I’ve heard the phrase the “Common Core way” several times this summer, as in “we used to teach math differently, but now we do it the Common Core way”. I want to unpack that idea.

What does the Common Core actually say about teaching and learning? Let’s look at the standards. There are exactly three points the standards make (pg. 3-8) before they dive into the content standards.

**Toward Greater Focus and Coherence**

To deliver on the promise of common standards, the standards must address the problem of a curriculum that is “a mile wide and an inch deep.”

We can argue about whether the standards actually achieve that goal, though I’m confident they are an improvement over the median state standards that preceded the Common Core.

**Understanding Mathematics**

One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity,

whya particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as(a + b)(x + y)and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding(a + b + c)(x + y).

We want students to understand, and one tool to probe for that understanding is to ask kids to explain a piece of mathematics. Nothing groundbreaking here.

**Standards for Mathematical Practice**

The Standards for Mathematical Practice describe the ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle, and high school years.

The Standards for Mathematical Practice focus on what students should be able to do — to reason abstractly, to construct arguments, to model, to make use of structure. Good to know.

**Key Shifts**

We can also look, separate from the standards themselves, at the key shifts:

- Greater focus on fewer topics
- Coherence: Linking topics and thinking across grades
- Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity

Nothing surprising here. Again, we can argue about whether the Common Core meets these goals, but these are goals worth working toward.

**The Standards**

Finally, there are the standards themselves. Does the content of the standards dictate instruction? Let’s look at the progression toward adding and subtracting fractions as an example.

**3.NF: **

- Develop understanding of fractions as numbers

**4.NF:**

- Extend understanding of fraction equivalence and ordering
- Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers
- Understand decimal notation for fractions, and compare decimal fractions

**5.NF:**

- Use equivalent fractions as a strategy to add and subtract fractions

These standards, like many other places in the Common Core, progress across several grades. First students should know what fractions are. The next year they should be able to compare fractions and think about them in multiple ways. Finally, they are ready to perform operations on them.

The standards also give an example of how students can link their previous knowledge to a new topic — using equivalent fractions (also called finding a common denominator) to add and subtract fractions.

This seems only to illuminate the point about coherence — a given grade is not an island, but a piece of a deliberate progression built around our best understandings of how children learn math.

**The Common Core Way?**

There are definitely differences here from standards that preceded the Common Core. My argument is not that everything is the same. Instead, I’m arguing that many teachers have always had these goals for students, and they represent common sense changes. Focus and coherence? Let’s do it. Standards that link content between grades? Awesome. Students who reason, argue, model? I’m in.

I don’t see any evidence that the Common Core is telling me *how* to teach. It’s not completely agnostic, but I see no evidence of a “Common Core Way”. The big difference I notice is when, as Dan suggests, I watch the verbs.

The Common Core asks students to understand, to explain, to reason, to argue, to model, to build on their knowledge from year to year, and to make sense of mathematics. It’s not just about what they know, it’s about what students are *doing* in math class. It’s about the verbs.

Maybe that’s what folks mean by the “Common Core way”. But the standards are still a political lightning rod, and the more they are framed as prescribing a new and different way of teaching math, the more polarizing they will be. Instead, I’d love to focus on the fact that the Common Core names some very reasonable goals for students, that none of these goals are particularly surprising, and that if anything we are raising the bar for what students are able to *do* in math class. With this focus, I think the Common Core will find more support and less polarization.

There are lots of tools to move students toward these goals. Some of them will continue to frustrate parents, as parents will naturally be frustrated when their children have a tough time with something new. But I think that if we say, “oh, well that’s just the Common Core way,” we’re setting the standards up for failure. Instead, we can frame it as, “I have ambitious goals for your daughter or son — to engage her or him in mathematical thinking, reasoning, and sense-making. It’s going to be hard sometimes. That’s fine — it’s hard because it’s worth doing.” That’s a message that is more likely to resonate with parents, and is faithful to the spirit of the Common Core.

We send a message, which is also my firm belief, that the Common Core is not some directive we received from on high to change everything. Instead, it’s one step forward, and the best tool we’ve got to reach the potential for teaching and learning mathematics for all students.

Michael Paul GoldenbergYou need to clearly distinguish between the Standards for Mathematical Practice (which in my view apply both to the teaching AND learning of mathematics and probably to the training of teachers of mathematics as well), and the Content Standards. The latter really are far more arbitrary and potentially fluid over the long haul, and while they are SEEMINGLY the part that has many parents, teachers, and “political” people up in arms to one degree or another, the question that they raise for me and some others is whether we need any such content standards at all.

Others would likely have been just ducky with the Content Standards had THEY been allowed to specify them in every detail (I’m thinking of the “traditionalists” in the Math Wars, including members of groups like Mathematically Correct and NYC-HOLD who were the most vehemently opposed to everything to emerge from NCTM starting with the 1989 Standards and running pretty much all the way until the release of the Common Core. Most of them oppose the Common Core, too, but more on that in a minute).

We also have to realize that when people (including ignoramuses in the media) write about “the Common Core way” of doing math: a) they don’t know what they’re talking about since there IS no such way discernable way explicit or even implicit in the Content Standards at all; b) they most are reacting to specific activities, worksheets, and/or assessments that have been published not by the people who wrote any of the Common Core, but rather by various publishers. And therein lies one of the biggest quandaries that arise with every attempt to have reform in mathematics education in this country: what actually represents the “reform,” and how can any for-profit, privately-owned company seriously assert that its latest “wonderful book(s)” really ARE an embodiment of the reform? And yet, every single time anyone – a state, NCTM, or now the Federal government – belches out the words “math standards,” the major publishers, who have been reduced to three mega monsters – Pearson, Houghton, and McGraw-Hill – crank out something new with a label that claims to be the imprimatur of the reform entity, or they slap a label on an old book/series and make the same claim. The wording is clever: “Aligned with the Blah Blah Blah Standards” is typical. They can’t say, “approved by” or “sanctioned by” or “prescribed by” anyone at the state or federal level, and NCTM by policy never endorses books. But teachers, book committees, parents, and politicians fall for this trick EVERY SINGLE TIME. And now that’s biting everyone, including the publishers and the Feds, on the ass, because with social media so widespread, Facebook and the rest of web crawl with complaints about some HORRIBLE worksheet or problem or test or activity that “proves” that the sky is falling (as it was in the ’90s and ’00s if you believe the old self-appointed math warrior types from the above-mentioned groups. And much of the screaming now sounds exactly like the screaming then, plus “Obama” appears throughout, with predictable rhetoric attached. And it turns out that the Federal government is trying to “dumb down” every American child so that martial law, an Islamic takeover, a Communist revolution, ad nauseam, can take place without opposition.

Now, aside from apparently substantive claims about particulars in the Content Standards, many of which at the upper level are bilge, in my opinion, and many of which at the lower level are inevitable given any attempt at imposing narrow standards on states, districts, communities, teachers, and – most importantly – children, because we can’t and should NOT be trying to standardize learning by age, no matter how hard Wall Street and the politicians it owns want the public to believe otherwise. So we wind up with parents and teachers flipping out – not unreasonably – when a topic has been shoved down a year or more in school and many kids are struggling with it. But the bitching at the upper level about not doing calculus in 9th grade (slight exaggeration) and selling the nation’s best and brightest out to the forces of darkness is much more political than it is anything of real substance. In this day of vast free on-line resources in mathematics at surprisingly high degrees of abstraction and sophistication, that dog doesn’t hunt if you actually think about it.

The REAL issue for many of those “Math Warrior” types isn’t the Content Standards at all, however, though they try to make it seem so. What REALLY bugs them is the Standards for Mathematical Practice. That’s where the old NCTM philosophy of teaching and learning is contained, and that is what these people will NEVER, EVER accept. They want math teaching done as it was in their day – teacher-centered, lecture-driven, no exploration, no “discovery,” no projects, no small groups, no calculators, and so forth. And anyone who can’t learn that way is “inferior”; anyone who advocates for alternatives is “fuzzy” and “dumbing down” the math, and “racist” and “sexist” (that’s right, folks – this is a lovely case of the pre-emptive strike: conservatives and reactionaries turning progressive criticism of traditional instruction and resources around on the liberals before the liberals can accuse these “geezers” (some of whom aren’t old at all) of being precisely what many of them in fact are.

So the real conversation, in the end, needs to focus on these philosophical precepts and the practices they imply (not so easy to pin down, after a quarter century+ of “progressive reform” math, while a separate discussion needs to take place about “the very idea” of national content and assessment. And to be clear, I am a vigorous opponent of the latter two things, while I generally favor some sort of fundamental unity of basic precepts in the philosophy of mathematics pedagogy. And hence, I aver that the Math Wars aren’t even close to being dead. The Common Core Standards aren’t going to last. Obama will be gone in a half-year. Arne Duncan already is gone, and his successor, John King, will have a very short reign indeed. David Coleman is ensconced at the College Board, and he is a truly annoying figure in the Common Core business, but he can be undermined if there was ever a rational public conversation about math education. Unfortunately, both NCTM and the US Dept. of Education have botched the job of conducting anything close to a sane conversation, and so the fight drags on with predictably awful results.

My advice to young math teachers is to connect with the Dan Meyers and dozens of other bright young math teachers online and figure out how to teach mathematics meaningfully and with integrity as long and as well as you can. The rest of this is noise and political posturing. Don’t sell out your kids for a still-born idea like the Common Core Content Standards.

dkane47Post authorThanks for this — good food for thought.

hpicciottoI agree: the goals of the Common Core are not far removed from common sense. However if you visit a lot of math classes, you’ll find that what is happening in too many classes is indeed far from common sense. The basic format in many American high schools is:

– go over homework too fast to help kids who need help, while kids who get it are bored

– the teacher carefully explains a new idea, sometimes by leading what appears to be a discussion, but is closer to a seemingly interactive lecture

– the students silently apply what the teacher hopes they learned from the lecture, and start their homework

Common sense says that while there is a place for any and all of those approaches. However they are in fact not effective if the students do not engage intellectually with the material. There are many ways to achieve that engagement, but the standard format does not make it possible, except for a minority of the students.

In other words, the “Common Core way” is indeed new and different for many, and frankly, I believe it is a good thing that many teachers are trying to move in that direction.

As for the polarization, in my view, it is not due to the failure to frame Common Core as common-sensical. But I can’t get into that right now.

dkane47Post authorThanks, Henri. I think a point worth making is that the Common Core Way is distinct — it’s different from what many teachers are doing — but it’s not prescriptive, in that there are a great deal of strategies teachers can use to meet the goals of the Common Core.

Michael Paul GoldenbergYes, the strategies are open to individual teachers. But that was true of the 1989 NCTM standards volume and all the ones that followed, and none of that seemed to convince the opponents of those volumes that the sky wasn’t falling.

In particular, the words “less emphasis on” and “more emphasis on” apparently changed into “eliminate entirely” and “do exclusively” in the copies that were read by members of Mathematically Correct, HOLD, and similar groups. Thus, arguing with them became pointless (nonetheless, I have tried for nearly a quarter-century to convince them or at least to publicly undo some of the damage they attempt).

hpicciottoRight. So maybe there is not a “common core way”, but there is a “common core goal”, perhaps encapsulated by “student understanding”. The fact that this is leading to some changes in many teachers’ practice is worth celebrating.