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At a high level you're right, Common Core philosophy does encourage this sort of lesson. The unfortunate part is that Common Core still is largely a list of fac

by j2kun 12y ago

At a high level you're right, Common Core philosophy does encourage this sort of lesson. The unfortunate part is that Common Core still is largely a list of facts that students need to know, and when they need to know them. This is why graph theory is not "compatible" with the standards, because in the huge list of topics they pretend these things don't exist. And since the Common Core is really a document for non-teachers, I agree with the original comment that this wouldn't fly. It's just due to opposition by administrators, test writers, and standards-compliance checkers who read the document too thoroughly and, paradoxically, too shallowly. They don't look at this lesson to see whether it fits with the philosophy of learning espoused by the standard; rather, they check off which standards it covers and complain when the answer is zero. I put some fault in the document for this.

kaitai 12y ago
I'd disagree that it's a list of facts; the high school modeling standards are skills. I've read some good discussions of whether the earlier-year standards are useful for their age groups and am not sure (I think they're pretty reasonable). The high school modeling and geometry components are great. But what does Common Core have to do with graph theory not being taught in elementary school? It never has been, and not because of new standards. It's not taught because too many teachers don't know it, and because too many "administrators, test writers, and standards-compliance checkers" have their noses where they shouldn't! It is terrible that in the US we have this attitude that teachers must be told exactly what to teach and when. We have it because we don't trust teachers, and swapping out NCTM standards for Common Core standards doesn't change that.
- j2kun 12y ago
  The modeling standard is, I feel, the most honest part of the standards. I'm arguing that if someone tried to teach graph theory as part of, say, modeling (which it is by all means), then they would see blowback from the people that make sure teachers are working toward meeting the standards.
gohrt 12y ago
There are so many hours in the day. Either you argue that graph theory is more important than the other topics (which?) or you acknowledge that graph theory is an enrichment topic for some students who learn the core material faster or devote more time to math study. It is true that Common Core lacks "enrichment" -- by defining a minimum standard, it doesn't specify what to do with student with more capacity to learn. But that's left to individual students, teachers, and schools, not incompatible. If a teacher can teach their students 7G math standards in 6 months of the year, the teacher has plenty of class time for other topics.
- j2kun 12y ago
  I don't want to argue that graph theory is more important (though I could list which topics I think it's more important than). Rather I want to argue that, partially because primary and secondary school educators don't have so many years of preconceptions about the right way to teach the subject, it can do a better job building the underlying skills we want to teach students in teaching them math. We don't teach math because we want students to know facts (the correct answer to "What's the derivative of arccsc(x^2)?" is almost always "who cares?"). I certainly don't think that basic graph theory should be reserved for "advanced students." This second grade experiment shows that it's accessible to everyone.

by j2kun 12y ago

kaitai 12y ago

I'd disagree that it's a list of facts; the high school modeling standards are skills. I've read some good discussions of whether the earlier-year standards are useful for their age groups and am not sure (I think they're pretty reasonable). The high school modeling and geometry components are great. But what does Common Core have to do with graph theory not being taught in elementary school? It never has been, and not because of new standards. It's not taught because too many teachers don't know it, and because too many "administrators, test writers, and standards-compliance checkers" have their noses where they shouldn't! It is terrible that in the US we have this attitude that teachers must be told exactly what to teach and when. We have it because we don't trust teachers, and swapping out NCTM standards for Common Core standards doesn't change that.

j2kun 12y ago
The modeling standard is, I feel, the most honest part of the standards. I'm arguing that if someone tried to teach graph theory as part of, say, modeling (which it is by all means), then they would see blowback from the people that make sure teachers are working toward meeting the standards.

gohrt 12y ago

There are so many hours in the day. Either you argue that graph theory is more important than the other topics (which?) or you acknowledge that graph theory is an enrichment topic for some students who learn the core material faster or devote more time to math study. It is true that Common Core lacks "enrichment" -- by defining a minimum standard, it doesn't specify what to do with student with more capacity to learn. But that's left to individual students, teachers, and schools, not incompatible. If a teacher can teach their students 7G math standards in 6 months of the year, the teacher has plenty of class time for other topics.

j2kun 12y ago
I don't want to argue that graph theory is more important (though I could list which topics I think it's more important than). Rather I want to argue that, partially because primary and secondary school educators don't have so many years of preconceptions about the right way to teach the subject, it can do a better job building the underlying skills we want to teach students in teaching them math. We don't teach math because we want students to know facts (the correct answer to "What's the derivative of arccsc(x^2)?" is almost always "who cares?"). I certainly don't think that basic graph theory should be reserved for "advanced students." This second grade experiment shows that it's accessible to everyone.