Dropping the Ball

The expert behind New York's bad plan to improve math instruction doubled down. We do, too. | Attacks on Excellence, Issue #6

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Let’s start with some good news. In her January State of the State address, New York Governor Kathy Hochul announced her “Back to Basics” proposal for math instruction. Hochul plans to require the New York State Education Department (NYSED) to “provide instructional best practices to school districts” that “equip teachers across the state with evidence-based teaching techniques and materials.” And in NYC, new Schools Chancellor Kamar Samuels is pledging a renewed focus on automaticity with basic math facts. “Knowing your times tables is very, very important in math,” Samuels told CBS. “You can’t factor on your fingers.” Even as Samuels helped roll out the city’s discovery-based math curriculum, NYC Solves, he now seems to acknowledge the value of prioritizing clear instruction that ensures fluency.

Now for the bad news. Even as Hochul and Samuels tout a return to fundamentals, the statewide education apparatus remains committed to the opposite message.

Back in October, we featured a guest post by professor Ben Solomon about his petition to retract the NYSED numeracy briefs. Commissioned as part of NYSED’s “Numeracy Initiative“ and written by Dr. Deborah Loewenberg Ball, the University of Michigan education professor behind TeachingWorks, the briefs were supposed to “highlight the evidence-based features and best practices of effective mathematics instruction.”

Yet despite their “evidence-based” framing and purported scientific rigor, the briefs stunned many educators by ignoring key research and regurgitating pernicious inaccuracies about effective math instruction. On October 10, Solomon’s petition (boasting 216 signatories at time of writing) was sent to Commissioner Betty Rosa. Then, on October 22, NYSED released its response. This response, written by Ball with an introduction by Assistant Commissioner JP O’Hare, doubled down on the contents of the briefs and accused the petitioners of politically motivated “misinformation.” Three months later, the briefs remain unchanged; under the aegis of “peer-reviewed, evidence-based research,” NYSED is marketing contested pedagogy as settled science.

In his piece, Solomon asked how it was possible that “university-affiliated professional development providers double-down on practices shown decades ago to be ineffective, ignoring hundreds of published empirical studies and meta-analyses.” Today, we explore how it is possible for the purveyors of bad pedagogy to defend their ideas with the imprimatur of a state’s education agency.

Ball’s response is disappointing, but it is also instructive. It shows us how advocates of these ideas continue to dodge criticism, and it shows us what arguments to expect when we see this happen again elsewhere.

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Ball’s Defense

The petition to retract the numeracy briefs identifies key ways in which they depart from recommendations grounded in rigorous research. As Solomon explained, good, evidence-based briefs would emphasize:

1. Ensuring fluency in core skills through practiced repetition and timed exercises;

2. Measuring student learning with regular, timed assessments to inform instruction;

3. Explicitly teaching and modeling fundamental principles; and

4. Deploying exploratory, inquiry-based learning only after explicit instruction and only for students who are competent with the basics.

The reasoning behind each of these points is straightforward and well-supported. Later math proficiency requires mastery of basic math facts to the point of fluency or automaticity; without these basics committed to memory, students will struggle with more complicated work. Deliberate practice with brief, timed exercises is among the most effective ways to ensure this basic fluency, and brief, timed assessments are a reliable gauge of how much students have learned. Moreover, clear, explicit instruction consistently leads to higher learning gains than competing approaches, especially for struggling students. While inquiry-based “discovery” approaches can benefit students who already grasp the fundamentals, they leave students without sufficient prior knowledge even further behind.

The NYSED briefs diverge from the research consensus on every one of these points.

A comprehensive response to the petition would need to justify why the best-supported instructional practices are not highlighted in due proportion to their effectiveness, why less effective practices are emphasized disproportionately, and why the research base on which the briefs rely omits the highest-quality evidence. Specifically, Ball would need to explain what basis she has for deemphasizing basic fluency, practiced repetition, timed assessment, and explicit instruction, while at the same time promoting inquiry-based approaches without cautioning about their limitations.

To be convincing, Ball would need to show either that the evidence in favor of the practices highlighted in the petition is contradicted by competing high-quality evidence, or that the evidence favoring the recommendations in the briefs is at least strong enough to warrant emphasizing them at the expense of those highlighted in the petition.

Ball’s response offers no such convincing justification. Although her response is structured as a point-by-point rebuttal to three discrete criticisms and four alleged inaccuracies, this structure obscures more than it clarifies. Ball’s responses to the first three criticisms all deploy the same argumentative move. Call it the “Scope-and-Methods Two-Step”: first, she defines mathematical proficiency broadly enough to claim that the petition’s evidence only addresses one component (procedural fluency), and is thus too narrowly scoped. Then she claims studying the remaining components of math proficiency require entirely different research methods — methods that conveniently cannot be held to the same exactly empirical standards as those in procedural fluency research.

This two-step strategy allows Ball, on the one hand, to dismiss any rigorous evidence as “narrow” without engaging with it directly, and on the other, to exempt the recommendations in the briefs from proper scrutiny. In doing so, she makes her position unfalsifiable by any evidence brought to bear in the petition, and only then responds to the individual charges of inaccuracy.

Let’s see the Two-Step in action.

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Dancing the Two-Step

“Criticism #1: The recommendations are not based on research.”

Consider Ball’s argument against what she identifies as the first criticism from the petition. The petition charges that the briefs fail to cite “the results of rigorous empirical studies”; the studies they do cite include “only 2 experimental studies and 2 meta-analyses,” and of the research they cite that is actually peer-reviewed, that research “is overwhelmingly articles reflecting personal experiences and opinions.” Given the briefs’ repeated framing as “evidence-based,” this is a serious charge.

How does Ball respond? She asserts that the petition only cites studies addressing how to develop “speed and accuracy,” which are only one component of math proficiency, whereas the NYSED briefs cite studies that address ways to develop all the components of math proficiency; and since, moreover, studies of different components appeal to “different methods,” the studies cited in the petition cannot contradict recommendations based on studies cited in the briefs:

[Although] the petition claims that only two experimental studies and two meta-analyses were used as the basis for the briefs, ... such methods are not the only kinds of research that are appropriate for decisions about mathematics instruction. Brief 1 … specifies … different methods and kinds of studies appropriate for different questions and components of mathematics instruction. For example, while … the development of speed and accuracy, may be appropriately studied through randomly controlled trials, other aspects, such as the development of the use of mathematical representations, language, and proving, require investigation in particular contexts of classroom learning across time. Similarly, issues related to grouping students, classroom discourse, and the use of manipulatives require close analysis of teaching in order to produce usable knowledge for instruction. … In contrast to this broad application of evidence, the citations included with the letter represent a narrow segment of the research ... [and] are not enough to address the complexity of mathematics teaching and learning.

Notice what this response does not do. This response does not refute, or even address, the petition’s claim that “performing fluently or automatically all the foundational skills” is the necessary foundation for “advanced math performance” (p. 3); neither does she show that we have reason to doubt the validity of the rigorous studies that support that claim. Instead, she uses the Two-Step to escape the responsibility to address the claim at all: “the development of speed and accuracy” is simply one among multiple “different … components of mathematics instruction,” and because these different components require “different methods,” the rigorous research cited in the petition has no bearing on her recommendations or the validity of the research they spring from.

Here we see the first core problem with the Two-Step: saying that there are other components of math proficiency besides the fluent, automatic performance of basic operations — “procedural fluency” in the briefs — says nothing about the necessary relation between procedural fluency and those other components.¹ The petition, too, identifies and stresses the importance of other components of math proficiency, such as “the rapid mastery of new concepts which then enables creative and generative problem solving” (p. 2). But procedural fluency is not merely one strand among others — it is necessary for building these other highly valuable, higher-order skills. This is precisely why the petitioners take issue with its unacceptable de-emphasis in the briefs, and it is precisely this claim that Ball would need to refute for a convincing response.

The Two-Step’s second problem also appears in this excerpt: when appealing to “evidence,” Ball cannot have it both ways. The entire selling point for why educators should care about the NYSED numeracy briefs is that they offer “Evidence-Based Practices for Teaching Mathematics” grounded in “substantial peer-reviewed, evidence-based research” — a label that, in other fields, means that the recommendations are informed by the kind of “rigorous, controlled studies of cause and effect” that best signal expertise and credibility.

But the briefs do not rely on studies using such rigorous research methods, and Ball’s response gives us no reason to doubt the findings of the petition’s studies, which do. The charge against the briefs was that they minimize the importance of the instructional practices best supported by the preponderance of rigorous evidence for teaching math effectively; they minimize the practices that best develop mastery of basic facts, including practiced repetition and timed tests, and they minimize the importance of explicit instruction, instead promoting “inquiry and discovery approaches to teaching and learning” out of proportion to what the evidence suggests.

Ball does not engage with these studies when making her rebuttals, nor does she offer competing evidence or critical responses. Instead, she uses the Two-Step to bypass these duties entirely: “studying different components requires different methods.”

Saying that there are other research methods besides RCTs and meta-analyses, however, is not yet demonstrating that these other methods and the studies that use them are rigorous enough to give us good evidence.

Fields with good epistemic hygiene rank the quality of their research methods based on how well they account for factors like confounding and bias, and the reason RCTs and meta-analyses are such respected methods is that well-conducted ones do this very well. As in any field — but particularly in education — much research that is cited as evidence is not good evidence because it accounts for confounding variables and bias poorly. For a piece of education research to give good evidence that an instructional practice is effective, that research has to give us good reasons to believe that practice will reliably promote student learning and retention for a wide variety of students when performed by a wide variety of teachers. Practices fail to meet this bar of reliable, wide applicability for many reasons, and high-quality education research is rigorous about controlling for factors that might explain why a practice that works in one context doesn’t in another, or why another practice that seems to be working may not be what’s causing the effect at all. If research is not sufficiently rigorous, the reasons it gives us for favoring one practice over another are not going to be good reasons.

The fact that one study uses different research methods or investigates different targets than another does not simply release that study or those methods from the demands of rigor. The methods by which astronomers determine the age of a star are different from the methods by which geologists determine the composition of a sample, but each is accountable to standards of rigor when they conduct and publish their studies. While the natural sciences are held up as paragons of methodology, this accountability is not unique to such fields.

Brief 1 offers “conceptual analysis” and “ethnography” as “different kinds and methods of inquiry” that can result in “valuable insight.” But different methods will still have internal standards of rigor, and crucially will also have different limits. Uses of conceptual analysis are better or worse based on, e.g., the quality of logical reasoning, the extent of engagement with critics, and ease of accounting for counterexamples; ethnographers that incorporate less data, take fewer meticulous notes, and follow the literature irregularly will be worse ethnographers.

But methods like conceptual analysis and ethnography are less equipped to offer rigorous, controlled, falsifiable explanations for phenomena than experimental methods that make and rigorously analyze testable, replicable predictions. That one uses “different methods” means neither that those methods are equivalent in rigor nor equivalent in explanatory power — and it certainly does not mean one has an excuse to discount the findings of multiple, rigorous, replicated studies that converge on conclusions that don’t fit one’s vision.

Moreover, unless those wildly underspecified, alternative research methods Ball mentions — like “investigation in particular contexts of classroom learning” and “close analysis of teaching” — measure up to exacting standards of clarity, testable predictions, meticulous observation, and corroboration by multiple data sources, those methods cannot provide good evidence for the kinds of claims Ball makes. Even if they did offer insights into “different components of math instruction,” that would not suffice to refute the evidence cited in the petition calling for retraction of her briefs.

All this is to say that if Ball is going to convince a methodologically literate reader by citing studies that use “different methods” for “different components,” she had better have the right receipts.

As we see from her next two responses, she does not.

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Rinse and Repeat

“Criticism #2: The briefs advance an approach to teaching mathematics that has been shown to be ineffective in developing students’ mathematical competence.”

Ball avoids responding to the substance of this criticism, too:

Brief 1 explicitly rejects ‘an’ approach [to teaching mathematics].... [R]ather than advocating for one approach or arguing against another, the brief ties mathematics teaching to specific aspects of mathematics … Learning to attend to mathematical structure, prove the completeness of a solution, or justify a geometric transformation requires different mathematical skills than does correctly solving … calculations. Each of these components of mathematical competence are specifically identified … [and] instructional methods cannot be generalized across these different forms of mathematical capability and skill.

Again, the charge in the petition is that the weight of the evidence shows specific approaches — explicitly teaching and modeling core principles, ensuring fluency in the basics, deferring discovery exercises until students are ready — are better for developing math proficiency than competing approaches, since a solid grasp of the basics is necessary to build proficiency in higher-order skills.

Ball’s response is a dodge: the “mathematical skills” required for “correctly solving … calculations” are different from the skills required for other math tasks, and the “instructional methods” that teach one skill “cannot be generalized across” different skills; accordingly, she concludes the briefs do not promote ineffective approaches, but rather promote approaches effective for different skills.

But Ball gives us no evidence or reason to believe that different instructional approaches are needed to teach different skills. Conversely, as Solomon wrote in October, the overwhelming research consensus gives us terrific reason to believe not only that the same approaches that build procedural fluency build math competence generally, but also that the same approaches that help students build literacy help them build numeracy:

The science of math shows that many of the lessons gleaned from the science of reading cross over, such as (a) explicitly teaching and modeling fundamental principles, (b) ensuring fluency in core skills, (c) measuring to inform instruction, and (d) saving exploratory and “hands on” learning for when students are ready for such. The skills and targets are different; the means to attain them the same. [Emphasis added.]

The briefs do not promote these evidence-based best practices for math instruction, and, in her response, Ball nowhere justifies her claim that “instructional methods cannot be generalized.” She simply asserts it. Where is her evidence that different methods are needed for the different components? Where is the evidence that Ball’s methods do better for these strands than explicit instruction and timed tests? Where is the evidence that Ball’s methods are better for different learners?

This last question is particularly important. Rigorous research finds that students who struggle with math and students with disabilities are even more in need of explicit instruction than students who are proficient. Yet Ball gets away with claiming, without justification, that the briefs “provide evidence-based guidance” for teaching “students with special needs and multilingual learners, as well as students who are denied opportunities to engage in mathematically challenging work.”

At this point, the reader should be able to predict what happens in her next response.

“Criticism #3: The briefs do not align with the ‘science of math’ and the ‘science of reading.’”

Ball asserts that “the ‘science of math’ is not ‘settled science’ and scholars … continue to research, develop, and critique the evidence base for each.” She continues:

The work conducted by psychologists focuses on particular versions of direct instruction and on basic arithmetic skills. These studies do not provide evidence related to the learning goals in the standards for mathematics learning. […] New York’s standards […] specify goals for mathematics learning that include but go beyond arithmetic computation with speed and accuracy [...] includ[ing] conceptual understanding and mathematical reasoning.

This is the Two-Step as usual. Ball first narrows the scope of her opposition: the work of “psychologists on particular versions of direct instruction and basic arithmetic skills” only concerns “speed and accuracy.” She then denies that studies or methods germane to speed and accuracy could also be germane to the recommendations in her briefs: “these studies do not provide evidence related to the learning goals” beyond speed and accuracy, such as conceptual understanding and mathematical reasoning. She does not mention that the petitioners also value conceptual understanding and mathematical reasoning, but stress that those goals are out of reach without sufficient procedural fluency. Neither does she allow that the studies themselves could be relevant; the evidence base is simply different.

The “not-settled-science” gambit offers one novel twist on the Two-Step, but no one claims the science is “settled” in some final sense. All education researchers — including Ball herself — are more than welcome to conduct and publish new rigorous research revealing data incompatible with the current consensus, or revealing that they tried and failed numerous times to replicate landmark experiments. These would be incredible findings; if such revolutionary studies stood up to scrutiny, they would be cited with alacrity and could certainly secure a tenure-track position for a junior co-author.

This is how healthy, evidence-based science works: the scientific consensus shifts when multiple rigorous studies produce results inconsistent with that consensus. What makes “the science of math” and “the science of reading” so impressive is that rigorous studies keep piling up that converge on the same results. But Ball cannot provide research that disproves that consensus on equal footing, so she deflects by mischaracterizing the goalposts of scientific inquiry instead.

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Setting the Facts Straight

After two pages spent poisoning the well, the final section of Ball’s response addresses the briefs’ alleged factual inaccuracies. The petition draws particular attention to four issues and the briefs where they occur:

1. The myth of math anxiety and timed testing being a cause of math anxiety (Brief 2);

2. The myth of explicit instruction (or direct instruction) being a selective instructional strategy, mostly useful for the disabled (Brief 2, 4, 7);

3. The myth that structured repeated practice of math facts and standard algorithms isn’t useful (Brief 2, 3, 7); and

4. The myth that discovery learning should be prioritized in the early stages of acquisition (Brief 2, 4, 7).

Because Ball’s approaches to myths 1 and 3 share a similar structure, as do her approaches to myths 2 and 4, it is helpful to treat them in these pairs.

Timed Tests and Repeated Practice (Myths #1 and #3)

The research consensus highlights two important functions for timed tests and assessments. First, they are essential for academic screening and formative assessment — assessment that informs teachers of how best to respond to students’ needs. Second, timed assessments are a valuable form of structured, repeated practice, which is highly effective for training students’ fluency and automaticity with basic math facts.

To the charge of perpetuating myth 1, Ball responds that “Brief 2 does not say that timed tests are the sole cause of math anxiety.” Instead, the brief merely “challenges the claim that such drills are the only way to develop fluency,” since although they do accomplish this, “they can raise anxiety, and … there are other approaches to develop fluency.”

To the charge of perpetuating myth 3, Ball responds in a similar way:

Brief 2 points out that timed practice of isolated facts is not the only way for students to develop fluency and procedural skill. It cautions that such methods can have negative effects and recommends considering other kinds of practice that involve quick repetition along with reasoning.

Notice the rhetorical sleight of hand. The petition does not accuse the briefs of saying that timed tests are the sole cause of math anxiety, nor that structured repeated practice is the only way to develop fluency. The accusation is that the briefs minimize the value of timed tests and repeated practice — practices that are among the very best supported by the evidence. Ball now spins this minimization as merely “challenging” the idea that these practices are the “only” way, a claim no one made. This is the classic motte-and-bailey: state strong claims, then when challenged, retreat to weaker, more defensible versions of those claims. Yet these more defensible versions still completely miss the point.

The petition makes clear that evidence-based timed tests are essential for formative assessment. It also addresses the true cause of math anxiety: poor math comprehension, which the best practices directly address. Teaching students the basics effectively reduces math anxiety, because students who understand math have less to be anxious about. Moreover, when Ball suggests “other approaches to develop fluency,” she cites no high-quality studies demonstrating that her alternatives are as effective as timed practice. The petition’s criticism stands: the briefs deemphasize what works in favor of what sounds good.

Explicit Instruction and Discovery Learning (Myths #2 and #4)

The research consensus also highlights the importance of explicit instruction, which the briefs disparage, and cautions of the limits of discovery learning for early instruction, which the briefs contravene. Ball responds that the briefs merely “challenge the universal recommendation that all mathematics is best taught through explicit and highly directed instruction.” Moreover, she claims, Brief 2 does not recommend “pure discovery,” but “guided discovery,” which purportedly does not suffer the same pitfalls as “pure discovery.” The brief “makes clear the need for structured and scaffolded instruction as well as for inquiry that is carefully set up and guided.”

Here in her response, finally, Ball concedes that explicit instruction is appropriate — a concession that any educators reading the briefs themselves would struggle to find. After diminishing the research on the effectiveness of explicit instruction, Brief 2 suggests it is often not “grounded in meaning” — whatever that means. Later, Brief 4 alleges that explicit instruction assumes students are “empty vessels” and not “sense-makers”; no evidence is offered to support this, nor is the construct “sense-making” ever defined. In Brief 7, this allegation is echoed with warnings (again without citations) that teachers must “consider with care whether explicit instruction guidance is mathematically accurate and not just getting students to get right answers” and that “explicitness … might constrain students’ sensemaking.”

In stark contrast to the now skeptical, now denigrating treatment of explicit instruction, discovery-based approaches are introduced enthusiastically and without similar caution. A teacher relying on the briefs for guidance would reasonably conclude that discovery learning is the preferred approach and explicit instruction a fallback for struggling students.

But Ball’s response ignores the petition’s central criticism: “Discovery learning is important, but it should occur for mastered concepts and skills … not when a new skill is being introduced….” The research is clear that discovery approaches work best after students have already developed fluency through explicit instruction — not before.

The briefs also fail to warn teachers about the significant limitations of discovery-based methods. Teachers must be extremely skilled to implement discovery methods effectively; discovery takes far longer than explicit instruction, meaning less material can be taught in the same time; and children can “discover” the wrong rules and go uncorrected, ingraining misconceptions that are difficult to undo. None of this appears in the briefs. A document claiming to offer “evidence-based” guidance should at minimum acknowledge these well-documented pitfalls.

Neither is Ball’s appeal to “guided discovery” a convincing defense. The extent that “guided” is better than “pure,” she says, is because “structured and scaffolded instruction” is important and “inquiry” should be “carefully set up and guided.” But these are precisely the virtues of explicit instruction! The more structured, the more scaffolded, the more carefully guided — the closer we get to explicit instruction by another name. At what point does “guided discovery” become simply explicit instruction with a progressive gloss?

This is not a minor terminological quibble. In any rigorous field, methods must be specified clearly enough to be replicated. “Guided discovery” fails this test. It functions less as a well-defined instructional method than as a rhetorical escape hatch — capacious enough to absorb any criticism by claiming to include whatever element the critic finds missing. If a study shows pure discovery fails, defenders claim they meant guided discovery. If explicit instruction outperforms inquiry methods, they claim guided discovery includes explicit elements. The term operates much like “balanced literacy” did in the reading wars: a catch-all that can never be pinned down, never be falsified, and never be held accountable for poor results.

Until Ball specifies what “guided discovery” involves concretely — what teachers should do, in what sequence, with what safeguards — it is not a method. It is an evasion.

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The Equity Contradiction

Three months after the petition was sent, the briefs remain in place. NYSED was sold a bill of goods: they trusted that “expert” recommendations were “evidence-based” without knowing how to evaluate the claim, and they have dismissed the concerns of the petitioners who pointed it out. One might wonder how Ball and her supporters at NYSED justify promoting pedagogical approaches that the best evidence shows are less effective. The answer lies in how they frame their goals.

Advancing equity is a core theme of the numeracy briefs, not merely a goal of math instruction but as a lens through which all instructional decisions must be filtered — curriculum content selection, assessment, representations, leadership. In practice, this lens consistently tilts in one direction: away from measuring whether students have mastered specific skills, and toward ensuring they feel affirmed and positively identified with mathematics. Brief 2 warns that “poor performance on timed tests” could lead students to be “labeled as ‘below’ or ‘behind.’” Brief 3 instructs teachers to “acknowledge” the “competence” of all “students’ mathematical ideas” so they can disrupt “patterns of inequity that position students as ‘struggling,’ a pattern that disproportionately affects students of historically marginalized identities.” Brief 5 cautions that identifying what students don’t know “can contribute to the reinforcement of deficit orientations associated with marginalized identities,” and when performance differences appear across demographic groups, tells teachers to “interrogate” whether “their results are accurate” — the implication being that the assessment, not the instruction, may be at fault. A teacher reading these briefs would learn to be suspicious of rather than responsive to her own assessments, and she would trust that the recommendations help her disadvantaged students on the basis of reassurances, not evidence of effectiveness.

This framing does not come from nowhere. TeachingWorks, Ball’s organization, markets itself as having “evolved to explicitly support teachers and teacher educators to disrupt persistent patterns of injustice.” A visitor to the Approach & Impact page is immediately assured that “Equitable practice is always at the core” of the TeachingWorks mission; their P–12 programs and services are “based in research that aim to disrupt injustice and advance equity in teaching and teacher learning.” These are each admirable goals. But in the briefs, “equity” and “evidence-based” are treated as though they mean the same thing. Brief 8 four times uses the phrase “equitable and impactful mathematics teaching” as a single concept — as though a practice cannot be equitable yet ineffective, or effective yet inequitable. The effect is to make the briefs’ recommendations unfalsifiable: if evidence-based instruction and equitable instruction are the same thing by definition, then no evidence can show that the briefs’ preferred methods fail disadvantaged students. The briefs simply beg the question that their approach is equitable because they intend it to be.

Ball and NYSED reinforce this insulation by framing their critics as politically motivated. O’Hare’s introduction to Ball’s response notes that the petition was publicized by the “conservative Manhattan Institute” and accuses critics of “politic[izing]” the work. But the petition opens by stating that its diverse signatories want to “equip all children with mathematical knowledge” and “close opportunity gaps” — hardly a conservative attack on equity. By dismissing critics as ideologically motivated, Ball and NYSED avoid engaging with their substantive arguments. This is an ad hominem defense, not an intellectual one.

And the substance matters, because the empirical evidence points in the opposite direction from the briefs’ assumptions. Explicit instruction significantly outperforms constructivist approaches for struggling students and students from disadvantaged backgrounds. When students lack background knowledge or foundational skills, they benefit most from clear, direct instruction that builds competence step by step. Discovery-based approaches tend to widen achievement gaps: students who already have strong foundations can “discover” new concepts, while those without the requisite fluency are left to flounder. As Carl Hendrick has written, there is a painful irony in progressive educators championing methods that further privilege already-privileged students while disadvantaging those most in need of structured support.

No one wants to talk about excellence in public schools

We have seen this pattern before. Whole-language instruction was promoted as more authentic and engaging than phonics, but it was students from disadvantaged backgrounds who suffered most when schools abandoned systematic reading instruction. Ball explicitly resists comparisons to “balanced literacy” and “the science of reading,” and for good reason: public sentiment has finally caught up to the reading reformers, and whole-language approaches are now broadly discredited. Ball knows where this story ends.

The briefs tell teachers that identifying struggling students reinforces “deficit orientations” and that assessments may reflect bias. But a child who cannot fluently add and subtract does not need her identity affirmed. She needs to be taught.

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Conclusion

Recall the good news: leaders like Governor Hochul and Chancellor Samuels are beginning to recognize the importance of evidence-based math instruction and automaticity. Yet they face an uphill battle against a throng of institutions — the education department, the associated ed schools, the professional development providers — committed to approaches that the evidence doesn’t support.

The point isn’t just that more math teachers in New York are going to be misled by the content of Ball’s math briefs. We may take some solace in knowing that these sorts of statewide instructional materials often go unread by many teachers; they are not the be-all-end-all for teaching kids, and even when poorly made likely can’t derail an entire state’s math instruction. But the briefs are an endorsed artifact of a state education agency. And not just any state’s, but New York’s. That means there are system-level issues with how we produce and signal educational expertise, on the one hand, and how we hold education agencies and officials accountable, on the other.

The emperor who has no clothes should be embarrassed, and the subjects who don’t speak up should be ashamed. So let’s keep the pressure on. The petition to retract the NYSED briefs has 216 signatories and counting, and it deserves even more attention — from parents, teachers, and the policymakers now pledging a “back to basics” approach. Every educator who reads the petition and Ball’s response can see the bad arguments and clichéd dodges for themselves. Public accountability matters, even when public pressure doesn’t produce immediate results. The embrace of science by the American education establishment is long overdue, it is only through that pressure that the “experts” who guide education policy will grow to deserve that title.

American students deserve math instruction grounded in the best available evidence, not meager reassurances that poor methods are just “different” from ideologues dressed in lab coats. The path forward is the same one the reading reformers eventually won: explicit instruction, practiced fluency, and honest assessment. The only question is how long it will take for the institutions to catch up.

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David Shuck is a contributing writer and editor at the Center for Educational Progress.

1. The briefs employ the five-strand model of math competence presented in the 2001 report Adding It Up. In this model, there are “five interwoven mathematical proficiencies necessary for student success”: “adaptive reasoning,” “strategic competence,” “conceptual understanding,” “productive disposition,” and “procedural fluency” (Brief 1, p. 1). While Adding It Up states that “All strands of proficiency can grow in a coordinated, interactive fashion,” it does not defend the stronger claim, found in Ball’s response, that different strands must be both a) developed via different instructional methods and b) studied via different research methods (Adding It Up, p. 11).