Gifted Issues Discussion homepage Forums Identification, Testing & Assessment Common Core Mathematics: background

I came across this article about Common Core mathematics tonight. It's wonkish but well worth the effort of reading in its entirety. A quote:




These are just bits and pieces. The author has a lot to say about how to teach math in a more meaningful way and deficiencies in teacher education in mathematics. I don't agree with everything he wrote, but the article is very thought-provoking and encouraging about the Common Core.

Here are some newer follow ups:

This one is by the author of the article quoted above.

A math ed. blogger

Thanks for the link. Very insightful. About halfway through, and the big point seems to be there is a common misunderstanding of the word understand. Existing, pre common core, textbooks have drifted away from teaching "understanding" of math to training in math techniques. If schools+parents+teachers+curriculum writers continue to misunderstand "understand", then the potential of common core would be lost.

I was blown away by his explanation of the distributive property proving that a negative times a negative equals a positive. I don't think that was taught in the seventies. Now I really want to make sure DS has that understanding (weekend mission, if sewing costumes leaves any time for it.)

i.e. you can't train thinking

Right.
(-1)x=-x
is not an axiom. It has to be deduced from the axioms.

I agree; good read. Thanks for sharing that. I'm just trying to really figure out what elementary math really is so I can figure out what DD needs.

Thanks so much for this link, Val.

Interesting - thanks for posting it. I read the entire article as well as the first follow up. They make some valid points. I also have no doubt that Professor Wu's assessment is correct for a subset of the schools in this country as well as for a subset of elementary teachers. However, many of his observations have not been my experience or my children's experiences over different decades. Many of the textbooks are definitely lacking. However, in our school district, the math textbook is not the only source of the math curriculum or math assessments. The distirct office develops curriculum and assesments to use with the textbooks and the gt classes in particular have utilized curriculum developed by well-known gt education experts. For example, the way of teaching fractions over several years that Professor Wu recommends is the way that I learned fraction at my school and the way that my three children have been taught in their school. That is one of the reasons that the elementary curriculum spirals because the ideas are presented with increasing complexity over the years. His criticism regarding the misfocus on "variable" rather than "symbol" in algebra was interesting. I do believe that one of the reasons why elementary schools started teaching "elementary algebra" was to emphasize/develop the symbolic aspect. That is why in first grade, the curriculum introduces 7 + ? = 9.

Based on our limited samples, I must also disagree with his thinking that university mathematics is not sufficient to provide capable elementary math teachers. All the competent math teachers that my children have had over the years were trained in higher mathematics and it appeared to me that was the reason why they taught elementary math so well. The incompetent teachers were ones who did not have the advance math background. Again, obviously Professor Wu had a large sample of his own students from his training camps with which to draw conclusions so surely there is some validity to his conclusions. However, I do posit that his sample may not have been entirely representative.

I agree with Quantum2003- my kids would be hard-pressed to tell you which textbooks their school uses (as would I!) because much of the curriculum is developed by the district/teachers themselves. They use textbooks, but only as one of many resources.

FYI for all, this document lays out Professor Wu's ideas about how to teach fractions. I'm about to go over the third grade stuff with my DD, having just written up 6 pages of lessons. To me the differences between what see coming home from school and his stuff are subtle, yet profound. Wu's stuff builds a foundation of knowledge about how everything fits together, whereas the stuff I've seen from my kids' schools doesn't. The kids can manipulate stuff very well, but they aren't shown all (or most, really) of the connections.

Quantum2003 and cricket3, did you and/or your kids learn Wu's ideas?

Thanks again, Val. These are great links.

Yes, Val, his examples are exactly how those topics were covered. The fraction examples in particular could have been straight from their materials.

I do think our school is an outlier, though. I still don't really understand why, but they began common core implementation much earlier than other NY schools, it seems. The kids were ready for the new assessments, and overall did quite well (tiny brag- both my kids, while good at math but not math-lovers, got perfect scores). But the real news, in my opinion, is that many of the kids seem to be learning it and learning it well.

Disclaimer- one big downside, (which I assume is related to the common core implementation, though not sure) is that the district does not accelerate or skip, until 8th grade. The "accelerated" class my 8th grader has been waiting for years for, a high-school credit regents class which supposedly covers about 2 years of material, is still agonizingly slow for her (and almost half the students are in this accelerated class). And she has an A+ average without studying, etc.- a real disappointment; we are hoping but not optimistic that by the time DS gets there things may change.