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This is the kind of experience would never be allowed with the Common Core type approach. I can't imagine people spending a classroom day on something like this (even though it's awesome and super valuable), but alas it's not content that will appear on the standardized tests.

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Why wouldn't this be allowed with the Common Core? The Common Core is a set of standards for what students should have learned by the end of a year, and for fourth grade, for instance, the Core consists of things like "Use the four operations with whole numbers to solve problems," "Understand decimal notation for fractions, and compare decimal fractions, " and "Generate and analyze patterns."

One can fault the Common Core for not including enough discrete math -- it really focuses on numbers, algebra, and eventually modeling with polynomial and trigonometric functions -- and one can fault America for putting people into the classroom who don't know math [1] and then telling them they'll be awarded tenure or not based on student performance on some test [2].

People are confusing the same old problems we've always had (poor teacher training, stupid cobbled-together curricula like Integrated Math mandates by school boards, teaching to tests with high stakes for teachers and little value for students, etc) with Common Core. Read the standards [3], folks, and decide based on what they actually say what you might actually think.

[1] http://www.nsf.gov/statistics/seind12/c1/c1s3.htm , http://www.math.vcu.edu/g1/journal/Journal7/Part%20I/Sterlin...

[2] http://education.ohio.gov/Topics/Teaching/Educator-Evaluatio...

[3] http://www.corestandards.org/Math/Practice/

That's a fair point - his content is certainly compatible with the Common Core's standard. I was really venting about your point [2] and shouldn't have implicated the standard for that. Thanks for the references.

There is so much to talk about re: point [2]...!

(Evaluating teachers using student test scores has been a push of the Bill & Melinda Gates Foundation, but it's not well-supported by evidence. One more link: http://www.latimes.com/opinion/editorials/la-ed-teacher-eval... )

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.

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.

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.

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.

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.

That's an incorrect slag on Common Core.

It is true that standardized tests would put pressure to ignore this sort of "enrichment" material, but that's a (Pearson) test problem and a (unfairly constrainted) teacher problem, not a Common Core problem.

Put another way:

If a student is exceeding the test standards, there is time to branch out to enrichment topics.

If a student is not passing the basic arithmetic standards of the standardized tests, it's open for debate how to reach a passing level, or if it is appropriate to engage in a major alternative curriculum.

> If a student

I think the problem is that in a vast majority of schools the classes are taught to the lowest common denominator. Sure, one , or two, or ten students could be exceeding the standards but if one or two other students are not passing the standards, I think teachers are very unlikely to introduce these enrichment topics.

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