Today I subbed in a seventh grade special ed science classroom. Since most of the classes are science and most have an aide or co-teacher, I won't write this in "A Day in the Life" format. Still, I have plenty to say about today's classes.
This is my fourth visit to this classroom and second this school year. I described my most recent visit here in my January 14th post. As I wrote in that post, this year, the only two classes she has in her own room are both science -- her only math class is as a co-teacher.
I sing different songs in the various classes, based on what is being taught in each one. In the lone math class, seventh graders prepare for tomorrow's test on percents and money, which also includes simple interest. Thus the "Interest Rap" (omitting the verses on compound interest) is in order here.
In seventh grade science co-teaching, the students watch a DVD called "Human Footprint." Here they learn about how much stuff each human consumes in a year or a lifetime. I rap out "One Billion Is Big" here, since millions and billions feature prominently in some of the video notes:
1. How many people are currently on the planet? Over 7 Billion
6. How many diapers are thrown away in the US every year? 18 Billion
16. As a nation, how many hot dogs do we eat on the 4th of July? 150 Million
24. How many gallons of water does a person use in a lifetime? 1.2 Million
26. As a nation, how many tons of waste do we generate each year? 2.46 Million
33. How many Christmas trees do we cut down each year? 20 Million
Indeed, we get as far as the fact about millions of hot dogs, which fits with the "One Billion Is Big" line about eating a billion hamburgers.
In eighth grade science co-teaching, the students are learning about the solar system. Back on January 14th, I sang "Earth, Moon, and Sun" for this class (my go-to song for physical science), and the resident teacher suggested that I come back one day during the astronomy unit to sing it again. Well, that day turns out to be today.
Finally, the seventh grade science class in my own room learns of plate tectonics and earthquakes. Of course, I don't already have an earthquake song. Instead, I finish a song that I mentioned earlier this week -- "When the Scientists Go Marchin' In" (since it's still the week of Mardi Gras, even if Lent has begun). The original idea behind this song is that I change the lyrics to whatever the class is currently studying. So here's how it goes today:
Refrain:
Oh when the scientists go marchin' in,
Oh when the scientists go marchin' in,
Oh how I want to learn some science,
When the scientists go marchin' in.
Verse:
We're gonna learn all 'bout earthquakes,
Oh when the whole world moves and shakes,
Building strong will take some designin',
When the scientists go marchin' in.
As for the Eleven Calendar, today is the first of three blank days that occur at the end of the year, just before New Year's Day on March 1st. I wrote that blank days will be just like Elevendays -- the rule to focus on will be any rule of my choosing.
The ninth resolution on attending every single second of class sort of comes up, as many students in each period ask for restroom passes. Usually, I defer to the aide or co-teacher who decides who gets to go, except for the last class of the day, a small solo seventh grade science class. There are only seven students present today, and I believe only one of them asks for a restroom pass.
Yesterday's first resolution on gaining confidence comes up in the math class, as students prepare for tomorrow's test. The resident teacher mentions two mnemonics to help students remember -- the first is PeDaL (Percent to Decimal, two spaces Left) and DiaPeR (Decimal to Percent, two Right). The other mnemonic is either "I'm PReTty" or "I PaRTy" for simple interest I = prt.
I also work on the millennium resolutions and communication skills. I interact with two teachers at lunch, as well as with the aide and each of the co-teachers.
As usual for days when I sub science, I must compare this to science at the old charter school. But first, I must point something out about today's science classes.
Last year when I subbed in a seventh grade science class, I blogged how one teacher had written a sort of "year in review" detailing the entire Science 7 curriculum for the year. I remember that the unit on plate tectonics was associated with a CER (Claim, Evidence, Reasoning) essay -- which I knew was also the format of the district Performance Task for English classes (a task that I mentioned on the blog earlier this week). I took a guess why that CER was listed there -- the science unit would be taught around the time of that ELA Performance Task in order help reinforce the CER format. So students would be more successful on the ELA essay. Moreover, unlike other other topics in science, plate tectonics doesn't naturally lend itself to a middle school lab experiment. So instead, my guess was that students would learn about it in the CER format -- a claim supporting tectonic theory is made, and we must find evidence and reasoning to show that the claim is true.
As it turns out, my guess was wrong. First of all, the CER in science is actually a district assessment that's completely separate from the English CER! I believe that the English CER has already been given, but the science CER will be on the last two days of the second trimester (which, as I wrote earlier, does not end today in this district). The topic for the seventh grade CER is indeed plate tectonics, but the topic for Science 8 is apparently the solar system.
And there actually are labs associated with the science CER's. For plate tectonics, students build a structure out of toothpicks (and stuff) that can withstand being shaken (as in an earthquake). They learn that their structures are stronger when they use plenty of tape. In eighth grade, the students must make a map of the solar system (on a long strip of paper) that's to "scale" -- that is, the distances between the planets and the sun follow one scale, while the sizes follow another scale. As it turns out, in a completely to-scale model of the solar system where the size of the earth is appreciable (say the size of a marble), the outer planets must be several miles away, as this video demonstrates:
OK, so let's compare all of this to science at the charter school from three years ago. Of course, there would not have been a required district CER assessment at the old charter school. But the labs that I see today might have been possible at the old school.
It's interesting that the above video is almost exactly three years old -- if we view it at YouTube directly, we see that it's dated March 2nd, 2017. This is right around the time I was teaching at the old charter school -- and indeed, it's right in the middle of the "Science Week" that I declared since I needed to establish student science grades (after failing to teach much science) for the trimester. In fact, March 2nd, 2017 was, just like today, the day after Ash Wednesday (hence my "Mardi Gras" song about science), with similar timing before the end of our trimester.
As I mentioned earlier, I stopped blogging about my class around this point (and I was very close to leaving the school altogether). But as it turns out, for eighth grade Science Week, the topic I'd chosen was outer space.
The project I started to give my eighth graders came from the Illinois State science text -- and as you recall, a major constraint on what projects I could give was the need to follow that text. In the Illinois State STEM text, students would measure objects with their own feet (or another body part) as a unit, just as the ancients did -- hence the unit name "foot." But instead of calling it a "foot," they would refer to it as one "body unit," in anticipation of the idea of one "astronomical unit" or AU.
The whole project only confused the students. Perhaps it would have gone better if I'd created my own worksheet for the project rather than adhere to the STEM text. But just as I'd done a month earlier with the Pythagorean Theorem, on March 2nd I could just replace it the something similar to the lab I see in today's classes. Here the students calculate how many AU each planet is from the sun and then mark it on the map using the scale 10 cm = 1 AU.
On Day 2 of the project (Friday in both years), the students calculate the relative diameters of the planets and draw them on the map using that scale. The final day of the project is Tuesday (assuming that the coding teacher comes in on Monday). And even though my charter school didn't have a CER, a similar write-up could have come at the end of this project, and this would be included in the trimester science grade.
I don't believe that I gave my seventh graders anything on plate tectonics for Science Week. (I think my lesson that week was on cells.) But it's possible for me to have given a lab similar to the one I see in Science 7 today and then have it culminate in a write-up similar to the seventh grade CER. (I'm not sure what I would have given my sixth graders.)
Right around the end of the trimester that year was the start of the environmental Green Team unit and project. The "Human Footprint" video that I see today would fit this unit perfectly.
And finally, today is the day of the Chapter 11 Test. All those other things might be fun, but this is a Geometry blog, so I must post the test -- sorry.
Today is a test day -- hence a "traditionalists" post. And the traditionalists have been especially active recently, going back to President's Day weekend:
https://traditionalmath.wordpress.com/2020/02/18/hows-that-been-working-out-for-you-dept/
A slump in math education through the early 21st century within the United States triggered the desire to improve how the country educated students in both math and language. That became known as the common core and was adopted by New York State in 2011.
That slump has been going on for some time as has the desire to improve math education. Every generation disparages the previous as having taught math wrong, with the principle reason being that it is being taught as “rote memorization” without understanding.
SteveH:
““It’s more of a focus on conceptual understanding, so whereas traditional math is more like procedural.”
Common core methods have been in place for about 10 years and data on whether it works has so far been inconclusive. A quick example would be 12 x 3. Traditional way might be to memorize this and get to the answer of 36. Common core teaches this as a distribution. Imagine (10 x 3) + (2 x 3) that gets to the answer of 36.”
Common core methods have been in place for about 10 years and data on whether it works has so far been inconclusive. A quick example would be 12 x 3. Traditional way might be to memorize this and get to the answer of 36. Common core teaches this as a distribution. Imagine (10 x 3) + (2 x 3) that gets to the answer of 36.”
Um, no. All of us old traditional kids learned left-right math from our right-left mastery of algorithms.
This is a tricky one. Often students did learn their times tables up to 12, so the standard algorithm wouldn't be needed until 13. Perhaps the article should have mentioned 7 * 3 instead, where we compare Common Core (5 * 3) + (2 * 3) to the traditionalist memorization of 7 * 3.SteveH:
“…in place for 10 years and data on whether it works has so far been inconclusive.”
The answer is no.
CC spells out a single (NON-STEM) slope from kindergarten to no remediation in a college algebra course – material they had in 8th or 9th grade?!?
This is another tricky one. SteveH tells us that "College Algebra" consists of material from Algebra I in Grades 8-9, and thus College Algebra is a priori "remediation." As usual, the goal for SteveH isn't College Algebra, but high school AP Calculus.Let's get to the other recent Barry Garelick post:
https://traditionalmath.wordpress.com/2020/02/21/another-math-miracle-dept/
This promo piece is about Nashua NH public schools adopting Eureka Math. In keeping with the tradition and style of such articles that pass as objective reporting, it contains the usual disparagement of algorithms, memorization, and of course tests that are not “formative”.
To wit and for example:
“It builds student confidence, year by year, by helping students achieve true understanding of math, not just algorithms,” said Fitzpatrick, adding students are focusing on applying math as opposed to memorizing math formulas. By implementing Eureka Math for kindergarten up to eighth grade, she said it will provide a continuous standard progression and help build conceptual understanding and abstract skills. It also encourages consistent math terminology and common assessments that are formative and summative, explained Fitzpatrick.
Our first featured commenter is KM Math Mom:
KM Math Mom:
I have been tutoring my kids in math almost every night and weekend since the dreaded CPM and Everyday Math curriculum (similar disasters to Eureka Math) were introduced (with zero Parental input) into our CA school system in 2015.
So, School Districts Everywhere, keep adopting these silly Discovery-Inquiry Reformist crap, parents will subvert it at home, and we will continue seeing these vacuous promo pieces with quotes from clueless teachers.
Here KM Math Mom mentions "Everyday Math" -- the U of Chicago elementary text. Once again, she mentions how she, like many other traditionalist commenters, "subverts" the U of Chicago text by tutoring her children.
Replying to her is SteveH:
SteveH:
I’m sure our K-8 schools take full credit for my son’s success in math with their MathLand and then Everyday Math curricula. Never mind that I (and the parents of all of my son’s STEM-ready friends) had to help out at home or with tutors. Never mind that I had to provide zero help once he got to our proper AP Calculus track high school.
Is this the new normal? They do the fun process at school and we parents have to enforce and ensure that mastery is done at home. That’s the whole purpose of “flipping the classroom.” They know that mastery doesn’t naturally flow from understanding. It’s the other way around. They know that most high schools are traditional AP/IB and completely different than what they offer, but nobody ever explains why that is. They claim more understanding with lower expectations. It’s a systemic fraud.
Of course, students who leave traditionalist p-sets blank gain neither mastery nor understanding.
SteveH:
Differentiated instruction (learning) is a failure unless they actually separate the kids by level. If they do that, then they might as well put walls up between the different groups and call them different classes. This can’t happen, so the difference ends up being enrichment rather than acceleration, or the acceleration ends when they get to the end of the low Common Core yearly expectations. It’s fake differentiation.
In other words, to SteveH, the only differentiation that actually works is outright tracking. And of course, "this can't happen" because tracking leads to racial and economic segregation. (This is a traditionalists' post, where race and economic class regularly come up.)
Our next commenter is Miss Friday, replying to SteveH's words about mastery and understanding:
Miss Friday:
I’m not too sure about this. You may be giving them far more credit than they deserve. I suspect that they have no idea how learning works, how teaching works or even how mathematics works.
I don’t think a fraud is being perpetrated, I believe it is sheer ignorance. Highly dangerous, civilization-destroying ignorance. You bring the popcorn, I’ll bring the fiddle and we can watch Rome burn together.
I've seen this malice vs. ignorance argument play out before -- for example, members of one political party ask whether members of the other party are malicious or ignorant. Here the traditionalists are so certain that they know "how mathematics works" that any dissent from their position must be due to either malice or ignorance.
SteveH responds to her:
SteveH:
When my son was in 7th and 8th grades, the teachers talked about having to toughen them up for high school. They are content certified and know that the learning slope is low in K-6 and that education changes completely to traditional honors/AP/IB classes in high school. High school math teachers aren’t ignorant about the problem. Perhaps they now think this nonlinear change is natural, but I don’t think so. They see kids like my son and his STEM-ready friends do well and don’t want to ask what we do at home. Deep down, they know.
OK, I agree with his point that secondary math teachers are "content certified" as opposed to most elementary school teachers who have multiple subject credentials. I'm not quite sure what a simple solution to this problem is. (The solutions that I've proposed on the blog are complicated.)
SteveH:
I’ve struggled with the idea that this is just ignorance, but my conclusion is that it’s not. It’s a systemic issue because many high school math teachers know what’s going on and this includes the proper Algebra I teachers in eighth grade. Before my son got to high school, I emailed the head of the math department at the high school about Everyday Math in K-6. The best she could say was that she didn’t approve of the use of too many do-overs, which had nothing to do with EM or what was going on. Word was that the high school math teachers trashed the mastery skills of incoming freshmen.
Deep down they know that facts are not “mere” and skills are not “rote.” Reality is showing them that they are wrong, but they have to make full inclusion work. As a parent, K-6 was a world where we parents learned quickly we better shut up and go with the program. It was not just ignorance. There was also academic turf and arrogance. Not only did they claim hegemony over the teaching process, but of the content. Incredibly, I had my son’s kindergarten teacher lecture me about understanding in math even though she knew my engineering background. My son’s first grade teacher told us to our faces that “Yes, your son has a lot of superficial knowledge.” However, some teachers did let on (in private) that they disagreed, and the principal did comment that the first grade teacher should have retired long ago. Clearly, something systemic is going on here that’s more than Ed Schools. So what happens to high school math teachers who get a degree from an Ed School? What mental machinations do they have to go through to reconcile the anti-content and anti-skill mastery tripe with the reality of having to teach AP Calculus? K-12 is not all one happy family, not even in K-8 where I recall during one parent/teacher meeting some teachers shushing up others because we parents were there. They have a product and we parents have no input or choice.
OK, there's the story about his son's "superficial knowledge" again. I wonder which teachers let on that they disagreed (with the first grade teacher, I presume).
Meanwhile, on the same day that Barry Garelick wrote about his "math miracle," another math article appeared at the Joanne Jacobs website:
https://www.joannejacobs.com/2020/02/3-1/
I hated trigonometry. Sines and cosines, secants . . . Logarithms were in there, right? I thought they had been invented by adults to torture children. They had suffered in 11th grade, so they wanted others to suffer. But I squeaked by with a B. Never since have I attempted to calculate the height of a flagpole by measuring its shadow.
Sandy Banks “needed three tries to pass trigonometry with a D,” she writes in the Los Angeles Times. She went to college and did OK in life without ever factoring another polynomial or calculating a cosine. Of course, like me, she went into journalism.
The article refers to a proposal that students be required to take four years of math (rather than the current three) to be admitted to the California State University system.
This article has drawn 30 comments. Two of our main traditionalists, Ze'ev Wurman and Bill, are among the commenters.
Let's start with Wurman first. He begins by responding to the commenter wahoofive:
wahoofive:
We have students entering who are so out of shape (or overweight) that they can hardly walk between classes without getting out of breath. Solution: require them to be in varsity sports in high school.
If we are enrolling students who think 1/4 + 1/3 = 2/7, requiring them to take trig (or statistics) isn’t going to help.
And Wurman responds:
Ze'ev Wurman:
Right. I agree about the trig. Still, and speaking of stats, if the student scored 1 out of 4 basket shots (1:4), and later in the day 1 out of 3 (1:3), what were his odds altogether that day? 🙂
Of course, Wurman's comment here is tongue-in-cheek, and this subthread continues with more jokes about situating when adding denominators actually works.
Responding to wahoofive's original comment though, students who are out of shape can benefit from being required to take general PE, but not Varsity sports. And I agree with the analogy that such students shouldn't be forced to take trig or Algebra II, but the real question, if such a student is getting straight A's in all non-math classes, should such a student be admitted to college as a non-STEM (say journalism) major? After all, the original article is about college admissions requirements.
Of course, I'm biased as the author of a Geometry blog. I have no problem with proposals that students not be required to take Algebra II -- but as soon as Geometry is named as the class that's not worth taking, then I get upset. That takes us to Dennis Ashendrof:
Dennis Ashendorf:
A different way to consider the “fourth year:” another attempt to sidestep the entrenched “Calculus-lobby.” I kid you not. Practically, most math teachers (and many professionals) think Algebra 2-PreCalc-Calculus is the holy grail.
The fourth year allows statistical or data science to creep into students’ minds – math they will really use! Spend one hour with the UCLA IDS program or the text “Financial Algebra” and see what really needs to be offered.
The problem isn’t four years of math, but 2 years of the wrong math for most people. BTW Geometry should be an pre-college elective not a requirement as it is in most high schools.
Recall that I recently subbed in a Business Math class. The real question is, should Geometry be the last class that's required before switching to the Business Math path, or should it be Algebra I? Well, here's Wurman's response:
Ze'ev Wurman:
Geometry used to be thought as foundational for two reasons.
First, it was typically the first student encounter with systematic logic proofs in mathematics. Second, it appealed to more spatially-oriented students, and was considered helpful in that sense too.
Since serious proofs went out of the window many years back anyway, perhaps you have a point. Yet auxiliary drawings are still helpful in many math problems, so perhaps there is still value to Geometry. And to anyone in STEM, both Geometry and Trig are indispensable. Now, if you are convinced in 9th grade you’re never going into any serious science or engineering, be my guest 🙂
How serious does Wurman mean by "serious proofs"? Of course, on the blog I often used to link to a "Dr. M" whose proofs are definitely serious. Also, as we've seen before, Wurman considers Common Core Geometry (with its transformations) and proof-based Euclidean Geometry to be mutually exclusive, when we've seen that this isn't really the case.
The last comment about "if you are convinced in 9th grade..." is the problem with second-decade math that I've discussed before on the blog.
Let's look at the Bill comments:
George Larson:
You need Trig for Calculus, survey, navigation cartography and as Joanne noted to be an Artilleryman, but they teach you Trig at the Field Artillery School and Defense Mapping School. You need Trig to go on in Science and Engineering. If people want to rule these out as a career or interest they should skip Trig.
Bill:
In CNC machining, you will destroy a very expensive machine without a working knowledge of trig, plain and simple.
Also, if people are asking if math is important, perhaps the FIU bridge collapse should be a lesson in what happens when engineers don’t compute load stresses properly (hint – people get injured and die).
And yet how many people who crossed that bridge before it collapsed said that they hated trig and wish that it didn't exist, or compared trig to torture? But once again, this ultimately goes back to the second-decade math problem again.
There's one more Larson-Bill exchange that returns us to the heart of the traditionalist debate:
George Larson:
Yes I agree that a lot of prior knowledge: arithmetic, algebra are needed to do trig and then calculus..I agree with you about the need for calculus to understand statistics and data science, but most people who use calculus don’t really understand calculus. They can integrate functions and solve differential equations, but they have never seen the proof of the fundamental theorems or learned the concepts that make calculus work or where it breaks down. On the intuitive level calculus is first taught it is difficult to absorb the ideas of limits and an infinitely decreasing ratio making a derivative or an infinite sum of decreasing values creating a definite integral. It took a long time for mathematicians to figure it all out. Arithmetic and algebra are fundamental. Maybe we should stop trying to teach arithmetic and algebra theoretically and rely more on rote memorization like we used to. We learn language before we learn grammar.
Bill:
Yeah, but that is information which should have been taught in grades 3-4 in most cases, the old plastic pizza is great for teaching fractions
I have nothing to say here as it's just a rehash of points made earlier in this post.
Here are the answers to today's test.
1. Using the distance formula, two of the sides have the same length, namely sqrt(170). This is how we write the square root of 170 in ASCII. To the nearest hundredth, it is 13.04.
2. The slopes of the four sides are opposite reciprocals, 2 and -1/2. Yes, I included this question as it is specifically mentioned in the Common Core Standards!
3. Using the distance formula, all four sides have length sqrt(a^2 + b^2).
4. Using the distance formula, two of the medians have length sqrt(9a^2 + b^2).
5. 60.
6. From the Midpoint Connector Theorem,
7. From the Midpoint Connector Theorem,
8. 4.5.
9. (0.6, -0.6). Notice that four of the coordinates add up to zero, so only (3, -3) matters.
10. At its midpoint.
11. 49.5 cm. The new meter stick goes from 2 to 97 cm and we want the midpoint.
12. Using the distance formula, it is sqrt(4.5), or 2.12 km to the nearest hundredth.
13. sqrt(10), or 3.16 to the nearest hundredth.
14. 1 + sqrt(113) + sqrt (130), or 23.03 to the nearest hundredth.
15. sqrt(3925), or 62.65 to the nearest hundredth. (I said length, not slope!)
16. -1/2. (I said slope, not length!)
17. (2a, 2b), (-2a, 2b), (-2a, -2b), (2a, -2b). Hint: look at Question 5 from U of Chicago!
18. (0, 5).
If you want, you can add the following questions, as the equation of a circle is still missing:
In 19-20, determine a. the center, b. the radius, and c. one point on the circle with the given equation.
19. (x - 6)^2 + (y + 3)^2 = 169
20. x^2 + y^2 = 50
Here are the answers:
19. a. (6, -3) b. 13
Possible answers for c: (19, -3), (18, 2), (11, 9), (6, 10), and so on.
20. a. (0, 0) b. 5sqrt(2)
Possible answers for c: (5, 5), (-5, 5), and so on.
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