Despite the progress schools and districts have made on returning fully to in-person instruction, some of the habits and apprehensions they’ve developed over the last thirteen months could impede their upcoming education recovery efforts. The global shock and disruption mean schools should not underestimate how this post-Covid hangover could linger in the weeks and years ahead, carrying with it significant repercussions as the work of stabilizing the system gets underway.

Even now, a whopping 70 percent of K–12 educators still believe the pandemic is a “real threat” to their school district. Parents, too, have their reservations, with some planning on waiting until their children have been vaccinated before sending them back to school, which for younger children probably won’t happen until next year. What’s more, low-income and minority students—especially those living in marginalized communities—are the most likely to be missing out on in-person learning and the least likely to return to school. Taken together, these philosophical and demographic divides might make the already formidable task of catching students up even more challenging.

Three things in particular could really gum up the works.

The first is whether mask-wearing should still be required in schools in 2022 and beyond, an argument that is as much about our raging culture wars as it is about public safety. Vaccines are now available to any adult that wants one, generally without delay. Partly because of this, some parents are beginning to wonder why their children should be compelled to wear masks if the adults in the school have already achieved immunity, or decided to take their chances without the miracle of modern medicine.

To be sure, some teachers and students could continue to wear masks in perpetuity; there should be no quarrel with those who make this choice. The tension arises now that we’ve entered a period of declining prevalence and rising vaccination rates. Case in point, Arizona’s governor just lifted the state’s mask ordinance in light of their rapid progress on vaccines. In response, the state’s schools chief threw a fit, calling the decision a “bomb” that’s been dropped upon Arizona’s schools. This kind of rhetoric may have been defensible in April 2020 when vaccines were a distant possibility, but it’s borderline irresponsible a year later given the tools and information now at our disposal.

Is it really a big deal to ask students to wear a mask? If the goal is to get more families—especially families of color—comfortable with sending their children back to school, there’s an argument to be made that mask mandates might help. The counterargument is that an indefinite enforcement of mask-wearing becomes superfluous as infection levels drop and as more students and teachers get vaccinated. Blanket mask edicts also fail to take into account local circumstances and other trade-offs to say nothing of the disincentives towards vaccination that can be created.

Regardless, this issue is coming to a head between parents and school districts across the country. Consider the words of Courtney Ann Taylor, a mother in Georgia who recently delivered an impassioned plea on behalf of her six-year-old daughter to her local school board:

It’s April 2021 and it’s time. Take these masks off of my child. And I know what I’m going to be met with: “But Ms. Taylor, the CDC.” We did not vote for people at the CDC. We did elect leaders who do create policy. We elected the five of you. We chose you to make difficult decisions for our children…

The video of her testimony has since gone viral, generating equal parts sympathy and scorn. But if left unresolved, this fracas could pose a real distraction to getting schools back to any semblance of the ordinary. It also illustrates the fact that not everyone is ready to rush headlong into a world where all schools are reopened as normal.

Second, the future of standardized testing and the information those exams provide will be in greater jeopardy following two consecutive years without them in many jurisdictions. From Los Angeles to Washington, D.C., millions of students, teachers, and families will have grown accustomed to the absence of a yearly academic checkup, and, the thinking goes among testing opponents, they will be none the worse for it. As a result, the never-ending debate is about to enter new and uncharted territory as more parents and educators alike question the whole premise of the current testing regime. Indeed, if federal education law has been tested by the pandemic, it’s by the stress that’s been exerted upon annual assessments and results-based accountability.

Finally, there’s the pernicious spread and stickiness of the four-day school week, a subject I’ve written about previously in this space. It was largely an Intermountain West phenomenon until the pandemic. The idea has since exploded as thousands of districts have used the discredited pretense of deep cleaning to dial back the amount of live instruction per week. To wit, the four-day model is now common in New England states, and there’s a real danger that schools and systems have become attached to it. If these districts carry the abbreviated school week into the next school year, there will be even fewer instructional minutes and hours available at a moment when time on task is of the essence.

We are nothing if not creatures of habit, and in the case of keeping masks on, testing off, and four-day school weeks the new normal, these routines may prove to be stubborn habits to break. According to the American Psychological Association, nearly half of Americans feel uneasy about returning to their pre-pandemic lives—including those that have already been vaccinated. Schools and districts will be called upon to help overcome this post-Covid hangover. So while it’s heartening to know that teachers are setting their sights on the tutoring and other programming that may soon be required—with policymakers laying out the tools to help—we would do well to keep an eye on the abiding crisis-mongering and bad-news bias that continue to shape habits and threaten to handicap the best laid plans for reopening schools.

Think of Michael Petrilli’s bold ideas and the Acceleration Imperative as newly designed Ford(ham) vehicles for K–12 recovery from the pandemic. Happily, there is much to admire in the showroom.

Fordham has two models in mind. The first is fairly conservative. It features improved instructional materials, professional learning, and accountability, while adding high-dosage tutoring and mental health services. The second is an experimental “move at your own pace” model, featuring personalized learning and up to an extra year of schooling, such as a 2.5 grade, for most students. “[W]e need to be willing to rethink our traditional ways of doing school,” he writes, and there’s no question he’s most excited about the experimental model.

Integral to both is the need for innovation and evolution based on research and development. And that is all to the good. It’s hard to fault the open and well-rounded approach that is embodied in the crowd-sourced Acceleration Imperative platform. Practitioners as well as policymakers are encouraged to drive the process with their own views.

And yet, despite all these praiseworthy attributes, Petrilli’s ideas and the Acceleration Imperative are unlikely to ever get up to full speed for two big reasons. One is the lack of money to pay for many of the ideas. The other is lack of enough attention to management support for frontline teachers and administrators.

Money is, of course, a familiar and contentious subject. But few would dispute that some of the proposals put forth by Fordham—for example, extended school time, an extra year of schooling, high-dosage tutoring, and mental health services—are pricey. Yet the price tags are almost never factored in or even mentioned. 

Yes, all the federal bucks flowing from pandemic relief bills seem to be creating a new education zeitgeist that is lifting educators from the depth of pandemic despair to the heights of reimagined, better—and more expensive—futures forever. But let the buyer beware. The money won’t be around longer than a few years. Plus there is the danger that much of it will be wasted because of pressures to spend rapidly, and to spread the money too thinly in response to the political clout of competing interests.

In any event, long-term implementation of reforms like those on Petrilli’s list and in the Acceleration Imperative will cost a lot more money than school systems will have after the federal funding bonanza runs out.

Further, management support for administrators and teachers has not gotten the attention it deserves—although it is, arguably, more important and riskier. For decades, education reforms, particularly instructional policies and programs, have petered out because of inept implementation. In part, that’s because of the well-recognized fact that education R & D is a near wasteland in comparison to medicine, industry, science, and technology. It’s also because of policy and practice churn caused by education politics. And most basic, educators are not generally good managers. They lack professional training and suffer from a professional culture that devalues managerial skills and accountability principles.

These management weaknesses call into question some of the benefits of that hardy perennial for reformers—innovation. Thinking outside of the box or letting a thousand flowers bloom are worthy principles, particularly for ossified education bureaucracies. Yet, as the late Robert Slavin, an expert on evidence-based best practices, said: “The problem of education reform is not a lack of good ideas, but a lack of good ideas sensibly implemented.”

So how do we balance being open-minded and experimental against making sure what we’re already supposed to be doing is being done effectively? For instance, would grade 2.5 be needed if early interventions were well funded and implemented efficiently—especially high-dosage tutoring within a Response to Intervention (RTI) framework. The weight of evidence says it wouldn’t.

To get to the right balance, state departments of education have an underappreciated role to play in high-quality implementation of current and future policies and practices. Contrary to conventional understandings, SEAs have legal control and responsibility under state laws and federal laws (such as ESSA, IDEA, and Title I) to ensure that funds are well spent. To this end, their critical role includes basic tasks that should influence what goes on in the classroom. They should presumptively require (subject to waivers for compelling reasons) evidence-based best instructional practices. At the same time, while empowering local educators, they must provide detailed technical assistance, including professional development and practice manuals. Then they must vigorously monitor for fidelity of implementation, collect data on outcomes, and guide continuous improvement.

An exemplar is John White’s past work in Louisiana. As state superintendent, he “quietly engineered a system of curriculum-driven reforms...with incentives for districts and schools statewide to adopt and implement [them].” However, few if any state departments have done the same. Robert Pondiscio recently noted the “open question...whether literacy laws—from mandating phonics to third grade retention policies—can have a beneficial effect on classroom practice.” We can’t answer that until such laws, far flung across the states, are adequately funded and well managed.

One illustration: The Council of Chief State School Officers, in a detailed report, Third Grade Reading Laws: Implementation and Impact, emphasizes “Passing a law is only the beginning.” I know from my current research on such laws that it is virtually impossible to get data on implementation or outcomes from the many states and national organizations I have contacted.

That doesn’t mean that federal or state dictates should emasculate local control, and it couldn’t happen even if desired, given the political potency of local control. But surely evidence-based best practices, as ESSA and many state laws already require, should be outside the realm of local autonomy.

While expressing these concerns about Petrilli’s proposals and the Acceleration Imperative, I root for what they’re driving at. I hope I have not undersold the value of their ideas and commitment to sustainable implementation. Still, without incorporating more money and much better management, the reform designs, I fear, will fall far short of their potential.

Numerous studies have found that the quality of child care is too low and that we need to do more to strengthen it. And the problem is not confined to center-based care. According to a 2014 report from the National Center for Education Statistics, 48 percent of home-based childcare rendered by a relative (sorry Mom!) or a non-relative was reported to be low- or medium-quality (based on everything from interactions with the child, to the quality of activities, to the adequacy of the space and furnishings). Moreover, childcare arrangements are often of poorer quality for disadvantaged children. For example, only 16 percent of children from families in the bottom income quintile received care rated to be good or better.

The ability of policymakers to make top-down changes in the quality of home-based care is limited, but better information about how parents perceive quality could make for bottom-up improvements, which are even more needed post pandemic. A recent study in the Economics of Education Review documents an experiment that sheds light on how parents think about childcare quality through their revealed preferences.

Researchers from American University and the University of Arizona designed a large field experiment that focuses exclusively on the “unlisted paid market of childcare,” meaning caregivers seeking work within the home of the family requesting childcare and paid by that family at a negotiated rate. Caregivers tend to be nannies, au pairs, and babysitters generally with no prior relationship with the family. They are unlicensed, operating outside of their state’s center-based regulatory regimes, and consequently are likely to be less skilled, younger, and more disadvantaged than their center-based peers.

Analysts randomly assigned several characteristics to fictitious caregiver profiles that they created on a large, online childcare job service that connects families with providers. More specifically, they assigned three dimensions of caregiving: affordability, which is the hourly price of childcare; quality, which is caregiver education and experience; and convenience, which is caregiver car ownership and availability. The randomization was carefully carried out to ensure that the treatment variables assigned to the profiles were balanced across families’ observable characteristics.

Between March 2017 and May 2018, they deployed these fictitious profiles to respond to 8,000 job advertisements in eight large cities across the United States. Job postings were chosen for a response based on an assessment of the perceived “seriousness” of the posting family, location of work within thirty miles of the central city zip code, an offer of ongoing employment, and a few other criteria.

Analysts used eight identical profiles (the only difference was the first name of the applicant), with one application submitted in response to each posting. All profiles were of a thirty-year-old white female with the same photo, who was English-speaking, non-smoking, completed first-aid training, and was comfortable around pets. In a nutshell, they examined the likelihood that their made-up applicant—with a given set of randomly assigned characteristics—would receive an interview request or an on-the-spot hire.

The topline finding is that parents are extremely sensitive to the cost of childcare. Caregivers charging $10 to $15 per hour had a one in three chance of receiving an interview; when the hourly wage increases to $20 to $25 per hour, the odds fell to one in eight. Parents also demonstrated strong preferences for quality, particularly caregivers with higher educational attainment. More specifically, compared to individuals with a high school degree, those profiles with an associate degree were 25 percent more likely to receive an interview, and those with a bachelor’s 37 percent more likely. There were declining returns to experience in that those with three, five, seven, and nine years of work experience were preferred over those with just one year, but the response rates fall off for those with more than nine years. Applicants with cars were 15 percent more likely to receive an interview, but parents seem indifferent to caregivers with a higher level of availability, which is defined as the flexibility to work nights and weekends, presumably because most are looking for caregivers to cover the traditional work day. Additional analyses find that the wage variable—specifically what looks like willingness to pay—is actually driven by ability to pay as reflected in the families’ income levels.

The researchers conclude that low-quality childcare may be explained by lack of affordability or information available to identify high-quality childcare, rather than parents not valuing it. Parents can only assess—and place a value upon—the information at their disposal. Thankfully, formal, state-licensed programs are now collecting more detailed measures of quality that are being linked to outcomes. As we get better measures of childcare quality, those definitions should trickle down to the home-based sector. Because, although it’s super convenient to have a provider come to your house to look after little Susie, they need to do far more than babysit.

SOURCE: James A. Gordon, Chris M. Herbst, and Erdal Tekin, “Who's minding the kids? Experimental evidence on the demand for child care quality,” Economics of Education Review 80 (2018): 102076.

Problem solving involves a complex set of mental steps, even when it happens quickly. A group of researchers from the University of Virginia sought to test one specific aspect of the process—the types of solutions people consider—and uncovered what could be an important human attribute, with significant implications for public policy.

They were interested in determining whether problem solvers have a tendency to opt for additive or subtractive solutions. That is, when faced with a problem that requires the transformation of an object, idea, or situation—say, a change to a recipe—how often do people add components (ingredients or steps, perhaps, if it’s a recipe) versus take them away?

The researchers conducted eight separate experiments, three in person and the rest virtually. Approximately 200 to 300 people participated in each for a total n-size of 1,585. Examples of experiments include modifying a Lego structure to support a brick, when adding pieces cost money and removing pieces is free; improving the design of a mini-golf hole, where multiple changes are allowed and recorded; and fixing a multi-colored asymmetrical digital grid pattern to be perfectly symmetrical by changing block colors, in which the only correct option was a subtractive one.

The bottom line is that no matter the problem at hand or the incentives provided, people tend to default to additive transformations and, in doing so, completely overlook subtractive options. For example, in the digital grid experiment, only 20 percent of participants favored subtracting blocks even though that was the only successful option. In another experiment, just 11 percent of improvement suggestions offered to an incoming university president via anonymous drop box were subtractive in nature. Across the board, participants choosing a subtractive transformation in an experiment never cracked 40 percent. In fact, most experiments were closer to 25 percent.

Participants did offer a greater number of subtractive solutions when they were given specific instructions to consider taking something away, when such options were made obvious (“Improve this grilled cheese and chocolate sandwich”), and when they were provided with several opportunities to propose solutions such as with the mini-golf example. But the researchers note that the need for such conditions underscores the human predisposition toward additive options.

The study concludes by saying that this bias toward addition—where “more” automatically equals “better”—could explain certain aspects of societal ills such as overburdened schedules, institutional red tape, and damaging effects on the planet. In a Washington Post analysis of the study, one of the researchers points to legislation and public policy as other areas where less might be more. In the realm of education, there is a tendency toward making teaching and the running of schools more complex over time, not less. We are forever adding new initiatives—putting new problems to solve on teachers’ plates while never taking anything off. If only decisionmakers could see and embrace “addition by subtraction,” new and better solutions may be more likely to emerge.

SOURCE: Gabrielle S. Adams, Benjamin A. Converse, Andrew H. Hales, and Leidy E. Klotz, “People systematically overlook subtractive changes,” Nature (April 2021).

• Yes, the pandemic affected the mental health of many young Americans, but the data don’t show a significant increase in suicides. —The Atlantic
• “Grade inflation is ruining education.” —Quillette

Cheers

• D.C. district leaders made it clear that they expect all children to be back in school in the fall unless students or families have a legitimate health concern. —Washington Post
• Tennessee’s department of education ruled that public school districts won’t be offering hybrid options in the fall, putting an end to the widely-despised “Roomers and Zoomers” model. —WBIR 10 News

Jeers

• Virginia's new approach to middle and high school math could “erode rather than advance equity.” —Andy Rotherham
• “Charter founder Seth Andrew charged with stealing over $200,000 from civics-focused network he created.” —The 74
• Parents, students, and teachers from both sides of the aisle are fed up with woke indoctrination. —Erika Sanzi
• Thousands of districts are doing four-day weeks this year, robbing students of learning time to follow costly and unnecessary cleaning protocols. —The 74
• Des Moines public school students, encouraged by teachers and principals, are missing class to protest a bill that could expand charter schools. —Des Moines Register

Bob Slavin was a force of nature, a world-famous education researcher who was also far more than that. A policy advocate (see for example his recent proposal for a post-Covid “Marshall plan” for schools, which strikes me as akin to what Biden is now proposing) and a major “doer” in his own right. Best known of course for the “Success for All” reading program, now more than three decades old. It’s a genuinely effective approach to early reading, validated both by the federal “What Works Clearinghouse” and by its acceptance and use in hundreds of school districts. Something over 1,000 schools today and several other countries. It dates to 1987, just a few years after “A Nation at Risk,” and the evidence suggests that it’s especially effective with poor and minority kids in the earliest grades of school, when getting a leg up on literacy matters most.

But Slavin wasn’t selfish about it. Success for All is nonprofit, and Slavin’s “evidence for ESSA” website lists a bunch of other effective reading programs besides his own.

And he was a lot broader than reading. He was also a major theorist of “cooperative learning.” Author of a much-used basic text in ed psych. I think the only Hopkins ed-school faculty member who qualified as a “university” professor, which generally means very broad-gauged, able to roam across the entire university.

But he was feisty, too, and willing to engage in combat. Check out the “backlash” section in this Fordham report on what happened to Bush 43’s “Reading First” program, and you’ll see Bob as a major combatant on behalf of (I would say) both Success for All and his own sense of right-and-wrong.

In February, Governor DeWine asked all public schools to create plans designed to address the learning loss caused by pandemic-related school closures. The governor requested that schools publish them by April 1, and the Ohio Department of Education has posted them on its website to make it easier for parents and stakeholders to find them.

The importance of summer programming cannot be overstated. Although education researchers are still working to pinpoint the breadth and depth of learning loss, there’s little doubt that it has occurred and still is. Offering some type of extended learning opportunity to students who need it is crucial. This is especially true in districts with large populations of low-income students and students of color, communities that were hit especially hard by the pandemic. In Ohio, there are several districts that fit that description, including the state’s largest district, Columbus City Schools (CCS). CCS has an enrollment of nearly 50,000 students, most of whom are economically disadvantaged and students of color.

So what does CCS plan to offer students? The answer is the 2021 Summer Experience, a program that aims to “provide enriching experiences for all students in PreK through 12th grade.” The initiative begins June 15 and continues through July 22, with students attending Monday through Thursday from 8:00 am to 1:00 pm. Programming will be housed in thirteen elementary schools, ten middle schools, and five high schools spread throughout the city. Transportation will be provided, as well as breakfast and lunch. The registration deadline is June 1.

As far as eligibility goes, the district appears to be trying to reach as many students as possible. There are some programs—like “enrichment extensions” or AP Bootcamp—that are capped at a certain number of seats and don’t last all summer, likely because they require staff with specialized training or knowledge. Generally speaking, though, any student who attends a district school can enroll in their grade-specific program. Summer Experience, much to CCS’s credit, is also open to students who reside in the district but don’t attend district schools. That means charter and private school students can also register to participate, free of charge.

But what, exactly, are students signing up for? Well, that largely depends on grade level. There aren’t a ton of details—we don’t know, for instance, what a daily schedule would look like for any given student—but here’s a brief overview of what’s available.

Elementary

Students in grades K–5 can register to participate in “mini camps” that are modeled after summer camp experiences but are aimed at “strengthening academic skills, leadership, and social-emotional learning.” All thirteen of the elementary sites will offer the same programming, and students are free to attend whichever site they choose, which should give parents some flexibility. For instance, instead of being required to send their child to the school closest to their home, parents could opt to enroll their child at a building that’s closer to a caregiver’s home, daycare, or a place of employment.

For students in grades K–2, camps have been “inspired” by programming offered by the Franklin Park Conservatory. Students will have a chance to interact with specialists from the Conservatory both inside and outside the classroom and will take a field trip to the Children’s Garden. Each of the six weeks is devoted to a camp with a distinct theme, such as Jurassic Franklin Park, Pirate Palooza, and Summer Science Nature Detective. (See here for information on programming available for rising kindergarteners.) Camps for students in grades 3–5, meanwhile, have been modeled on COSI programming and will provide students with an opportunity to visit the science museum. These camps will also have distinct themes, such as Gadgets to Go, Mission to Mars, and Superhero Science.

Middle school

Unlike their younger peers, middle schoolers won’t be attending a differently themed mini-camp each week. Instead, each school site will offer its own themed camp for the duration of the summer. Programming for these camps was designed by CCS staff and teachers in collaboration with the PAST Foundation, and will “use design-thinking strategies to solve real-world problems.” Students can choose to attend whichever camp interests them, with options including aviation, cyber security, the business side of eSports and gaming, fashion in STEM, food science, medicine, robotics, and 3D modeling. A small number of seats will also be available for middle schoolers interested in two-week long “enrichment extensions” offered at Spruce Run—the district’s environmental education center—with transportation provided. There are five options, including a Survivors Camp where students will read Hatchet by Gary Paulson and work on mastering survival skills. 

High school

At the secondary level, Summer Experience offerings get a little more complex in order to reflect the broad needs of high schoolers. There are six options:

• Credit recovery. Students in grades 9–12 who failed a course this year can complete credit recovery through APEX, the district’s virtual learning platform. 

• Credit advancement. The Virtual Credit Advancement Program (VCAP) allows students in grades 10–12 to complete self-paced courses that combine technology and individualized teacher instruction. Students who successfully complete these courses will be awarded high school credit.

• Traditional summer school. Current eighth and ninth graders—rising ninth and tenth graders—can enroll in a six-week, in-person learning experience focused on interdisciplinary “community-based impact projects.” This program will be instructor-led through a partnership between CCS teachers, The Ohio State University, and the Korda Institute of Teaching. Classes include English 9, Physical Science, Algebra I, and World Studies.

• College Credit Plus. The opportunity to earn college credit will be available at several higher education institutions for students who meet College Credit Plus eligibility qualifications.

• AP Bootcamps. Students who are enrolled in AP Calculus and AP English for the upcoming 2021–22 school year can enroll in a weeklong bootcamp that will introduce them to the content and skills that will be taught in the upcoming year.

• Outdoor programs and enrichment at Spruce Run.
  • Students in grades 8–11 can complete a six-week course that will give them credit for Physical Education I and II courses.

  • Eleventh and twelfth grade students who have completed biology can earn a credit for environmental science—an advanced science class—by passing a six-week course that includes the completion of three independent, research-based environmental projects.

  • Students can participate in a two-week Counselor-In-Training program that allows them to earn up to fifty volunteer hours per session. (Volunteer hours can be used to earn several seals needed for graduation.)

***

It’s hard to tell based on the limited information that’s available whether these programs will help students regain academic ground they lost over the last year. But to be fair, it would be impossible to judge any new program that’s been built from scratch in a matter of months to address fallout from a never-before-seen pandemic. There are several aspects of Summer Experience that seem promising, such as STEM-focused camps for third through fifth graders, and the wide variety of themed camps available for middle schoolers. But there are also aspects of the plan that should give parents and advocates pause. For instance, offering online credit recovery programs is probably cheap and easy. But after a year of virtual learning where many students struggled because their classes were online, having them take yet another online class seems unfair.

Overall, though, the extended learning plan put forth by CCS deserves praise. Like the summer offerings at affluent private schools and high-performing suburban districts, the CCS Summer Experience reflects an intentional effort by district leaders and teachers to offer students engaging summer programming that will improve hard and soft skills. The district has made that programming available to all of Columbus’s children, even if they don’t attend district schools. And in every grade band, the district has chosen to collaborate with at least one well-respected community partner in ways that will have a direct impact on students. There’s always room for improvement and growth, but CCS deserves a whole lot of kudos for this plan.

1. Brunswick City Schools recently celebrated its third “clean audit” award over the last seven years, bestowed by the Auditor of State. (Cleveland.com, 4/27/21)
    
2. However, the true award for fiscal excellence must go to Chloe Green. Hands down. The 19-year-old central Ohioan graduated from her charter school at age 16, started her own business while holding down two other jobs, invested like a savant, and saved zealously toward her goal. She has now become what some folks believe is the youngest DIY home buyer ever in the area. “Kudos” seems a little tepid for such a mighty accomplishment, but I get the feeling we’ll be needing even more and greater accolades for Ms. Green in the future. (Columbus Dispatch, 4/28/21)

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Editor’s note: The Thomas B. Fordham Institute recently launched “The Acceleration Imperative,” a crowd-sourced, evidence-based resource designed to aid instructional leaders’ efforts to address the enormous challenges faced by their students, families, teachers, and staff over the past year. It comprises four chapters split into nineteen individual topics. We're publishing each as a stand-alone blog post.

What little data we have indicates that remote learning has been particularly challenging for students in mathematics. Schools will need to ensure that their recovery strategies allow ample opportunities for students to complete unfinished learning before moving on to new concepts.

Adopting and faithfully implementing a high-quality elementary mathematics curriculum that is aligned to college and career-ready standards—the same curriculum across all grade levels—is one essential step. Such a curriculum does the following:

• Concentrates heavily on arithmetic. Students analyze and solve word problems, practice calculating fluently with mental math and written algorithms, and use the four basic operations on whole numbers, fractions, and decimals.


• Provides sufficient practice with procedures and basic math facts—all developed on a basis of concepts and understanding.


• Enables teachers to orchestrate effective forms of mathematical discourse during lessons, such as eliciting connections between different representations of a problem, or connections between different student strategies.


• Includes effective supports for English learners.


• Enables teachers to involve parents in their children’s mathematical education.

Recommendations

• Adopt and implement a single, high-quality elementary mathematics curriculum across all grades and schools that is aligned to college and career-ready standards. EdReports has given strong favorable reviews to several products, including two we consider exemplars: Eureka Math and Zearn. Their materials are free or low-cost, and both have been adopted widely by some of the best-performing elementary schools in the country.


• Use the same curriculum for interventions and supports—including high-dosage tutoring—that is used for regular classroom instruction.


• Dedicate training and planning time to help teachers develop expertise in the curriculum, including building on what students already know to connect them to grade-level work. In math professional-learning sessions, as in other areas of the curriculum, staff developers should explicitly link what teachers are learning to the curriculum they are using.

Rationale

The research base identifying what works in mathematics education is substantial—probably more so than any other subject. There are, for example, four different Institute for Educational Sciences Practice Guides that contain a total of twenty-eight recommendations, all of which are backed by an extensive body of high-quality research. These three are particularly important and instructive:

• Studies show that students become more efficient and flexible in selecting appropriate ways to solve problems when they have been regularly exposed to questions that require different strategies to answer. For example, in Eureka Math and Zearn, teachers facilitate classroom discussions about the strategies selected, with questions such as “Which strategy do you prefer and why?” or “Which strategy is the most efficient?”


• Research also underscores the importance of teaching students how to use visual representations. Students who learn to visually represent the mathematical information in problems prior to writing an equation are more effective at problem solving. High-quality curricula build this progression into the development of all concepts.


• How fractions are treated, beginning in the earliest grades, is another hallmark of high-quality programs. IES reviews the research and concludes that “a high percentage of U.S. students lack conceptual understanding of fractions, even after studying fractions for several years.” This conclusion supports using a curriculum that places a high premium on building a conceptual understanding of fractions and the ability to use them to think mathematically.

Reading List

Achieve the Core. (2013). K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics.

• The basis for the quality indicators used by EdReports in its curriculum reviews. Describes necessary instructional shifts and establishes criteria for how those should show up in curriculum.

Atkinson, R., Derry, S., Renkl, A., and  Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181–214.

• Curricula that include multiple worked examples for math problems are effective at promoting conceptual understanding.

Cooper, G., and Sweller, J. (1987). The effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347–362.

• When lessons teach students the concepts (schema) under certain math rules, students’ conceptual understanding and fluency are improved.

Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., and McDowell, J. (2013). “Teaching math to young children: A practice guide.” Washington, D.C.: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., and Witzel, B. (2009). “Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools.” Washington, D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Halpern, D., Aronson, J., Reimer, N., Simpkins, S., Star, J., and Wentzel, K. (2007). “Encouraging Girls in Math and Science.” Washington, D.C.: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education.

Jacobs, V., Franke, M., Carpenter, T., Levi, L., and Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258–288.

• Professional development on bringing in algebraic reasoning to elementary math lessons improved students’ grasp of mathematical content. Speaks to potential benefits of using a curriculum that builds in the teaching of algebraic thinking at the elementary level.

Ng, S.F., and Lee, K. (2009). The model method: Singapore children’s tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282–313.

• The method of model drawing used in Singapore’s national math curriculum for nearly all word problems has had a positive impact on student achievement.

Rittle-Johnson, B., Star, J. R., and Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836–852.

• Students’ prior conceptual and procedural knowledge is essential at the elementary school level and even more important in middle-school Algebra classes.

Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., and Wray, J. (2010). “Developing effective fractions instruction for kindergarten through 8th grade: A practice guide.” Washington, D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Tajika, H., Nakatsu, N., Nozaki, H., Neumann, E., and Maruno, S. (2007). Effects of self-explanation as a metacognitive strategy for solving mathematical word problems. Japanese Psychological Research, 49(3), 222–233.

• Promoting students’ ability to explain their thinking has a positive impact on their ability to solve math word problems.

Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., and Ogbuehi, P. (2012). “Improving mathematical problem solving in grades 4 through 8: A practice guide.” Washington, D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.