The above is an exercise from my favorite Geometry textbook.
You know when you're going to need to find the area of a 30 degree sector? In Trigonometry, when quickly knowing how to transform a central angle into a proportion of a circle is crucial for quickly moving between degrees and radians.
That's why you need a good curriculum, to start helping these kids get ready for Trigonometry a solid two years before they've even enrolled in the course. That sort of thoughtfulness is so, so hard to achieve while trying to make sure each individual class session is awesome.
Here's another bit of curricular thoughtfulness that amazed me this week.
Do you see it? (Actually, this picture is pretty small so you might literally not be able to see it.)
Question 1: Make an angle that measures 60 degrees.This is the sort of little touch that makes this such a lovely 4th Grade curriculum. It's like, forget the progressive, weirdly controversial activities and lessons. Does your curriculum go the extra mile to make sure that kids can actually read mathematical notation?
Question 2: Explain how you know that this is a 60[degree symbol] angle."
I didn't even notice this genius move until a little 4th Grade girl asked me what that symbol meant in class.
If you're making your own curriculum -- using all your own worksheets, your own activities and assignments and everything -- you need to take a close look at some of the best work out there in curricular design. Every time I get cocky, I take a look at CME, CMP or TERC and I realize that they're thinking like ten steps ahead of me.
I'm not saying that a great curriculum's activities and tasks are better than mine. Sometimes they're great for my kids, usually I at least have to turn them inside out before using them. But for previewing, reviewing, and a general sensitivity toward common student pitfalls, I think it's going to be a long time before I can do better than these guys.
Michael,
ReplyDeleteYou've hit the nail on the head. It is so important to be thinking vertically about mathematics, what they need to understand now, to be successful at all levels. I have not been as cognizant of this in the past few months, I realize I got caught up in too many things around me and forgot about good teaching. We have so much going on at our school this year, so many changes and new initiatives and instead of just focusing on good teaching and allowing the rest to fit in, I have become a part of the problem. Thank you for reminding me what it was that interested me in teaching in the first place, and that the students and good learning have got to be the priority.
Which of the curriculum you have mentioned above are the secondary level?
Thanks again, Teresa Ryan
Which of the curriculum you have mentioned above are the secondary level?
DeleteI <3 CME. And I'm not the only one.
Thanks. I'll be checking it out. I believe that collaboration gives us much better products. That's why I have my students work together.
DeleteImportantly, none of these curricula was written by an individual. All were highly collaborative efforts.
ReplyDeleteWhat's the takeaway from that? That this sort of thoughtfulness and care is beyond what can be expected from any single individual? That these sorts of efforts ought to be highly collaborative?
DeleteI'm catching up on my reading, so I just got to this post today. The timeliness of it struck me, as I touched briefly and less eloquently on the same idea in my post yesterday. I think there are some things I can make well, but I don't have the luxury of continually refining every problem set I write until they have the right mix of all the parts kids need to be successful. A good curriculum really is invaluable. There are so many teachers I see blogging that seem to create every thing their students use. Whether that's by choice or necessity, I don't know. Personally, I wouldn't choose that for my classroom.
ReplyDeleteFirst, I dunno about anyone else but I'm always reading new comments on any post, so no need to apologize.
DeleteSecond, yeah. And as Christopher mentions, great curricular work might be the sort of thing that's beyond the abilities of any individual teacher.
Personally, this year I've leaned on curricular materials as a sort of constant safety net. The day's activity is usually basically my own, but the problems and benchmarks of the curriculum have got my back.