A couple of months ago, before I got sucked back into the black hole of my SAT vocabulary book, I wrote a post about the importance of time constraints in standardized testing. In it, I briefly discussed some reasons for why current students find timed assignments/assessments so overwhelming; and in particular, I voiced my concern that the loosening of academic standards during the pandemic resulted in pupils’ becoming (further) accustomed to endlessly flexible deadlines and high grades for “fuzzy” assignments such as posters, Power Points, and projects designed to disguise gaps in basic subject knowledge.

There are additional factors that play a role in declining expectations and concurrent SAT score inflation, however—and the situation long predates the pandemic. I originally started to discuss it in my previous post, but the issues seemed too complex and distracting to really get into, so it made more sense to explore them in a separate piece.

Let m start here. In terms of the timing changes on the digital SAT, the increase in the amount of time allotted to each Math question is really striking: from 25 minutes for 20 questions on the paper-based exam to 35 minutes for 22 questions. (Although slightly more time is given per Writing questions than on the paper-based test, Writing is now rolled in with Reading, which is generally more time consuming.) The more I thought about it, the more the disparity seemed odd—why give so much more time for Math questions than for Reading and Writing?

One obvious factor is that the proficiency score for Math is set 50 points higher than for Reading and Writing (530 vs. 480). Between 2016, when scores were “recentered” from the already-recentered 1995 scale, and 2023, the last year of the paper-based administration, Math scores declined from an average of 527 to 508—a 19-point drop, in contrast to the 13 for Reading/ Writing (533 down to 520, but still well above the suspiciously low proficiency bar). Score declines = bad press, a further decline in the number of students sitting for the SAT, which is something the College Board would obviously prefer to avoid. .

In addition, eight states require the SAT for high school graduation, with another three allowing either the SAT or ACT. An exam that produces too many scorers below the proficiency level could threaten the College Board’s state contracts, and so it is in the organization’s interest to tweak the parameters of the exam in order to ensure that too many students are not hindered from graduating.

Then, of course, there is the College Board’s standing with its private market. It must make the digital test as appealing as possible if it is to retain its traditional clientele, and improving students’ chances of scoring well on the STEM side will obviously help boost its standing in the minds of the paying customers.

Beyond all that, however, it seems reasonable to wonder why test-takers would now require so much additional time on this particular part of the exam. And the answer, I think, involves Common Core.

I recognize that Common Core has more or less faded from public consciousness and is increasingly regarded as a better-forgotten debacle of the mid-2010s. That does not mean, however, that its effects have been erased, or that it did not do serious damage to the way half a generation of students learned—and are still learning—math. Indeed, in many states, the Standards have simply been repackaged and renamed.

Granted, mathematics is not my area of expertise, but most of the debates surrounding math instruction have extremely close parallels in reading and writing; I’ve followed them closely over the years and have just enough experience to grasp the depth of some of the problems that have been created.

In a nutshell, for those of you unfamiliar with the issue: the main criticism of Common Core math is that it taught simple procedures in overly complex, convoluted ways; delayed the introduction of standard algorithms for up to several years; and left students ill-prepared to handle advanced topics, including calculus, in high school.

Not surprisingly, this characterization received a fair amount of pushback in certain educational circles, whose members insisted that the Standards were designed to foster “deep conceptual understanding” rather than the “rote memorization” and “drill n’ kill” that turned students into “math zombies” able to memorize and spit back formulas without truly understanding how they worked.** **

In a 2014 *Atlantic *article, the math teacher and author of *Traditional Math* Barry Garelick summarized the problem with what he has termed the “fetish over conceptual understanding” and the downplaying of procedural fluency:

*It’s an odd pedagogical agenda, based on a belief that conceptual understanding must come before practical skills can be mastered. As this thinking goes, students must be able to explain the “why” of a procedure. Otherwise, solving a math problem becomes a “mere calculation” and the student is viewed as not having true understanding.*

*This approach not only complicates the simplest of math problems; it also leads to delays. Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them “understand” the conceptual underpinnings. *

I realize that personal anecdotes are of limited value when discussing national movements, particularly given the decentralized nature of the American school system. For what it’s worth, though, watching an elementary schooler spend approximately 20 minutes drawing out an array of 81 dots to show “deep understanding” of 9 x 9 remains one of the most surreal experiences of my career. Given that this took place in a very affluent community in the highest achieving state, I find it difficult to even fathom what math education might consist of elsewhere.

Provided that a child grasps the most basic principle of multiplication—namely, that the word “times” literally indicates the number of times a number is added to itself—there is no reason on earth not to ensure that the times tables are committed to memory as quickly as possible *so that they can be applied to more advanced contexts*. If students never master such fundamental pieces of knowledge, it is not difficult to imagine why problems requiring simple calculations might pose a time challenge (no pun intended) down the line. When one considers that many of the students taking the SAT in the early 2020s have spent their entire school careers in Common Core-influenced classrooms, it is not surprising that these issues would be surfacing now.

However appealing an emphasis on “deep understanding” sounds on the surface, it overlooks the fact that in math, a fluency with facts provides the framework for conceptual understanding—a point on which Garelick expanded in several posts on his personal blog:

*For many concepts in elementary math, it is the skill or procedure itself upon which understanding is built. The child develops his or her understanding by repeatedly practicing the pure skill until it is realized conceptually through familiarity and tactile experience that forges pathways and connections in the brain. But in terms of sequential priority, there is no chicken-and-egg problem: more often than not, skill must come first, because it is difficult to develop understanding in a vacuum. Procedural fluency provides the appropriate context within which understanding can be developed…*

A rough verbal analogy here might be something like prepositions (“time” and “position” words), which are tested in relation to the misuse of commas on the SAT and ACT. The vast majority of my students could not form an abstract category for these words in the absence of specific knowledge of them, and so it was necessary to drill them repeatedly on individual examples in order to help them build a mental framework for the concept.

A more recent piece that appeared on Diane Ravitch’s blog (authored anonymously and originally posted on eduissues.com) emphasizes the gap between what is intended by the Standards and what was (and presumably still is) actually being taught:

*The content pieces are too numerous and detailed for any but the most proficient of students to actually know, given the current trends in teaching, and the practices are abstracted so far from any actual skills or tasks that they become little more than empty platitudes to normalize flagging proficiency.*

*Without adequate support for this procedural mastery, the clustered conceptual outline scheme by which the content standards are subdivided and organized becomes too smart for its own good. The result is too much reductionism in each of the standards, forcing rote memorization of isolated topic points without adequate context to frame them and hold them together…The standards become little more than testing points for rote practice and memorization, with the focus shifted from mathematical calculation to linguistic verbalization.*

One of my great takeaways from following media discussions of education for the last decade is that claims of being against “rote memorization” and in favor of “critical thinking” are nearly always sufficient to shut down any meaningful scrutiny of what is actually happening (see: Balanced Literacy and rote memorization of phonetic “sight words”). It does not matter if children are actually learning to parrot explanations to please their teachers as long as the theory holds that they are doing otherwise.

Regarding the emphasis on verbalization: not only does it pose a major obstacle for English-language learners, as well as children whose verbal and writing skills have not caught up to their numerical ones, but it also fails to recognize that the language of math is *math*. Children who are gifted, or merely highly proficient in that subject, may not have the language to, say, write a paragraph about why it is necessary to multiply in a given situation—even if they can automatically recognize that the operation is called for. However, according to ed-school logic, only the ability to write or talk expressively (in a small group, of course) about what one is doing is considered evidence of “real learning.”

Thus, a student who can easily solve challenging, above-grade-level problems using numbers and symbols, but who cannot engage in “rich” conversation or write a detailed paragraph about how and why they do so, is held to not truly understand math.

No system based on this kind of absurdity could possibly function outside of ed-school professors’ heads. And in fact, according to Chalkbeat, a 2019 study found that less than a decade after Common Core was rolled out:

*[S]tates that changed their standards most dramatically by adopting the Common Core didn’t outpace other states on federal NAEP exams. By 2017 — seven years after most states had adopted them — the standards appear to have led to modest declines in fourth-grade reading and eighth-grade math scores.*

*“It’s rather unexpected,” said researcher Mengli Song of the American Institutes for Research. “The magnitude of the negative effects tend to increase over time. That’s a little troubling.” *

In fact, there is absolutely nothing surprising about it. On the contrary, assuming that the criticisms of people like Garelick are valid, it is precisely what would be expected. When fundamental skills are not mastered early on, the gaps become progressively more detrimental over time. The College Board can add as much time and “recenter” its scoring as often as it wishes, but that will do nothing to actually make students more proficient. Eventually, the bill for all that pretending will come due.

The gap between Math and RW proficiency is curious, but also consistent with the ACT. The ACT College Readiness Benchmark for English is only 18, ostentatiously lower than the benchmarks for Math (22), Reading (22), and Science (23). I’d love to hear your conclusions if you dig into these numbers.

Mike, as you know, the ACT scores roughly correspond with percentiles. In contrast, the readiness benchmarks correspond with the the minimum level of rigor a student is expected to encounter at the college level. Thus, the way I interpret this gap is that a greater share of students are capable of completing college coursework that requires “English” as a core component than that which requires math, reading or “science.”

Thank you for this important, well-written, and thoroughly researched post! Even with a master’s degree in education and a career in education, I find it a requirement to continually stay on top of this type of information not only for my high school students but also as a parent of a kindergartener. I am grateful you take the time to post about these issues, which are relevant in every discipline, but especially for those of us in the humanities field. Thank you!

Thanks for this post. There is definitely an obsession over students obtaining “understanding” — most times at the expense of knowing the procedure. You may wish to look at this recent post regarding the delaying of teaching the standard algorithm for addition/subtraction and Common Core’s role in same.

https://barrygarelick.substack.com/p/teaching-math-with-fidelity