Articulating why the Common Core State Standards are such a big change for mathematics can be challenging, especially if your audience is unfamiliar with them, like parents and other non-educators. After all, isn’t it just changing the standards? Fellow educators also feel the stress, but may have trouble stating exactly why that is. How do you describe what is so different?

The major changes seem to fall into five categories which form the acronym SPARCK. Looking at each category, you get a better sense of why this is such a big deal.

The most obvious change is that 45 of 50 states and 5 of 6 districts or territories have adopted the Common Core State Standards in lieu of their previous standards. If you’ve ever been to a grocery store that decided to reorganize the location of its products, then you’ll know what it feels like. At first you wonder if you are even in the right store. Looking around, you notice that some of the items you regularly buy are in the same place you expect them. Other products have moved to locations unknown and you either have to ask for help or find yourself wandering around looking all over for them. You even encounter new products you’ve never heard of and wonder what they’re for. This alone is a notable change and it will take teachers time to acclimate to these new standards. Real problems include dealing with students who have content knowledge gaps as a result of the transition and learning how the grade level standards fit together to form a cohesive understanding.

Teachers are not only expected to change what they teach but how they teach it. Students must have conceptual understanding and know how to apply the mathematics in addition to having procedural skill and fluency. Children will be expected to articulate their mathematical understandings orally and in writing. Some teachers have already been doing these things with their students for years and will see it as a validation of all their hard work. For other teachers it will be another huge change. It is notable that many teachers were not taught this way when they were students nor was this style of teaching emphasized when they were getting their credential. Accordingly, it is not as simple as telling someone what to do. Educators will require significant amounts of professional development to improve.

This is the biggest change in educational assessment in decades. Previous assessments were rather straightforward: paper and pencil multiple choice tests. The new assessments from Smarter Balanced Assessment Consortium (SBAC) and Partnership for Assessment of Readiness for College and Careers (PARCC) will be computer-based, have several types of questions including those that require students to explain themselves in writing, and are computer adaptive (meaning that they will change in difficulty, getting harder if students get questions right and easier if they get them wrong). Most teachers and students have never done anything like this and it will take practice to get used to it.

Some people may compare adopting the Common Core State Standards to adopting new resources like textbooks. Educators may be accustomed to using activities, lessons, or problems that were aligned to their state’s outgoing standards, so integrating new resources will take time. This alone would be a significant change. However, normally when you adopt new resources, the standards, pedagogy, assessments, and content knowledge needed to teach them do not also change. It is a different magnitude of adjustment.

Perhaps the biggest elephant in the room is that some educators will be expected to teach lessons on mathematics that they currently do not understand themselves. It isn’t their fault either, as many of the new standards were not part of the curriculum when they were in school. I am certainly one of them. I was a mathematics major at the University of California, Los Angeles (UCLA). However, in retrospect, I realize I was a math robot. I could do the mathematics well but I didn’t really understand why it worked. For example, I’ve known for years how to find the area of a circle using the formula πr^

^{2}. However it wasn’t until after graduating from UCLA that I had any clue where the formula came from or why it worked. How can teachers be expected to help students fill in these missing gaps when they haven’t had the professional development to fill their own? This too will take time.

To be clear, I am a strong supporter of the Common Core State Standards. I believe they represent a large step forward for mathematics education in the United States. If educators are feeling stressed out over this change, it is rightfully so. However, with time and support, this will get easier for all.

Robert, you make many good points, but I think you miss many important ones. First, there’s little that’s new under the sun here in terms of the Practice Standards (what you are really talking about under pedagogy). Those ideas are distilled for the most part from NCTM standards volumes dating back at least to 1989. The problem now is: 1) people who don’t have any understanding or knowledge of the history of reform efforts in US math education think that the CCSS-M Practice Standards have arrived from some NEW thinking on the part of whomever put together these standards and that is simply untrue; 2) ignorance, rejection, distortion, and misunderstanding of those Practice Standards (or Process Standards, as NCTM used to call them) is hardly new. It dates back to the early 1990s and resulted in vehement anti-progressive math groups like Mathematically Correct and NYC-HOLD. Their willful misreadings of those standards informed their ceaseless propagandizing against any meaningful reform in K-12 math teaching, fed the growth of smaller local groups throughout the country, and can still be seen, sometimes word for word, in the current attacks on the math standards the Common Core has produced; 3) there really are problems with the new Content Standards, not the least of which is the insane and often arbitrary push-down of topics into the primary grades, at the expense of what most developmental psychologists and lower-elementary teachers tell us about children. Of course, caring about children’s emotional health is not on the radar screen of many current corporate deformers, sad to say. Their focus has very little to do with kids, with teachers, with parents, with schools, or anything but $ $ $ $. And it’s damned difficult to separate in the mind of many people the truly heinous things about the overall Obama-Duncan (and Bush, and Clinton, and Bush the First and Reagan) educational policies from specific pedagogical or content changes.

So while you’re right that we need lots of professional development to improve math education, it’s not ONLY because teachers might have to teach some math content with which they are less familiar, though that’s a possible concern. It’s because many teachers in this country are well below where they need to be in their own mathematics knowledge to begin with, coupled with their staunch resistance to teaching methods that require that not only kids deepen their thinking but that TEACHERS leave their procedural comfort zone and start doing a lot more thinking about math themselves. That’s why they fought the NCTM Standards in many instances, and it’s why only a madman could believe that things are different now than they were a quarter century ago so that many teachers will warmly embrace the Practice Standards now.

On my view, even if I could support the overall CCSSI, which unlike you I don’t, I would have to assert gross idiocy or incompetence on the part of those in charge in their failure to adequately try to change teachers’ thinking about math and to prepare them for the requisite shifts in pedagogy that should have taken place over the last 25 years and did not. There is too much greed coupled with too much blindness to the reality of K-12 math classrooms pushing the standards juggernaut. It is a recipe for disaster that, coupled with anti-Obama right-wing lunacy, is going to set US math education back even further.

I agree with you that the Practice Standards are not new to mathematics education and that they come from the NCTM process standards as well as the National Research Council’s Adding It Up report. However, as these standards were not adopted at the state level, they were generally not required to be implemented in the classroom. Previous state mathematics standards, for example in California, primarily covered content and not pedagogy. Now the pedagogy is explicitly a part of what teachers will be required to do.

The other critical change is that this pedagogy will also be assessed. Previous standards may have stated that students needed rigorous mathematical understandings, but didn’t assess it on the standardized tests so it wasn’t implemented by teachers with fidelity. I also agree with you about pedagogy training being very important as I stated under “Pedagogy” that “educators will require significant amounts of professional development to improve.”

Thank you Michael for your thoughtful reply and for pushing the conversation further.

Nice (but discouraging) breakdown of the challenges facing CCSS. Also discouraging is why it is supposed to work anyway:

“However, as these standards were not adopted at the state level, they were generally not required to be implemented in the classroom. … Now the pedagogy is explicitly a part of what teachers will be required to do…The other critical change is that this pedagogy will also be assessed.”

“Required”, “required”, and “assessed”. What plan do we have when the elephantine teacher community sits down and just looks at us? Fire them all? Then whom do you hire? Uh-oh, CCSS just fell on its face after wasting everyone’s energy for years when that energy could have gone into much more interesting experiments in leveraging technology and new models such as learner-centric study.

Teachers can no longer threaten students with bad grades (thank goodness). Instead, they have to figure out conditions under which students will choose to learn. Great. Likewise CCSS enforcers need to step up their game: when has top-down mandatory global curriculum change ever worked? Math education has tried that several times since Sputnik and accomplished nothing.

The CCSS premise is that better teaching can be squeezed out of teachers by doing nothing more than setting a new bar and standing back while teachers figure out how to jump it, which presupposes that teachers are the problem. Lip service to teacher training is precisely that.

While CCSS is huffing and puffing its thinly veiled threats, educators on the ground are exploring ways to engage and energize students with, again technology and new models of education, a thousand experiments in a thousand classrooms.

If CCSS thinks it is so hot, just do a convincing pilot somewhere like the rest of us explorers. Win on the merits, not by coercion.

Thank you for your thoughts Kenneth.

Appreciate the reply, Robert. My sense of where things are heading is that the generally sound ideas in the Practice Standards will be thrown under the bus by a combination of the right-wing lunatic reactions to Common Core (e.g., “The Common Core Standards were written by Bill Ayers” – which must be a shock to Bill, who has been consistently critical of the Obama-Duncan education policy package) and broader negative reaction to the high stakes tests and their consequences. In NY State last year, for example, we got a chance to sample what public reaction is going to look like in June 2015. Instead of focusing on the absolutely crucial professional development, the folks in the USDOE will continue to play political/rhetorical games and fail to take useful action.

I’ve written more than once that for this set of standards to work (to the extent that it should work), a year-by-year roll-out coupled with serious training of cadre after cadre of teachers who actually get the Practice Standards, and a moratorium on the high-stakes testing would be absolutely necessary. Didn’t happen and won’t. The horse long ago left the barn, and 10-20 years from now, the next “Big Fix” will likely make most of the same dumb-ass mistakes this one already has. A lot of well-paid people should be giving their salaries back to the American people. And that won’t happen, either. ;^)

Personally, I stay out of the politics as much as possible. I focus on ideas that everyone can rally around such as:

– “We all want students to make sense of problems”

– “We all want students to be able to articulate their understandings”

I don’t see how anyone can be against those ideas so I spend my time working on ways to make them happen.

But in fact, there is a lot of anger directed at both of those ideas, particularly the latter. Not only students resent having to write or explain in math class. That is one of the many buttons groups like Mathematically Correct love to press. To them, coming up with the correct answer suffices and anything else is “fuzzy.” I don’t think it’s possible, in the long run, to avoid the politics, even if it isn’t manifesting itself as partisan party politics. After all, some of the most vocal members of Mathematically Correct are self-proclaimed Socialists, though the majority are libertarian, conservative, reactionary and/or Republican.

It has been my experience as both a classroom teacher and district math teacher specialist that any resistance students have to explaining themselves is temporary and more often stems from a change in the status quo. In fact, I also see students who resent NOT being asked to explain themselves when they go to a math class where that is not valued.

What I find, in general, is that students love explaining the creative ways they approached a problem. They are excited by seeing how the different approaches connect and build upon each other.

Perhaps it isn’t possible to avoid politics in the long run, but for now I am enjoying being able to focus on helping kids make sense of mathematics and becoming more articulate members of our society.

Thanks again for helping me broaden my thinking, Michael.

I am impressed with how efficiently distilled your SPARCK list is Robert. I believe it can be a very useful tool for my work with nearby districts in communicating with teachers, parents, principles, etc. what the CCSS-M “change” means. For many, it is a large hurdle to consider an integrated rather than segmented approach to implementation. The more difficult challenges are not yet understood.

I also greatly appreciate Michael’s comments. My first take on them is that they live in a discussion space not as immediate to classroom teachers. But, that district math leaders and administration need to fully understand–both the radical cultural change called for, the historic difficulties of making such changes, and the backlash that will come with high levels of certainty.

I, like Michael, don’t think the “law” will make a difference. I live and work in CA where since 1997 all students were supposed to take the equivalent of Algebra in 8th grade, and that never happened. Also in CA, the CCSS-M were adopted in 2010 and 3.5 years later I don’t believe there has been much pedagogical change at all–my focus is the HS level.

And finally, I am less certain that the CCSS-M prescribe or define a pedagogy, nor will it be assessed. I think I understand your notion that it emphasizes understanding, which to do will require a different pedagogy. But I don’t quite see any “standard” for that pedagogy defined, or a manner in which it will be assessed. I see pedagogy as teacher actions.

However, the 1991 NCTM Professional Standards for Teaching Mathematics “present[s] a vision of what teaching should entail to support the changes in curriculum set out in the Curriculum and Evaluation Standards. This document spells out what teachers need to know to teach toward new goals for mathematics education and how teaching should be evaluated for the purpose of improvement” (p. vii). This to me has been one of NCTM’s finest documents, and quite sadly largely ignored.

Thank you Brian. You mentioned that you “don’t quite see any ‘standard’ for that pedagogy defined, or a manner in which it will be assessed.” The CCSS for Mathematics require that educators “pursue with equal intensity” conceptual understanding, procedural skill and fluency, and applications. The standards that define what that pursuit will look like are the Standards for Mathematical Practice (SMP). In terms of how the SMP will be assessed, in California we are part of the Smarter Balanced Assessment Consortium. They have listed four claims that each problem they include must be connected back to. Those four claims are:

Claim #1 – Concepts & Procedures

“Students can explain and apply mathematical concepts and interpret and carry out

mathematical procedures with precision and fluency.”

Claim #2 – Problem Solving

“Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.”

Claim #3 – Communicating Reasoning

“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”

Claim #4 – Modeling and Data Analysis

“Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”

These claims match up nicely with the SMP. For example, Claim 3 is nicely connected to MP3 and MP6.

So, while I do not believe that all teachers will be proactive in adjusting their pedagogy, I do believe some will and others will follow as they see that their students are not performing as well as they hoped.

“3) there really are problems with the new Content Standards, not the least of which is the insane and often arbitrary push-down of topics into the primary grades, at the expense of what most developmental psychologists and lower-elementary teachers tell us about children. Of course, caring about children’s emotional health is not on the radar screen of many current corporate deformers, sad to say. Their focus has very little to do with kids, with teachers, with parents, with schools, or anything but $ $ $ $. And it’s damned difficult to separate in the mind of many people the truly heinous things about the overall Obama-Duncan (and Bush, and Clinton, and Bush the First and Reagan) educational policies from specific pedagogical or content changes.”

I will agree here with Michael. From my perspective as an elementary school math specialist working to help teachers and struggling students, the point he makes above is most relevant. Take a look at the difference between the grade 2 standards related to fractions (they’re not so easy to find) and the grade 3 fraction standards.

I also agree with Brian that this conversation is taking place in a discussion space “not as immediate to classroom teachers.” But the sad fact is that it is classroom teachers who have to deal with the fall-out from the emotional and psychological trauma that the testing-industrial complex inflicts on their children. Perhaps if the writers of the common core standards (math and ELA both) were not themselves part of this complex, I might view them with a different lens. But I can’t and I don’t.

Thanks Joe. I appreciate your comments. Yes, there is going to be a lot of fall out from the transition to the Common Core State Standards. Clearly there is no perfect solution, but I believe that they are a step in the right direction.

Also, thank you for the kind words. I just checked out your post on the highway sign lesson. Very cool. Do you mind if I link to it from the lesson? Have you seen the new butter fraction number line lesson?

Go right ahead and link away!

I have not seen the butter fraction number line lesson yet, but will check it out.

Thanks again.

And Robert, I’d also like to let you know how important your work has been to mine. I’ve used the highway sign project and the movie theater project, which have been the subjects of detailed posts at my blog: exit10.blogspot.com

I continue to mine your site for meaningful activities and thought-provoking content. Thanks!

Typo: that’s exit10a.blogspot.com