ABSTRACT—

The International Fund for Agricultural Development (IFAD) has for many years stressed innovation, knowledge and scaling up as essential ingredients of its strategy to combat rural poverty in developing countries. This institutional review of IFAD’s approach to scaling up is the fi rst of its kind: A team of development experts were funded by a small grant from IFAD to assess IFAD’s track record in scaling up successful interventions, its operational policies and processes, instruments, resources and incentives, and to provide recommendations to management for how to turn IFAD into a scaling-up institution. Beyond IFAD, this institutional scaling up review is a pilot exercise that can serve as an example for other development institutions.

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2015 is a pivotal year. Three major workstreams among all the world’s nations are going forward this year under the auspices of the United Nations to develop goals, financing, and frameworks for the “post-2015 sustainable development agenda.” First, after two years of wide-ranging consultation, the U.N. General Assembly in New York in September will endorse a new set of global goals for 2030 to follow on from the Millennium Development Goals (MDGs) that culminate this year. Second, to support this effort, a financing for development (FFD) conference took place in July in Addis Ababa, Ethiopia, to identify innovative ways of mobilizing private and public resources for the massive investments necessary to achieve the new goals. And third, in Paris in December the final negotiating session will complete work on a global climate change framework. 

These three landmark summits will, with luck, provide the broad strategic vision, the specific goals, and the financing modalities for addressing the full range of systemic threats. Most of all, these three summit meetings will mobilize the relevant stakeholders and actors crucial for implementing the post-2015 agenda—governments, international organizations, business, finance, civil society, and parliaments—into a concerted effort to achieve transformational outcomes. Achieving systemic sustainability is a comprehensive, inclusive effort requiring all actors and all countries to be engaged.

These three processes represent a potential historic turning point from “business-as-usual” practices and trends and to making the systemic transformations that are required to avoid transgressing planetary boundaries and critical tipping points. Missing from the global discourse so far is a realistic assessment of the political decisions and institutional innovations that would be required to implement the post-2015 sustainable development agenda (P2015).

For 2015, it is necessary is to make sure that by the end of year the three workstreams have been welded together as a singular vision for global systemic transformation involving all countries, all domestic actors, and all international institutions. The worst outcome would be that the new Sustainable Development Goals (SDGs) for 2030 are seen as simply an extension of the 2015 MDGs—as only development goals exclusively involving developing countries. This outcome would abort the broader purposes of the P2015 agenda to achieve systemic sustainability and to involve all nations and reduce it to a development agenda for the developing world that by itself would be insufficient to make the transformations required.

Systemic risks of financial instability, insufficient job-creating economic growth, increasing inequality, inadequate access to education, health, water and sanitation, and electricity, “breaking points” in planetary limits, and the stubborn prevalence of poverty along with widespread loss of confidence of people in leaders and institutions now require urgent attention and together signal the need for systemic transformation.

As a result, several significant structural changes in institution arrangements and governance are needed as prerequisites for systemic transformation. These entail (i) political decisions by country leaders and parliaments to ensure societal engagement, (ii) institutional innovations in national government processes to coordinate implementation, (iii) strengthening the existing global system of international institutions to include all actors, (iv) the creation of an international monitoring mechanism to oversee systemic sustainability trajectories, and (v) realize the benefits that would accrue to the entire P2015 agenda by the engagement of the systemically important countries through fuller utilization of  G20 leaders summits and finance ministers meetings as enhanced global steering mechanisms toward sustainable development.   Each of these changes builds on and depends on each other.

I. Each nation makes a domestic commitment to a new trajectory toward 2030

For global goal-setting to be implemented, it is essential that each nation go beyond a formal agreement at the international level to then embark on a national process of deliberation, debate, and decision-making that adapts the global goals to the domestic institutional and cultural context and commits the nation to them as a long-term trajectory around which to organize its own systemic transformation efforts. Such a process would be an explicitly political process involving national leaders, parliaments or rule-making bodies, societal leaders, business executives, and experts to increase public awareness and to guide the public conversation toward an intrinsically national decision which prioritizes the global goals in ways which fit domestic concerns and circumstances. This political process would avoid the “one-size-fits-all” approach and internalize and legitimate each national sustainability trajectory.

So far, despite widespread consultation on the SDGs, very little attention has been focused on the follow-up to a formal international agreement on them at the U.N. General Assembly in September 2015. The first step in implementation of the SDGs and the P2015 agenda more broadly is to generate a national commitment to them through a process in which relevant domestic actors modify, adapt, and adopt a national trajectory the embodies the hopes, concerns and priorities of the people of each country. Without this step, it is unlikely that national systemic sustainability trajectories will diverge significantly enough from business-as-usual trends to make a difference. More attention needs to now be given to this crucial first step.  And explicit mention of the need for it should appear in the UNGA decisions in New York in September.

II. A national government institutional innovation for systemic transformation

The key feature of systemic risks is that each risk generates spillover effects that go beyond the confines of the risk itself into other domains. This means that to manage any systemic risk requires broad, inter-disciplinary, multi-sectoral approaches. Most governments have ministries or departments that manage specific sectoral programs in agriculture, industry, energy, health, education, environment, and the like when most challenges now are inter-sectoral and hence inter-ministerial. Furthermore, spillover linkages create opportunities in which integrated approaches to problems can capture intrinsic synergies that generate higher-yield outcomes if sectoral strategies are simultaneous and coordinated.

The consequence of spillovers and synergies for national governments is that “whole-of-government” coordinating committees are a necessary institutional innovation to manage effective strategies for systemic transformation. South Korea has used inter-ministerial cabinet level committees that include private business and financial executives as a means of addressing significant interconnected issues or problems requiring multi-sectoral approaches. The Korea Presidential Committee on Green Growth, which contained more than 20 ministers and agency heads with at least as many private sector leaders, proved to be an extremely effective means of implementing South Korea’s commitment to green growth.

III.  A single global system of international institutions

The need for a single mechanism for coordinating the global system of international institutions to implement the P2015 agenda of systemic transformation is clear. However, there are a number of other larger reasons why the forging of such a mechanism is crucial now.

The Brettons Woods era is over. It was over even before the initiative by China to establish the Asia Infrastructure Investment Bank (AIIB) in Beijing and the New Development Bank (NDB) in Shanghai. It was over because of the proliferation in recent years of private and official agencies and actors in development cooperation and because of the massive growth in capital flows that not only dwarf official development assistance (concessional foreign aid) but also IMF resources in the global financial system. New donors are not just governments but charities, foundations, NGOs, celebrities, and wealthy individuals. New private sources of financing have mushroomed with new forms of sourcing and new technologies. The dominance of the IMF and the World Bank has declined because of these massive changes in the context.

The emergence of China and other emerging market economies requires acknowledgement as a fact of life, not as a marginal change. China in particular deserves to be received into the world community as a constructive participant and have its institutions be part of the global system of international institutions, not apart from it. Indeed, China’s Premier, Li Keqiang, stated at the World Economic Forum in early 2015 that “the world order established after World War II must be maintained, not overturned.”

The economic, social and environmental imperatives of this moment are that the world’s people and the P2015 agenda require that all international institutions of consequence be part of a single coordinated effort over the next 15 years to implement the post-2015 agenda for sustainable development. The geopolitical imperatives of this moment also require that China and China’s new institutions be thoroughly involved as full participants and leaders in the post-2015 era. If nothing else, the scale of global investment and effort to build and rebuild infrastructure requires it.

It is also the case that the post-2015 era will require major replenishments in the World Bank and existing regional development banks, and significantly stronger coordination among them to address global infrastructure investment needs in which the AIIB and the NDB must now be fully involved. The American public and the U.S. Congress need to fully grasp the crucial importance for the United States, of the IMF quota increase and governance reform.  These have been agreed to by most governments but their implementation is stalled in the U.S. Congress. To preserve the IMF’s role in the global financial system and the role of the U.S. in the international community, the IMF quota increase and IMF governance reform must be passed and put into practice. Congressional action becomes all the more necessary as the effort is made to reshape the global system of international institutions to accommodate new powers and new institutions within a single system rather than stumble into a fragmented, fractured, and fractious global order where differences prevail over common interests.

The IMF cannot carry out its significant responsibility for global financial stability without more resources. Other countries cannot add to IMF resources proportionately without U.S. participation in the IMF quota increase.   Without the US contribution, IMF members will have to fund the IMF outside the regular IMF quota system, which means de-facto going around the United States and reducing dramatically the influence of the U.S. in the leadership of the IMF. This is a self-inflicted wound on the U.S., which will damage U.S. credibility, weaken the IMF, and increase the risk of global financial instability. By blocking the IMF governance reforms in the IMF agreed to by the G-20 in 2010, the U.S. is single-handedly blocking the implementation of the enlargement of voting shares commensurate with increased emerging market economic weights.  This failure to act is now widely acknowledged by American thought leaders to be encouraging divergence rather than convergence in the global system of institutions, damaging U.S. interests.

IV. Toward a single monitoring mechanism for the global system of international institutions

The P2015 agenda requires a big push toward institutionalizing a single mechanism for the coordination of the global system of international institutions.  The international coordination arrangement today, is the Global Partnership for Effective Development Cooperation created at the Busan High-Level Forum on Aid Effectiveness in 2011.  This arrangement, which recognizes the increasingly complex context and the heightened tensions between emerging donor countries and traditional western donors, created a loose network of country platforms, regional arrangements, building blocks and forums to pluralize the architecture to reflect the increasingly complex set of agents and actors. This was an artfully arranged compromise, responding to the contemporary force field four years ago.

Now is a different moment. The issues facing the world are both systemic and urgent; they are not confined to the development of developing countries, and still less to foreign aid. Geopolitical tensions are, if anything, higher now than then.  But they also create greater incentives to find areas of cooperation and consensus among major powers who have fundamentally different perspectives on other issues. Maximizing the sweet spots where agreement and common interest can prevail is now of geopolitical importance.  Gaining agreement on institutional innovations to guide the global system of international institutions in the P2015 era would be vital for effective outcomes but also importantly ease geopolitical tensions.

Measurement matters; monitoring and evaluation is a strategic necessity to implementing any agenda, and still more so, an agenda for systemic transformation.  As a result, the monitoring and evaluation system that accompanies the P2015 SDGs will be crucial to guiding the implementation of them.  The UN, the OECD, the World Bank, and the IMF all have participated in joint data gathering efforts under the IDGs  in the 1990s and the MDGs in the 2000s.   Each of these institutions has a crucial role to play, but they need to be brought together now under one umbrella to orchestrate their contributions to a comprehensive global data system and to help the G20 finance ministers coordinate their functional programs.   

The OECD has established a strong reputation in recent years for standard setting in a variety of dimensions of the global agenda.  Given the strong role of the OECD in relation to the G20 and its broad outreach to “Key Partners” among the emerging market economies, the OECD could be expected to take a strong role in global benchmarking and monitoring and evaluation of the P2015 Agenda.  The accession of China to the OECD Development Centre, which now has over fifty member countries, and the presence and public speech of Chinese Premier Li Keqiang at the OECD on July 1^st, bolsters the outreach of the OECD and its global profile.

But national reporting is the centerpiece and the critical dimension of monitoring and evaluation.  To guide the national reporting systems and evaluate their results, a  new institutional arrangement is needed that is based on national leaders with responsibility for implementation of the sustainable development agendas from each country and is undertaken within the parameters of the global SDGs and the P2015 benchmarks.

V.   Strengthening global governance and G20 roles

G-20 leaders could make a significant contribution to providing the impetus toward advancing systemic sustainability by creating a G-20 Global Sustainable Development Council charged with pulling together the national statistical indicators and implementing benchmarks on the SDGs in G-20 countries.  The G-20 Global Sustainable Development Council (G-20 GSDC) would consist of the heads of the presidential committees on sustainable development charged with coordinating P2015 implementation in G-20 countries.  Representing systemically important countries, they would also be charged with assessing the degree to which national policies and domestic efforts by G20 countries generate positive or negative spillover effects for the rest of the world.  This G-20 GSDC would also contribute to the setting of standards for the global monitoring effort, orchestrated perhaps by the OECD, drawing on national data bases from all countries using the capacities of the international institutions to generate understanding of global progress toward systemic sustainability. 

The UN is not in a position to coordinate the global system of international institutions in their functional roles in global sustainable development efforts.  The G-20 itself could take steps through the meetings of G-20 Finance Ministers to guide the global system of international institutions in the implementation phase of the P2015 agenda to begin in 2016. The G-20 already has a track record in coordinating international institutions in the response to the global financial crisis in 2008 and its aftermath. The G-20 created the Financial Stability Board (FSB), enlarged the resources for the IMF, agreed to reform the IMF’s governance structure, orchestrated relations between the IMF and the FSB, brought the OECD into the mainstream of G-20 responsibilities and has bridged relations with the United Nations by bringing in finance ministers to the financing for development conference in Addis under Turkey’s G-20 leadership. 

There is a clear need to coordinate the financing efforts of the IMF, with the World Bank and the other regional multilateral development banks (RMDBs), with the AIIB and the BRICS NDB, and with other public and private sector funding sources, and to assess the global institutional effort as whole in relation to the P2015 SDG trajectories.  The G-20 Finance Ministers grouping would seem to be uniquely positioned to be an effective and credible means of coordinating these otherwise disparate institutional efforts.  The ECOSOC Development Cooperation Forum and the Busuan Global Partnership provide open inclusive space for knowledge sharing and consultation but need to be supplemented by smaller bodies capable of making decisions and providing strategic direction.

Following the agreements reached in the three U.N. workstreams for 2015, the China G-20 could urge the creation of a formal institutionalized global monitoring and coordinating mechanism at the China G-20 Summit in September 2016. By having the G-20 create a G-20 Global Sustainable Development Council (G-20 GSDC), it could build on the national commitments to SDG trajectories to be made next year by U.N. members countries and on the newly formed national coordinating committees established by governments to implement the P2015 Agenda, giving the G-20 GSDC functional effectiveness, clout and credibility.   Whereas there is a clear need to compensate for the sized-biased representation of the G20 with still more intensive G-20 outreach and inclusion, including perhaps eventually considering shifting to a constituency based membership, for now the need in this pivotal year is to use the momentum to make political decisions and institutional innovations which will crystallize the P2015 strategic vision toward systemic sustainability into mechanisms and means of implementation.

By moving forward on these recommendations, the G-20 Leaders Summits would be strengthened by involving G-20 leaders in the people-centered P2015 Agenda, going beyond finance to issues closer to peoples’ homes and hearts. Systemically important countries would be seen as leading on systemically important issues.  The G-20 Finance Ministers would be seen as playing an appropriate role by serving as the mobilizing and coordinating mechanism for the global system of international institutions for the P2015 Agenda.  And the G-20 GSDC would become the effective focal point for assessing systemic sustainability not only within G20 countries but also in terms of their positive and negative spillover effects on systemic sustainability paths of other countries, contributing to standard setting and benchmarking for global monitoring and evaluation.    These global governance innovations could re-energize the G20 and provide the international community with the leadership, the coordination and the monitoring capabilities that it needs to implement the P2015 Agenda. 

As the MDGs culminate this year, as the three U.N. workstreams on SDGs, FFD, and UNFCC are completed, the world needs to think ahead to the implementation phase of the P2015 sustainable development agenda. Given the scale and scope of the P2015 agenda, these five governance innovations need to be focused on now so they can be put in place in 2016.

These will ensure (i) that national political commitments and engagement by all countries are made by designing, adopting, and implementing their own sustainable development trajectories and action plans; (ii) that national presidential committees are established, composed of key ministers and private sector leaders to coordinate each country’s comprehensive integrated sustainability strategy; (iii) that all governments and international institutions are accepted by and participate in a single global system of international institutions;   (iv) that a G-20 monitoring mechanism be created by the China G-20 in September 2016 that is comprised of the super-minister officials heading the national presidential coordinating committees implementing the P2015 agenda domestically in G-20 countries, as a first step;  and (v) that the G-20 Summit leaders in Antalya in November 2015 and in China in September 2016 make clear their own commitment to the P2015 agenda and their responsibility for its adaption, adoption and implementation internally in their countries but also for assessing G-20 spillover impacts on the rest of the world, as well as for deploying their G-20 finance ministers to mobilize and coordinate the global system of international institutions toward achieving the P2015 agenda.

Without these five structural changes, it will be more likely that most countries and actors will follow current trends rather than ratchet up to the transformational trajectories necessary to achieve systemic sustainability nationally and globally by 2030.

Ye Yu, Xue Lei and Zha Xiaogag, “The Role of Developing Countries in Global Economic Governance---With a Special Analysis on China’s Role”, UNDP, Second High-level Policy Forum on Global Governance: Scoping Papers, (Beijing: UNDP, October 2014).

Zhang Haibing, “A Critique of the G-20’s Role in UN’s post-2015 Development Agenda”, in Catrina Schlager and Chen Dongxiao (eds), China and the G-20: The Interplay between an Emerging Power and an Emerging Institution, (Shanghai: Shanghai Institutes for International Studies [SIIS] and the Friedrich Ebert Stiftung [FES], 2015) 290-208.

Global Review, (Shanghai:  SIIS, 2015,) 97-105.

Colin I. Bradford, “Global Economic Governance and the Role International Institutions”, UNDP, Second High-level Policy Forum on Global Governance: Scoping Papers, (Beijing: UNDP, October 2014).

Colin I. Bradford, “Action implications of focusing now on implementation of the   post-2015 agenda.”, (Washington: The Brookings Institution, Global Economy and Development paper, September 2015).

Colin I. Bradford, “Systemic Sustainability as the Strategic Imperative for the Future”, (Washington: The Bookings Institution, Global Economy and Development paper; September 2015). 

Wonhyuk Lim and Richard Carey, “Connecting Up Platforms and Processes for Global Development to 2015 and Beyond:  What can the G-20 do to improve coordination and deliver development impact?”, (Paris: OECD  Paper, February 2013).

Xiaoyun Li and Richard Carey, “The BRICS and the International Development System: Challenge and Convergence”, (Sussex: Institute for Development Studies, Evidence Report No. 58, March 2014).

Xu Jiajun and Richard Carey, “China’s Development Finance: Ambition, Impact and Transparency,” (Sussex :  Institute for Development Studies, IDS Policy Brief, 2015).

Soogil Young, “Domestic Actions for Implementing Integrated Comprehensive Strategies:  Lessons from Korea’s Experience with Its Green Growth Strategy”, Washington: Paper for the Brookings conference on “Governance Innovations to Implement the Post-2015 Agenda for Sustainable Development”, March 30, 2015).

This post continues a series begun in 2014 on implementing the Common Core State Standards (CCSS).  The first installment introduced an analytical scheme investigating CCSS implementation along four dimensions:  curriculum, instruction, assessment, and accountability.  Three posts focused on curriculum.  This post turns to instruction.  Although the impact of CCSS on how teachers teach is discussed, the post is also concerned with the inverse relationship, how decisions that teachers make about instruction shape the implementation of CCSS.

A couple of points before we get started.  The previous posts on curriculum led readers from the upper levels of the educational system—federal and state policies—down to curricular decisions made “in the trenches”—in districts, schools, and classrooms.  Standards emanate from the top of the system and are produced by politicians, policymakers, and experts.  Curricular decisions are shared across education’s systemic levels.  Instruction, on the other hand, is dominated by practitioners.  The daily decisions that teachers make about how to teach under CCSS—and not the idealizations of instruction embraced by upper-level authorities—will ultimately determine what “CCSS instruction” really means.

I ended the last post on CCSS by describing how curriculum and instruction can be so closely intertwined that the boundary between them is blurred.  Sometimes stating a precise curricular objective dictates, or at least constrains, the range of instructional strategies that teachers may consider.  That post focused on English-Language Arts.  The current post focuses on mathematics in the elementary grades and describes examples of how CCSS will shape math instruction.  As a former elementary school teacher, I offer my own personal opinion on these effects.

Certain aspects of the Common Core, when implemented, are likely to have a positive impact on the instruction of mathematics. For example, Common Core stresses that students recognize fractions as numbers on a number line.  The emphasis begins in third grade:

CCSS.MATH.CONTENT.3.NF.A.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.

CCSS.MATH.CONTENT.3.NF.A.2.A
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

CCSS.MATH.CONTENT.3.NF.A.2.B
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

When I first read this section of the Common Core standards, I stood up and cheered.  Berkeley mathematician Hung-Hsi Wu has been working with teachers for years to get them to understand the importance of using number lines in teaching fractions.^[1] American textbooks rely heavily on part-whole representations to introduce fractions.  Typically, students see pizzas and apples and other objects—typically other foods or money—that are divided up into equal parts.  Such models are limited.  They work okay with simple addition and subtraction.  Common denominators present a bit of a challenge, but ½ pizza can be shown to be also 2/4, a half dollar equal to two quarters, and so on. 

With multiplication and division, all the little tricks students learned with whole number arithmetic suddenly go haywire.  Students are accustomed to the fact that multiplying two whole numbers yields a product that is larger than either number being multiplied: 4 X 5 = 20 and 20 is larger than both 4 and 5.^[2]  How in the world can ¼ X 1/5 = 1/20, a number much smaller than either 1/4or 1/5?  The part-whole representation has convinced many students that fractions are not numbers.  Instead, they are seen as strange expressions comprising two numbers with a small horizontal bar separating them. 

I taught sixth grade but occasionally visited my colleagues’ classes in the lower grades.  I recall one exchange with second or third graders that went something like this:

“Give me a number between seven and nine.”  Giggles. 

“Eight!” they shouted. 

“Give me a number between two and three.”  Giggles.

“There isn’t one!” they shouted. 

“Really?” I’d ask and draw a number line.  After spending some time placing whole numbers on the number line, I’d observe,  “There’s a lot of space between two and three.  Is it just empty?” 

Silence.  Puzzled little faces.  Then a quiet voice.  “Two and a half?”

You have no idea how many children do not make the transition to understanding fractions as numbers and because of stumbling at this crucial stage, spend the rest of their careers as students of mathematics convinced that fractions are an impenetrable mystery.   And  that’s not true of just students.  California adopted a test for teachers in the 1980s, the California Basic Educational Skills Test (CBEST).  Beginning in 1982, even teachers already in the classroom had to pass it.   I made a nice after-school and summer income tutoring colleagues who didn’t know fractions from Fermat’s Last Theorem.  To be fair, primary teachers, teaching kindergarten or grades 1-2, would not teach fractions as part of their math curriculum and probably hadn’t worked with a fraction in decades.  So they are no different than non-literary types who think Hamlet is just a play about a young guy who can’t make up his mind, has a weird relationship with his mother, and winds up dying at the end.

Division is the most difficult operation to grasp for those arrested at the part-whole stage of understanding fractions.  A problem that Liping Ma posed to teachers is now legendary.^[3]

She asked small groups of American and Chinese elementary teachers to divide 1 ¾ by ½ and to create a word problem that illustrates the calculation.  All 72 Chinese teachers gave the correct answer and 65 developed an appropriate word problem.  Only nine of the 23 American teachers solved the problem correctly.  A single American teacher was able to devise an appropriate word problem.  Granted, the American sample was not selected to be representative of American teachers as a whole, but the stark findings of the exercise did not shock anyone who has worked closely with elementary teachers in the U.S.  They are often weak at math.  Many of the teachers in Ma’s study had vague ideas of an “invert and multiply” rule but lacked a conceptual understanding of why it worked.

A linguistic convention exacerbates the difficulty.  Students may cling to the mistaken notion that “dividing in half” means “dividing by one-half.”  It does not.  Dividing in half means dividing by two.  The number line can help clear up such confusion.  Consider a basic, whole-number division problem for which third graders will already know the answer:  8 divided by 2 equals 4.   It is evident that a segment 8 units in length (measured from 0 to 8) is divided by a segment 2 units in length (measured from 0 to 2) exactly 4 times.  Modeling 12 divided by 2 and other basic facts with 2 as a divisor will convince students that whole number division works quite well on a number line. 

Now consider the number ½ as a divisor.  It will become clear to students that 8 divided by ½ equals 16, and they can illustrate that fact on a number line by showing how a segment ½ units in length divides a segment 8 units in length exactly 16 times; it divides a segment 12 units in length 24 times; and so on.  Students will be relieved to discover that on a number line division with fractions works the same as division with whole numbers.

Now, let’s return to Liping Ma’s problem: 1 ¾ divided by ½.   This problem would not be presented in third grade, but it might be in fifth or sixth grades.  Students who have been working with fractions on a number line for two or three years will have little trouble solving it.  They will see that the problem simply asks them to divide a line segment of 1 3/4 units by a segment of ½ units.  The answer is 3 ½ .  Some students might estimate that the solution is between 3 and 4 because 1 ¾ lies between 1 ½ and 2, which on the number line are the points at which the ½ unit segment, laid end on end, falls exactly three and four times.  Other students will have learned about reciprocals and that multiplication and division are inverse operations.  They will immediately grasp that dividing by ½ is the same as multiplying by 2—and since 1 ¾ x 2 = 3 ½, that is the answer.  Creating a word problem involving string or rope or some other linearly measured object is also surely within their grasp.

I applaud the CCSS for introducing number lines and fractions in third grade.  I believe it will instill in children an important idea: fractions are numbers.  That foundational understanding will aid them as they work with more abstract representations of fractions in later grades.   Fractions are a monumental barrier for kids who struggle with math, so the significance of this contribution should not be underestimated.

I mentioned above that instruction and curriculum are often intertwined.  I began this series of posts by defining curriculum as the “stuff” of learning—the content of what is taught in school, especially as embodied in the materials used in instruction.  Instruction refers to the “how” of teaching—how teachers organize, present, and explain those materials.  It’s each teacher’s repertoire of instructional strategies and techniques that differentiates one teacher from another even as they teach the same content.  Choosing to use a number line to teach fractions is obviously an instructional decision, but it also involves curriculum.  The number line is mathematical content, not just a teaching tool.

Guiding third grade teachers towards using a number line does not guarantee effective instruction.  In fact, it is reasonable to expect variation in how teachers will implement the CCSS standards listed above.  A small body of research exists to guide practice. One of the best resources for teachers to consult is a practice guide published by the What Works Clearinghouse: Developing Effective Fractions Instruction for Kindergarten Through Eighth Grade (see full disclosure below).^[4]  The guide recommends the use of number lines as its second recommendation, but it also states that the evidence supporting the effectiveness of number lines in teaching fractions is inferred from studies involving whole numbers and decimals.  We need much more research on how and when number lines should be used in teaching fractions.

Professor Wu states the following, “The shift of emphasis from models of a fraction in the initial stage to an almost exclusive model of a fraction as a point on the number line can be done gradually and gracefully beginning somewhere in grade four. This shift is implicit in the Common Core Standards.”^[5]  I agree, but the shift is also subtle.  CCSS standards include the use of other representations—fraction strips, fraction bars, rectangles (which are excellent for showing multiplication of two fractions) and other graphical means of modeling fractions.  Some teachers will manage the shift to number lines adroitly—and others will not.  As a consequence, the quality of implementation will vary from classroom to classroom based on the instructional decisions that teachers make.  

The current post has focused on what I believe to be a positive aspect of CCSS based on the implementation of the standards through instruction.  Future posts in the series—covering the “bad” and the “ugly”—will describe aspects of instruction on which I am less optimistic.

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.

The release of 2015 NAEP scores showed national achievement stalling out or falling in reading and mathematics.  The poor results triggered speculation about the effect of Common Core State Standards (CCSS), the controversial set of standards adopted by more than 40 states since 2010.  Critics of Common Core tended to blame the standards for the disappointing scores.  Its defenders said it was too early to assess CCSS’s impact and that implementation would take many years to unfold. William J. Bushaw, executive director of the National assessment Governing Board, cited “curricular uncertainty” as the culprit.  Secretary of Education Arne Duncan argued that new standards typically experience an “implementation dip” in the early days of teachers actually trying to implement them in classrooms.

In the rush to argue whether CCSS has positively or negatively affected American education, these speculations are vague as to how the standards boosted or depressed learning.  They don’t provide a description of the mechanisms, the connective tissue, linking standards to learning.  Bushaw and Duncan come the closest, arguing that the newness of CCSS has created curriculum confusion, but the explanation falls flat for a couple of reasons.  Curriculum in the three states that adopted the standards, rescinded them, then adopted something else should be extremely confused.  But the 2013-2015 NAEP changes for Indiana, Oklahoma, and South Carolina were a little bit better than the national figures, not worse.[i]  In addition, surveys of math teachers conducted in the first year or two after the standards were adopted found that:  a) most teachers liked them, and b) most teachers said they were already teaching in a manner consistent with CCSS.[ii]  They didn’t mention uncertainty.  Recent polls, however, show those positive sentiments eroding. Mr. Bushaw might be mistaking disenchantment for uncertainty.[iii] 

For teachers, the novelty of CCSS should be dissipating.  Common Core’s advocates placed great faith in professional development to implement the standards.  Well, there’s been a lot of it.  Over the past few years, millions of teacher-hours have been devoted to CCSS training.  Whether all that activity had a lasting impact is questionable.  Randomized control trials have been conducted of two large-scale professional development programs.  Interestingly, although they pre-date CCSS, both programs attempted to promote the kind of “instructional shifts” championed by CCSS advocates. The studies found that if teacher behaviors change from such training—and that’s not a certainty—the changes fade after a year or two.  Indeed, that’s a pattern evident in many studies of educational change: a pop at the beginning, followed by fade out.  

My own work analyzing NAEP scores in 2011 and 2013 led me to conclude that the early implementation of CCSS was producing small, positive changes in NAEP.[iv]  I warned that those gains “may be as good as it gets” for CCSS.[v]  Advocates of the standards hope that CCSS will eventually produce long term positive effects as educators learn how to use them.  That’s a reasonable hypothesis.  But it should now be apparent that a counter-hypothesis has equal standing: any positive effect of adopting Common Core may have already occurred.  To be precise, the proposition is this: any effects from adopting new standards and attempting to change curriculum and instruction to conform to those standards occur early and are small in magnitude.   Policymakers still have a couple of arrows left in the implementation quiver, accountability being the most powerful.  Accountability systems have essentially been put on hold as NCLB sputtered to an end and new CCSS tests appeared on the scene.  So the CCSS story isn’t over.  Both hypotheses remain plausible. 

Reading Instruction in 4^th and 8^th Grades

Back to the mechanisms, the connective tissue binding standards to classrooms.  The 2015 Brown Center Report introduced one possible classroom effect that is showing up in NAEP data: the relative emphasis teachers place on fiction and nonfiction in reading instruction.  The ink was still drying on new Common Core textbooks when a heated debate broke out about CCSS’s recommendation that informational reading should receive greater attention in classrooms.[vi] 

Fiction has long dominated reading instruction.  That dominance appears to be waning.

After 2011, something seems to have happened.  I am more persuaded that Common Core influenced the recent shift towards nonfiction than I am that Common Core has significantly affected student achievement—for either good or ill.   But causality is difficult to confirm or to reject with NAEP data, and trustworthy efforts to do so require a more sophisticated analysis than presented here.

Four lessons from previous education reforms

Nevertheless, the figures above reinforce important lessons that have been learned from previous top-down reforms.  Let’s conclude with four:

1.  There seems to be evidence that CCSS is having an impact on the content of reading instruction, moving from the dominance of fiction over nonfiction to near parity in emphasis.  Unfortunately, as Mark Bauerlein and Sandra Stotsky have pointed out, there is scant evidence that such a shift improves children’s reading.[vii]

2.  Reading more nonfiction does not necessarily mean that students will be reading higher quality texts, even if the materials are aligned with CCSS.   The Core Knowledge Foundation and the Partnership for 21^st Century Learning, both supporters of Common Core, have very different ideas on the texts schools should use with the CCSS.[viii] The two organizations advocate for curricula having almost nothing in common.

3.  When it comes to the study of implementing education reforms, analysts tend to focus on the formal channels of implementation and the standard tools of public administration—for example, intergovernmental hand-offs (federal to state to district to school), alignment of curriculum, assessment and other components of the reform, professional development, getting incentives right, and accountability mechanisms.  Analysts often ignore informal channels, and some of those avenues funnel directly into schools and classrooms.[ix]  Politics and the media are often overlooked.  Principals and teachers are aware of the politics swirling around K-12 school reform.  Many educators undoubtedly formed their own opinions on CCSS and the fiction vs. nonfiction debate before the standard managerial efforts touched them.

4.  Local educators whose jobs are related to curriculum almost certainly have ideas about what constitutes good curriculum.  It’s part of the profession.  Major top-down reforms such as CCSS provide local proponents with political cover to pursue curricular and instructional changes that may be politically unpopular in the local jurisdiction.  Anyone who believes nonfiction should have a more prominent role in the K-12 curriculum was handed a lever for promoting his or her beliefs by CCSS. I’ve previously called these the “dog whistles” of top-down curriculum reform, subtle signals that give local advocates license to promote unpopular positions on controversial issues.

For many years, Africans have complained that the International Criminal Court (ICC) has concentrated its efforts exclusively in Africa, a process that has made a mockery of the court’s claims to bring about an end to global impunity. Some Africans have even argued that the ICC’s claims that it is helping bring about justice in Africa are not unlike those made by proponents of the colonial order established by the Berlin Conference in 1884-1885.

On Tuesday, March 11, I participated in a panel discussion entitled, “The International Criminal Court in Africa: Bias, Legitimate Objections, or Excuses for Impunity?” co-hosted by New York University’s School of Continuing and Professional Studies (SCPS), Center for Global Affairs and the International Center for Transitional Justice (ICTJ).  The program brought together experts interested in justice and peaceful coexistence in Africa to examine the role that the International Criminal Court (ICC) can play in minimizing impunity in the continent.

I was joined by Ambassador Tiina Intelmann, president of the Assembly of States Parties of the International Criminal Court; Richard Dicker, director of the International Justice Program at Human Rights Watch; and Jennifer Trahan, clinical associate professor at the New York University’s School of Continuing and Professional Studies (SCPS), Center for Global Affairs.  David Tolbert, president of the International Center for Transitional Justice, moderated the discussion.

The most important conclusions from what was a robust dialogue were that (i) it is very important that African countries develop the legal and institutional capacity to deal effectively and fully with impunity and other extra-legal activities that impede human development and peaceful coexistence; (ii) the international community should help African countries develop that capacity; (iii) the ICC should make a concerted effort to open dialogue with the African Union in particular and Africans generally in order for the court to gain a better insight into African problems, while, at the same time, help Africans understand and appreciate the nature of the ICC’s work, how it functions, and why it is a critical international body in the fight against impunity; and (iv) the ICC needs to improve openness and transparency in its activities. To make the ICC a truly international court, important countries such as the United States, India, the People’s Republic of China and the Russian Federation need to be brought aboard. Obviously, more dialogue is needed and it is my hope that soon, we will be able to undertake a discussion of this type somewhere in Africa.

During my presentation, I argued that an important part of improving relations between Africa and the ICC is that Africans must take ownership of their problems and find ways to resolve them themselves. For one thing, justice is most effectively delivered locally. Hence, the first line of business is for each African country to develop the legal and institutional capacity to deal with impunity and other governance problems. External actors, notably the ICC, should only be considered conflict-resolution instruments of last resort.

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