ABSTRACT

Recent literature has expressed considerable pessimism about the prospects for both productivity and overall economic growth in the U.S. economy, based either on the idea that the pace of innovation has slowed or on concern that innovation today is hurting job creation. While recognizing the problems facing the economy, this paper offers a more optimistic view of both innovation and future growth, a potential return to the innovation and employment-led growth of the 1990s. Technological opportunities remain strong in advanced manufacturing and the energy revolution will spur new investment, not only in energy extraction, but also in the transportation sector and in energy-intensive manufacturing. Education, health care, infrastructure (construction) and government are large sectors of the economy that have lagged behind in productivity growth historically. This is not because of a lack of opportunities for innovation and change but because of a lack of incentives for change and institutional rigidity.

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• U.S. Productivity Growth: An Optimistic Perspective

In his presidential campaign in 1928, Herbert Hoover promised to help impoverished farmers by increasing tariffs on agricultural products; after the election, he also asked Congress to reduce tariffs on industrial goods. In April 1929, well before Black Thursday, U.S. Representative Reed Smoot, a Republican from Utah, introduced a bill that passed the House in May. The bill increased agricultural and industrial tariffs at levels that had not been seen for a century. This was a relatively benign beginning of what would become one of the most tragic policy measures of the 1930s. Within a few months of the bill being passed in the Senate as the Smoot-Hawley Tariff Act, other countries in response raised their own trade barriers, which started a vicious circle of contracting world trade flows and economic activity, and rising unemployment from 1930 to 1933.

There are three main lessons from the policies mentioned above: 

1. “Beggar-my-neighbor” policies are bad.
2. Bad policies can have tragic consequences.
3. Beware of benign measures that can ignite uncontrollable chain reactions.

Indeed, these lessons have been in every policymakers’ mind since the Lehmann Brothers failure. In fact, the creation of the G-20 was a spectacular effort by the major economies of the world to cooperatively answer the challenges raised by the most severe financial crisis since the 1930s. The G-20 coordinated the management of strong macroeconomic policies, including huge deficits and easy monetary policies. These were bold decisions but not radical, and those who condemned government intervention have been rebutted by the urgency of these measures. And it is now widely acknowledged that these unconventional measures successfully avoided the transformation of the Great Recession into another Great Depression.

In the U.S., the recovery is at best shaky, unemployment is artificially reduced by the growing number of discouraged workers who have stopped looking for work, and the median income is dramatically lagging.

Today, there are reasons of hope that have been eloquently described by Roger Altman [1]: it can be argued that in the U.S., and to a lesser degree in Europe, the crisis has inspired significant reforms that have pushed the economy closer to a sound and sustainable growth trajectory. However others rightfull so object that enormous challenges are still facing the populations and their respective governments. The price paid for curing the damages of the global financial crisis is extremely high everywhere. In the U.S., the recovery is at best shaky, unemployment is artificially reduced by the growing number of discouraged workers who have stopped looking for work, and the median income is dramatically lagging. In Europe, austerity is the name of the game in every country except Germany and despair is growing among the populace. Japan has been stuck for two decades in deflation. Many citizens around the world feel that the efforts have gone too far, yet the benefits and retribution have benefitted too few. Electoral frustrations are on the rise as demonstrated in Italy where Mario Monti’s wise policies have been followed by the success of the Five Stars Movement of Beppe Grillo. Italy turning ungovernable is a bad sign for democracies. Could we see a comeback of desperate national policy experiments like the ones that democracies were progressively pushed to adopt after facing insurmountable difficulties in the early 1930s?

Now, a really radical policy experiment is already taking shape in Japan with the introduction of what has been named “Abenomics” after the name of the newly-elected prime minister, Shinzo Abe. It has taken only one election and one nomination at the head of the Bank of Japan to really revolutionize monetary policy. This revolution can be qualified in two ways, one benign, one threatening.

There is first reason to rejoice. After two decades of failed policies, it’s finally good to see bold politicians ready to do whatever it takes to extract Japan from its deflationary trap. Should Mr. Abe succeed, he would unclench the domestic brakes to economic growth, which deflation has so lengthily opposed: declining prices in effect are discouraging consumption (goods will be better and cheaper tomorrow, why spend now?) and investment (facing massive excess capacity of production and weak final demand, why invest now?). The new mission of the governor of the Bank of Japan is to raise inflationary expectations to 2 percent, which would make Japan converge with the world average inflationary trend and monetary policy. Demand would restart and Japan would contribute to an improved global economic outlook. This is the view that the IMF chief recently endorsed. As expected, Mr. Kuroda last week unveiled a much more aggressive package of quantitative easing than what we have previously witnessed, with a view to double the monetary base. Japan’s central bank will buy more long-term government bonds, pushing private investors to invest more in risky assets. Since the election, the Nikkei has risen 34 percent. Different polls and surveys suggest that the public is positively reacting to Mr. Abe’s promises.

Is success already underway? That would be good news for Japan and for the world. But it is clearly too soon to celebrate because this virtuous circle can simply fail to happen. No central bank until now has ever tried to raise inflationary expectations and no one knows if this can turn to be a practical and manageable reality. Inflationary expectations could also easily turn out of control. Before exercising traction on the economy, they could impose higher interest rates that would have devastating consequences for the Japanese Treasury in the management of a huge public debt (more than twice the size of the GDP). But there is something worse than the risk of Abenomics having poor or adverse domestic consequences.

The other side of Abenomics is currency management, a much less propitious theme for a government to communicate in the weeks leading up to the IMF Spring Meetings in Washington. This aspect of the policy is not only bold, it’s actually radical. As a candidate, Mr. Abe made extremely clear that he was willing to help the manufacturing sector by depreciating the yen and that monetary policy would be designed with this goal in mind. Remember that Japan, despite all its woes, remains a formidable exporter with an external surplus close to ¥650 billion in February (approximately $6.5 billion). As my fellow economists at Brookings have recently shown [2], the Japanese bilateral surplus with the U.S., which is $23 billion according to reported trade statistics, would dramatically increase by 60 percent and reach $36 billion if measured in added-value terms. Mr. Abe’s message was well received by investors who quickly after the election started to short the yen. As a result, the yen has slumped 21.5 percent in the past five months— the worst (or the best?) performance among the currencies of the developed economies. Following last week’s announcement that the Bank of Japan was really acting to debase monetary policy, the yen weakened beyond 99 yen per dollar and dropped against 15 major currencies.

A weakening yen also poses challenges for China, complicating the China’s strategy to reach its 8 percent target growth for this year; it could also trigger huge capital flows into China destabilizing the delicate control of financial stability

This is where Mr. Abe and Mr. Smoot cross ways: both are local politicians inspired by the difficulties facing their countries; both are willing to use every available policy tool to soften these difficulties; neither is willing to shock the global economy, which has never been the case when arguing in favor of protectionism or competitive devaluations. But these measures are nonetheless radical because they have the potential to ignite uncontrollable chain reactions. South Korea for one already declared itself very concerned by this aggressive policy, which is totally understandable. For instance, when Toyota and Sony take some advantage of Abe’s policy, the ones that would likely be first to suffer are Hyundai and Samsung. South Korea has vital interests at stake and, over In the last five months, it has been struggling with a pernicious appreciation of its currency. A weakening yen also poses challenges for China, complicating the China’s strategy to reach its 8 percent target growth for this year; it could also trigger huge capital flows into China destabilizing the delicate control of financial stability; SAFE, the financial institution that manages China’s huge official reserves, last week published its yearly report for 2012. Commenting on the global environment, the report emphasized that “a yen’s depreciation can’t solve Japan’s structural problem, … [but] could turn out of control and trigger a suspicion about its sustainability,… and finally have dangerous spill-over-effects”[3]. Chinese officials at the Boao Forum also expressed similar concerns.

We still don’t know the end. Hope is that we could see the positive interpretation of a bold Japanese policy experiment contributing to a better functioning world economy. Experience should nonetheless make us cautious. What the movement by the Bank of Japan does is to increase an already huge excess liquidity, inundating global markets. In addition, the Japanese government has added a dangerous touch of currency manipulation. Both aspects should be alerts for the IMF rather than too quickly fuel the artificial satisfaction of promises regarding higher inflationary expectations and increased domestic demand. In the end, competitive devaluations always prove inefficient and dangerous because they inevitably provoke reactions and retaliations. “Currency wars” have made headlines from time to time in the recent years but these were skirmishes. This time it could be for real, and this should be a major concern for the United States. It is a great thing that Japan recently expressed interest in joining the Trans-Pacific Partnership, but these are words with long delayed potential results. A more constructive and immediate task is to continue the cooperative global approach of exchange rate policies and to strongly discourage any temptation of national radical policy experiments. This should be a central issue next week during the IMF Spring Meetings in Washington.

[1] Roger C. Altman: “The Fall and Rise of the West”, Foreign Affairs, January-February 2013

[2] Kemal Dervis, Joshua Meltzer and Karim Foda: “Value-Added Trade and its Implications for International Trade Policy”, Brookings Opinion, April 2, 2013

[3] http://www.safe.gov.cn/resources/image/076044004f1fb34a9da59ff675a23beb/1365377817854.pdf?MOD=AJPERES&name=2012年中国国际收支报告.pdf

The replenishment process for concessional resources of the multilateral development banks is broken. We have come to this conclusion after a review of the experience with recent replenishments of multilateral development funds. We also base it on first-hand observation, since one of us was responsible for the World Bank’s International Development Association (IDA) replenishment consultations 20 years ago and recently served as the external chair for the last two replenishment consultations of the International Fund for Agricultural Development (IFAD), which closely follow the common multilateral development bank (MDB) practice. As many of the banks and their donors are preparing for midterm reviews as a first step toward the next round of replenishment consultations, this is a good time to take stock and consider what needs to be done to fix the replenishment process.

So what’s the problem?

Most of all, the replenishment process does not serve its key intended function of setting overall operational strategy for the development funds and holding the institutions accountable for effectively implementing the strategy. Instead, the replenishment consultations have turned into a time-consuming and costly process in which donor representatives from their capitals get bogged down in the minutiae of institutional management that are better left to the boards of directors and the managements of the MDBs. There are other problems, including lack of adequate engagement of recipient countries in donors’ deliberations, the lack of full participation of the donors’ representatives on the boards of the institutions in the process, and inflexible governance structures that serve as a disincentive for non-traditional donors (from emerging countries and from private foundations) to contribute.

But let’s focus on the consultation process. What does it look like? Typically, donor representatives from capitals assemble every three years (or four, in the case of the Asian Development Bank) for a year-long consultation round, consisting of four two-day meetings (including the meeting devoted to the midterm review of the ongoing replenishment and to setting the agenda for the next consultation process). For these meetings, MDB staff prepare, per consultation round, some 20 substantive documents that are intended to delve into operational and institutional performance in great detail. Each consultation round produces a long list of specific commitments (around 40 commitments is not uncommon), which management is required to implement and monitor, and report on in the midterm review. In effect, however, this review covers only half the replenishment cycle, which leads to the reporting, monitoring, and accountability being limited to the delivery of committed outputs (e.g., a specific sector strategy) with little attention paid to implementation, let alone outcomes.

The process is eerily reminiscent of the much maligned “Christmas tree” approach of the World Bank’s structural adjustment loans in the 1980s and 1990s, with their detailed matrixes of conditionality; lack of strategic selectivity and country ownership; focus on inputs rather than outcomes; and lack of consideration of the borrowers’ capacity and costs of implementing the Bank-imposed measures. Ironically, the donors successfully pushed the MDBs to give up on such conditionality (without ownership of the recipient countries) in their loans, but they impose the same kind of conditionality (without full ownership of the recipient countries and institutions) on the MDBs themselves—replenishment after replenishment.

Aside from lack of selectivity, strategic focus, and ownership of the commitments, the consultation process is also burdensome and costly in terms of the MDBs’ senior management and staff time as well as time spent by ministerial staff in donor capitals, with literally thousands of management and staff hours spent on producing and reviewing documentation. And the recent innovation of having donor representatives meet between consultation rounds as working groups dealing with long-term strategic issues, while welcome in principle, has imposed further costs on the MDBs and capitals in terms of preparing documentation and meetings.

It doesn’t have to be that way. Twenty years ago the process was much simpler and less costly. Even today, recent MDB capital increases, which mobilized resources for the non-concessional windows of the MDBs, were achieved with much simpler processes, and the replenishment consultations for special purpose funds, such as the Global Fund for HIV/AIDS, tuberculosis, and malaria and for the GAVI Alliance, are more streamlined than those of the MDBs.

So what’s to be done?

We recommend the following measures to fix the replenishment consultation process:

1. Focus on a few strategic issues and reduce the number of commitments with an explicit consideration of the costs and capacity requirements they imply. Shift the balance of monitoring and accountability from delivery of outputs to implementation and outcomes.
2. Prepare no more than five documents for the consultation process: (i) a midterm review on the implementation of the previous replenishment and key issues for the future; (ii) a corporate strategy or strategy update; (iii) the substantive report on how the replenishment resources will contribute to achieve the strategy; (iv) a financial outlook and strategy document; and (v) the legal document of the replenishment resolution.
3. Reduce the number of meetings for each replenishment round to no more than three and lengthen the replenishment period from three to four years or more.
4. Use the newly established working group meetings between replenishment consultation rounds to focus on one or two long-term, strategic issues, including how to fix the replenishment process.

The initiative for such changes lies with the donor representatives in the capitals, and from our interviews with donor representatives we understand that many of them broadly share our concerns. So this is a good time—indeed it is high time!—for them to act.

The European Union (EU) is confronting a series of potentially existential threats, including the refugee crisis, ISIS terror, Russian adventurism, and Brexit (the potential exit of the U.K. from the EU).  I hosted Czech Prime Minister Bohuslav Sobotka at Brookings to get his fundamentally (but carefully) optimistic take on how he and his fellow EU leaders can meet those challenges. Here are five reasons for optimism that emerged from our conversation: 

1. Take the Fight to Daesh.  The PM made clear Europe’s determination to take on the terror and refugee issues at their source in Iraq, Syria, and Libya.  Just this week, the Czech Republic upped its commitment to the international coalition, announcing that it will send a team to train Iraqis using U.S. made L-159 fighter jets (also sold to Iraq by Prague).  With transatlantic leadership, these efforts are starting to bear fruit in the decay of ISIS.
2. Never Let a Good Crisis Go to Waste. As part of addressing today’s refugee crisis, Europe is exploring multi-lateral efforts to construct a common European border service, integrate refugee populations, and promote internal security.  The process is painful, but filling these gaps will make the European Union stronger.
3. Stand Strong With Ukraine.  Some predicted that European unity against Putin’s expansionism would not hold.  Instead, the EU and the United States have maintained their resolve in enacting sanctions.  That has strengthened the EU, but as the PM pointed out, now Ukraine and its supporters must make sure that state moves towards good governance and functionality. 
4. Taking the Exit Out of Brexit.  The PM predicted that the U.K. would not exit the EU.  When I pressed him on why, he acknowledged that there were elements of wishing and hoping in that forecast, and that the vote comes at a tough moment.  But I share the PM’s hopes—the U.K. is not one to leave friends when times get tough.
5. Never Forget to Remember.  The PM and I spent a lot of time discussing the ups and downs of Central Europe’s experiment with democracy over the past century.  He and his Czech colleagues—of all mainstream political parties—are acutely aware of that history, and that too gives me hope that it will not be repeated.

Immense challenges can destabilize and divide—but they also present opportunities for new collaboration and cohesion. If addressed in partnership, Europe’s current trials can ultimately strengthen the ties that bind the EU together.  

Watch the full discussion here.

Andrew Kenealy contributed to this post. 

This is part two of my analysis of instruction and Common Core’s implementation.  I dubbed the three-part examination of instruction “The Good, The Bad, and the Ugly.”  Having discussed “the “good” in part one, I now turn to “the bad.”  One particular aspect of the Common Core math standards—the treatment of standard algorithms in whole number arithmetic—will lead some teachers to waste instructional time.

In 1963, psychologist John B. Carroll published a short essay, “A Model of School Learning” in Teachers College Record.  Carroll proposed a parsimonious model of learning that expressed the degree of learning (or what today is commonly called achievement) as a function of the ratio of time spent on learning to the time needed to learn.     

The numerator, time spent learning, has also been given the term opportunity to learn.  The denominator, time needed to learn, is synonymous with student aptitude.  By expressing aptitude as time needed to learn, Carroll refreshingly broke through his era’s debate about the origins of intelligence (nature vs. nurture) and the vocabulary that labels students as having more or less intelligence. He also spoke directly to a primary challenge of teaching: how to effectively produce learning in classrooms populated by students needing vastly different amounts of time to learn the exact same content.^[i] 

The source of that variation is largely irrelevant to the constraints placed on instructional decisions.  Teachers obviously have limited control over the denominator of the ratio (they must take kids as they are) and less than one might think over the numerator.  Teachers allot time to instruction only after educational authorities have decided the number of hours in the school day, the number of days in the school year, the number of minutes in class periods in middle and high schools, and the amount of time set aside for lunch, recess, passing periods, various pull-out programs, pep rallies, and the like.  There are also announcements over the PA system, stray dogs that may wander into the classroom, and other unscheduled encroachments on instructional time.

The model has had a profound influence on educational thought.  As of July 5, 2015, Google Scholar reported 2,931 citations of Carroll’s article.  Benjamin Bloom’s “mastery learning” was deeply influenced by Carroll.  It is predicated on the idea that optimal learning occurs when time spent on learning—rather than content—is allowed to vary, providing to each student the individual amount of time he or she needs to learn a common curriculum.  This is often referred to as “students working at their own pace,” and progress is measured by mastery of content rather than seat time. David C. Berliner’s 1990 discussion of time includes an analysis of mediating variables in the numerator of Carroll’s model, including the amount of time students are willing to spend on learning.  Carroll called this persistence, and Berliner links the construct to student engagement and time on task—topics of keen interest to researchers today.  Berliner notes that although both are typically described in terms of motivation, they can be measured empirically in increments of time.     

Most applications of Carroll’s model have been interested in what happens when insufficient time is provided for learning—in other words, when the numerator of the ratio is significantly less than the denominator.  When that happens, students don’t have an adequate opportunity to learn.  They need more time. 

As applied to Common Core and instruction, one should also be aware of problems that arise from the inefficient distribution of time.  Time is a limited resource that teachers deploy in the production of learning.  Below I discuss instances when the CCSS-M may lead to the numerator in Carroll’s model being significantly larger than the denominator—when teachers spend more time teaching a concept or skill than is necessary.  Because time is limited and fixed, wasted time on one topic will shorten the amount of time available to teach other topics.  Excessive instructional time may also negatively affect student engagement.  Students who have fully learned content that continues to be taught may become bored; they must endure instruction that they do not need.

Jason Zimba, one of the lead authors of the Common Core Math standards, and Barry Garelick, a critic of the standards, had a recent, interesting exchange about when standard algorithms are called for in the CCSS-M.  A standard algorithm is a series of steps designed to compute accurately and quickly.  In the U.S., students are typically taught the standard algorithms of addition, subtraction, multiplication, and division with whole numbers.  Most readers of this post will recognize the standard algorithm for addition.  It involves lining up two or more multi-digit numbers according to place-value, with one number written over the other, and adding the columns from right to left with “carrying” (or regrouping) as needed.

The standard algorithm is the only algorithm required for students to learn, although others are mentioned beginning with the first grade standards.  Curiously, though, CCSS-M doesn’t require students to know the standard algorithms for addition and subtraction until fourth grade.  This opens the door for a lot of wasted time.  Garelick questioned the wisdom of teaching several alternative strategies for addition.  He asked whether, under the Common Core, only the standard algorithm could be taught—or at least, could it be taught first. As he explains:

Delaying teaching of the standard algorithm until fourth grade and relying on place value “strategies” and drawings to add numbers is thought to provide students with the conceptual understanding of adding and subtracting multi-digit numbers. What happens, instead, is that the means to help learn, explain or memorize the procedure become a procedure unto itself and students are required to use inefficient cumbersome methods for two years. This is done in the belief that the alternative approaches confer understanding, so are superior to the standard algorithm. To teach the standard algorithm first would in reformers’ minds be rote learning. Reformers believe that by having students using strategies in lieu of the standard algorithm, students are still learning “skills” (albeit inefficient and confusing ones), and these skills support understanding of the standard algorithm. Students are left with a panoply of methods (praised as a good thing because students should have more than one way to solve problems), that confuse more than enlighten. 

Zimba responded that the standard algorithm could, indeed, be the only method taught because it meets a crucial test: reinforcing knowledge of place value and the properties of operations.  He goes on to say that other algorithms also may be taught that are consistent with the standards, but that the decision to do so is left in the hands of local educators and curriculum designers:

In short, the Common Core requires the standard algorithm; additional algorithms aren’t named, and they aren’t required…Standards can’t settle every disagreement—nor should they. As this discussion of just a single slice of the math curriculum illustrates, teachers and curriculum authors following the standards still may, and still must, make an enormous range of decisions.

Zimba defends delaying mastery of the standard algorithm until fourth grade, referring to it as a “culminating” standard that he would, if he were teaching, introduce in earlier grades.  Zimba illustrates the curricular progression he would employ in a table, showing that he would introduce the standard algorithm for addition late in first grade (with two-digit addends) and then extend the complexity of its use and provide practice towards fluency until reaching the culminating standard in fourth grade. Zimba would introduce the subtraction algorithm in second grade and similarly ramp up its complexity until fourth grade.

It is important to note that in CCSS-M the word “algorithm” appears for the first time (in plural form) in the third grade standards:

3.NBT.2  Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

The term “strategies and algorithms” is curious.  Zimba explains, “It is true that the word ‘algorithms’ here is plural, but that could be read as simply leaving more choice in the hands of the teacher about which algorithm(s) to teach—not as a requirement for each student to learn two or more general algorithms for each operation!” 

I have described before the “dog whistles” embedded in the Common Core, signals to educational progressives—in this case, math reformers—that  despite these being standards, the CCSS-M will allow them great latitude.  Using the plural “algorithms” in this third grade standard and not specifying the standard algorithm until fourth grade is a perfect example of such a dog whistle.

It appears that the Common Core authors wanted to reach a political compromise on standard algorithms. 

Standard algorithms were a key point of contention in the “Math Wars” of the 1990s.   The 1997 California Framework for Mathematics required that students know the standard algorithms for all four operations—addition, subtraction, multiplication, and division—by the end of fourth grade.^[ii]  The 2000 Massachusetts Mathematics Curriculum Framework called for learning the standard algorithms for addition and subtraction by the end of second grade and for multiplication and division by the end of fourth grade.  These two frameworks were heavily influenced by mathematicians (from Stanford in California and Harvard in Massachusetts) and quickly became favorites of math traditionalists.  In both states’ frameworks, the standard algorithm requirements were in direct opposition to the reform-oriented frameworks that preceded them—in which standard algorithms were barely mentioned and alternative algorithms or “strategies” were encouraged. 

Now that the CCSS-M has replaced these two frameworks, the requirement for knowing the standard algorithms in California and Massachusetts slips from third or fourth grade all the way to sixth grade.  That’s what reformers get in the compromise.  They are given a green light to continue teaching alternative algorithms, as long as the algorithms are consistent with teaching place value and properties of arithmetic.  But the standard algorithm is the only one students are required to learn.  And that exclusivity is intended to please the traditionalists.

I agree with Garelick that the compromise leads to problems.  In a 2013 Chalkboard post, I described a first grade math program in which parents were explicitly requested not to teach the standard algorithm for addition when helping their children at home.  The students were being taught how to represent addition with drawings that clustered objects into groups of ten.  The exercises were both time consuming and tedious.  When the parents met with the school principal to discuss the matter, the principal told them that the math program was following the Common Core by promoting deeper learning.  The parents withdrew their child from the school and enrolled him in private school.

The value of standard algorithms is that they are efficient and packed with mathematics.  Once students have mastered single-digit operations and the meaning of place value, the standard algorithms reveal to students that they can take procedures that they already know work well with one- and two-digit numbers, and by applying them over and over again, solve problems with large numbers.  Traditionalists and reformers have different goals.  Reformers believe exposure to several algorithms encourages flexible thinking and the ability to draw on multiple strategies for solving problems.  Traditionalists believe that a bigger problem than students learning too few algorithms is that too few students learn even one algorithm.

I have been a critic of the math reform movement since I taught in the 1980s.  But some of their complaints have merit.  All too often, instruction on standard algorithms has left out meaning.  As Karen C. Fuson and Sybilla Beckmann point out, “an unfortunate dichotomy” emerged in math instruction: teachers taught “strategies” that implied understanding and “algorithms” that implied procedural steps that were to be memorized.  Michael Battista’s research has provided many instances of students clinging to algorithms without understanding.  He gives an example of a student who has not quite mastered the standard algorithm for addition and makes numerous errors on a worksheet.  On one item, for example, the student forgets to carry and calculates that 19 + 6 = 15.  In a post-worksheet interview, the student counts 6 units from 19 and arrives at 25.  Despite the obvious discrepancy—(25 is not 15, the student agrees)—he declares that his answers on the worksheet must be correct because the algorithm he used “always works.”^[iii] 

Math reformers rightfully argue that blind faith in procedure has no place in a thinking mathematical classroom. Who can disagree with that?  Students should be able to evaluate the validity of answers, regardless of the procedures used, and propose alternative solutions.  Standard algorithms are tools to help them do that, but students must be able to apply them, not in a robotic way, but with understanding.

Let’s return to Carroll’s model of time and learning.  I conclude by making two points—one about curriculum and instruction, the other about implementation.

In the study of numbers, a coherent K-12 math curriculum, similar to that of the previous California and Massachusetts frameworks, can be sketched in a few short sentences.  Addition with whole numbers (including the standard algorithm) is taught in first grade, subtraction in second grade, multiplication in third grade, and division in fourth grade.  Thus, the study of whole number arithmetic is completed by the end of fourth grade.  Grades five through seven focus on rational numbers (fractions, decimals, percentages), and grades eight through twelve study advanced mathematics.  Proficiency is sought along three dimensions:  1) fluency with calculations, 2) conceptual understanding, 3) ability to solve problems.

Placing the CCSS-M standard for knowing the standard algorithms of addition and subtraction in fourth grade delays this progression by two years.  Placing the standard for the division algorithm in sixth grade continues the two-year delay.   For many fourth graders, time spent working on addition and subtraction will be wasted time.  They already have a firm understanding of addition and subtraction.  The same thing for many sixth graders—time devoted to the division algorithm will be wasted time that should be devoted to the study of rational numbers.  The numerator in Carroll’s instructional time model will be greater than the denominator, indicating the inefficient allocation of time to instruction.

As Jason Zimba points out, not everyone agrees on when the standard algorithms should be taught, the alternative algorithms that should be taught, the manner in which any algorithm should be taught, or the amount of instructional time that should be spent on computational procedures.  Such decisions are made by local educators.  Variation in these decisions will introduce variation in the implementation of the math standards.  It is true that standards, any standards, cannot control implementation, especially the twists and turns in how they are interpreted by educators and brought to life in classroom instruction.  But in this case, the standards themselves are responsible for the myriad approaches, many unproductive, that we are sure to see as schools teach various algorithms under the Common Core.

Only days before her retirement at age 71, Kathleen Elliott Yinug succumbed to a recurrence of cancer, which had been in remission for fifteen years. Over a Brookings career spanning four decades, she not only assisted several members of the Brookings community, but also became their valued friend. A woman of intelligence and liberal values, she elicited, demanded, and merited the respect of all with whom she worked.

After college, she joined the Peace Corps and was sent to the island of Yap. There she met her husband to be and there her son, Falan, was born. The family returned to the United States so that her husband could attend law school. Kathleen came to work at Brookings, helping to support her husband's law school training. When he returned to Yap, Kathleen assumed all parental responsibility. Her son has grown into a man of character, a devoted husband and father of two daughters. He and his wife, Louise, with compassion and generosity, made their home Kathleen's refuge during her final illness. Over extended periods, she held second jobs to supplement her Brookings income.

Her personal warmth, openness, and personal integrity made her a natural confidante of senior fellows, staff assistants, and research assistants, alike. She demanded and received respect from all. Her judgment on those who did not meet her standards was blunt and final; on one occasion, she 'fired'—that is, flatly refused to work with—one senior staff member whose behavior and values she rightly deplored.

With retirement approaching, Kathleen bought a condominium in Maine, a place she had come to love after numerous visits with her long-time friend, Lois Rice. After additional visits, her affection for Maine residents and the community she had chosen deepened. She spoke with intense yearning for the post-retirement time when she could take up life in her new home. That she was denied that time is a cruel caprice of life and only deepens the sense of loss of those who knew and loved her.

Far too many people reach their advanced years without planning for how they want their lives to end. The result too often is needless suffering, reduced dignity and autonomy, and agonizing decisions for family members.

Addressing these end-of-life issues is difficult. Most of us don’t want to confront them for ourselves or our family members. And until recently, many people resisted the idea of reimbursing doctors for end-of-life counselling sessions. In 2009, Sarah Palin labelled such sessions as the first step in establishing “death panels.” Although no such thing was contemplated when Representative Earl Blumenauer (D- Oregon) proposed such reimbursement, the majority of the public believed that death panels and euthanasia were just around the corner. Even the Obama Administration subsequently backed away from efforts to allow such reimbursement.

Fortunately, this is now history. In the past year or two the tenor of the debate has shifted toward greater acceptance of the need to deal openly with these issues. At least three developments illustrate the shift.

First, talk of “death panels” has receded, and new regulations, approved in late 2015 to take effect in January of this year, now allow Medicare reimbursement for end of life counselling. The comment period leading up to this decision was, according to most accounts, relatively free of the divisive rhetoric characterizing earlier debates. Both the American Medical Association and the American Hospital Association have signaled their support.

Second, physicians are increasingly recognizing that the objective of extending life must be balanced against the expressed priorities of their patients which often include the quality and not just the length of remaining life. Atal Gwande’s best-selling book, Being Mortal, beautifully illustrates the challenges for both doctors and patients. With well-grounded and persuasive logic, Gwande speaks of the need to de-medicalize death and dying.

The third development is perhaps the most surprising. It is a bold proposal advanced by Governor Jeb Bush before he bowed out of the Presidential race, suggesting that eligibility for Medicare be conditioned on having an advanced directive. His interest in these issues goes back to the time when as governor of Florida he became embroiled in a dispute about the removal of a feeding tube from a comatose Terry Schiavo. Ms. Schiavo’s husband and parents were at odds about what to do, her husband favoring removal and her parents wishing to sustain life. In the end, although the Governor sided with the parents, the courts decided in favor of the husband and allowed her to die. If an advanced directive had existed, the family disagreement along with a long and contentious court battle could have been avoided.

The point of such directives is not to pressure people into choosing one option over another but simply to insure that they consider their own preferences while they are still able. Making this a requirement for receipt of Medicare would almost surely encourage more people to think seriously about the type of care they would like toward the end of life and to talk with both their doctors and their family about these views. However, for many others, it would be a step too far and might reverse the new openness to advanced planning. A softer version nudging Medicare applicants to address these issues might be more acceptable. They would be asked to review several advance directive protocols, to choose one (or substitute their own). If they felt strongly that such planning was inappropriate, they could opt out of the process entirely and still receive their benefits.

Advanced care planning should not be linked only to Medicare. We should encourage people to make these decisions earlier in their lives and provide opportunities for them to revisit their initial decisions. This could be accomplished by implementing a similar nudge-like process for Medicaid recipients and those covered by private insurance.

Right now too few people are well informed about their end-of-life options, have talked to their doctors or their family members, or have created the necessary documents. Only about half of all of those who have reached the age of 60 have an advanced directive such as a living will or a power of attorney specifying their wishes. Individual preferences will naturally vary. Some will want every possible treatment to forestall death even if it comes with some suffering and only a small hope of recovery; others will want to avoid this by being allowed to die sooner or in greater comfort. Research suggests that when given a choice, most people will choose comfort care over extended life.

In the absence of advance planning, the choice of how one dies is often left to doctors, hospitals, and relatives whose wishes may or may not represent the preferences of the individual in their care. For example, most people would prefer to die at home but the majority do not. Physicians are committed to saving lives and relatives often feel guilty about letting a loved one “go.”

The costs of prolonging life when there is little point in doing so can be high. The average Medicare patient in their last year of life costs the government $33,000 with spending in that final year accounting for 25 percent of all Medicare spending. Granted no one knows in advance which year is “their last” so these data exaggerate the savings that better advance planning might yield, but even if it is 10% that represents over $50 billion a year. Dr. Ezekiel Emanuel, an expert in this area, notes that hospice care can reduce costs by 10 to 20 percent for cancer patients but warns that little or no savings have accompanied palliative care for heart failure or emphysema patients, for example. This could reflect the late use of palliative care in such cases or the fact that palliative care is more expensive than assumed.

In the end, Dr. Emanuel concludes, and I heartily agree, that a call for better advance planning should not be based primarily on its potential cost savings but rather on the respect it affords the individual to die in dignity and in accordance with their own preferences.

Editor's note: This piece originally appeared in Inside Sources.

Throughout the past year, we have heard paid leave debated in state houses and on the campaign trail. I am all in favor of paid leave. As I have argued elsewhere, it would enable more people, especially those in lower-paid jobs, to take time off to deal with a serious illness or the care of another family member, including a newborn child. But we shouldn’t stop with paid leave. We should also consider shortening the standard work week. Such a step would be gender neutral and would not discriminate between the very different kinds of time pressures faced by adults. It might even help to create more jobs.

The standard work week is 40 hours -- 8 hours a day for five days a week. It’s been that way for a long time. Back in 1900, the typical factory worker spent 53 hours on the job, more than a third more hours than we spend today. The Fair Labor Standards Act was passed in 1938, and set maximum hours at 40 per week. Amazingly, more than three quarters of a century after passage of the FLSA, there has been no further decline in the standard work week. Not only has the legal standard remained unchanged, but 40 hours has become the social and cultural norm.

What’s going on here? Economists predicted that as we became more prosperous we would choose to work fewer hours. That hasn’t happened. Instead we have kept on working at about the same pace as we did earlier in our history, but have poured all of the gains from productivity growth into ever-higher levels of consumption – bigger houses, more electronic gadgets, fancier cars. With increased prosperity, people are buying more and more stuff, but they don’t have any more time to enjoy it. A reduction in the standard work week would improve the quality of life, especially for those in hourly jobs who have benefitted hardly at all from economic growth in recent decades.

Two-earner couples would also benefit. Among couples between the ages of 25 and 54, the number of hours worked increased by 20 percent between 1969 and 2000, from 56 hours to 67 hours (for both husband and wife combined). As Heather Boushey notes in her new book, Finding Time, we no longer live in a world where there is a “the silent partner” in every business enterprise, the iconic “American Wife,” who takes care of the children and the millions of details of daily living. With a shorter work week, both men and women would have more time for everything from cutting the grass to cooking dinner with no presumption about who does what. Although much of the debate this year has been about work-family balance, empty nesters or singles without young children might also welcome a shorter work week. For them it would provide the chance to follow their dream of becoming an artist, a boat builder, or the creator of their own small business.

Shorter hours could have another benefit and that is more jobs for workers who would otherwise be left behind by technological change. Many economists believe that as existing jobs are replaced by machines and artificial intelligence, new jobs will be created in technical, management, and service fields. But will this happen fast enough or at sufficient scale to reemploy all those who now find themselves without decent-paying work? I doubt it. A shorter work week might help to spread the available jobs around. Germany and other European countries, along with a few U.S. states used this strategy during the Great Recession. It kept more people on the job but at shorter hours and reduced unemployment. Using a similar strategy to deal with automation and long-term joblessness, although controversial, should not be dismissed out of hand.

Of course, shorter hours can mean lower total pay. But in one typical survey published in the Monthly Labor Review, 28 percent of the respondents said they would give up a day’s pay for one fewer day of work per week. Any new movement to reduce the work week would need to be phased in slowly, with flexibility for both employers and employees to negotiate adjustments around the standard. Yet if done correctly, the transition could be accomplished with little or no reduction in wages, just smaller raises as a bigger slice of any productivity improvement was invested in more free time. When Henry Ford reduced the work week from 6 to 5 days in 1926, he did not cut wages; he assumed that both productivity and consumption would rise, and his example encouraged other employers to follow suit.

I am not talking about reducing hours for those of us who want to spend long hours at work because we enjoy it. We would still be free to work 24/7, tied to our electronic devices, and no longer knowing exactly when work begins and ends. A new hours standard would primarily affect hourly (nonexempt) employees. These are the people in the less glamourous jobs at the bottom of the ladder, many of them single parents. Right now they finish work exhausted only to come home to a “second shift” that may be equally exhausting. A reduction in the standard workweek would almost certainly improve the quality of life for these hard-pressed and overworked Americans.

By all means, let’s enact a paid leave policy, but let’s also debate some even bigger ideas – ones that could lead to greater work-life balance now, and more job opportunities in the longer run.

Editor's note: This piece originally appeared on The Washington Post's In Theory Blog.