Today I subbed in a middle school special ed English class. This is the third time I've visited this class this month -- I most recently described the class in my Valentine's Day post. This time, I won't do "A Day in the Life," but I will discuss some of the things I see today.
The middle school rotation is set up to begin with the co-teaching class today. As she often likes to do, the resident teacher begins with silent reading, even though the official silent reading time isn't until after lunch. Afterward, she starts talking about the district Performance Task.
What, you're now thinking, we're still talking about that darn Performance Task! I thought there'd be no more mention of Performance Tasks after President's Day! Well, this teacher decides to take the Performance Task a step further. First, she gives the seventh graders their scores -- and the rubric specifically states that the scale is based on the SBAC, with 4 as the top score. Then she tells them that this entire week will be for editing the essay and resubmitting it for a higher score.
To accomplish this goal, the teacher divides the class into five groups and assigns each group to a particular station. That's right -- this teacher is implementing Learning Centers. And once again, each time I see Learning Centers implemented, I can't help but think back two years to the old charter school and my failure to do Learning Centers properly.
Since I'm here to co-teach, she assigns me one of the groups. This is the top group, and the goal here is to partner up for peer review and editing. Only one student, a girl, has earned a perfect 4, but there are several scores of 3.5. The lowest score in my group appears to be 2.5. (Hmm -- she claims that these are SBAC scores, but I see no evidence that the SBAC uses half-integer scores like 3.5 or 2.5.)
It appears that the students will rotate through the groups throughout the week. The resident teacher is giving weaker students more help before they rotate into the editing station. This is very different from Learning Centers as envisioned by Illinois State, since students aren't expected to spend the entire week in Learning Centers. Then again, some of my colleagues suggested that, considering all the management problems I had that year, I try implementing a full week of Learning Centers.
(What's worse -- "Big Essay" or "Big March"? That's easy -- continuing to work on the Big Essay during the Big March, as this class is doing.)
After this class, I returned to my own classroom with the special aide. Just as we did on Valentine's Day, there is an assignment where students read two articles on a point/counterpoint, answer ten questions about the articles, and then do a current event on the topic.
This time, the topic is year-round schools. I wrote about year-round schools on the blog before -- about 2.5 years ago, just before I started working at the old charter. Let me reblog a little of what I wrote back then:
Here's how students can attend 3/4 of the year on the Year-Round Calendar -- we divide all students into four tracks, labeled by the first four letters A, B, C, and D. At any point three of the tracks attend school while the fourth track is off. The result is that all students attend school for 3/4 of the year, or 180 days, just like the Traditional Calendar students.
You might think that the A-Track student would take, say, the summer off, B-Track students would take the fall off, C-Trackers the winter, and D-Trackers the spring. But the actual Year-Round calendar in the LAUSD wasn't as simple. Students didn't have a single three-month break -- instead, the break was divided in half, so they had two breaks, each a month-and-a-half, during the year.
In today's class, the students consider the pros and cons of this schedule. On the Year-Round calendar there are more breaks, but the traditional calendar summer break lessens the need for air conditioning.
(Notice that on some tracks, there is no "Big March" since students are off-track in March. But on other tracks, the "Big March" may be even longer than on the traditional calendar!)
The worst period of the day, when I must write two names on my bad list, is second period. A seventh grade boy and girl start tearing each other's papers -- and then when I hand them Scotch tape to repair the papers, they just play with the tape.
As for the troublesome third period students from Valentine's Day -- the ones who were making fun of my raggedy shoes -- the girl is one of the hardest working students today. But the boy, meanwhile, is absent. We suspect that he's ditching, since he's present for homeroom (which has the same kids as third period at this school). It's not raining, so there's no double lunch or two-minute period before the lunch starts.
(Oh, and speaking of V-Day, two girls -- one in each grade -- still have the holiday pencils that I gave them that day!)
You might notice that I've labeled this post as traditionalists. Over the weekend, yes, our favorite traditionalist posted, and yes, our favorite commenter commented.
But let me start with something I saw on Facebook yesterday. One poster wrote that Algebra II should be replaced with a basic finance class. Another user -- a former classmate (which is why I'm able to read her post), agreed and added that all math beyond Geometry should be elective.
I expressed partial agreement in my response. We can all get behind the idea that prospective STEM majors should take Algebra II. On the other hand, non-college bound students shouldn't have to take Algebra II at all -- I have no problem ending with our favorite class, Geometry. The gray area is for future humanities/liberal arts majors. On one hand, I can see why such students shouldn't have to take such a difficult math class, but on the other, if we propose eliminating the Algebra II requirement, traditionalists will complain that we're trying to "water down" a college degree (even for non-STEM).
By the way, my classmate also posted a picture of awards earned by her sixth-grade daughter. One of the awards is for academic achievement in "accelerated math" (which I assume is for middle school students who are headed for eighth grade Algebra I). I assume that this girl will have no problem passing advanced courses in high school such as Algebra II.
Ironically, after responding to my classmate yesterday, I did my taxes -- a task for which that finance class might have been useful.
OK, let's get to the traditionalists. Here is Barry Garelick's post from yesterday -- yes, he wrote this just as my classmate was Facebooking and I was signing my tax return:
https://traditionalmath.wordpress.com/2019/02/24/revisit-of-rote-understanding/
I originally wrote about this in an October 2014 article published in Heartlander. I re-read it recently and decided it’s still true. I have reprinted it here with minor updates.
Well, I guess I reblog my old posts all the time, so I can't blame Garelick for reblogging here.
During a course in math teaching methods I took in ed school, I watched a video of a teacher leading his students to do a variety of tasks, ostensibly to teach them about factoring trinomials, such as x2 + 5x + 6. But rather than teaching factoring techniques, as is done in traditionally taught classes, the session was a mélange of algebra tiles (plastic squares and rectangles used to represent algebraic expressions) and a graph of the equation being factored (a parabola).
I have mixed feelings on this. Recall that algebra tiles are one of the manipulatives that I was supposed to use in Learning Centers at the old charter school. I believe that students might be more willing to use the algebra tiles (for factoring, the challenge is to make a rectangle with the tiles) than complete a traditional factoring p-set. On the other hand, I suspect that they'd be less likely to want to graph the function (unless maybe if they're using technology to do the graphing, such as on a graphing calculator or Desmos).
Garelick continues:
I recount the above because of an eighth-grade math course I observed as an instructional assistant (a role which one assumes after doing countless hours of subbing, and is generally the last step before being hired as a teacher). The math course was given just before full-fledged adoption of the Common Core standards in California and was piloting lessons that aligned with Common Core math standards. The teacher was quite good, and I do not hesitate to say she is excellent at what she does. But I also add that one can be very good at implementing things that are horrible. Her sessions were a mixture of letting the students “struggle” with a problem and then providing some explanation through limited direct instruction and questioning. During one session the class was learning about linear equations, graphing and functional form.
Garelick doesn't state whether this class is Common Core Math 8 or Algebra I, since he writes that this class takes place during the transition. Linear equations appear in both Math 8 in Algebra I. But he strongly implies later in this post that this is Math 8, not Algebra I.
Then Garelick links to some pages from the Golden Age of math textbooks, and tells us that these texts also promoted the same kind of understanding that the Common Core encourages. Then he adds on the following:
Those who view the traditional approach as strictly procedural believe it does not result in a “deep understanding.” They believe students do not learn the “why” of a procedure, just how to do it through “meaningless” drills. Yet the teacher I observed was still giving the students instruction after allowing them some time to “struggle.” She also gave them opportunities to practice. The difference was that her exercises included having to explain (orally and in writing) various connections—i.e., how the table of values related to the equation of the line, how the line related to equation, and so forth. The writing was also instructed: she gave them examples of sentences that she would say aloud but with blanks where key words would go.
SteveH's short comment is to express agreement here:
SteveH:
A classic. They are parroting and applying their rote understanding of math education from ed school.
Here Garelick and SteveH highlight what they consider to be ironic. The Common Core wants students to show deep understanding -- but to them, the Golden Age texts lead to understanding, while the Common Core lessons lead to rote learning of what the teacher (and ultimately, what the SBAC) wants them to write.
Once again, my biggest concern isn't a definition of "deep understanding" vs. "rote learning." My concern is that when students are bored, they're likely to leave assignments blank or give complaints such as "When will I use this in real life?" No one gains rote knowledge or deep understanding from assignments that are left blank.
And so I want to promote lessons that students are more likely to do and less likely to leave blank. I believe that algebra tiles (a puzzle that looks like fun) are more likely to be done than traditional factoring (a p-set that doesn't look like fun).
Just today, one eighth grader asks me the question "When will I use this in real life?" -- actually, I think he uses the phrase "adult life." Notice that this isn't even math, but English, so I can only imagine what he thinks about his math classes. Of course, the ability to make a claim and defend that claim using evidence ("I think the traditional school calendar is better than a Year-Round calendar.") is a useful skill in real life. It's probably easier to defend the real-life utility of defending claims than, say, algebraic factoring. But I was unable to convince him of anything.
In the end, the student completes the English assignment quickly, then goes to the restroom. When he returns, he threatens another student -- and the aide ends up giving him a referral. I was almost about to place him on the good list for doing his work, but of course I write him on the bad list instead.
A student who asks "When will I use this?" in math might be a typical math hater, but someone who asks it in a non-math class probably just hates school altogether. His assumption is that nothing he's taught in any class these days will be useful in real life. In other words, he's already learned everything he needs to know, so he should be allowed to graduate and spend all the hours he's awake on entertainment.
I ultimately tell the class that in the old days, we did let students graduate at their age. But they didn't have fun all day -- instead, they were expected to work. This is the idea of Dickens age -- teenagers worked long hours for little pay. And this is still the case in Third World countries today.
I actually say of this to the other students, when the "When will I use this?" boy is in the restroom. I know that if I say it directly to him, it would likely lead to an argument. (Notice that if I'd waited until he is in the office with a referral to talk about this, it might count as continuing to discuss past incidents, hence a violation of the third resolution.) I might as well practice saying all of this, since I know I'll hear "When will I use this?" all the time in my own math class.
But it's the traditionalists like Garelick and SteveH who forget about "When will I use this?" They assume that just because we hand the students a traditional p-set, the students will just do it without any questions. That assumption isn't even true in English, much less math.
Before I leave the traditionalists, I do wish to comment on the latest teacher strike. I won't blog about every teacher strike, but I feel I should mention the Oakland labor dispute since it's in California. (I do point out that Oakland is in Northern California, and thus it's much closer to Garelick's home than my own.)
Unlike the LAUSD strike, the Oakland strike apparently doesn't have "overtesting" as a major point of contention. Once again, we see the impact of standardized testing firsthand in my district. First there's a Performance Task for the actual SBAC. Then the district gives its own Performance Task in order to prepare students for the SBAC. Then an individual teacher in the district decides that she wants to extend the district assessment to give her students extra practice -- probably in the name of making sure that the students are ready for the SBAC.
(Today's co-teacher is the only teacher I know who is making her students rewrite their essays. In particular, in the main class I subbed for, the students haven't even seen their scores yet -- and as far as I know, there's no plan to have these special ed students edit and resubmit their essays.)
Once again, I have no problem with the idea of different tests at different levels, but this easily leads to overtesting when districts add tests to prepare for the state assessment, and teachers add tests to supplement the district assessment.
This is what I wrote last year about today's lesson -- which is based on something that I found in a math class I subbed in last year:
I also find a copy of a Performance Task, similar to what students may find on the SBAC. There's a hole in my U of Chicago pacing plan since Chapter 11 has only six sections. And I've never posted a Performance Task before, despite this being a Common Core blog.
And so I post this task as an activity for today and tomorrow. Actually, I create my own version of the problem rather than the district copy. This is to block out the name of the district since I don't post identifying information (and to avoid any issues with SBAC, which might mistake this practice question for a real test question). Also, I changed it from one day to two days. On the actual SBAC, students are typically given a two-hour block to complete the Performance Task, so they should have two days to complete it.
The question is about the coordinates of a square. It fits perfectly with Chapter 11 of the U of Chicago text -- and indeed it's similar to the Lesson 11-1 activity from two weeks ago.
In the Glencoe text, the Performance Task fits with Chapter 6, on quadrilaterals. Glencoe Chapter 6 is similar to Chapter 5 in the U of Chicago text (and Chapter 6 in the Third Edition), except that coordinates appear early. Indeed, I lamented three years ago that the Distance Formula appears as early as Chapter 1 in the Glencoe text!
2019 update: So now I'm writing about Performance Tasks in math after blogging so much about the Performance Task in English. I have no idea when this task was actually given in the district. I assume that it was well before winter break, since the English Performance Task is after winter break.
Traditionalists probably won't like the explanation required for Part III of this task. They'd say, just graph the quadrilateral and classify it. There's no need for students to explain anything.
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