After testifying in Indianapolis, Jason Zimba reflects on what he learned about the entrenched opposition to the Common Core State Standards. Photo by W9NED |

Earlier this week, I spent a day visiting Indiana’s beautiful nineteenth-century statehouse in Indianapolis, where I testified about the Common Core State Standards for Mathematics. Testimony in favor of the standards was also given to legislators by in-state experts, like Warren Township school superintendent Dena Cushenberry and Purdue Dean of Admissions Pamela Horne. Afterwards, I reflected about what I had learned about the entrenched opposition to the standards.

The first thing I learned is that there is a significant gap in the quality of the evidence being brought forward in this debate.

- In my testimony, I cited a peer-reviewed journal study by a distinguished university researcher on international mathematics performance about the grades and topics in the standards—research concluding that the Common Core agrees with high-performing countries better than any previous state standards, including those of Indiana. During his testimony, noted critic of the standards Dr. Williamson Evers cited an online news article.
- At a previous hearing, Mr. Ze’ev Wurman apparently told legislators[1] that “Common Core completely forgot conversion among fractional forms—fractions, percent, and decimals.” But standard 7.EE.3 on page 49 includes the language “…calculate with numbers in any form; convert between forms as appropriate,” as well as an example problem that involves a fraction, a percent, and a decimal.
- An editorial yesterday in a Utah newspaper claimed that the standards set “no expectation of competency in, or even a basic familiarity with, trigonometry.” Pages 71 and 77 disprove this claim; see standards F-TF.8 and G-SRT.8, among others.[2]

The quality of information being provided by the critics isn’t serving policymakers, who are trying to make important decisions on behalf of the teachers, students, and parents they represent.

Second, as I prepared for my Indiana testimony, I learned that the most prominent CCSS opponents lack intellectual consistency:

- In 2012, in a debate about the math standards published in
*Education Next*, Mr. Wurman quoted a research conclusion from a study that the math standards aren’t very focused. But then in March 2013, he apparently testified to the Indiana legislature that they were too focused.[3] - In July, Professor R. James Milgram testified to the Arkansas legislature that the standards were “better than 90% of the state standards…they replace.” Then he turned around and quickly wrote a scary-sounding editorial about how the Common Core was “a massive, risky experiment with your kids.”
- In a generally negative critique of the standards from 2010, Professor Milgram said of the Common Core that “…there are also very real strengths in the document. Many of the discussions, among them ratio and rate in grade 6, and proportion in grade 7, are excellent. They are clear and mathematically correct presentations of material that is typically very badly done in most state standards in this country.” But in his recent editorial, he wrote, “There are also severe problems with the way Common Core handles percents, ratios, rates, and proportions – the critical topics that are essential if students are to learn more advanced topics such as trigonometry, statistics, and even calculus.”

Third, I learned that these critics believe wrongly that the standards require a constructivist approach to pedagogy. In my testimony previous to Dr. Evers’s, I had noted that

###### [T]here are no expectations in the Common Core for students to invent, construct, or discover algorithms. One reason no such expectation can be found is that “constructivism,” whatever you think of it, is a teaching method—and the standards do not prescribe teaching methods.

Dr. Evers, however, pointed out in subsequent testimony that in several places, framing language in the grade overview pages includes language about students “developing” computational methods. Here for example is one of these instances (this is from the Grade 1 overview on page 13):

###### “Students develop…efficient, accurate, and generalizable methods to add within 100….”

Before I say anything further about this, I would like to note that Mr. Wurman has assailed the Common Core in legislative testimony for, as he claims, requiring “crude strategies” and “invented algorithms applicable only to specific cases.” But the incredibly careful adjectives that were used in this framing language (*efficient*, *accurate*, *generalizable*) tell a different story.

Nevertheless, I appreciated Dr. Evers’s observation,[4] and I noted it. It would have been more correct for me to say that there are no *standards* in the Common Core that call for students to invent, construct, or discover (or “develop”) algorithms. I was using “expectation” as a synonym for “standard,” just because I think people get tired of hearing the word “standard” all the time. But I won’t do so in the future.

Those who know the ways in which standards documents actually relate to tests and to textbooks will recognize, however, that this is a very weak argument that the standards require students to invent, construct, discover, or even “develop” algorithms. That’s because no single standard (or even cluster heading) tells people that students have to do so. Consequently, for example, if one examined the PARCC test blueprints, I doubt that one would find any so-called ‘evidence statements’ there that require students to develop, invent, construct, or discover computation algorithms—for the simple reason that no standard in CCSSM requires them to.

I don’t make much of the fact, which critics like to repeat, that Professor Milgram was the only mathematician on the validation committee and that he didn’t sign off on the standards. The fact is true, but the impression it gives that the standards are mathematically unsound is false. Professor Emeritus of mathematics Hung-Hsi Wu has said that “the statements of the standards are mathematically correct and the progression from topic to topic is logical.”

It won’t do to counter, as critics sometimes do, that Professor Wu must be biased because he worked on the standards. People seem to forget that Professor Milgram also worked on the standards. In fact, it is doubtless thanks in part to Professor Milgram’s input during the development of the standards that they are, at least in his view, “better than 90% of the state standards…they replace.” However, they clearly didn’t turn out a hundred percent his way—or indeed any one person’s way.

Professor Milgram occupies one extreme side in the Math Wars; there was another distinguished validation-committee member who happens to occupy the other extreme side. Neither signed. The standards don’t please everybody, but they represent a broad consensus-point in the long discussion between mathematicians and mathematics educators that this country has been having for a quarter century. That is one reason why the presidents of every major society of mathematicians *and* every major society of mathematics educators in the country strongly support the Common Core.

The support and agreement that the Common Core has earned are unprecedented in the history of American mathematics education over the past twenty-five years. The standards aren’t perfect, but the presidents of all of the major mathematical societies in America have said that the Common Core is an “auspicious advance.” They have also urged that this is “not the time to turn away from our good fortune.”

The word *auspicious* evokes thoughts of the future. If we want our future mathematics performance to improve upon our past and present, then I think is time to stop warring over the ends so that we can begin concentrating everywhere on improving the means—for the means we have at our disposal today are hobbling our performance. Textbooks are a mile wide and an inch deep; teachers are too often denied the preparation in mathematics that they and their future students deserve; and assessment developers have seldom created tests that showcase mathematics or reward teachers for good work. That is where states are today, but that is not where they have to stay forever. Widely shared goals give the fragmented education sector a shared agenda for gradually strengthening practitioners’ mathematical knowledge base; improving the tests we rely on to know how we are doing; accumulating the research to resolve important disputes; and, instead of waging ideological wars over textbooks, achieving a rational materials marketplace in which schools more reliably choose to purchase the tools that actually work best.

Finally, I learned that the opposition continues to misrepresent my views. Substantively speaking, this is the least important thing I learned in Indiana. Readers who are uninterested in a he-said/he-didn’t-say sort of debate may wish to skip down to the ### symbol at this point. Those who are interested in such things, please settle in.

First, the facts about the standards themselves. As I testified in Indiana, and as I wrote in an editorial,

###### The definition of college readiness in the standards is readiness for entry-level, credit-bearing courses in mathematics at four-year colleges as well as courses at two-year colleges that transfer for credit at four-year colleges. It is incorrect to say, as critics sometimes claim, that the definition of college readiness in the Common Core is pegged to a community college level.

This language does not appear in the standards document itself, but from what I can tell, everybody who is working on implementation of the standards understands this to be the case. Here is PARCC, using language pretty similar to mine:

###### The PARCC CCR Determinations in ELA/literacy and mathematics describe the academic knowledge, skills, and practices in English language arts/literacy and mathematics students must demonstrate to show they are able to enter directly into and succeed in entry-level, credit-bearing courses and relevant technical courses in those content areas at two- and four-year public institutions of higher education. The CCR Determination will provide policymakers, educators, parents, and students with a clear signal about the level of academic preparation needed for success in these postsecondary courses. It will provide a strong indicator of college and career readiness that can be used to set performance goals at any level and show progress towards those goals. Finally, students who attain a CCR Determination in ELA/literacy and/or mathematics will have a tangible benefit – direct entry into relevant entry-level, credit-bearing courses without need for remediation.

I call this level of college and career readiness minimal, for the reason that the mathematics in the Common Core—easily three years of mathematics reaching the level of Algebra II—will not by itself prepare students for STEM majors or meet admissions criteria for top universities. As I explained in response to a legislator’s question in Indiana, for example, the flagship campus of the state university system, Bloomington, requires four years of math reaching the level of precalculus. Purdue University also requires four years of math, which puts students beyond Algebra II.

And yet, the Dean of Admissions of Purdue University testified in favor of the Common Core in Indiana. But there is no paradox here. As I wrote in my editorial,

###### Just because the Common Core standards end with Algebra II, that doesn’t mean the high school curriculum is supposed to end there. California, for example, had calculus standards before adopting the Common Core, and the state still has them now, as it should. The difference in California today is that better standards can help more of California’s students gain the strong foundations they need to succeed in calculus.

###### States still can and still should provide a pathway to calculus for all students who are prepared to succeed on that pathway—not only because it is at the heart of many STEM fields, but also because the calculus is one of the greatest intellectual developments in human history.

It occurs to me now that people will criticize me from the other side for characterizing Algebra II as “minimal” preparation for college. That’s because two-year colleges typically don’t require Algebra II for admission. A person focusing on community colleges might even define Algebra II as “maximal.” The words “maximal” and “minimal” are part of the mathematician’s lexicon, and I suppose that’s why they come so easily to mind for me; I’m not expressing value judgments, just trying to characterize a factual situation as I perceive it. And I apologize if, at any point in this discussion or elsewhere, I have given the appearance of disdain or disrespect for two-year colleges, elite colleges, or anything in between.

Speaking of “minimal,” critics refer ceaselessly to the March 23, 2010, meeting of the Massachusetts Board of Elementary and Secondary Education, at which I testified about the March 10 public draft of the standards (not the final version; many details of the discussion held on March 23 are now outdated). The video of this meeting is available to anyone who wishes to see it. There I said many times what I have just said above: Algebra II is a minimal definition of college readiness. And again, that’s true if you ignore community colleges and focus your attention on the needs of STEM majors and the admissions criteria of top colleges.

So while we may one day see viral videos of myself repeatedly saying the scary word “minimal,” in the meeting I think it was clear that I wasn’t using the word as a pejorative. I was simply using it to agree with Dr. Sandra Stotsky (a board member at the time) that Algebra II isn't enough preparation for a STEM major and won’t satisfy admissions criteria at top colleges. I think that is not so much a smoking gun as a statement of the obvious.

Who could look at what’s in the Common Core State Standards for Mathematics and see a program designed primarily to prepare people for community college? At one point in the meeting, I can hear from the video that I almost said the word "non-selective." Halfway through the word, it seems clear that I realized that it would be incorrect and could give a false impression. So halfway through the word, I managed to correct myself. Here is a transcript of that moment in the video:

###### You can look at, um, college admissions requirements in, you know, reasonable—um, non-ssss—uh, colleges at which 80% of kids today attend. And you’ll see that they all require pretty much three years of math, they often describe it as Algebra II. There’s a—there’s a broad consensus of what it takes to basically get into college, and it’s Algebra II.

This passage is hardly eloquent, what with all of the um’s and ah’s. But the latter two sentences clarify the first sentence beyond dispute. I was trying to truthfully separate out the beyond–Algebra II cases of STEM majors and top universities. Try inserting the word “community” into the third sentence, just before the word “college”—it doesn’t fit. Likewise, replacing the word “they” in the second sentence with “community colleges” yields nonsense.

At another point in the video, Dr. Stotsky and I can be seen agreeing with one another repeatedly about the fact that Algebra II won’t prepare you for a STEM major or meet the admissions criteria for a top college (UC Berkeley was the example I used). I could understand somebody concluding from this exchange that, since I agreed that Algebra II doesn’t get you into what we were calling “selective” institutions (like Berkeley), I must have meant equally that Algebra II only gets you into “non-selective” institutions. But I didn’t say those words, and I didn’t mean that statement. I had in mind for the purposes of this conversation a rather simple model of the world, in which one might say that there are three categories: selective, non-selective, and, in between those two extremes, something we might as well for lack of a better word call “normal.” (This simple model was also the source of my choice of the word “reasonable” in the excerpt quoted above.) When I was agreeing here yet again with Dr. Stotsky, I was saying yes to the normal portion of the distribution, not to the lower extreme. And—to belabor this to the point of fatigue—I had already said anyhow that the standards were aiming at colleges that require Algebra II.

For my part, I wouldn’t say that my testimony that day was especially eloquent. It has been distressing to see that testimony misused. I wish I had been clearer, and I hope that what I have written here clarifies matters, not only about what I said, but about what is so.

In case anybody is interested in the further history of this—skip down to the ###, if not—the minutes published after the board meeting in Massachusetts carried the following one-sentence summary of my remarks: "Mr. Zimba said the concept of college readiness is minimal and focuses on non-selective colleges." I wasn’t given an opportunity to review the minutes before they were published (that isn’t how these things work in any case), but if I had, I would have objected to this as apt to give a false impression of my testimony.

Not long afterwards, in a report written by Mr. Wurman and Dr. Stotsky and published by the Pioneer Institute, there appeared the following:

###### Jason Zimba, a member of the mathematics draft-writing team who had been invited to speak to the Board, stated, in response to a query, that “the concept of college readiness is minimal and focuses on non-selective colleges.”

Only by consulting the footnotes would a reader be likely to realize that the clause in quotation marks was somebody else’s sentence, not mine.

And the sentence continues to grow by accretion. Professor Milgram has now added the dread word “community” to the minutes of the meeting:

###### One of the main authors of the Core Math Standards, Jason Zimba, testified to the Massachusetts State Board of Education in 2010 that Common Core is only designed to prepare students for an entry level job or a non-selective community college, not a four year university.

I hope the absurdity of this is apparent.

The critics are also getting increasingly creative with CCSSM project lead Professor William McCallum’s quote (also from 2010, and also an indirect quote) that the standards are "not too high." In context, Professor McCallum clearly meant “not excessively high, as compared to East Asian countries.” But soon Mr. Wurman was suggesting that Professor McCallum had said that the standards were *not very high*. And I was astonished to hear, as I believe I heard during Dr. Evers’s testimony in Indiana, that now Professor McCallum has said that the standards are *not high*, period. How long before we are told that Professor McCallum has said the standards are too low?

###

Evidence from international comparisons, domestic research, and major reports, as well as a wide range of expert opinion, affirm that the Common Core State Standards for Mathematics are a blueprint for a strong mathematical education. They do this by first erecting a focused, coherent staircase in grades K–8, and then in high school calling for students to learn the math they need for college (recognizing that STEM majors need more, and so do students who want to meet the admissions criteria of top colleges). If students want to go further and gain the additional mathematics they need for STEM majors or admission to a top university, the Common Core, implemented faithfully, will help more of them to do so.

To this point, I have been critical of the critics. Where do we agree? What do I think they have added to the debate about the Common Core?

I appreciate that they have highlighted a risk that I too believe is worth taking seriously: namely, the possibility that the “hard skills” in the standards are being underemphasized in implementation. That is why my editorial in response to Professor Milgram, as well as my testimony in Indiana, emphasized this issue and urged states to attend to it.

I also appreciate that they are focusing discussion on the interests of prospective STEM majors and those who aspire to top universities. Perhaps because of my own life experiences, the educational fate of mathematically talented students in our public schools matters to me.

I don’t claim to have all the answers. In fact, I have many questions. For example, should Algebra II be a required course for high school graduation? Should passing a state test of Algebra II be a graduation requirement? Or, to put it another way: Should every student be held to a college- and career-ready standard in order to receive a high school diploma? I am not sure that states would naturally agree upon these matters (as opposed to, say, the multiplication table).

Another set of important questions for math education, and for our international competitiveness, would center on providing a sturdier pathway to calculus for all students prepared to succeed in it—and increasing the number of truly viable candidates year upon year. I believe the Common Core is the beginning of that process, but not the end of it.

Finally, it is highly urgent that we improve our systems for the mathematical education of teachers. Every mathematician I work with on Common Core implementation shares this sense.[5] My instinct is that the Common Core is the most promising development on that front in decades. But that is a subject for another time.

(For a PDF version of this article, click here.)

*Jason Zimba was a lead author of the Common Core State Standards for Mathematics and is a founding partner of Student Achievement Partners, a nonprofit organization. He holds a BA from Williams College with a double major in mathematics and astrophysics; an MSc by research in mathematics from the University of Oxford; and a PhD in mathematical physics from the University of California at Berkeley.*

[1] I only say “apparently,” because my source for this statement is the website “Hoosiers Against Common Core,” which is not a legislative record.

[2] The “TF” in “F-TF” stands for “Trigonometric Functions,” the name of the domain that contains, e.g., standard F-TF.8.

[3] Again I only say “apparently,” because my source for this statement is the same document from “Hoosiers Against Common Core” cited above.

[4] The verb “develop” also occurs transitively with “methods” as its object in two footnotes in the document.

[5] Dr. Evers and Dr. Stotsky also both stressed the importance of this issue in their testimony.