These characteristics are combined with an incremental approach to public policy, which seems especially relevant in the political and social instability of Latin America. Unlike studies that concentrate their focus on policy prescriptions to be implemented beyond contexts, such as the well-known McKinsey Report (Mourshed et al., 2010), what we found in our previous research is that improvement is constructed in a dynamic and flexible manner. As Oszlak (1980) pointed out, the attempt at excessive planning does not provide the necessary doses of realism of the unstable territories of actors in Latin America. Unlike ex ante approaches, the incremental tradition points to the importance of intermediate steps or "snowball" effects of policies that make their way through gaining legitimacy and continuity.

This is found in problem-solving iterations approaches (Andrews et al., 2017): it´s more important to achieve step-wise progress and build confidence in the ability to solve issues relevant to system actors than to follow universal policy prescriptions. Thanks to these feedback loops, more trust is generated in the different spheres of government and a flexible path is built with a focus on improvement through different doors to enter the educational system. This approach builds what we have called in previous studies, an "education governance platform," without which it is not possible to effectively implement the complex policies that alter learning outcomes on a large scale (Rivas & Scasso, 2020).

Systemic governance generates combined effects in the symbolic and material dimensions of the space and time of educational systems. In the symbolic field, it entrenches a series of priorities, motivations and shared visions in the actors of the system. In terms of temporal sequence, it generates guarantees of policy continuity and sustainability.

The second axis, referring to the capacities of the system's actors, defines the conditions for the dynamics of improvement processes. Educational practices have the characteristic of being highly decentralized and interpersonal: they operate at the micro level of classrooms mediated by the personal intervention of thousands of individual teachers. Improvement cannot be forced or digitized from outside: participation, and involvement of individual and collective actors are necessary.

Burns & Koster (2016) develop an approach to the capabilities of an educational system at four levels: individual, institutional (at the school level), systemic and societal. The individual level is defined from the possibilities that the subjects of the system have to develop new ideas in the local context from existing knowledge. This expands from the institutional level where school management is key to generate learning environments and constant reflection.

This axis may involve the generation, expansion and liberation of capacities within the educational system, three different processes that can be combined with each other. What is relevant in this axis is the construction of a growing dynamic of learning, reflection and power of agency on the part of educators. Without this dynamic approach, improvement processes can happen in one first stage (perhaps more instrumental and technocratic) but not be sustained over time. Moving in this direction implies the construction of a certain ecosystem where learning processes are valued and effectively communicated at the local level so that they are not dispersed and, in this way, avoid dependence on policies that intervene from the top down in hierarchical terms.

In Latin America we find diverse contexts of interaction of educational actors. In some educational systems, such as Colombia, there is a strong tradition of autonomy of schools and teachers, while in other cases, such as Mexico, there are more rigid and structured centralized pedagogical regulation mechanisms (such as textbooks produced by the State and delivered to all students in the country). Beyond certain shared characteristics in the region, this dimension varies widely both in initial teacher training circuits and in school regulation and control practices.

The third axis refers to accountability processes that express the alignment and control of education systems. Accountability indicates the existence of a set of shared, clearly defined, communicable and achievable objectives that are regularly monitored and produce a certain systemic consistency between the practices, motivations and expectations of educational actors and institutions.

Accountability depends on the creation of a data dashboard that indicates achievements at the level of educational institutions. In all the studied cases of systemic improvement, this systemic and detailed information base appears as a necessary condition for action planning and for the shared allocation of responsibilities. This is what we called in previous studies the "multifocal approach" to improvement: a constant information flow mechanism that informs the achievements of each school on multiple indicators to define an improvement plan, external assistance and/or incentives to push the various actors towards shared goals.

Previous studies have particularly focused on accountability schemes as the core of systemic improvement. Pritchett (2015) developed a theoretical model on systemic coherence. Coherence is built when there is a balance between autonomy, capabilities, and accountability. This process relates to clear information flows that define purposes. These purposes should be coherent at the scale of the whole system, demarcating a shared direction (Pritchett, 2015).

Our theoretical hypothesis here is that accountability processes in Latin America are inseparable from systemic governance: they need solid, reliable and enduring governance institutions to settle on actors in a way that is neither excessively rigid nor stifling. The cases of systemic improvement we have previously studied show the importance of accountability systems: in Ceará, Pernambuco (Brazilian states) and Puebla (Mexican state) we found aligned systems of objectives, incentives and constant measurement. However, these systems were accompanied by large doses of trust in government institutions and processes of constant support to schools with more adverse conditions. These are not systems of exclusionary competition but combine "positive pressure" for results with preventive support mechanisms based on collaboration and coordination between schools.

The fourth axis opens the black box of improvement processes and refers to the structure of school knowledge translation. In the words of Basil Bersntein (2000) we refer to the processes of pedagogical recontextualization that condense the systemic organization and management of the curriculum.

Curriculum governance refers to studies on the pedagogical flow that travels from policies to classrooms. The pioneering work of Cohen & Spillane (1992) pointed out the importance of combining consistency, specificity and clarity with levels of curriculum prescription, hierarchization and sequencing. Perhaps the most emblematic study of this current theory is the book "Why Schools Matter", which studied the flow of curriculum policy in the 54 countries participating in the TIMMS test. There it was highlighted that the countries with the best results have a curriculum structure with more focus, clarity, articulation and rigor (Schimdt et al., 2001).

The hypothesis behind this fourth axis of the theory is that systemic improvement cannot occur without understanding the internal dynamics of school knowledge management. In some cases of small subnational educational systems, improvement processes can occur relatively independently of the curricular governance structure. But in these cases, improvement will always be limited by a non-controllable external factor that can be enhanced by the agencies that have the greatest capacity for curricular regulation (in many countries these attributions are in national hands, while local governments have limited curricular powers).

The capacity for curricular and pedagogical adaptation requires a combination of technical knowledge, dialogue with multiple stakeholders and continuity over time. These three factors are scarce in Latin America. Perhaps this is one of the reasons why it is so difficult to find systemic improvement processes in the region. Previous studies in the region have highlighted the low level of clarity, focus and rigor in curricular instruments (Valverde, 2009). A comparative research on the educational systems of Cuba, Chile and Brazil highlighted how Cuba achieved better educational results based on a strong integration between the curriculum, teacher training and teaching materials (Carnoy, 2007).

The cases we have found in our own research on subnational education systems in Latin America confirm these hypotheses. The cases of Ceará and Pernambuco in Brazil, Córdoba in Argentina and Puebla in Mexico had an outstanding capacity for curriculum management, with strong technical competencies and coordinated devices that produce materials and guides in dialogue with teachers and schools (Rivas, 2021). These are examples of the use of curricular and pedagogical policy channels to work together to achieve better results.

Again, this axis is strengthened by the development of the previous analytical axes. For example, curricular policies are also combined with the legitimacy of government institutions. Previous comparative studies indicate that countries with better results in standardized assessments have a reliable curricular governance system that offers teachers content that they can interpret, understand and apply, with constant feedback and calibration processes (Schimdt & Prawat, 2006).

5. METHODOLOGICAL STRATEGIES

The theoretical framework for the analysis of the improvement of educational systems in Latin America has a direct empirical derivation. This section presents some methodological strategies to apply the theoretical framework in future studies.

5.1. Multiplying sources of data on improvement processes and analyzing the intertemporal validity of each source

The first methodological strategy takes up one of the central obstacles of studies on the improvement of educational systems: the fragile methodological validity of the intertemporal comparison of standardized assessments and other educational indicators.

There are different methodological strategies to face this obstacle. The first involves methodological analysis of the intertemporal validity of standardized assessments. An analysis of the methodological documents of the tests is a first step, but often in Latin America the tests do not explicitly define these technical aspects and it is necessary to conduct interviews with the official specialized agents to better understand the possible biases and methodological problems of the tests. Unfortunately, standardized tests are instruments with a high margin of error and can end up generating studies on cases of improvement that in reality only crystallize some methodological flaw in the application of the tests.

A second complementary strategy is to multiply the sources of data to measure processes of improvement. We recommend comparing different standardized assessments: national and international tests (most Latin American countries have their own evaluations and participate in international tests). Another way of multiplying sources is to appeal to a broader vision of the data ecosystem that countries have: data on access to education, students´ trajectories, educational equity, among others. In this way, it is possible to select cases of improvement in various indicators that are consistent over time, avoiding large jumps from one year to the next in standardized assessments that may be the result of statistical problems rather than real improvements.

Other more sophisticated quantitative strategies is to compare different variables associated with the tests and in particular the value-added effect between different test editions, controlling for other factors such as the social context of the students (Carnoy et al. 2017).

Finally, another way to escape the pitfalls of standardized assessments is to broaden the perspective on what systemic improvement means. For example, interviews can be conducted with experts in the education systems analyzed to find possible improvement processes that are not captured in the evaluations, or system actors can be consulted on educational aspects that are not evaluated in a standardized manner.

5.2. Comparison of cases using multiple quantitative and qualitative variables

In order to generate hypotheses on the processes of systemic improvement, it´s key to use the comparative method of description, interpretation, juxtaposition and simultaneous comparison (Beraday, 1964). An individual case that achieves improvements in its own test has notable limitations that can be overcome by the comparative method analyzing multiple cases that participate in international or subnational comparative tests. Many of the singular explanations can be falsified by comparing similar cases.

Quantitative strategies can be useful if comparable data exist to measure associated factors over time in a set of cases. This allows multiple regression analysis to isolate variables.

The study of macro-structural factors that affect educational outcomes is a necessary complementary strategy to avoid the possible biases of the available databases. For example, it is key to study differences in standardized test scores in different learning areas and years assessed to confront different types of educational policies implemented.

The falsification principle requires comparing multiple variables with different types of available data. If the improvement process was concentrated in reading but not in mathematics, are there possible hypotheses of differential policy interventions? If the improvement was greater in primary than in secondary education, was it because there were differences in policies, subsystem governance, or factors exogenous to education that affected one age group more than the other? If the improvement was over a period of time and then stopped, were there specific policies that were discontinued? If the improvement was in one edition of the test, what is the time frame of the effects of the policies, considering that students begin their schooling long before they are assessed and carry those learnings longitudinally?

To investigate these major questions, it is important to map educational policies in their historical context. Document analysis and interviews with key actors are the best known methodologies for this task of reconstructing policy trajectories (Gale, 2001). It´s key to construct a systematic map of interventions over a period of time that should go back to the moment when the students participating in the first edition of the tests being compared began their educational journey up to the final year of those same tests. The sequencing of the socio-economic context and of each of the relevant policy strategies will make it possible to construct different scenarios and contrast hypotheses that often appear a priori and that do not survive the systematic comparison of variables in time and space.

5.3. Analyzing the reception of educational policies and the culture of the system

Policy mapping and macro-structural variables are vital but limited tools for understanding the complexity of education systems. Even questionnaires complementary to tests, which provide relevant information on the actors and institutions of the system, have obvious methodological limitations. That is why it´s so important to implement a third methodological strategy to grasp the complexity of an educational system. Conducting interviews with teachers, students and actors of the educational community is a key step, but it requires a lot of resources and time in order to achieve representative samples. It should be noted here that even if they do not correspond to a representative sample, these interviews can be important to take the temperature of the system and to learn from the testimonies some visions that allow for the sophistication or nuance of macro-political arguments.

Conducting interviews or focus groups with school principals can be a valuable strategy to capture the representations of the actors in the system on a more limited scale. A further step, always desirable but very costly to practice, is the observation or filming of classes or the ethnographic work of participant observation of the daily life of educational institutions. This approach makes it possible to analyze the practices in their natural environment, unmediated by the representations of the testimonies of the actors interviewed.

The analysis of the interior of the educational system favors the reconstruction of the paths, translations and reinterpretations of educational policies. This makes it possible to review often naïve or incomplete hypotheses about the effects of policies on educational outcomes. In turn, the vision of the actors in the system (including students) is a recommendable way to analyze what improvement means beyond measurements. Many interviews and observations can escape the prison of quantitative data to interpret how an educational system generates multiple effects and learning that cannot be captured by standardized systems.

5.4. Curriculum flow analysis

A methodological strategy complementary to the previous ones is the study of the flow of curriculum policy. This strategy makes it possible to open the black box of translations of the structure of school knowledge. Some international studies have analyzed the impact of the prescribed curriculum, textbooks and teacher planning on the results of standardized assessments (Schmidt et al., 2001; Westbury & Hsu, 1996). These lines of research have not generally been applied in Latin America and much remains to be known about the processes of curriculum translation, its evolution over time and the comparison of contexts and countries.

The central purpose of this strategy is to compare models of curriculum organization, prescription, coherence and extension in order to understand how they affect learning processes.

6. DISCUSSION

The four analytical axes of systemic improvement are pieces that fit together in a jigsaw puzzle. They cannot be viewed in isolation. It is in combination that they generate what we might call the "combustion" necessary for continuous sustainable improvement. This does not imply that systems improve only when these four axes are present, since some may be more developed than others and may be tuned in different ways in each context to the existing traditions of that educational system.

The proposed theoretical framework is intended to provide a framework for the development of empirical studies. It comes from and returns to research in comparative systems. Grounded theory is built on the basis of previous research that allows the development of categories based on concrete evidence and a framework that can pass through the verification of multiple cases of improvement.

It is a theoretical model that relies especially on the previous studies compiled by Ehren & Baxter (2021). These scholars developed an analytical framework of systemic reforms based on three backbones: trust, accountability and capabilities. These three dimensions are complemented in our theoretical framework by a fourth one, referring to the process of curriculum translation, which gives more emphasis to the ways in which macro policies are linked to local practices with a focus on the system's curriculum coherence and alignment.

In turn, our theory seeks a specific design for the Latin American context. Based on the study of improvement cases in the region and the adaptation of the categories to the particularities of the context, this article favors a comparative view of educational systems based on the juxtaposition of similarity and proximity factors. Can this same theoretical framework be useful for analyzing systemic improvement in other contexts? Of course, but starting from the conception of grounded theory, based on multiple previous empirical studies, it is more appropriate to present the theoretical proposal adjusted to the context from which it starts.

The dialogue of this theoretical model with some relevant antecedents in the field of educational policy is inevitable. There is a central anchor in the study of systemic improvement which is the well-known McKinsey Report (Mourshed et al., 2010). Our previous studies find many similarities with some of the central findings of this report. We see the flow that occurs between centralized regulation for low development contexts and the extension of local capabilities to achieve consolidate improvement processes. However, our approach differs in a central axis, which is the reading of contexts and the analysis of governance modalities.

Unlike the universal recipes proposed by the McKinsey Report, our theory argues that improvement is possible under conditions of flexibility and with incremental approaches. It´s not so decisive what policies are implemented but how the system is governed: it´s more important to achieve concrete progress, generate trust, build legitimacy and open doors than to apply a specific textbook recipe. Latin American education systems are fragile and uncertain: what generates improvement processes is dynamic, contextualized and strongly supported by the resolution of concrete problems experienced by the system's actors. This more territorial, situated and incremental logic is combined with the other axes analyzed: capacity building; the clear definition of objectives and the coherence of accountability; and the systemic alignment of curricular frameworks that feed pedagogical practices.

Finally, it is worth noting the blind spot of our theory. One of the axes that explain the low theoretical and empirical density of the academic debate on the improvement of educational systems in Latin America is the meaning acquired by standardized measurements of quality. Reduced to biased cut-offs on the purposes of education, tests are an iron cage for education systems. When they are strong markers of the way forward -through high-stake assessments- they have the risk of reducing non-assessed areas and teaching to the test.

Can our theory be capable of escaping the magnetism of the measurable? There are two ways to answer this question. The first is empirical and requires studies that analyze whether standardized tests correlate well with non-measurable learning. We know little in this area, but it is possible to advance from research in measuring in broader ways and in analyzing that which is not measured with other methodological strategies.

The second answer is anchored in the political positioning of our theoretical proposal. It is not necessary to fall into a "black-white" polarization. Standardized tests may well have or generate biases, but they also have a value in themselves. It´s enough to look at the most basic: whether students can read and understand a text is a central component of their right to education and this can indeed be measured. This pragmatic attitude, as we have defined it, does not fall into the technocratic view of assessments as mirrors of education systems. It is precisely the theoretical layer that allows us to conceptualize the complexity of what is measured and, above all, how the practices of an entire system are modified so that its results change.

Moving away from simplistic analytical biases that propose linear hypotheses to explain the results is a necessary step to review what systemic improvement is and what it means. We hope to contribute to this search with a theory that is both applicable and open to other visions of what are the goals of educational systems in diverse contexts and in a changing and uncertain world.

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