Introduction

The interest of studying the Distributed Leadership (DL) style is becoming increasingly important. The predominant position in contemporary literature regarding DL establishes the following fundamental theories: The Theory of Activity (Spillane et al., 2004); The Theory of "Substitutes for Leadership" (Jermier and Kerr, 1997); Theories on Located and Distributed Cognition (Brown and Duguid, 1991;) Gronn, 2002); the Institutional Theory (Ogawa and Bossert, 1995), and the Theory of Motivation (Bandura, 1989) (Locke, 2003) (Mentioned by García, 2017b). The perspective of distribution focuses on how the practice of leadership is distributed among the formal and informal leaders, and how the analyzed construct is a new leadership model based on morals, and centered on values, which promotes its own socialization, and its distribution as a whole. In theoretical terms, DL corresponds to the means of multiple sources of guidance and direction, following the contours of experience in an organization, made coherent through a common culture. This research arises in the first place, following the relevance of the DL phenomenon in improving the effectiveness of primary schools, and, secondly, in order to enrich the studies related to the primary centers in Madrid. The aim of this article is to present the results obtained, in relation to the perception of directors, and according to the DPL dimension in the selected primary schools. To this end, a research has been designed using a quantitative methodology with a descriptive cut, in order to identify how the actors value the DL process. To achieve these objectives an ad hoc questionnaire has been applied in 25 public and concerted schools in Madrid, Capital.

An approximation to the concept of distributed leadership

At present, there are many definitions and interpretations of the DL, but few are clear, and the definitions that exist seem to differ from one another, such is the case of the area of organizational restructuring, that focuses much of the research on DL's conceptions; as horizontal, organic, and multifunctional structures that replace hierarchical structures (Day, 2000). Evidence from different types of educational institutions confirms the idea that some leadership practices are valuable, in almost all contexts (Leithwood, 2011). For Spillane (2017) there is a perspective of DL, which recognizes the existence of several leaders, and as explained by Harris (2012), the activities are widely shared within and between the organization. Primarily, The characteristics of the distribution model focus on interactions, rather than actions, supervisors, and on informal leadership roles. Secondly, it is the direction and influence of leadership, as well as the improvement of the organization's instruction (Spillane, 2012), that recognizes the work of all people rather than contributing to the practice of leadership, if not formally designated or defined as the leaders. Third, the DL is also fundamental to the reconfiguration of the system and organization, as well as the redesign that requires horizontal decision making (Hargreaves and Fink, 2000). This model leads to a leadership perspective, as a phenomenon involving the organization as a whole. For Bennett (2003) DL appears at the end of 1990; it is there when the definition of DL actually arises. Harris (2009) points out that the definition and understanding of DL fluctuate between the normative and the theoretical; hence, the literature supporting the definition of DL remains diverse and broad-based. Despite these solid investigations, it is during the last decades, the approach on the DL (Gronn, 2002, Spillane, 2012) has emerged in the educational research; and it must be highlighted that this new position has been driven by a change of Paradigm, which moves the individual leader, by the leader or distributed leaders, being the main cause for the demands for educational leaders in the world of the Education (Gronn, 2002, Hulpia et al., 2009). For Elmore (2005) the important thing is instruction, improvement and school performance. To a large extent, Spillane (2017) based the study on distributed cognition to generate the theory of DL. The DL of the school center is one of the most vibrant elements with which schools have in order to be effective and to achieve quality results; school leaders are able to influence and shape the conditions in which they occur (Leithwood et al., 2006).

The examination of the investigations claims that to achieve the improvement of learning the performance of the directors, they must have traits of an up-down model of rather than a bottom-up one; it should be taken into account that it is noticed that a up- down authority model can be more effective for improving student learning outcomes.

Problem approach

School leadership makes a difference in schools; it is one of the most influential factors in a student academic achievement, and it accounts for 25% of all school effects. It means that if the directors exert the educational leadership, they can influence the work of teachers and improve the conditions in the development of the processes of teaching and of learning. The importance of the school management, as the performance of the management teams has evolved over time and is currently aiming, is to balance among all the members of the school’s community and the constant improvement in the academic results (Leithwood and Seashore-Louis, (2011); Knapp et al., 2014; Spillane, 2017). The attitude of the person who assumes the functions of management in the school is a key element that determines the success of processes of change in the institution, as well as for the development of the institutions (Firestone and Riehl, 2005). There are new social demands that require reform at the school level, these reforms or transformations must be promoted from within each school center. In this context, a strong direction is a basic, whose aptitudes have competences to perform all functions, from the perception of DL. It urges in the Spanish centers a school director that acts as an engine of change, committed with the whole educational community and whose project is common (García, 2017a). Two unfavorable factors must be pointed out for Spain, firstly, exposes the OECD (2016), in Spain, the school management is very weak, there is a model of direction very different from the rest of the European countries, with the exception of Portugal. Both countries have built an address with very different characteristics, full of difficulties and unfortunately, in the case of Spain, there is no professionalization or leadership. The characteristics of the system itself are transformed into barriers to the exercise of leadership. Secondly, the new Education law (of Spain, 2013), further closes the doors to an autonomy of the centers, scarcing curricular, pedagogical competencies. Spain is one of the countries where school managers play lower leadership quotas. Spain has a weakened direction, and it must go with international trends where leadership and an effective direction are key to school improvement (Bolivar and San Fabián, 2013). The research has shown that the behavior and attitude of the person assuming the functions of management in the school are a key element that determines the existence, quality, and success of processes of change in the institution (Garcia, 2017b).

Method

A mixed methodology is used in this research, part quantitative, descriptive, and the pilot test is developed. Also, in order to study DL from an educational perspective, the methodology corresponds to a descriptive study, and quantitative analysis techniques. We present the sample, description of the data collection instruments, and data analysis techniques that allow the integration of the data to make a global vision of the phenomenon studied, in this case, the DL. The "distributed leadership of the school management" questionnaire is used as an ad hoc instrument.

We describe the DL of primary school principals, in terms of the DLP dimension of Madrid's 23 primary schools, in the presence of a set of management characteristics. The population is the group of Directors of primary education centers of the Autonomous Community of Madrid (CAM), corresponding to 244 public primary schools and 277 private, according to the database of the cam (Educa. Madrid, 2014).

The exhibition was made up of 23 primary school principals from the autonomous community of Madrid. Incorporated public, private and concerted centers, located in the different geographical areas according to the direction of the territorial area of Madrid (central Madrid, north, south, and east). This type of sampling was chosen considering only that obtaining the collected information depended exclusively on the authorization of the managers to implement the instrument. The composition of the schools is given by 7 concerted (31%) and 16 public (69%). 13 women directors (57%) and 23 men (43%). The age of the participants maintain the proportionality of the composition of the directors, there is a predominance between the 52-58 years (35%), however, it is significant the existence of directors with ages between 32-51 years. 17% is between 32-51 years respectively. 35% corresponds to 52 and 58 years and 13% to 59-64 years. Within the research, the experience of the directors is relevant. Most of the managers are 30% of their ages between 13 and 18 years of experience. 13% have between 19-24 years of experience; 25-30 years correspond to 22%; 31-37 years are 26%, and only 9% corresponds to 38-43 years. Most of the executives agreed to their positions on the opposition route, which is 44%. 30% got their charges for managing projects. Finally, 26% did it for the contest.

The collection of information was carried out through a questionnaire, previously validated (validity and high reliability-ΑCronbach = 0,933). A Likert scale of DL was constructed, made up of 54 items, 9 referred to the context variables, and DL 45, with five response alternatives graduated. Validity is related to the fact that the instrument measures what is intended to be studied. In this case, the validity of construct was initially worked through the number of elements (45), to guarantee the correspondence between each item and the dimensions of the construction. The design is a field, since the data that was used was collected directly from the reality and the pertinent information for the development of this research was obtained from living or direct sources in its natural environment. In this communication, some of the results obtained in the quantitative and descriptive research are exposed, based on the questionnaire "The distributed leadership of the school management" an ad hoc instrument, realizes the results obtained for one of the Four dimensions: "DLP" (12 items). The validation by experts allowed to evaluate the correspondence of the dimensions included in the scale with its conceptual definition, and with the items. In this way, it was attempted to ensure that the scale items were relevant to the concept of distributed leadership. Six experts were used for validation. The selection was done in response to its experience in methodological aspects, educational research, and knowledge on the theme of leadership. For the calculation of the reliability a ΑCronbach was used and the results are shown below (table 1). The value of 0.933 certifies that the total instrument is highly reliable for 45 elements.

To ensure that each of the dimensions of the test was equally reliable, the Αlpha Cronbach was also applied to each of them. The DLP dimension has a reliability of 0.759 and consists of 7 elements. Then the shared decisions dimension presents a reliability value of 0.787 with 11 elements. The mission, vision and shared goals have a value of 0.839 and 11 elements. Finally, the professional development, complexity of the task and incentives have a 0.754 of reliability for 13 elements (table 2).

The variable to describe is DL, it focuses on the interaction between the employees, in which it recognizes the work of all the individuals by contributing in the practice, in the decision making, and in the delegation of responsibilities and authority, even if they are not formally defined as leaders, and it is fundamental in the configuration of the system and of the organization, because the redesign of the Organization requires a process of shared decision making (Garcia, 2017a). The dimensions of Distributed leadership consist of four dimensions, which are listed below:

1. · Shared vision, mission and goals: it is the aspect of distributed leadership that implies that everyone is committed to the shared goals of the institution with a sense of purpose or long-term vision; It is considered that the school has a set of shared values that guide the efforts, promote confidence and commitment among teachers, managers, administrative staff and educational community. There is a strong commitment to the shared goals of the Organization as a whole, and the philosophy of the school, as well as a long- term vision of the college that are shared with all staff; The school is sensitive to the needs of the students, parents, and community, and it generates support in helping, establishing and communicating the group clearly about the course of the institution.

   · Distributed Leadership Practices: there is a delegation of work, and the Director assumes that the sum of the shares represents more than the parties because the participative work translates into a learning for the organization. The management considers that the most participatory forms of leadership work best and allow access to the collective knowledge of the organization, as well as to manage democratic processes to use the conflicts productively, which requires to arrange and regularize informal relations to improve existing agreements.

   · Professional development of teachers, complexity of the task: relates to reflection and dialogue to delegate, orient, leverage and improve the skills and knowledge of all teachers, and create a positive and effective common culture, as well as to provide a consistent and coherent school curriculum between subjects and levels, as well as a system of goals and incentives. Leadership actions contribute to the development of people in order to advance productively in the institution. Management and leadership are practiced as a reflection of the school's culture, ethics, and traditions. In addition, it includes the planning of the professional development of the team, through assistance to seminars, courses, workshops, etc., and supports the allocation of the necessary resources to promote the efforts of school improvement. Shared decisions of the Organization: we work on the basis of cooperation rather than competition, to promote productivity within the school, with a "holistic" vision of the organization and with flexible professional practices. The members of the organization discuss and help each other in a spontaneous way to solve any problem, through agreements to modify certain organizational structures, and through parental involvement, in order to make decisions about teaching and learning for their children in school.

In addition to DL, some demographic and context variables were also incorporated. These are the conditions under which the event is manifested to describe, then each one of them is defined. The variable to describe is distributed leadership, which is defined below:

1. • Age: Defined as the number of years elapsed from birth to the time of investigation.

   • Experience as a manager: it is defined as the number of years elapsed since its incorporation to the position of Director (a), until the time of the investigation.

   • Academic experience: Refers to the number of years elapsed since its inception in work as teachers until the time of the investigation.

   • Experience in the position of the executive: refers to the number of years as a director until the time of the investigation.

   • Type of entry to the position of Director: refers to the way in which managers enter the Spanish educational system according to the education law. In Madrid they are by regulation.

   • The educational project of the management: it is one of the forms established to participate in the selection of the schools in the incorporation to the directors (as) in the offices (cases Studied in Madrid).

   • Election by the school board and faculty of Professors: corresponds to the appointment of the principal.

   • Direct designation by the administration: assignment chosen by the school board and other members of the school.

   • The character of the institution: it has to do with the type of school. The Spanish educational system includes three types of primary schools: public, private and concerted.

   • Public schools: They are lay centers, financed and managed by the Government with the help of the local administrations of each zone. The majority of these centers have all levels of basic and compulsory education (children, primary, secondary and baccalaureate, although some centers delegate the higher cycles to public institutes).

   • Concerted schools: They are private-nature centers (not created by the administration) but subsidized largely by the Central Administration. They have freedom of management with an adaptation to certain conditions established by the government like, for example, the limit of students by class, dates, admissions, etc. They finance part of their offer with subsidies, and another with parental payments.

   • Private schools: These are private-nature centers (not created by the administration). They have freedom of management with an adaptation to certain conditions established by the government as the limit of students by class, dates, admissions, etc. They finance their offer with parents ' payments.

   • Gender of Directors: it has to do with male or female sex.

   • The tendency of the enrolment of the schools of Madrid: measures the behavior of admission and withdrawal of students compared with previous years.

   • Dropout of students from the Madrid colleges: measures the population of students who retire from a school to migrate to another.

Analysis and presentation of DLP data and information

As part of the descriptive analysis, it is essential to examine the results of the study, and the calculation of the response distributions of the subjects for each item for each dimension. These analyses have been taken as indispensable to discover the reality and problems of the directors’ DLP. In order to obtain an even more detailed view of the dimension, the study was made by item (table 3), this information is represented in Figure 2. The seven items are taken (P10, P15, P16, P17, P18, P34 and P35) Table 5 details the same of the DLP dimension and estimated the percentage of directors who responded to each option (Total disagreement (TD), Disagreement (D), Regular (R), Total agreement (TA) and Agreement (A)). Below are the items that make up the DLP dimension.

It highlights the result related to the item: The Division of labor according to the specialization of competencies (P10), 95.66% of the directors located between total agreement and agreement with these practices, i.e., with the division of labor according to the Specialization of competencies. Directors consider that the division of labor produces the crucial differentiation between individual action and collective activity. It is understood that the division of labor in an activity creates different positions for the participants, and involves agents with multiple viewpoints, interests, and traditions. The idea of the division of the work is understood in all the tasks, and for the accomplishment of the work is added the technological capacity (the tools and the knowledge). In the analysis of the P10, it is observed that no manager disagreed with the position of the Division of labor. It also stands out, with a 95.65% agreement and total agreement, the perception of the directors to the affirmation: participatory work results in learning (P16), directors value participatory work as a way to learn the people and the organization. It is, thus, suggested that a director can hardly serve as a distributed leader for a school, without the active and substantial participation of other teachers or educators, and the development of a leadership capacity among all members of the Community School. Then with a 91.3% agreement and total agreement is the approach: the most participatory forms of leadership work best in Complex tasks (P34) for directors to distribute leadership, it is a strategy with some potential to access the Collective knowledge of the Organization, to carry out complex tasks and achieve the organizational objectives. It is related to the division of labor as an activity that generates different positions for the participants. Not all directors agree with a form of shared leadership, which is based on a more collective and inclusive philosophy of traditional leadership theory, which focuses on the skills and behaviors of the leading individuals, note that the percentage of disagreement is very small (8.7 %).

Given the opinion about: by delegating their work and distributing it the sum is more than the parties (P15) The directors show a percentage of 86.96 of agreement and total agreement, and no manager disagrees in this item. This aspect relates to the delegation and the distribution that translate into the synergy effect. Directors agree that the sum of all the leadership from different sources or people in the school results in a significant variation in school outcomes and the effectiveness of schools. In relation to the item: the work of two or more leaders is made separately and interdependently (P18) shows, 47.82% are in total agreement and agreement, and 52.18% say regular, disagree and in total disagreement. This means that directors do not agree with the work of two or more leaders, or with spontaneous collaboration, which refers to groups of people with different skills and knowledge, from different levels of the organization, who they unite to share their expertise and regularize their behaviours during a task by exercising their own leadership, and then separating them.

Given the approach related to the distribution of leadership as a strategy, with some potential to access the collective knowledge of the organization, to perform complex tasks and achieve organizational objectives (P35), it is obtained 21.74% of total to regular disagreement; one should mention the fact that there was a significant percentage of agreement and total agreement (78.25%). This means that P35 is not one of the most valued aspects of distributed leadership practices. The scholars of the organizations have long argued that the complexity of the task is a key variable that determines the productive leadership responses. This argument is based on the more directive forms of leadership (similar to the "oversight" for most people) being productive when the tasks to be done are relatively simple. Finally, in accordance with the question related to the leadership practices that are based on the work of two or more leaders (P17), 30.43% were totally in agreement, and 52.17% agreed. It does not always agree with delegating and passing power to others, as seen with an 8.70% disagreement and 8.70% in regular opinion.

Conclusions

Theoretical research and analysis is evidenced, as proposed by Gronn (2002), in the practice of the three conditions (collaborative, collective and coordinated distribution), by the directors of the schools of Madrid. From this analysis, it is key to understand that by working collaboratively with the committed, capable actors, and locally adapting some general suggestions, to retake the strengths and overcome the weaknesses of individual leadership, you could get a formula with good results, and, of course, a first-rate education with quality.

The management model prevailing in Spain is Democratic (Arias and Canton, 2006), and for these directors, participatory work is a practice of DL. Redesigning the organization has proven that educational leaders develop their schools as effective organizations that support and maintain the performance of teachers and students, contributing to teamwork and student learning.

Changes in the division of labor occur with the incorporation of new tasks and new requirements - this seems to have two parts: the technical, and the social form. In the DLP, the division of labor becomes evident, when individuals and groups do so on the basis of their values and interests. These relationships are a key source of social and organizational power, if compared to exclusively hierarchical or centered forms of leadership, it is thought that distributed leadership reflects more accurately the division of labor that is lived within the Organizations on a day-to-day basis.

Participatory work results in learning. The concept of DD is significantly overlapping with the concepts of shared leadership (Pearce and Conger, 2003), Collaborative (Wallace, 1989) Democratic (Gastil, 1997) and participatory (Vroom and Jago, 1998) mentioned by García (2010). DL represents a set of practices to set course and exert influence, potentially "by people at all levels, more than a set of personal characteristics and attributes of people at the organizational cusp" (Fletcher and Kaufer, 2003, p. 22). For these directors, participatory work is a DLP, redesigning the organization has proven that educational leaders develop their schools as effective organizations that support and maintain the performance of teachers and students, their contribution to the work of the team, and to the learning of the students. The DLP assumes that the purpose of the cultures and organizational structures is to generate the flexibility of the structures, which must be combined with the changing nature of the school improvement agenda.

The most participatory forms of leadership work best in complex tasks. Experts in the theory of the school organization (Leithwood et al., 2006; Leitwood, 2009) have argued that the complexity of the task is a variable key, which determines DL's responses. In this dimension, it is where the 23 directors are best served; they tend to distribute the tasks according to the competencies and skills of those who work with them, inclined to delegate aspects of their position, and to encourage the emergence of other leaders within the organization, as a way to tackle complex tasks and to achieve institutional goals. The directors base the work mostly on the participation.

According to the results, it seems that the DLP has spread more than it could be, and it is accepted by most of the principals of the schools studied in Madrid. It is evident in this study that the DLP most valued by the directors consulted are: • Division of the work according to the specialization of competencies. • The delegation of work and distributing it is more than the parts. • Participatory work results in learning.

The worst positions valued by the directors are related to: the work of two or more leaders is made separately and interdependently (P18), 52.18% of directors disagree with the work of two or more leaders, and the distribution of leadership as a strategy with some potential to access the collective knowledge of the organization, to perform complex tasks and achieve organizational objectives (P35), 21, 74% disagree.

A high percentage of directors consider working on the basis of cooperation as the best way to promote productivity within the school. Cooperation is related to the concept of planned alignment which is comparable to the holistic modality already mentioned in the previous development of this work (institutionalized practice) (Gronn, 2002, 2008). In most cases where the DLP is applied, teachers, who are sometimes individualistic (Lopez and Sánchez, 2004), brings out the best of their talents and abilities, offering to the service of the community and the school, to exercise leadership roles in various areas.

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