This is what I wrote last year about today's lesson:
This isn't exactly a filler chapter, since students indeed must remember surface area and volume formulas. It's just that students can learn all of these formulas without the benefit of Lesson 10-6. The important part is that some formulas are clearly linked -- such as the formulas for a prism and a cylinder. It's no wonder then that the text calls both of these "cylindric solids."
...and that's all I wrote last year! That's going to be a problem on the blog now that we've passed the one-year anniversary of my first day in the new district. When I try to quote posts from last year, notice that on some days I wrote more about my subbing that day than the U of Chicago lesson -- and that includes the day I posted Lesson 10-6 last year.
And so let me fill the rest of this post in with some assorted topics. First, even though today's Pappas problem isn't a Geometry question, I do want to mention it as it contains an error (likely just a typo):
Set A = {whole #s 5} has cardinality ______.
The problem is that "whole #s 5" is meaningless. Pappas probably left out a symbol between whole #s and 5, so let's fill it in for her:
Set A = {whole #s < 5} has cardinality ______.
The set A is now {0, 1, 2, 3, 4, 5}. This set of course has six elements. Thus the desired cardinality is six -- and of course, today's date is the sixth.
Of course, I already knew the date, which explains why inserted the < sign. Had I used < instead, the set would have contains only five elements, yet today's date isn't the fifth. And had I used > instead, the cardinality would have been infinite (aleph-null), yet today's date isn't the aleph-nullth (or the infinite ordinal "omega," since dates are ordinals).
Actually, there's a way to connect this question to the U of Chicago text after all. In Lesson 6-1, we learn that the symbol "N" stands for "cardinality." So we could have written this question as:
Set A = {whole #s < 5}. What is N(A)?
Once again, I'm trying to avoid traditionalists' posts this week. But I couldn't help but notice another link at the Joanne Jacobs website today that's all about grading:
https://www.joannejacobs.com/2019/02/grade-students-on-knowledge-growth/
The 0-100 point scale is “mathematically oriented toward failure, writes Feldman. Teachers can reward learning if the use a 0-4 scale, “stop assigning a zero for missing work, and weight recent performance and growth instead of averaging performance over time.” In addition, letting students “retake tests and projects (with the chance to replace previous scores)” helps “students who enter classrooms with weaker academic backgrounds.”
Even though author Joe Feldman doesn't mention the controversial 0=50 scale (that is, counting a zero as 50%), his idea mentioned above clearly reminds us of 0=50.
One commenter, Darren -- I believe this is Darren of "Right on the Left Coast" -- responds:
Darren:
If this *truly* works, if students really *do* learn more this way, if grades “correlate” better this way, then why not just let the overall grade be the grade the student earns on the final exam? Think about it:
1) not turning in homework isn’t an issue,
2) students can take as long as they need (in a semester) to learn a certain topic, and
3) today’s knowledge, not last month’s, is what’s graded.
Win-win!
Joanne Jacobs responds to this comment herself -- this is what many college classes are like. The problem is that a college student is more mature than a K-12 student -- collegians are more likely to do the homework even if it's worth nothing because he/she knows that doing so serves as preparation for the exam. Less mature K-12 students are unlikely to think this way -- if something doesn't benefit or hurt them right away, they don't consider the consequences.
Instead, here's yet another compromise between traditional grading and 0=50 -- we count zeros as 50% only in the first month. Then they count as 40% in the second month, then 30%, 20%, and 10% in the last month of the semester. A zero on the final counts as 0%.
I'm hoping that this compromise really does increase student learning. Students are more likely to work harder if they're near the boundary between two grades -- thus the best system has as many students near grade boundaries as possible.
Under the traditional system, students who earn zeros at the start of the semester are mathematically eliminated from reaching 60% by the end of the semester -- that is, they're too far below the D-F boundary to care much about the final. On the other hand, too many zeros converted to 50%+a few completed assignments might result in students being too far above the D-F boundary (or the C-D boundary, etc., depending on their parents' expectations) to care much about the final.
To get students to care about the final, they must come in near a grade boundary. My hope is that the compromise (0=50 in first month, 0=40 in second month, etc.) results in many students near the grade boundaries leading up to the final. It also encourages students to keep on doing homework as the semester progresses so that they'll be more prepared for the final.
I don't want to make this a habit on the blog, but since I didn't sub today, I wish to take a second look at the subbing day that I quoted in last year's Lesson 10-6 post. I wrote:
This is also a tricky one. In third period, three seventh graders fail to turn in the homework -- or even produce a blank HW sheet -- and start talking loudly. I write down the names, and the aide suggests that these students receive a Saturday detention, but this doesn't deter the trio. Eventually, the aide calls the office, and security comes to escort the three out of the room.
At the time I didn't note this, but as I revisit this a year later, I must admit that this was one of my worst days of subbing in my new district. I consider any day when security must be called to be a failure on my part. It shows that I can't control the class without outside help.
What should have I done in this case? The best plan of action was probably nothing -- this was a special ed class with an aide. Even though she was to one to call the office, I suspect that I'd been the one to provoke the students by asking for the homework (after all, they started talking loudly only after I asked them for the HW). The special aide knew the strengths and weaknesses of the students, including who could and couldn't handle the homework. But by repeating that they should turn in the HW, all I did was get the boys angry, and they respond by arguing which ultimately leads to security being called.
Once again, I had problem with distinguishing "no work" from "bad behavior." I tried to punish the boys for "no work" instead of "bad behavior," which is a bad idea in any class, but even more so in special ed. In the end, I'd provoked the students into bad behavior that might have been avoided. So instead, I should have let the aide deal with the missing work.
As a sub, I should worry only about bad behavior -- for example, if the boys had started talking loudly in the middle of a lesson for no reason (as opposed to arguing with me). My problem is that it's much easier to identity who didn't turn in the work (just look to see whose paper is blank) as opposed to who's talking. ("I wasn't the one talking!"). When it comes to classroom management, I need to get away from what's easy and focus on what's right.
Also, last year I wrote:
The problem is that I continue to discuss the incident the remainder of the day. For example, I tell a pair of eighth graders in sixth period that I'm about to write their names for the teacher. One of them tells me that writing down his name means nothing to him, so I tell him about the earlier class and how three students earned Saturday school and a referral to the dean. This, therefore, constitutes a violation of the third resolution.
How should I have handled this situation? Perhaps instead of saying, "I'll write your names on the bad list" (What's a bad list?), I could have said, "I'll explain to the teacher how you acted today." In this manner, the students understand exactly what I'm about to write for the teacher. If the students persist in failing to my threat seriously, I could inform them that students whose names are left might wind up in Saturday school, without any further explanation.
This part is on the right track. I could have simply said "If you don't change your behavior, I'll write your name on the bad list and you'll get Saturday school," without mentioning the earlier class at all.
OK, that's enough for today's hodgepodge. Let's get to today's worksheet:
END
No comments:
Post a Comment