# Some Perspective on Common Core

Policymakers and reform advocates alike have rallied around introducing a set of national content standards, suggesting that this will jump start the stagnating achievement of U.S. students. As history clearly indicates, simply calling for students to know more is not the same as students actually knowing more. The largest problem is that the discussions of common core suck all of the air out of the room, distracting attention from any serious efforts to reform our schools.

To be sure, it is a real problem when students in one state learn very different things than those in other states, and in particular when students from some states lack the skills needed for our modern economy. We really do have a national labor market, and significant numbers of our population end up living and working in a state different than that where they were born and went to school. The presumption behind having national standards is that having a clearer and more consistent statement of learning objectives across states would tend to lessen the problem of heterogeneous skills that students bring to the labor market. Again, however, the fundamental problem is lack of minimal skills and not the heterogeneity of skills per se.

We currently have very different standards across states, and experience from the states provides little support for the argument that just more clearly declaring what we want children to learn will have much impact. Proponents of national standards conventionally point to Massachusetts: strong standards and top results. But, it is useful to expand thinking from just Massachusetts to include California, a second state noted for its high learning standards. California balances Massachusetts: strong standards and bottom results.

In other words, what really matters is what is actually taught in the classroom. Just setting a different goal – even if backed by intensive professional development, new textbooks, and the like – has not historically had much influence as we look across state outcomes.

The continuing emphasis on common core standards, including the debates about the legality of them, is often interpreted as indicating that the common core is a really big deal in school reform. The data suggest otherwise.

The one possible complementary gain from the move to national standards is that the assessments of performance might become better. It is widely recognized that the current tests used to judge outcomes within individual states tend to be quite weak. If the new standards lead to better tests – something that might come out of the two testing consortia funded by the U.S. Department of Education – we might have the basis for improved school policies. But, that is also not certain and cannot be used as a primary justification for the focus on common core standards.

Indeed, moving to these new, untested tests may make it impossible to have continued accountability of the schools for results. At the very least it will cause a moratorium in continuation of state accountability programs even though these programs have had a consistently positive impact on student performance.

One interpretation of the emphasis on developing the common core curriculum is that these debates provide a convenient diversion from potentially more intractable fights over bigger reform ideas like using improved teacher evaluations for personnel decisions, expanded school choice, or enhanced accountability systems.

I am not against having better learning standards, but I also believe that we cannot be distracted from more fundamental reform of our schools. My recent book with Paul Peterson and Ludger Woessmann, * **Endangering Prosperity*, argues that the future economic well-being of the U.S. is entirely dependent on improving the achievement and skills of today’s students. The Common Core per se does little to ensure improved student outcomes.

-Eric A. Hanushek

*Eric Hanushek is the Paul and Jean Hanna Senior Fellow at the Hoover Institution of Stanford University.*

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You have omitted one important aspect with respect to mathematics education. The Common Core has tried to replace what Hung-Hsi Wu has called “textbook school mathematics”, which bears little resemblance to mathematics. For example, in the 2011 TIMSS eighth grade test, one question was which of the following four methods should be used to compute 1/3 – 1/4. The first is (1-1)/(4-3) which cannot be correct since it is 0 and 1/3 – 1/4 is not. The second is 1/(4-3) which cannot be correct since this is 1 and 1/3 – 1/4 is less than 1. The third is (3-4)/(3*4) which cannot be correct since it is negative. The last is (4-3)/(3*4) which is correct, since 1/3 – 1/4 = 4/(3*4) – 3/(3*4) = (4-3)/(3*4).

Here are a few representative results, percent for each.

1 2 3 4

International Average 25 26 9 37

South Korea 3 7 4 86

US 32 26 11 29

Finland 42 29 9 16

Some countries know how to teach fractions, others do not. The Common Core does this well, and many teachers now want help in learning the material so they can teach it as suggested in the Common Core. The realization of need for better content knowledge is new and may make the it easier for the Common Core to lead to better results.

If readers find the result for Finland surprising, here is a link which helps explain why this was not a surprise to some:

http://solmu.math.helsinki/fi/2005/erik/PisaEng.html

How will national standards assist the intellectually impoverished children modern families deposit on the doorstep of politically focused and controlled schools? It seems professional educators of all sides are afraid to address the fundemental problems of America’s schools: poorly prepared and unsupported children in the home; and, control of the local schools by teachers’ unions whose interests conflict with the interests of the children and public. If I am correct, why is this? If I am wrong, how so?

The Common Core has several virtues. Richard Askey (above) has pointed out one, a better approach to fractions. It also has some better approaches to place value, and to word problems, than most previous state standards. These are major pieces of elementary math education, and improving our approaches to them sets the stage for substantial improvement. However, the article is quite correct to point out that standards by themselves do not guarantee high achievement. The most disappointing aspect of the essay above, and of many discussions of the Common Core, is the failure to call for using the standards as an occasion to provide support to teachers to do better. Lack of adequate formation and ongoing education for teachers is the major source of failure in our education system. To the extent that the Common Core is used as a way to avoid addressing that issue, its impact will be negative.

The link to comments on math education in Finland is

http://solmu.math.helsinki.fi/2005/erik/PisaEng.html

Sorry about the typo.

I will limit my comments to mathematics education only.

Professor Hanushek correctly identifies the problem: “what really matters is what is actually taught in the classroom.”

In order to improve what is actually taught in the classroom, two among the many obvious issues are critical. One is that the content must be good enough, and the second is that the teachers must be able to teach this content.

The CCSSM represents an attempt to address the first issue. It falls short of the ideal, but comes closer than any other sets of standards in the past 24 years. To address the second, we need massive content-based professional development. As of 2013, there has been basically no movement in this direction.

I am dismayed that Professor Hanushek is completely silent on the second issue. There is a tremendous disconnect between the existing content-knowledge gap among math teachers and what Professor Hanushek seems to consider to be more pressing: “bigger reform ideas like using improved teacher evaluations for personnel decisions, expanded school choice, or enhanced accountability systems”. None of these matters one bit if teachers have to teach what they don’t know.

The following passage may explain this disconnect: “intensive professional development, new textbooks, and the like – has not historically had much influence as we look across state outcomes.” Professor Hanushek may have been misled into believing that the so-called “intensive professional development” have really addressed this content-knowledge deficit, and that the “new textbooks” have been an upgrade over the older ones. I wish either were even remotely correct.

In Askey’s example of an international math exam I already found it disheartening that the word “method” was used to describe a formula. The method for subtracting fractions gives the teacher (and the composer of exams) a wonderful opportunity to teach something very mathematical, while what has been happening, as the international choices of the answer exhibit, has been nothing but wild international guesswork, senseless attempts to evade what today’s teachers and examiners consider “too hard” for the sensitive youngsters to obtain by means of mathematical reasoning.

One should teach students at that level about equivalent fractions and how to create them, and how to add or subtract two fractions with the same denominators. (Both of these are easily understood when exhibited on a number liine.) It then becomes easy to arrive at a fraction for 1/3 – 1/4 without floundering in search of “the formula” for the result. Does common core mention “equivalent fractions”?

Ralph,

The Common Core does treat (and mentions) equivalent fractions extensively starting in grade 3 and through grade 5, and then it continues with the concept through equivalent ratios, and then equivalent expressions, in grades 6 through 8.

So, in one sense, one can say that the Common C ore represents a clear improvement and that it addresses very well the mathematics you think is important. That is the case that Wu, Askey, and also many less astute observers of the Common Core argue.

Yet there is another way to view the Common Core effort, while accepting that their mathematical content is reasonably coherent and that it overwhelmingly stresses points that make a lot of sense to mathematicians.

This view has to do with pedagogical efficacy and pedagogical evidence of Common Core’s approach. Taking the concept of equivalent fractions (EF) as your example, it is not only that they are mentioned, but they are *extensively* mentioned. So, in grade 3, we have four (out of 37) standards dealing with EF. In grade 4, we have six (out of 37) and in grade 5 another four (out of 38). And not only is the concept mentioned, but the standards are strongly prescriptive as to *how* EF must be presented — and tested — to student in each and every grade. In a similar vein, triangle congruence and similarity are handled in grade 8 and HS geometry not as a standard or two along the lines of ” “Prove that triangles are congruent [or similar]” but rather as a massive number of detailed and prescriptive standards (7 out of 36 in grade 8, 13 out of 45 in HS geometry) that dictates to teachers and students *how* precisely they are expected to go about it — and how precisely they will be tested on it.

The problem with this approach is twofold. First, we have no idea whether the *pedagogical approaches* peddled by the Common Core with such doctrinaire zeal are actually helpful for mathematics *instruction.* Certainly they are absent (or at least invisible) in the standards of high achieving countries like Singapore or Korea. Even more worrisome is that we know from the original New Math experience that ideas that make a perfect sense to *mathematicians* are not necessarily helpful — to put it mildly — in the context of large-scale instruction. The above-mentioned example of congruence-related standards is a classic example of this danger – – it may make a lot of sense to mathematicians yet it was an abject failure with actual students, even very gifted ones, when tried in school. Expecting that it will beget anything but failure when imposed on the nation’s 50 million students is (non-mathematically) naïve.