kitchen table math, the sequel: Should We Be Worried? (YES)

Sunday, June 5, 2011

Should We Be Worried? (YES)

Core Standards Are Very Different
The new standards are supposed to be internationally benchmarked. Yet Common Core’s eighth-grade math standards don’t match Finland (0.21), Japan (0.17) or Singapore (0.13), primarily because these countries stress performing procedures. On language arts and reading, alignment ranges from 0.09 with Finland to 0.37 with New Zealand.

Should we be worried? Common Core Standards represent “a change for the better” when it comes to “higher order cognitive demand,” Porter concludes, but the “answer is less clear” when it comes to the topics that are covered.

Personally, I would say the "answer" is perfectly clear!

How Big a Change are the Common Core Standards?


gasstationwithoutpumps said...

I wouldn't put much credence in the results of this study. The paper published in Educational Researcher was very sloppy. See my blog post at

Allison said...

The study has a lot of issues. GSW/OPs has done a lot of work showing the bizarre methodology
(or lack thereof. ) Read that. In addition, I'll add some other issues that are ignored by the paper.

They cite "eighth grade math standards" but fail to address that these nations do something very very different than we do. Singapore, for example, splits its population after grade 6 into different math curricula--because by grade 6, they are tracked for different kinds of education. The US does nothing comparable at all. So what does it even mean to "match" three different sets of standards? Nothing, Assuming they compared against one, why didn't they discuss which one? Japan, for example, covers much LESS material than the US does, even in the Common Core--they have even fewer topics, and cover it much more slowly but deeply. (The idea that Japan is stressing procedures at this point is bizarre--the 8th grade Japanese textbook has nothing of the kind in it. Where did they get this notion?) How do you value the matching issue when the US teaches measurement and Japan doesn't? Does CC "match" better than current states or not in this regard? Next, why did they pick 8th grade? Because that's the data they had--not because they were determining the cumulative math taught in, say, grades 6-8.


Allison said...

Now, to the bigger issue: the oft cited complaint about Common Core is that it doesn't move "fast enough" to get all students to algebra 1 by 8th grade--and that some states have more "rigorous" standards by demanding that all students take algebra 1 in 8th grade. Critics suggest that the International standard of algebra 1 in 8th grade is not met by Common Core.

First, many people think that the earlier we get to algebra, the better. Their idea, implied if not explicit, is that acceleration is really is equal to rigor, and we can get rigor if we just get to more rigorous math faster. They come to this conclusion because what the US does prior to algebra is utterly non-rigorous, even in states like MA, and they mistakenly assume that there is/was never any rigor in the arithmetic/fractions/pre algebra courses taught to children--so they just want to get to the rigorous algebra course.

Generally then, US students are moving through a shallow curriculum prior to algebra and then find themselves completely unprepared for an authentic algebra course. Getting to algebra faster does nothing to better prepare our students. Worse, the move to "teach algebra earlier" has resulted in algebra classes being even less rigorous than before, since the students can't really handle this material, since they were never given the breadth and depth of preparation needed to master it.

Of course, there are some students who can handle the acceleration, and some students who need to be moved ahead much more quickly. But even these students find themselves ill served by the elementary and middle school math they took before moving on to algebra, because they were mistaught.

This shallow math curriculum in middle school (grades 4-8) lacks
1) coherence
2) appropriate precision--the use of precise definitions to work with mathematical ideas
3) exposure to symbolic manipulation and abstraction

Without all of these three elements, students do not develop mastery of school mathematics.
International comparisons in 8th grade, then, are apples and oranges. Each country has tackled the problem of weak math knowledge in elementary school in different ways: most have created national curricula, most have vastly different requirements for teacher training, vastly different models of preservice and inservice, exceptionally different methods of tracking/sorting students. Many of these changes result in more rigorous elementary mathematics education than the US has because the teachers' knowledge of mathematics is much stronger; some result in big changes in the population being taught. Should CC standards be written so as to be impossible to implement practically?

The math standards in the Common Core for these grades are significant improvements along these lines. The standards are coherent from year to year, and demand teachers incorporate more precision, more definition, and more exposure to symbolic manipulation and abstraction than any other standards out there have done previously.

So, while Common Core doesn't push a full year of authentic algebra in 8th grade, it does push the underpinnings to be solid--and that is a necessary condition for success in getting to algebra.

Should they have done more? Given how difficult it is to get consensus, my vote is no, they shouldn't have pushed to get to algebra 1 faster. There is no fundamental need to get to it earlier; there IS a fundamental need to get to it with sufficient mastery of the underpinnings to ensure success when it's reached.