (an extra tune I played while waiting for a girl to perform) and the Big March Song (which I played since in this district, we are indeed still in the Big March).
Eventually, all the girls performed as the entire class sang the song "Joshua," which is all about the Biblical Battle of Jericho.
Even though sixth period already had their own songs to sing for Carnegie Hall, I couldn't help but sing one more song for them, just as all four groups were returning to the choir room right at the end of the period. Since it was a science song that started it all, I played my science song -- "Earth, Moon, and Sun," a parody of "Hava Nagila." That's right -- even my science song was a parody, and I ended up singing basically all of my parodies yesterday.
Spring Break Mocha Music
Let's get back to second period Guitar class. The songs that I'll convert to Mocha today are the spiritual "Peace Like a River" and the round "Scotland's Burning."
Both of these songs are in the key of A major. The students are playing rhythm guitar, where they learn how to strum the chords. The songs contain the three main chords in this key -- A, D, E7.
Of course, for Mocha we're not coding the chords -- we're coding the melody. Fortunately for us, neither melody contains the full A major scale. "Peace Like a River" is pentatonic -- it contains only five notes, namely A, B, C#, E, F#.
And "Scotland's Burning" is even easier as it contains only four notes -- A, B, C#, E. This makes the song Fischinger playable -- referring to the Fischinger Google Doodle, which was the last musical doodle before the Bach one.
Then again, the Fischinger doodle contained only four bars while "Scotland's Burning" has eight. But we can take advantage of the song's structure as a four-part round (similar to Kristin Lawrence's "Ghost of John" from Halloween). On the Fischinger player, we code all four parts to play at the same time. Actually, the first and fourth parts are identical, so only three parts are coded. Since each part is two bars, we repeat it twice to fill the four bars. As the Fischinger player loops, it sort of sounds like a multi-part round.
I'm not quite sure how the round is played in the actual Guitar class. I asked a few students, who inform me that the class hadn't reached that song yet. The song repeats only the E7 and A chords in each part, and so the four parts would sound identical in the classroom unless they are switching to lead guitar (where the melody is played) instead of rhythm guitar.
But that's enough about Fischinger and the guitar -- we're trying to play these songs in Mocha. We've coded pentatonic scales in Mocha before, but those weren't based on simple EDL scales (instead we searched for all of the "white," or Pythagorean, notes in Mocha).
The simplest EDL containing five notes is 10EDL. But unfortunately, while four of the notes fit a major pentatonic scale (1/1 tonic, 10/9 major 2nd, 5/4 major 3rd, 5/3 major 6th), the perfect fifth is missing from 10EDL. In its place we a have 10/7 tritone.
Our most promising EDL for anything resembling a major scale is 18EDL. This scale also contains four of the five pentatonic notes (1/1 tonic, 9/8 major 2nd, 9/7 supermajor 3rd, 3/2 perfect 5th). But fortunately, the lack of a major 6th is is irrelevant for "Scotland's Burning," which doesn't even contain the sixth.
As for "Peace Like a River," our only available sixth is the 18/11 neutral 6th. Fortunately, the sixth only appears in this song as eighth notes, so the difference between the sixths are less noticeable.
Both songs span an octave, but the span is from fifth-to-fifth, not tonic-to-tonic. Therefore the version of the scale we'll use for both songs is:
Degree Note Function
12 white A perfect fifth
11 lavender B neutral sixth ("Peace" only)
10 green C not used in either song
9 white D tonic
8 white E major second
7 red F# supermajor third
6 white A perfect fifth ("Scotland" only)
Here white D is the tonic, not white A. But due to our span, the scale ends up turning into 12EDL rather than 18EDL. So far, I've never thought of using 12EDL in this manner -- a no-fives version of the major pentatonic scale starting on the perfect fifth. (Here "no-fives" means that the only multiple of five, namely the 10, has been omitted.)
It's possible to use the basic 10EDL/20EDL framework for "Peace Like a River." Instead of a perfect fifth, we use the wide fifth 20/13. Like the sixth, the fifth only appears as eighth notes. But these eighth notes are consecutive, so it's easier to hear the defect here than with the neutral sixth above. I thus recommend that we use 12EDL for both songs. (And 13 for the fifth is completely unacceptable for "Scotland," which needs the fifth in the higher octave.)
Let's code the songs now. First is "Peace Like a River."
10 FOR V=1 TO 3
70 N=1
80 FOR X=1 TO 48
90 READ A,T
100 SOUND 261-N*A,T
110 NEXT X
120 DATA 7,2,8,2,9,4,9,2,9,2,9,2,7,2
130 DATA 8,2,9,2,9,4,9,2,9,2,11,2,12,2
140 DATA 12,2,11,2,9,4,9,2,9,2,7,2,7,2
150 DATA 8,2,9,2,8,12
160 DATA 7,2,8,2,9,4,9,2,9,2,9,2,7,2
170 DATA 8,2,9,2,9,4,9,2,9,2,11,2,12,2
180 DATA 12,2,11,2,9,4,9,2,9,2,7,2,7,2
190 DATA 8,2,8,2,9,12
200 RESTORE
210 NEXT V
Don't forget to click on the "Sound" button. The song repeats thrice as there are three verses:
First Verse:
I've got peace like a river,
I've got peace like a river,
I've got peace like a river in my soul;
I've got peace like a river,
I've got peace like a river,
I've got peace like a river in my soul.
Second Verse:
I've got joy like a fountain...
Third Verse:
I've got love like an ocean...
And here is "Scotland's Burning." Of course, Mocha doesn't play it as a round:
NEW
70 N=1
80 FOR X=1 TO 24
90 READ A,T
100 SOUND 261-N*A,T
110 NEXT X
120 DATA 12,4,12,4,9,4,9,4
130 DATA 12,4,12,4,9,4,9,4
140 DATA 8,8,7,8,8,8,7,8
150 DATA 6,8,6,8,6,8,6,8
160 DATA 12,4,12,4,9,4,9,4
170 DATA 12,4,12,4,9,4,9,4
Lyrics:
Scotland's burning,
Scotland's burning!
Look out!
Look out!
Fire! Fire!
Fire! Fire!
Pour on water,
Pour on water.
Once again, these songs play in the key of white D major pentatonic. The closest we can get to the key of A is to change line 70 to N=11 (key of lu A below white A) or N=21 (key of red A).
New Xenharmonic Wiki
Last year, I wrote that the Xenharmonic Wiki would no longer exist. Well, as it turns out, the Xenharmonic Wiki is back:
https://en.xen.wiki/
Even though I've linked to this site in the past, recall that most of the links at this site are EDO's, or equal divisions of the octave. But Mocha music is based on EDL's, or equal divisions of length. But there are a few pages on this wiki that are relevant to Mocha music.
First of all, it's possible to approximate some of the EDO's in Mocha EDL. This is mainly true for the macrotonal EDO's -- the ones where each step is larger than the usual standard (12EDO) steps. Here are the best approximations to the macrotonal EDO's in Mocha EDL:
7EDO: Degrees 156, 141, 128, 116, 105, 95, 86, 78
8EDO: Degrees 202, 185, 170, 156, 143, 131, 120, 110, 101
9EDO: Degrees 132, 122, 113, 105, 97, 90, 83, 77, 71, 66
10EDO: Degrees 256, 239, 223, 208, 194, 181, 169, 158, 147, 137, 128
11EDO: Degrees 162, 152, 143, 134, 126, 118, 111, 104, 98, 92, 86, 81
Subtract 261 from each of these Degrees to obtain the corresponding Sounds.
Extending this to the microtonal EDO's -- the ones where each step is smaller than the usual 12EDO steps -- is less accurate and is not generally recommended. But then again, last year I wrote an Easter song in 28EDO and played it on Mocha. To understand why I did so, you must know what I was thinking when I created that song.
I was fascinated by the fact that the Easter date, while seemingly random, followed patterns. For example, the next three Easters fall on April 21st, 12th, 4th. The first two dates are nine days apart and the last two are eight days apart. There are other sequences of three consecutive years that follow this same pattern:
1995-1996-1997: April 16th, April 7th, March 30th
2063-2064-2065: April 15th, April 6th, March 29th
I was hoping to take advantage of these patterns to make a tune based on the Easter dates -- for example, nine days could be a major third and eight days a minor third. Then all three of these patterns correspond to triads -- either major or minor, depending on how I decided to convert dates into notes.
At the time, I'd never heard of alternate scales (other than 12EDO, of course). But a simple correspondence didn't work out.
Then when I read a book written by Theoni Pappas, I learned about EDO scales. I was researching these scales and realized that 28EDO best preserves the patterns found in the Easter dates.
It was afterward when I discovered the Mocha emulator of my old computer. I remembered the Sound command and was curious about how the computer could play microtonal music. After a few tries, I learned that Mocha used EDL's, not EDO's. Still, it was the only way I knew to play music in anything other than 12EDO, and so I composed the 28EDO Easter song in it. It's not quite as accurate as a real 28EDO instrument, of course.
Since I wrote my 28EDO song in Mocha EDL, I suppose it's reasonable to estimate all microtonal scales between 12EDO and 28EDO in Mocha. But no higher EDO beyond 28EDO is recommended.
As a microtonal scale, 28EDO isn't one of the more common scales. It is notable for having a very accurate 5/4 major third at the ninth step of 28EDO. (Thus all those nine-day intervals between Easters map to major thirds.) But unfortunately, 28EDO lacks an accurate 3/2 perfect fifth. As we saw when trying to convert the guitar songs into EDL's above, I keep using 18EDL (with a just perfect fifth on the root note) over 20EDL (with a just major third over the root instead). This is especially true because the usual 12EDO scale has such an accurate perfect fifth, so our ears demand more accurate fifths compared to accurate thirds.
Is it possible to write the Easter song in an EDL scale instead of an EDO? For example, what if we were to map March 22nd-31st to Degrees 22-31 and April 1st-25th to Degrees 32-56? The resulting song would be considered 56EDL. Notice that 56EDL and 28EDO have the same number of steps in an octave, namely 28.
But unfortunately, EDL's hide the patterns we find in the Easter dates. For example, let's revisit the pattern I mentioned above:
1995-1996-1997: April 16th, April 7th, March 30th
2019-2020-2021: April 21st, April 12th, April 4th
Converting these to 56EDL, the first triad is 47:38:30 while the second is 52:43:35. These are not the same triad. For example, 47/38 is about 368 cents while 52/43 is about 329 cents. Neither one of these is equivalent to the major third of 28EDO (386 cents) -- and indeed, both of these would be the same triad in 28EDO while they are distinctly sounding triads in 56EDL.
Then again, EDL scales contain just major thirds, even more accurate than 28EDO. We might at least wish to modify the Mocha approximation of 28EDO (which, as I wrote above, isn't accurate) to include as many just 5/4 intervals as possible.
Here is Mocha's best approximation of 28EDO:
28EDO: Degrees 210, 205, 200, 195, 190, 186, 181, 177, 172, 168, 164, 160, 156, 152, 148, 145, 141, 138, 134, 131, 128, 125, 122, 119, 116, 113, 110, 108, 105
And here is our modified version:
28EDO: Degrees 210, 205, 200, 195, 190, 185, 180, 176, 172, 168, 164, 160, 156, 152, 148, 144, 141, 138, 135, 132, 129, 126, 123, 120, 117, 114, 111, 108, 105
Here we start with multiples of five from Degree 210 to 180 and then switch to multiples of four from Degree 180 to 144. This allows several 5/4 major thirds to appear: 210/168, 205/164, 200/160, 195/156, 190/152, 185/148, and 180/144 are all just major thirds. After 144 I switched to multiples of three instead. This results in several 4/3 perfect fourths appearing as well: 180/135, 176/132, 172/129, 168/126, 164/123, 160/120, 156/117, 152/114, 148/111, and 144/108 are all just fourths. In fact, this is an improvement over pure 28EDO, which lacks just fourths (and fifths).
The modified version of 28EDO can be coded in Mocha. We either use three For loops -- one loop each for five-, four-, and three-degree steps -- or include the whole list in Data lines.
Here is the link to 28EDO on the new Xenharmonic Wiki:
https://en.xen.wiki/w/28edo
And before we leave the Xenharmonic website, let me link to Kite's color notation, which I still use to describe EDL scales as well:
https://en.xen.wiki/w/Color_notation
This link includes the new version of Kite's color notation (including the use of "azure" or "zo" to mean "blue," and "lavender" to mean 11-limit).
Notice that Mocha EDL's are utonal. This means that only the colors that contain "u" in their symbols (plus white) are needed for Mocha:
Limit Color
3 white (wa)
5 green (gu)
7 red (ru)
11 lavender (lu)
13 thu
Coding Kite Colors in Mocha
It's possible to write a simple program in Mocha where we enter a Sound from 1-255. The program converts this to a Degree (by subtracting it from 261) and then naming it using Kite colors.
NEW
10 INPUT "SOUND";S
20 D=261-S
30 C$=" ":L=2:K=3
40 P=2:S$="":GOSUB 200
50 P=3:S$="":GOSUB 200
60 P=5:S$="GU":GOSUB 200
70 P=7:S$="RU":GOSUB 200
80 P=11:S$="LU":GOSUB 200
90 P=13:S$="THU":GOSUB 200
100 IF D>1 THEN P=D:S$=STR$(P)+"U":GOSUB 200
110 IF C$=" " THEN C$="WA"+C$
120 A=INT(L*12/7+.4)-K
130 L=L-INT(L/7)*7
140 N$=CHR$(71-L)
150 IF A>0 THEN N$=N$+STRING$(A,"#")
160 IF A<0 THEN N$=N$+STRING$(-A,"-")
170 PRINT C$+N$
180 SOUND S,16
190 END
200 Q=D/P
210 IF Q>INT(Q) THEN RETURN
220 D=Q
230 C$=S$+C$
240 L=L+INT(LOG(P)/LOG(2)*7+.5)
250 K=K+INT(LOG(P)/LOG(2)*12+.5)
260 GOTO 200
20 D=261-S
30 C$=" ":L=2:K=3
40 P=2:S$="":GOSUB 200
50 P=3:S$="":GOSUB 200
60 P=5:S$="GU":GOSUB 200
70 P=7:S$="RU":GOSUB 200
80 P=11:S$="LU":GOSUB 200
90 P=13:S$="THU":GOSUB 200
100 IF D>1 THEN P=D:S$=STR$(P)+"U":GOSUB 200
110 IF C$=" " THEN C$="WA"+C$
120 A=INT(L*12/7+.4)-K
130 L=L-INT(L/7)*7
140 N$=CHR$(71-L)
150 IF A>0 THEN N$=N$+STRING$(A,"#")
160 IF A<0 THEN N$=N$+STRING$(-A,"-")
170 PRINT C$+N$
180 SOUND S,16
190 END
200 Q=D/P
210 IF Q>INT(Q) THEN RETURN
220 D=Q
230 C$=S$+C$
240 L=L+INT(LOG(P)/LOG(2)*7+.5)
250 K=K+INT(LOG(P)/LOG(2)*12+.5)
260 GOTO 200
Here's how the program works. After the Sound is converted to a Degree (D), Mocha starts finding the factors of D. Here C$ (the color) starts out as blank space (Line 30), and if it remains as a blank space (Line 110) then the color must be "white" (the syllable "wa"). Lines 40-90 contain syllables for the primes 2 through 13, including a null string "" for primes 2 and 3.
Line 100 assumes that any factor left after sieving out primes 2 through 13 must be prime (since the smallest possible composite would be 17^2 = 289, but the highest Degree in Mocha is 260). The syllable for these primes is the prime followed by "u" (17u, 19u, 23u, and so on).
The subroutine starts at Line 200. Here we keep track of both the letter name in L and the keyspan (which determines sharp of flat) in K. The flats are printed as "-" in Mocha because this is what the Play command also uses for flats.
Lines 240 and 250 use a 12EDO framework to determine the name of the note. Here Degree 11 ends up as Bb and Degree 13 becomes G#. Even Kite himself admits that the names for 11 or 13 can go either way (lu B or lu Bb for 11, thu G or thu G# for 13). I myself tend to use B and G for 11 and 13, but the 12EDO framework requires Bb and G# (since 11/8 is closer to an augmented 4th than a perfect 4th, and 13/8 to a minor 6th than a major 6th in 12EDO). Kite would write "ilo 4th=P4, tho 6th=M6) for my method and "ilo 4th=A4, tho 6th=m6" for Mocha's.
After returning from the subroutine, L and K are used to determine the note name. Here L=0 denotes the note G, L=1 is F, and L=2 is E, and so on. (The note names are backwards because EDL's are utonal/undertones.) And K=0 is also G, but K=1 is F#, K=2 is F, K=3 is E, and so on. (Line 30 starts at N=2, K=3 because the fundamental corresponding to Degree 1 is E.) Line 120 uses .4 for the rounding instead of .5 only because .5 happens to place a 12EDO note between B and C instead of between A and B as is proper for (American) 12EDO. (Germans like Bach actually would put an extra note between B and C, called H! But we don't want Mocha to follow the German convention.)
Line 170 prints the color and note name, Line 180 plays the Sound, and Line 190 ends the program.
Here are the names determined by Mocha for all the Sounds in the 200's (Degrees 6-61):
Sound Degree Note
255 6 wa A
254 7 ru F#
253 8 wa E
252 9 wa D
251 10 gu C
250 11 lu Bb
249 12 wa A
248 13 thu G#
247 14 ru F#
246 15 gu F
245 16 wa E
244 17 17u D#
243 18 wa D
242 19 19u C#
241 20 gu C
240 21 ru B
239 22 lu Bb
238 23 23u A#
237 24 wa A
236 25 gugu Ab
235 26 thu G#
234 27 wa G
233 28 ru F#
232 29 29u F#
231 30 gu F
230 31 31u E#
229 32 wa E
228 33 lu Eb
227 34 17u D#
226 35 rugu D
225 36 wa D
224 37 37u Db
223 38 19u C#
222 39 thu C#
221 40 gu C
220 41 41u B#
219 42 ru B
218 43 43u B
217 44 lu Bb
216 45 gu Bb
215 46 23u A#
214 47 47u A
213 48 wa A
212 49 ruru G#
211 50 gugu Ab
210 51 17u G#
209 52 thu G#
208 53 53u G
207 54 wa G
206 55 lugu Gb
205 56 ru F#
204 57 19u F#
203 58 29u F#
202 59 59u F#
201 60 gu F
200 61 61u E#
Notice that I use the syllables ("gu," "ru") rather than the full colors ("green," "red"). This is so that Mocha can combine the syllables if needed ("gugu," "rugu"). I could have used "white" in Line 110 since this is never combined with another color, but I used "wa" for consistency.
Operation Varsity Blues
I did say earlier that I'd write about the recent college admissions scandal. Yes, on the anniversary of the day I got into UCLA, I'm discussing how others got into UCLA, USC, and other schools. As it turns out, this scandal has a name, "Operation Varsity Blues." It's named for a movie that came out 20 years ago -- just two and half months before I received my UCLA admissions letter.
Operation Varsity Blues is causing everyone to rethink about what students need to do to gain admissions to selective college. We all agree that students who pretend to play sports that they don't actually play is an illegitimate way to get into selective colleges.
But some people are starting to wonder whether colleges admissions offices are too reliant on SAT, ACT, and AP exams. Just this month, I've written extensively about how my new district, unlike many others, offer AP English Language to sophomores and AP English Literature to juniors.
Again, I wonder whether these early AP's are intended to help students get into colleges. After all, the AP's I personally took in my senior year didn't help me get into UCLA, since I didn't get the scores of those AP's until about four or five months after I received my fat envelope from UCLA. The only AP scores that helped me get into UCLA are the ones I took as a junior -- and in general, only AP's taken no later than 11th grade are seen by admission decision makers. By taking the AP exams a year early, this allows an extra score to be seen by decision makers before fat envelopes are sent out.
So far, I haven't seen as much for early AP math classes -- but then again, AP Calculus is much more difficult than AP English Lit. I did write earlier about the two seventh graders in Algebra I -- those two students might be headed for junior year Calculus.
I often consider the tweeter CCSSIMath to be a traditionalist. This user has retweeted several articles this month pertaining to the Operation Varsity Blues scandal:
https://twitter.com/CCSSIMath
But unlike the other traditionalists, CCSSIMath doesn't agree completely with the push to place everyone in Algebra I in seventh or eighth grade. The user links to the following article:
https://www.chicagotribune.com/suburbs/deerfield/news/ct-dfr-district-109-math-curriculum-concerns-tl-0321-story.html
Some said they’re starting to see negative results with the district’s decision to cut the “regular” math course for seventh graders this year, leaving them with the options of taking an accelerated or advanced class.
Here the accelerated class leads to completing Algebra I in eighth grade, while the advanced class is itself seventh grade Algebra I. What I'm wondering is, is the reason to dropping regular Common Core Math 7 related to making students more competitive for college.
I'm not quite sure whether there is a simple solution to this problem. I recall reading about how college admissions are different from most other businesses. For example, successful eateries such as McDonalds used to brag about how many customers they had -- "99 billion served." But Ivy League colleges do the opposite -- they brag about how few students get into their schools, not how many.
But the only way to make colleges more like fast food is if the most successful colleges -- say the Ivy League trio of Harvard, Princeton, and Yale -- educated the most people. Imagine if almost every college -- even community colleges -- were run by Harvard, Princeton, and Yale. Then many more people could earn diplomas from those schools, and so Operation Varsity Blues would disappear.
Of course, I can't see how that could work in reality. So far, I don't know a solution to the college admissions scandal.
Bruce William Smith
Yes, this means that the schools in Deerfield, Illinois (CCSSIMath link above) are placing all students into either accelerated (SteveH-level) or advanced (Smith-level) classes. And I subbed in two eighth grade Algebra I classes (SteveH-level), and in each class there was one seventh grader (Smith-level).
Anyway, Smith has now been posting at the Joanne Jacobs site -- a site I often go to in order to find certain other traditionalists. So let's find out what he's been up to:
https://www.joannejacobs.com/2019/03/why-kids-need-to-learn-standard-english/
This post is a who's who among traditionalists. Not only does Smith make his first comment in response to this post, but also among the commenters are Bill (a regular at the Jacobs site) and Ze'ev Wurman (who occasionally comments here). Moreover, Jacobs even links to a blog (co-)authored by another traditionalist I haven't seen in some time -- Katharine Beals!
But the post that has drawn so many traditionalists has nothing to do with math. The topic of this post is English -- standard English, to be exact. And unfortunately, this post is racial, since it's all about black students and whether they should speak Standard American English or the dialect known as African-American Vernacular English.
So far, I've seen Smith mainly write about math in his traditionalism comments. But Bill, Wurman, and Beals have all discussed traditional English instruction as well. On the other hand, we already know that race (specifically tracking) is a fairly common talking point among traditionalists.
Since this is a racial discussion, that's why I had to delay writing about this grand traditionalists' reunion until spring break. I try to bury controversial racial discussions at the bottom of vacation posts (though this was impossible when reading Eugenia Cheng's latest book).
Let's start with the original Jacobs post, which as usual contains a link of its own:
Black kids need to learn Standard American English (SAE), writes Jasmine Lane, an English teacher in training, in her excellent blog.
It was called “talking white” when she was growing up as “a poor, Black girl from the north side of Minneapolis with two working-class parents and one who didn’t finish the 9th grade.”
Now here are our traditionalists. Let's start with Smith, whose return first drew me to this post:
brucewilliamsmith:
Standardization in English (and other languages) is more applicable to its written than its spoken form; AAVE is distinguished from standard English in its grammar as well as its vocabulary, to a point, in extreme versions (such as Gullah), where it may be argued to be a separate dialect rather than a mere variety of English.
Next up is Bill:
Bill:
Does anyone remember ebonics, which was derided even by Jesse Jackson when it proposed many years ago in the Oakland school district (at least I think it was Oakland)…
As I recall it wasn’t around for very long
As a Californian, I'll inform readers that yes, it was indeed Oakland. The third traditionalist to comment is Wurman:
Wurman:
I would agree too, not only Henry Higgins. 
I welcome the dose of common sense she represents.
Here "Henry Higgins" is a character from the My Fair Lady clip that Jacobs includes in her post. I assume that "she" refers to Lane, the author of the blog at the first link.
I won't quote Katharine (or Catherine) here on this blog, but it's significant to note that the post at the link is all about diagramming sentences -- something that traditionalists (of English class) wish that students still do nowadays.
Yesterday I subbed in a music class. The students were singing spiritual songs to prepare for their trip to Carnegie Hall. Many spirituals have their roots in the black church, and so some of their lyrics are written in AAVE. I heard the sopranos (none of whom are black, by the way) sing about going to the "promis' lan'," and I believe the word "nevah" appeared in the song as well.
So let me conclude the racial portion of this post with my own opinion on this issue. We might wonder why black students speak AAVE and have trouble learning Standard English. Well, the answer is that from ages 0-5, all the young black students hear nothing but AAVE from the parents, and old habits are hard to break once they reach school age. So now we wonder do the parents speak AAVE and have trouble learning Standard English. Well, the answer is that from ages 0-5, all the parents heard nothing but AAVE from the grandparents, and old habits are hard to break once they reach school age. So now we wonder do the grandparents speak AAVE and have trouble learning Standard English. Well, the answer is that from ages 0-5, all the parents heard nothing but AAVE from the great-grandparents...and so on.
And after we go back sufficiently many generations, we reach one where during ages 0-5, the language they spoke wasn't any English dialect, but an African language that they were speaking on the continent of Africa. This language probably wouldn't have been Swahili (which I mentioned earlier in this post). For example, Kunta Kinte in Alex Haley's Roots spoke Mandinka. As the Africans began to learn English, their speech was influenced by their native languages, and hence AAVE was born.
Thus in order to break the AAVE cycle, we'd need a generation that hears nothing but Standard English for the first sixty months of their lives. Then this generation can grow up and teach Standard English to their children. But once again, I don't know how achievable this is.
Jasmine Lane (the author of the link above) tells us that black students must make a choice between their native dialect that they naturally want to speak (AAVE) and the dialect that leads to success in the real world (Standard English). On the other hand, whites don't have to make such a choice, since their native dialect is the same as the dialect that leads to success. This is the source of the debate -- blacks must make a choice that whites don't have to make.
Unlike Lane, I am not an English teacher, and so much of the AAVE debate isn't relevant to me. But there is one part of AAVE that is relevant to me as a math teacher -- student names.
It's well-documented that certain names are the equivalent to AAVE -- they are strongly associated with being black. And ceteris paribus, job candidates with resumes containing the AAVE names are less likely to be called for interviews than those containing SAE names. (Notice that some of these names actually are Swahili, such as Imani -- named for the last principle of Kwanzaa and is equivalent to the name Faith in SAE.) And no matter how much black students change their dialect from AAVE to SAE, they can't as easily change their name.
When I was at the old charter school two years ago, recall that almost all of the eighth graders there were black. At the start of the year, one girl was clearly at the top of her class. I won't reveal her name here, but I will say that her name contains an apostrophe. Names with apostrophes (unless they are Irish names beginning with "O'-") are strongly associated with being black. (This is the "neutral girl" from my January 6th post.)
And even this week, I notice that one of the two seventh graders in the Algebra I class was black. He has a common Biblical name, except that one of the letters is replaced with a "z."
These two students are clearly strong math students and might even apply for high-paying STEM jobs in the future. But I fear that the apostrophe or "z" in their names might lead to their resumes being rejected.
At the old charter school, I was considering telling the girl that when she sends a resume to a company someday, she should spell her name without an apostrophe. (Save the apostrophe for after she's hired and she's filling out her W-4 forms.) But she moved away from the school after a month and I never got to say this to her.
And of course I didn't give this sort of advice to the Algebra I seventh grader, since I only knew him for two days. (He was also in one of the science classes I subbed for later in the week.) Indeed, this is the sort of thing I'd only tell a student at the end of the year, after the student has attended my class for an entire year and learned to trust me.
Conclusion
Notice that race isn't the only controversial topic I wrote about in this spring break post. Somehow, religion has quietly dominated the two spring break posts, from calculation of the date of the religious holiday Easter to the lyrics of spiritual songs to students with Biblical names.
Just as I ordinarily don't post "A Day in the Life" when one of my districts is on spring break, I normally wouldn't post a worksheet from such a day. But I can't help but post the following worksheet today because it fits my most recent U of Chicago lesson like a glove.
On the day I subbed for Algebra I, the teacher assigned an extra credit worksheet. One side of the worksheet was a Pizzazz worksheet on simplifying radicals. But the other side just happened to be a logic problem about college roommates.
Of course I have to post the logic problem today, since it fits perfectly with Lesson 13-6 and the logic problem I posted last week. And it's all about college roommates, which also goes well with today's UCLA anniversary post.
As for our next lesson, spring break ends and I'll cover Lesson 13-7 in my next post, scheduled for Monday, April 1st. For those who have completed spring break, I hope you enjoyed it. For those who are just starting spring break, I hope you'll have fun. And those of you for whom spring break is still a week or more away, just sing the Big March song and hopefully you'll get through this tough time.
