$\begingroup$

I'm really wondering if this is the end of the world or the beginning of an improvement in the way we teach math.

I'll answer this first, and then talk a little bit about the rest of the question. Please excuse my bluntness. I will try to give you the opinion you ask for by weighing what I think may be most important relative to quality of math education. Black and white is not my usual style.

When you say "Common Core" you must, primarily, be referring to the Common Core State Standards (CCSS). And in this context, the Common Core State Standards for Mathematics (CCSS-M)

No, it is not the end of the world. Yes, it is (or should be) the beginning of an improvement in the practice of math education here in the US.

WHY? The shortest answer as to why this is definitely an improvement lies in the CSS-MP, the practices portion of the Common Core State Standards. In short, the CCSS-M include a list of eight practices which, as a math person, you would likely recognize as good mathematical habits of mind related to the sense-making aspect of mathematics. Summarized, they are:

Problem solving and perseverence Quantitative reasoning Mathematical argumentation (reasoning and proof) Mathematical modeling with data Strategic use of tools (representations, technology, etc.) Attention to appropriate precision in calculation, communication, claims, definitions Seek and make use of structure Generalize from repeated reasoning

(Some may not like my summaries, so it's best just to look at the descriptions themselves.)

It is the case that not all states had these practices (or the notion of an explicit focus on mathematical practices) in mind in their existing frameworks and standards. So, this standardizes the recognition that there should be an explicit focus on these aspects of mathematical thinking in mathematics education rather than standards simply existing as a list of what content comes in what order and hoping that the students develop good habits of mind along the way.

Here you can listen to Prof. Alan Schoenfeld briefly make a similar argument.

This may not be the argument you hear most often in defense of the CCSS. There is the general defense of standardization, which is described in this short video. Essentially, that IES noticed great variability in the quality of education from state to state. NAEP testing revealed that the states had varying expectations, the results of which were only uncovered in NAEP testing done across the nation.

That is an important issue in itself, but in the potential CCSS-M has for improving math instruction, I see the mathematical practices as their best contribution.

NOW - These are standards, not curriculum. For political reasons, it was important to not dictate curriculum or specific pedagogy. Therefore, how a state adopts these standards, what curriculum they choose, and whether they put any effort toward supporting teachers in doing what is necessary to develop students' mathematical habits of mind is a local decision. And it is a decision with fiscal and other resource implications. There are some serious political implications here that I will not divert into.

Suffice it to say, YES to that part of your question, though states and districts will have to take the practice standards to heart, lead teachers to appropriate formative assessment lessons that both develop student mathematical reasoning and help teachers determine their students' progress in that development.

But why do I "hear all sorts of stories ... horror stories mostly ... about the Common Core math curriculum?"

Firstly, the reason you're hearing "Common Core math curriculum" because there is curriculum that claims to be "aligned with the common core." The actual problems you may see with this curriculum may have nothing to do with the standards. You may even be seeing problems arising from a misinterpretation of what the standards call for. Or a pedagogy that does little to encourage the practices, but it claimed to be aligned simply because it took a traditional approach and mapped it to the content standards.

Or, you could also be seeing an actual attempt to help students reason in some way aligned with one or more of the practices, but at an appropriate grade level. For instance, before students can do formal proving, they may be developing an understanding of the role of justification in mathematical reasoning, and engage in informal proving and argumentation. Students may well be asked to do things that their parents simply do not recognize as mathematics because they were never asked to, for example, reason quantitatively (Smith III & Thompson, 2008).

Why have I maybe heard "that it's better for the smart kids but it's elitist?"

I'm actually not sure. I haven't actually heard this. It is possible that some are worried that higher standards, in some cases will cause test scores to temporarily drop. That may well be the case. But a period of transition may not be able to avoid this, and the point is really the learning, not the scores themselves.

What other attacks are there on the CCSS?

Some see it as a states rights issue. But you asked about education, and I think that is the appropriate focus, unless it is a discussion among lawyers, which can happen elsewhere.

Some want more local control of the content standards. Today, a wise math ed researcher I know pointed out that the NCTM Principles and Standards for School Mathematics takes a wider grade-band approach, which would have given states, districts, and teachers more flexibility in their local use of the standards. My personal opinion is that a desire to hold individual teachers accountable within a school year (i.e. the ability to use standardized assessments to apply a Value Added Model to teacher evaluation) is embedded in these standards and some of the standardized assessments that are being developed. This is something I wish they'd change about the standards (and something I think they could change). Combine grades into bands and hand some flexibility to the states. But I'm not in charge of them. And I see the presence of the mathematical practices to be more significant in possibly improving instruction.

Some are disturbed by all the standardized testing that is going on. This is reflected in some states that have withdrawn from the common core-aligned assessments. I will note that this is not necessarily related to the question about improving math instruction, however, it definitely could be depending on how districts change their schools to prepare for tests. It is understandable that a burden of test preparation is a serious concern for teachers, and it is also understandable that it has so often been conflated with the standards themselves (we call them standardized tests, after all, and they are definitely related). However, getting rid of the CCSS-M wouldn't stop standardized testing. In that sense, attacking Common Core State Standards because of issues over testing is barking up the wrong tree. This is a bad thing because it won't lead to desired results.

I think there are no publications on this yet, but there are people working on providing tests that score along multiple dimensions and help teachers gain an understanding of how to help their students rather than just one score that will be used to evaluate teacher performance. And there are people working to provide materials that help teachers "teach to the test" in a way that develops mathematical reasoning rather than just developing a higher score on the test. That sort of thing is possibly coming in the near future. But it depends on the type of tests states adopt.

Anything else?

Yes. There are people who fundamentally disagree with certain research-based approaches to math education, preferring a more traditional didactic approach. See my previous answer here for just one thread of research that shows how there are multiple dimensions to mathematics education, and implications in traditional approaches that we did not realize were interfering with both math learning and with how students decided to go on to further study in math and related fields.

There are political wars that buffet math education, and math wars (Schoenfeld, 2004) that have produced political movements to quash certain kinds of curriculum and instruction reforms. Some of these people tour the country to fan the fires of their complaints, knowing that parents showing up at school boards has been effective for them in the past in opposing the kind of instruction reform they disagree with. While I respect differences of opinion, I cannot always say I respect the political approach to winning this sort of debate, or other, even less noble, approaches.

Long story short, some of this stuff will also show up on social media because some people are specifically attacking Common Core State Standards as the new manifestation of reform they have long opposed. Ironically, many of the reformers they oppose would not have written the standards this way. They're very much a compromise. I wanted to include this information mainly to explain that there is another motivation out there for some of these attacks/complaints.

Finally

I have not gone into legitimate, educational complaints about the CCSS-M (other than the grade band issue) mainly because you asked for an opinion and I have provided the arguments to explain my opinion. There are ways to improve the standards that I think are worth exploring some time later.

Cited:

Schoenfeld, A. H. (2004). The Math Wars. Educational Policy, 18(1), 253–286. doi:10.1177/0895904803260042

Smith III, J. P., & Thompson, P. W. (2008). Quantitative reasoning and the development of algebraic reasoning. In J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 95–131). New York, NY: Taylor & Francis Group.