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I have a background in math but no contact with secondary education or kids. I hear all sorts of stories ... horror stories mostly ... about the Common Core math curriculum in the USA. Then I hear that it will lead to more mathematical thinking so it's actually better. Or maybe that it's better for the smart kids but it's elitist.

Can I get some opinions from people who have actually seen or dealt with the Common Core material? I'm really wondering if this is the end of the world or the beginning of an improvement in the way we teach math.

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This question tackles an important point that we should discuss and I am eager to see answers, but I have somhow the feeling this is a bit broad and should somheow made more focused. –  András Bátkai Apr 30 at 6:29
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This is yet another country-dependent question on MESE. While I have no problem with such questions, I'd love to see an explanation (or at least a link to one) of what "Common Core" is/consists of exactly. –  mbork Apr 30 at 8:40
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Perhaps the usa tag should be added to the post? –  Joel Reyes Noche Apr 30 at 14:07
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It is a problem in this domain that people may need assistance in getting to the point where they can ask more focused questions. I am not confident editing people's questions at the moment; a more focused version of (or addition to) this question might be: Can we expect the Common Core State Standards in Mathematics to improve mathematical thinking in US schools? If so, how? If not, why not? –  JPBurke Apr 30 at 14:10
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"Common Core" implies "USA" only to people who already know what the Common Core is. For everybody else, it implies nothing at all! It would be helpful if people asking questions about a specific country could include the name of that country explicitly in the question. –  David Richerby Apr 30 at 17:19

4 Answers 4

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:

  1. Problem solving and perseverence
  2. Quantitative reasoning
  3. Mathematical argumentation (reasoning and proof)
  4. Mathematical modeling with data
  5. Strategic use of tools (representations, technology, etc.)
  6. Attention to appropriate precision in calculation, communication, claims, definitions
  7. Seek and make use of structure
  8. 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.

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In addition to what you listed, I've noticed that some people also look at any attempt at math ed reform and run for the hills going "math reform = another new math = bad because pop culture told New Math was bad!" (I'm not qualified to offer a reasoned critique of New Math either, mind you, but I find this chain of reasoning pretty common in Common Core criticisms). –  Jsor Apr 30 at 6:35
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Yes, it's pretty explicit in the term "New new math" that you will hear. If you want to know more about "the New Math" you might be interested in Bob Davis' chapter on education reform in which he argues that "any claim that there was a well-defined 'new math' is entirely unfounded." –  JPBurke Apr 30 at 6:52
    
Davis, R. B. (2003). Changing school mathematics. In G. M. A. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 623–646). Reston, VA: National Council of Teachers of Mathematics. –  JPBurke Apr 30 at 6:53
    
+1 for the formative assessment link to map.mathshell.org -- I think anyone with a math background looking through those will be able to appreciate that it's really good math being taught, but might also be able to appreciate why "traditionalists" might feel that it's less "efficient" than just drilling standard algorithms. –  PurpleVermont May 14 at 21:46

Edit (7/17/14): You can find a very informative flow chart about CCSSM here to show dependencies among standards. At the time of posting, the page covers the standards included for K-8.


If by "material" you mean CCSSM lesson plans, then it is important to draw the distinction between standards and curricula. JPBurke makes this distinction in his answer, but I re-iterate here that there is a dearth of standards-aligned material (which will be important when students - and probably teachers, schools, and so forth - are assessed based on CCSSM).

For example, a major difference between CCSSM and previous standards and curricula is its inclusion of mathematical modeling (as both a Standard for Mathematical Practice at all ages, and its own strand at the secondary school level). I have yet to see real materials for teaching modeling; moreover, I think many teachers are not only unsure as to how they should teach modeling, but - in many cases - are not even sure what "mathematical modeling" means. The short bit in the standards is not very illuminating, even with its diagrammatic representation of the process. Others have written about the subject (e.g., Blum, Ferri, Pollak) and there is a recent thesis by Gould on teachers' (mis)conceptions about modeling:

Gould, H. (2013). Teachers’ Conceptions of Mathematical Modeling (Doctoral dissertation, Columbia University). Link.

As for personal experiences with the Common Core State Standards for Mathematics: A former classmate of Gould's, "Master [mathematics] teacher" Heidi Reich, recently had her letter about CCSS impressions published in the New York Times. It is entitled: A Teacher's View of Common Core.

The full version is available on the site (and was linked to by this blog); here is the main part:

I am a teacher and have been for 15 years, which means I am right in the middle of my career. I have been recognized for my teaching by Math for America (I have been a “Master Teacher” for eight or so years now), am locally respected (sorry, no data to support that) and have loved my job for all of these years. Now I find that the nutty wacky whims of the Department of Education under Bloomberg and Klein have been dwarfed by NYS and the federal government’s desire to implement truly difficult standards in a matter of months. We (teachers) are required to write curriculum based on almost NO information, tailor said curriculum to testing about which there are NO data, and still teach our five classes of 34 students a day without skipping a beat.

I imagine you are thinking, why do you need to tailor curriculum to tests, especially if the tests don’t even exist yet? Sure, it has something to do with our jobs being on the line if our students don’t surpass some standard or other (sorry, but to us it all seems just so very arbitrary), but more to the point, no reform means anything until you see what assessment is going to be. We are accustomed to writing our curricula by determining what it is we want our students to be able to do and then designing activities and lessons to convey those expectations and to train students to accomplish goals. It would be duplicitous for the powers that be to withhold those expectations from us if they were even close to having established them, but we are all too aware that, unfortunately, Pearson and others are scrambling madly to write tests (for billions and billions of dollars) that they have no time to field test, which has already resulted in chaos and utter confusion in lower grades in NY State. My colleagues and I have NO problem holding students to high standards as long as those standards are clearly conveyed to us and as long as we have time to develop appropriate curricula and activities. (We would have used the summer to do this if the standards had been available before September — not happily, but we would have done so.) The current situation is diametrically opposed to that. And I must reiterate my disappointment that The Times, the only paper of record as far as I am concerned, totally missed the point: that parents and students and educators are ALL up in arms about the Common Core, not just extremist politicians on both sides, because to us, the Common Core standards are not even standards. They are vague ideas being developed (for huge personal profit) by billionaires and testing companies, imposed upon teachers, students and parents with complete disregard for education, learning and progress.

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MAP is developing lessons targeted to the standards. Here is an example of a lesson on Modeling in Grade 8. –  JPBurke Apr 30 at 14:19
    
@JPBurke I suppose I am mostly skeptical about materials for teaching mathematical modeling without knowing what the subsequent assessments will look like. COMAP published a handbook on mathematical modeling lessons (to which I contributed a few at the behest of those involved) but I cannot say how valuable a resource it is/will be. I am familiar with the UCB/Shell Center collaboration; I recently co-edited a festschrift for Henry Pollak (the mathematical modeler) with articles from Schoenfeld (UCB) and Burkhardt (Shell). There should be a copy online soon that talks a bit about modeling... –  Benjamin Dickman Apr 30 at 15:00
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I understand your skepticism. I maintain that the standards can improve instruction, but tests will likely drive what really happens in classrooms. My state is testing out PARCC tests now. I won't go into detail about my opinion there, right now, but I prefer the approach that Smarter Balanced is supposed to be taking. I am disturbed that tests today seem more about supposed accountability and less about learning and the instruction we need to support it. It's an odd situation when the test is no longer a tool for teachers, but teachers seem to become subject to the test results. –  JPBurke Apr 30 at 15:16
    
The standards give many examples of modeling in Appendix A, in the places marked with a star. The stars are explained at the bottom of corestandards.org/Math/Content/HSM, and the stars appear starting on p. 17 in the appendix at corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf. While this does not cover assessment, I do find it illuminating on "what mathematical modeling means" in this context. –  Matt F. May 12 at 20:20
    
@MattF. Thanks. I am aware of the asterisked points; some remaining issues are: (1) what will mathematical modeling mean once the corresponding examination/assessments are instituted; (2) how will teachers who have never learned about mathematical modeling develop lesson plans and/or teach these examples effectively (what does the average secondary school teacher glean from: "Engaging in critical path analysis, e.g., applied to turnaround of an aircraft at an airport" from your first link); and (3) objections to the CCSSM modeling definition... see some of the authors I cited in my post... –  Benjamin Dickman May 12 at 20:33

Working in a district that has been "ahead of the curve" in preparing teachers about the CC, I feel confident in what the Core has to offer. On the other hand, the parents are still unsure about it. The negative feedback is the typical stuff you see on FB, etc., coupled with the statement, "My kid already knows how to ______ (in math)." The reality is that they have memorized a process, but don't understand the process or concept. Ok, so they are efficent at something -- they aren't quite sure what though. The sad examples of someone's attempt to show what CC is on social media is a joke. Plus, the dad's angry letter to his son's teacher about math homework shows how ignorant parents are about this topic.

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Plus, the dad's angry letter to his son's teacher about math homework shows how ignorant parents are about this topic. Are you referring to something that you forgot to link to? –  Ben Crowell Apr 30 at 18:55
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Referring, undoubtedly, to this piece which was viral on Facebook earlier in the year about a dad with an engineering degree not understanding a number line. A very good example of someone wholly misunderstanding the common core standards and what they're trying to teach. –  Joe Apr 30 at 20:32
    
@Joe: That is a bad example of a number line.. probably due to the rush to create curriculum for the new standards. My daughter is in 2nd grade and we see her homework with number lines often. I can see how this example is confusing. The pieces of bad curriculum and worksheets do nothing to advance the Common Core cause. My daughter's teacher is smart enough to throw out bad worksheets or tell the kids not to do that page because it's either too confusing or wrong. A better number line would have had bigger bullets for the 10's place. "Jack" should have subtracted one ten and 5 ones to get 111 –  staticx May 1 at 14:59
    
@staticx, I think you mean "one ten and 6 ones" –  Joel Reyes Noche May 1 at 22:29
    
@Joel: yes, but does it matter? –  staticx May 1 at 22:31

In regards to early education and specifically the math of the CCSS, I have a link. This is a new blog post that ultimately tries to wade in by outlining several OTHER blog posts that all make good points.

Some of the main points being offered is that you have to separate the STANDARDS themselves from the question of whether they are being implemented well, whether there is the professional development and knowledge amongst teachers to use them the way they are meant to be used, whether the textbooks that are "aligned" are actually well done, etc etc etc.

As many are stating, there is plenty of good that can come from the standards, but there are many other things at play. They can be implemented poorly and actually make things worse... or at least not any better.

4 Blog Posts to Help Understand the Common Core Math Standards Debate

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