Pedagogical Coordination in Secondary Schools from a Distributed Perspective. Adaptation of the Distributed Leadership Inventory (DLI) in the Spanish Context

education sciences Article Pedagogical Coordination in Secondary Schools from a Distributed Perspective. Adaptation of the Distributed Leadership Inventory (DLI) in the Spanish Context Inmaculada García-Martínez 1, Pedro J. Arrifano Tadeu 2,* , JoséLuis Ubago-Jiménez 3and Carlos Brigas 2 1Department of Pedagogy, University of Jaén, 23071 Jaén, Spain; [email protected] 2Centre for Studies in Education and Innovation (CI&DEI-ESECD), Polytechnic Institute of Guarda, 6300-559 Guarda, Portugal; [email protected] 3Department of Didactics of Musical, Plastic and Corporal Expression, University of Granada, 18071 Granada, Spain; [email protected] *Correspondence: [email protected] Received: 13 April 2020; Accepted: 27 June 2020; Published: 1 July 2020   Abstract: Introduction: Leadership as the second factor in school improvement needs potential leaders to be effective. Method: The present study aimed to know the potential capacity of leaders in Spanish secondary schools through the adaptation of the DLI questionnaire to Spanish. To accurately adapt this questionnaire, the present research group conducted content validity processes in 2017, using the Delphi Method, in which eight experts from the Spanish Network for Research into Leadership and Academic Improvement were invited to participate (RILME). As part of a pilot test, preliminary tools were administered to 547 participants from secondary schools in Granada and Ja é n (Spain). Results: The present study reports on the adaptation of the DLI instrument within the Spanish context. Acceptably high values were obtained in the analysis of reliability and internal consistency, suggesting that this item can be reliably utilised for the exploration of the dynamics of internal functioning in secondary education and the evaluation of the distribution of leadership characteristics. Conclusions: The pilot study highlights how heads of studies and department heads are potential leaders, making it easier to set up and sustain educational projects in schools. Keywords: pedagogical coordination; distributed leadership; high schools; adaptation; questionnaire 1. Introduction Leadership is one of the most valuable indicators in the context of education and the achievement of academic improvement. Previous research on leadership has focused on the profile possessed by leaders [ 1 ], in addition to the different forms leadership takes and the contexts in which it is developed [ 2 ]. Other studies have instead placed the focus on the educational organisation itself as a place in which individuals can learn and interact with their educators [3,4]. Recently, research has emerged targeting the identification of leaders within the school environment, analysing different types of leaders [ 5 ], and highlighting the inconsistencies between their identity owed to differences in their educational formation, socioeconomic and cultural context, experiential baggage and their degree of commitment and involvement [6,7]. Recent studies have identified the positive impact of leadership in high schools, relating it with improvements in the development of professional teacher training, the working climate, and the establishment of a system of confidence based on professional participation and learning. These studies Educ. Sci. 2020,10, 175; doi:10.3390/educsci10070175 www.mdpi.com/journal/education Educ. Sci. 2020,10, 175 2 of 19 have also highlighted the leadership figure as the key individual driving change [ 8 ]. Key individuals will be those who are trusted by their management, while they are able to mobilize other colleagues to achieve a common project. Authors such as Siskin [ 9 ] have pointed to departments as suitable places to bring about change in schools. Thus, department heads would be key figures, as they are the link between the management team and the teaching staff[ 10 ]. These findings imply important actions for schools. Firstly, it is beneficial for educational schools to initiate educational projects to secure high levels of participation from within the general educational community [ 11 ]. Secondly, there exists a large managerial responsibility to initiate a set of positive practices oriented towards the improved learning of students [ 4 ]. Finally, it is important to channel leadership in a form that distributes responsibility amongst several key individuals in schools, to support the professional development of teachers and improve the quality of teaching [12,13]. Leadership is an improvement factor if we understand it as the capacity of one or several people to involve others in a common project [ 14 ]. Building a positive school environment, establishing the conditions for a common pedagogical project, as well as promoting processes of change and internal exchanges aimed at improving student and teacher learning means improving the social and professional capital of the whole school and its agents. Often, the high demands of accountability cause principals to be unable to assume pedagogical leadership functions. Therefore, they must delegate responsibilities and empower others, such as heads of studies or department heads [15]. From this perspective, it is understood that the head of studies is the key individual who acts as the link between the groups that compose an educational school and their wider context [ 16 ]. Along with this approach, the head of studies assumes pedagogical, administrative and management roles [ 17 , 18 ]. Domingo-Segovia and Ritacco-Real [ 19 ] consider research management to be one of the main supports for the achievement of a distributed pedagogical leadership. According to their pertinent research, strong management enables the heads of studies to be key components in the initiation and development of processes targeting improvement in secondary schools. Similarly, Paranosic and Riveros [ 20 ] highlighted the importance of management research into key leadership figures working together towards the school’s objectives. In addition to the directors and the heads of both research studies and of schools, the head of the department is a key figure [ 21 , 22 ]. The head of the department is responsible for ensuring the coherence of pedagogical coordination within the research or educational institution. Besides, the head of the department is typically delegated tasks such as delivering the educational projects of the school, organising the spaces and facilities assigned to their department, and collaborating in evaluations. This takes place within the operational needs of the school, which functions according to the structural models of the individual bodies and organisational units held within it. In the same way, the relationships developed between the staff(both vertical and horizontal) to achieve efficient pedagogical coordination are also important [23]. It is therefore supported that the type of leadership exercised by management is related to the organisational disposition and professional involvement of the teaching staff. The scientific literature indicates the potential of the DLI instrument to analyse the capacity of schools or educational schools to incorporate distributed leadership modalities within their organisation and to examine the management dynamics of high schools and their tendency towards collaboration [24]. Once the heroic leadership patterns have been overcome, there is a need to find potential leaders in the schools. The construction of educational projects oriented towards school improvement needs people involved in achieving it. Moreover, given the relevance and currency of studies on educational leaders, it was found essential to provide a tool to measure the educational leadership of others who might be leaders in the school. Many instruments have been developed to evaluate the principal’s leadership capacity [ 25 , 26 ], although this number is smaller when referring to middle leaders [ 27 , 28 ]. Many of the instruments validated in the field have focused on a person’s leadership capacity. In this case, it was interesting to analyse the role of principals, but also the leadership potential of middle leaders. In turn, the importance focuses not on the leadership capacity of the people, but on their potential and action to promote Educ. Sci. 2020,10, 175 3 of 19 processes and carry out internal changes aimed at a common Project. The instrument that has been adapted to the Spanish context has items that go beyond valuing the leadership and management capacity of leaders. In the updated Spanish context, importance is given to the school functioning as the main context in which people involved or not, with common goals, work and interact. The involvement of teaching staffin designing and supporting the school’s goals ensures that this instrument not only evaluates leadership capacity from a distributed perspective, but also discusses the capacity of the school as a whole, where people work and whose actions must be translated into the internal changes necessary for its pedagogical improvement. Similarly, it also includes the professional identity for assuming leadership and job satisfaction, both crucial and required aspects for the correct school functioning, as well as for identifying effective leaders. Therefore, this study aims to know how pedagogical coordination is carried out in high schools based on the existence of distributed leadership modalities. At the same time, it is also intended to adapt the DLI Questionnaire to the Spanish context. 2. Methods 2.1. Study Sample The study aimed to analyze the leadership capacity of formal and middle leaders in secondary schools in the areas of Ja é n and Granada. Due to the fact that there is no official number of principals, heads of studies and department heads, we carried out an estimation of population based on the number of schools. Thus, it was found that in the area of Ja é n there were 87 secondary schools and in Granada there were 94. An average of 18 participants per school was estimated, in order to balance small, medium and large schools. Consequently, it was estimated that the total population was 3709. Subsequently, we calculated the minimum sample needed to achieve a sampling error of 0.05, giving a sample of 364. The final study sample consisted of 547 educational leaders, with 54.1% men and 45.9% women, with a mean age of 47.31 (SD =9.42). The participants were distributed in 83 principals, 97 heads of study and 367 heads of department from schools in the provinces of Granada and Ja é n. Ethical approval was obtained from the University of Granada Research Ethics Committee and all participants provided informed consent. 2.2. Instrument The instrument used was the DLI Questionnaire developed by Hulpia et al. [ 24 ]. The purpose of this questionnaire was to establish the relationships existing between the perception of distributed leadership and job satisfaction in secondary schools, and between organisational commitment of teachers and teaching leaders. A previous study, which collected 2198 responses from teachers and teaching leaders belonging to 46 schools in Flanders (Belgium) [ 24 ], interpreted findings as demonstrating “three core functions of successful leaders mentioned in the instructional and transformational leadership models (. . . ) and in the educational change literature ( . . . ): (a) setting a vision, (b) developing people, and (c) supervising teachers’ performance” (p. 1015). In the first section of the DLI, respondents are asked to rate the individual leadership functions of the school head teacher, head of studies and teaching leaders. For each subgroup, items were scored on a 5-point Likert scale (0 =never to 4 =always). When initially developing the item, Hulpia et al. [ 24 ] stated that it was based on “strength of the vision ( . . . ), supportive leadership behavior ( . . . ), providing instructional support, and providing intellectual stimulation ( . . . ). For supervision, we developed a scale based on the literature concerning supervising and monitoring teachers” (p. 1018). To facilitate response-giving with regards to the characteristics of the leadership team, questions are directed towards characteristics of the school leaders when considered as a team. To this end, subscales are based on “the subscales Role Ambiguity, Group Cohesion and the Degree of Goal Consensus” (p. 1018). Items are evaluated on a Likert scale with five response options (0 =totally disagree to 4 =completely agree). Educ. Sci. 2020,10, 175 4 of 19 2.3. Procedure For the adaptation of DLI [ 24 ] into Spanish, experts were asked to review the instrument according to the Delphi Method [ 25 – 31 ]. The panel of experts selected was formed by university teachers and researchers with a recognised prestige for their expertise in the field of study, and who belonged to the RILME network. The number of individuals on expert panels of previous studies varies between two and 20 experts [ 32 , 33 ]. Eight experts participated in the present study, all of them being university teachers with Terminal Degrees who worked in the departments of Didactics and School Management and Pedagogy at different universities (37.5% male and 62.5% female). Review by the expert panel followed a pre-planned systematic approach that was structured according to three phases: preliminary, exploratory and final. In the first phase, the research team explained the objective of the study. Next, a collaboration agreement was made with the participating experts. Coordinators were charged with interpreting and making relevant adjustments and corrections to the questionnaire. The original questionnaire valuable was the leadership capacity of principals. The experts decided that it would be valuable to learn about the possibilities of the leadership of other leading figures in high schools such as head of studies (responsible for pedagogical issues in Spanish secondary schools, who belongs to the management team) and department heads. Therefore, the first 13 items of the original questionnaire were tripled (Appendix A). The exploratory phase consisted of development and adaption of the questionnaire, and finalisation of the definitive version. To achieve this, the questionnaire was sent by email to the participating experts. This email explained the objective of the research and included a registration form for each expert to complete data collection. The final questionnaire was composed of 65 items pertaining to seven dimensions contemplated on a scale described by Hulpia et al. [ 24 ]. A 5-point Likert scale was used with 0 describing “complete disagreement” and 4 describing “complete agreement.” In the third and final phase, outcomes from the process of adaptation of the final questionnaire were synthesised. These were then administered to 53 secondary school leaders in Andalusia. This stage aimed to find the wrong items and potential errors in the items’ comprehension and redaction. Once the final test was obtained, we contacted high schools in the areas of Ja é n and Granada via telephone and through institutional mail. However, due to the low response achieved, a researcher from the study team visited all schools and invited them to participate directly in person. During this visit, the researcher explained to the management teams all of the study processes, study objectives and data collection measures. The schools were assured that feedback on the study findings relating to their centre would be provided to them, should it be requested. In addition, schools were offered the option of completing the questionnaire in paper format or online, through a Google tool called Google Forms. Once agreement to participate was received from the school, data collection began with questionnaires administered between January and April of 2018. Finally, 565 answers were obtained. A total of 18 questionnaires were excluded as they were not properly completed. The study followed directives provided by the Declaration of Helsinki in relation to research projects. 2.4. Data Analysis Content analysis was conducted to analyse the qualitative data collected. Quantitative data were analysed via descriptive statistics, exploratory factor analysis (EFA) and internal consistency estimations using the statistical software SPSS version 24.0. Confirmatory factor analysis (CFA) was conducted using the statistical software AMOS version 21. The Factorial Analysis (FA) is an exploratory data analysis technique that aims to discover and analyse the structure of a set of interrelated variables in order to construct a measurement scale of factors that somehow control the original variables. The main components method was used to extract these factors, it is a multivariate statistical procedure that allows transforming a set of initial quantitative variables correlated with each other into another set with fewer orthogonal variables and designated by main components. The main components were calculated in decreasing order of Educ. Sci. 2020,10, 175 5 of 19 importance, namely, the first one explained the maximum variance of the data, while the second one explained the maximum variance not explained by the first one, thus, successively. The last component was the one that least contributes to the explanation of the total variance of the data. In order not to find problems of assigning the item to the factor (dimension; component), the rotation of the variables is used to produce an interpretable solution in such way that the higher weights are even higher and the lowest even lower, disappearing the intermediate values, so that the factors are easily interpretable. In this work, the varimax rotation procedure was used, because we wanted to obtain a structure in which variables would only be associated to a single factor and less associated to the remaining ones (process developed by Kaiser 1958, that later comes to be known as KMO (Kaiser–Meyer–Olkin)). In order to apply the factorial model, there must be a correlation between the variables; if these correlations are small, they are unlikely to share common factors. The KMO (Kaiser-Meyer-Olkin) and the Barthel test are statistical procedures that allow to measure the quality of correlations between variables in order to continue with factor analysis. KMO is a statistic that varies between zero and one and compares the zero-order correlations with the correlations observed between the variables. The KMO near one indicates small partial correlation coefficients, while values close to zero indicate that factor analysis may not be a good idea, because there is a weak correlation between the variables. Barthel’s sphericity test allows us to ascertain whether the correlations are high enough for FA to be useful in estimating common factors. It is also common to evaluate the reliability and validity of measurement instruments in FA. The reliability of the instrument refers to the ownership of consistency and reproductively of the measure [ 34 ] (p. 174). An instrument is said to be reliable if it consistently and reproducibly measures a particular characteristic or interesting factor. Cronbach’s alpha coefficient was used as a measure of reliability. This extraction was at the original meeting, hence it proceeded to confirmation. For the evaluation of the psychometric properties of the latent variables of 1st order of the perception of the culture of reliability; for the analysis of the measurement model and the structural model, the Amos v.21 software was used using the maximum likelihood method applied to the original items. The results obtained were considered in the analysis of the adjustment: for the comparative fit index (CFI), which should be greater than 0.9; for the Parsimony Goodness-of-Fit Index, which should be higher than 0.6; and for the root-mean-square error of approximation (RMSEA), which should be less than 0.10, in order to consider the quality of the good adjustment. Also, in the confirmatory factor analysis it is pertinent to evaluate the reliability and validity of the measurement instruments. The reliability of the instrument refers to the consistency and reproductively of the measure [ 34 ] (p. 174). An instrument is said to be reliable if it consistently and reproducibly measures a particular characteristic or interesting factor. Cronbach’s alpha coefficient and composite reliability are used as reliability measures; the latter gathers greater consensus among the different authors, estimates the internal consistency of the reflective items of the factor or construct, indicating that these are consistently manifestations of the latent factor. Composite reliability values above 0.7 are considered to indicate a reliability of the appropriate construct. For Cronbach’s alpha values between 0.7 and 0.8, the internal consistency is reasonable, values between 0.8 and 0.9 consistency are good and values above 0.9 consistency are very good [ 35 ]. Validity is the property of the instrument or scale of measure that evaluates whether it measures and it is the operationalization of the latent construct that is really intended to evaluate. Validity is composed of three components: factorial, convergent and discriminant. Factorial validity is generally evaluated by standardized factor weights, it is usual to assume that if these are at least 0.5, the factor has factorial reliability. The square of the standardized factor weights designates the individual reliability of the item, this is appropriate if the value obtained is at least 0.25. Convergent validity occurs when items are a reflection of a factor, that is, they strongly saturate in this factor, that is, the behavior of the items is essentially explained by this factor. This validity is evaluated using the average variance extracted (AVE); if this value is at least 0.5, then there is adequate convergent validity. Educ. Sci. 2020,10, 175 6 of 19 3. Results 3.1. Exploratory Factor Analysis Firstly, the initial dimensions of support and supervision by leadership were transformed in the adaptation carried out. When the first 13 items were tripled to assess the leadership capacity not only of the management, but also of the head of studies and the head of department, two factors emerged from the factor analysis in the second one: leadership of the head of the department and management of the head of the department. The cohesive leadership team shared decision-making, and commitment dimensions were transformed by school functioning and leadership identity, according to the suggestions of the experts and what was found in the literature. The job satisfaction dimension was maintained with respect to the original instrument. For the development and translation of the questionnaire, the original DLI was divided according to its six dimensions: support, supervision, cohesive leadership team, shared decision-making, the commitment of the organization and job satisfaction [ 24 ]. Then we applied the exploratory factor analysis with varimax rotation. Like we stated before, this was used due to the fact that we wanted to obtain a structure in each variable that would only be associated to a single factor and less associated to the remaining ones. According to the groupings of the questionnaire, we identified the following dimensions: management leadership, the leadership of the head of studies, leadership and management of the head of the department, school functioning, job satisfaction and leadership identity. Exploratory factor analysis outcomes were interpreted using KMO (with value 0.897) indicators and the Bartlett test (p=0.000). The exploratory results presented in Table 1corroborate the theoretical constructs proposed by the research team of the present study and the expert panel. Table 1. Factor loadings of DLI items adapted to Spanish. Item Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 10.713 20.821 30.763 40.788 50.781 60.722 70.780 80.765 90.731 10 0.741 11 0.690 12 0.618 13 0.593 14 0.708 15 0.782 16 0.790 17 0.702 18 0.643 19 0.740 20 0.769 21 0.775 22 0.835 23 0.720 24 0.672 25 0.666 26 0.712 27 0.738 Educ. Sci. 2020,10, 175 7 of 19 Table 1. Cont. Item Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 28 0.777 29 0.749 30 0.685 31 0.772 32 0.803 33 0.816 34 0.762 35 0.733 36 0.831 37 0.915 38 0.863 39 0.827 40 0.840 41 0.850 42 0.766 43 0.621 44 0.795 45 0.840 46 0.755 47 0.757 48 0.648 49 0.579 50 0.681 51 0.719 52 0.708 53 0.774 54 0.742 55 0.769 56 0.794 57 0.735 58 0.412 59 0.842 60 0.746 61 0.769 62 0.588 63 0.889 64 0.817 As can be seen in Table 2, all questionnaire dimensions demonstrated high reliability, with the lowest Cronbach’s alpha produced being 0.84. Table 2. Reliability coefficients of the dimensions of DLI. Dimensions Items Cronbach’s Alpha Management leadership 13 0.958 Leadership of the head of studies 12 0.954 Leadership of the head of department 10 0.940 Management of the head of department 3 0.915 School functioning 18 0.968 Job satisfaction 6 0.859 Leadership identity 2 0.840 Educ. Sci. 2020,10, 175 8 of 19 3.2. Confirmatory Factor Analysis Confirmatory factor analysis followed exploratory factor analysis to solidify the dimensions. Models are deemed to have a very good fit if values for CFI (Comparative Fit Index), GFI (Goodness of Fit Index) and AGFI (Adjusted Goodness of Fit Index) are greater than 0.90 [ 36 ], or if RMSEA (Root Mean Square Error of Approximation) produces a coefficient that is lower than 0.05. If these same values are greater than 0.05 and lower than 0.10, respectively, good model fit is suggested ([ 34 ] (p. 51). Estimation of relationship effects is based on the covariance matrix developed between the considered variables. In the present study, the maximum likelihood estimation method was used to freely interpret the data. This is the method most recommended when assumptions of normal distribution may be violated within the examined population [35,37]. Table 3presents the findings from the analysis of quality of model fit, reliability and validity of the seven dimensions. The dimension describing management demonstrated good quality of fit to the measured data χ ˆ2/df =3562 <5; CFI =0.967 >0.90; TLI =0.956 >0.90; RMSEA =0.070 <0.08. The composite reliability value was sufficiently high (0.937), and the average variance extracted (AVE) indicator of convergence factors was adequate (0.538). Standardised factor weights ( γ _ij) greater than 0.50 and squared standardised factor weights ( γ _ijˆ2) greater than 0.25 suggest factorial reliability and reliability of individual items, respectively. Table 3. The goodness of fit of the measurement’s models. Dimensions χ2/df CFI TLI RMSEA AVE CR Management leadership 3.562 0.967 0.956 0.070 0.683 0.965 Leadership of the head of studies 3.949 0.968 0.957 0.075 0.687 0.963 Leadership of the head of department 3.742 0.921 0.912 0.072 0.712 0.961 Management of the head of department 3.837 0.947 0.936 0.072 0.893 0.962 School functioning 4.279 0.963 0.951 0.079 0.693 0.976 Job satisfaction 3.932 0.956 0.943 0.076 0.619 0.904 Leadership identity 3.886 0.949 0.938 0.079 0.835 0.910 Note: CFI: Comparative Fit Index, RMSEA: Root Mean Square Error of Approximation, TLI: Tucker-Lewis Index, AVE: Average Variance Extratected, CR: Composite Reliability. The dimension describing head of studies demonstrated good fit to the observed data χˆ2/df =3.949 <5 ; CFI =0.968 >0.90; TLI =0.957 >0.90; RMSEA =0.075 <0.08. The component reliability value was sufficiently high (0.933), and the average variance extracted (AVE) indicator of factor convergence was adequate (0.541). Standardized factor weights ( γ _ij) greater than 0.50 and squared standardized factor weights ( γ _ijˆ2) greater than 0.25 suggest factorial reliability and reliability of individual items, respectively. The dimension describing head of department demonstrated good fit to the observed data χˆ2/df =3.742 <5 ; CFI =0.921 >0.90; TLI =0.912 >0.90; RMSEA =0.072 <0.08. Values for component reliability were sufficiently high (0.930 for the leadership of the head of department component and 0.903 for the management of the head of department component), and the average variance extracted (AVE) indicators for factor convergence were adequate (0.571 for the leadership of the head of department component and 0.757 for the management of the head of department component (Table 3). Standardized factor weights ( γ _ij) greater than 0.50 and squared standardized factor weights ( γ _ijˆ2) greater than 0.25 suggest factorial reliability and reliability of the individual items, respectively. The dimension describing school functioning demonstrated good fit to the observed data χˆ2/df =4.279 <5 ; CFI =0.963 >0.90; TLI =0.951 >0.90; RMSEA =0.079 <0.08. Component reliability values were sufficiently high (0.958 for the school functioning component, 0.844 for the job satisfaction component and 0.843 for the leadership identity component), and average variance extraction (AVE) indicators of factor convergence were adequate (0.565 for the school functioning component, 0.4854 for the job satisfaction component and 0.7289 for the leadership identity component). Standardised factor Educ. Sci. 2020,10, 175 9 of 19 weights ( γ _ij) greater than 0.50 and squared standardised factor weights ( γ _ijˆ2) greater than 0.25 suggest factorial reliability and reliability of individual items, respectively. 3.3. Distribution and Descriptive Statistics of Items in the Adaptation of the DLI Questionnaire The following Table 4includes a brief description of the seven dimensions. Table 4. Distribution and descriptive statistics of items according to dimensions. DIMENSIONS Items Min. Max. M SD Management leadership 1 to 13 1 4 3.462 0.630 Leadership of the head of studies 14 to 25 0.83 4 3.417 0.636 Leadership of the head of department 26 to 35 1 4 3.222 0.671 Management of the head of department 36 to 38 0.00 4 3.000 0.958 School functioning 39 to 56 0.72 4 3.500 0.627 Job satisfaction 57 to 61, 64 0.83 4 3.667 0.628 Leadership identity 62–63 0.00 4 3.000 0.891 With regards to the management leadership dimension, reported values were between 1 and 4, with an M =3.462 and an SD =0.630, suggesting moderate dispersion of reported responses. Reported values for the leadership of the head of studies were between 0.83 and 4, with an M =3.417 and an SD =0.636. The median indicating that a large majority of the responses reported were shared between “mostly agree” and “completely agree.” Values for the leadership of the head of the department dimension generally were slightly lower than the two aforementioned dimensions, reporting values between 1 and 4, with a mean of 3.180 and a slightly larger standard deviation of 0.671. These results suggest greater variability of reported responses and a lower influence of this indicator relative to the other measured dimensions. The median score was 3.222, which is, however, similar to the medians reported for the other dimensions. Minimum and maximum values for the management of the head of the department dimension were 1 and 4, respectively. The mean value was 2.756, which is moderately lower than those found for the other measured dimensions, while the standard deviation of 0.958 is higher, suggesting a large dispersion of individual responses. The median value reported was 3. Concerning the school functioning dimension, minimum and maximum values were 0.72 and 4, respectively, with a mean value of 3.359 and a standard deviation of 0.627, suggesting marked variability between questionnaire responses. For the median, it can be seen that this value was slightly larger than the mean, rising to 3.5, suggesting that more than 50% of individual responses reported the value describing “complete agreement.” The job satisfaction dimension scores obtained ranged between 0.83 and 4. Further, this dimension obtained the highest mean value of 3.412 and a median of 3.667. Dispersion of reported responses is marked, with a standard deviation of 0.628. Finally, values reported for the leadership identity dimension fell between 0 and 4. With regards to the mean and the median, the values produced from the observed data were 2.748 and 3, respectively, which are considerably lower than the values reported for all other dimensions, apart from the management of the head of studies dimension. Further, the high value obtained for standard deviation, 0.891, reveals a very high dispersion of responses to the item about these dimensions. In summary, it is evident that the most influential dimensions as suggested by the calculated means and medians are management leadership, the leadership of the head of studies, school functioning and job satisfaction, with all values reported being 3.417 and above and 3.324 and above, for the median and mean, respectively. According to the original authors’ instructions of the DLI Questionnaire [ 24 ], the aim is also to analyze in detail the validity of the construction of the Spanish version of this psychometric instrument; besides, a Confirmatory Factorial Analysis was applied. Figure 1presents the analysis confirmatory factorial performed through the structural equation model. As can be seen, the DLI Questionnaire Educ. Sci. 2020,10, 175 16 of 19 Table A2. Cont. 31. Estádisponible después de las clases para ayudar al profesorado cuando necesitan ayuda 01234 32. Busca el bienestar personal de los profesores 01234 33. Me anima a crecer profesionalmente 01234 34. Me anima a innovar mis prácticas docentes 01234 35. Procura que los profesores tengan “tiempos y espacios” para interaccionar profesionalmente 01234 36. Evalúa el desempeño del personal 01234 37. Participa en la evaluación del proceso de enseñanza y aprendizaje del profesorado 01234 38. Participa en la evaluación formativa de los profesores 01234 Second part Ítem Valoración 39. En nuestro instituto hay un equipo directivo eficaz 01234 40. El equipo directivo gestiona el centro de forma eficiente 01234 41. El equipo directivo apoya las metas que me gustar í a alcanzar en nuestro centro 01234 42. Todos los miembros del equipo directivo están involucrados con la misma intensidad en el logro de los objetivos centrales del instituto 01234 43. En nuestro instituto, cada docente ocupa la función que le pertenece, teniendo en cuenta sus competencias 01234 44. Los miembros del equipo directivo distribuyen su tiempo equitativamente 01234 45. Los miembros del equipo directivo tienen claros los objetivos escolares 01234 46. El equipo directivo asume las responsabilidades ligadas a su cargo 01234 47. El equipo directivo muestra disposición hacia la innovación 01234 48. Están delimitadas las funciones del equipo directivo 01234 49. La coordinaci ó n y supervisi ó n de tareas y responsabilidades entre el personal, es una forma de liderazgo que permite alcanzar las metas de la escuela 01234 50. El liderazgo es compartido entre el personal 01234 51. Como docente considero que se me permite participar en la toma de decisiones del centro 01234 52. Como docente, considero que participo en la toma de decisiones del centro 01234 53. Existe una estructura de comisiones de coordinación que hace eficaz la toma de decisiones 01234 54. Se facilita una comunicación funcional entre el personal 01234 55. Existe un nivel óptimo de autonomía en la toma de decisiones 01234 56. Mi instituto me motiva a desarrollar mi capacidad docente 01234 57. Estoy orgulloso de formar parte del equipo de este centro 01234 58. Realmente me preocupa el destino de nuestro centro 01234 59. Encuentro que mis valores y los valores este instituto son similares 01234 60. Habitualmente hablo con mis amistades sobre lo encantado/a que estoy de trabajar en este instituto 01234 Educ. Sci. 2020,10, 175 17 of 19 Table A2. Cont. 61. Me alegra haber elegido este instituto para trabajar 01234 62. En quémedida considero que mi trabajo es de profesor líder 01234 63. Me gusta desempeñar mi función de liderazgo. 01234 64. Quiero continuar desempeñando mi función profesional en este instituto 01234 65. Si pudiera elegir otra vez, cambiaría mi trabajo por otra profesión 01234 References 1. Verger, A.; Normand, R. Nueva gesti ó n p ú blica y educaci ó n: Elementos te ó ricos y conceptuales para el estudio de un modelo de reforma educativa global. Educ. Soc. 2015,132, 599–622. [CrossRef] 2. Maureira-Cabrera, O. Pr á cticas del liderazgo educativo: Una mirada evolutiva e ilustrativa a partir de sus principales marcos, dimensiones e indicadores más representativos. Rev. Educ. 2018,42, 1–19. [CrossRef] 3. Hulsbos, F.; Evers, A.; Kessels, J.W. Learn to lead: Mapping workplace learning of school leaders. Vocat. Learn. 2016,9, 21–42. [CrossRef] 4. Louis, K. Changing the culture of schools: Professional community, organizational learning, and trust. J. Sch. Leadersh. 2007,16, 477–489. [CrossRef] 5. Garc í a-Mart í nez, I.; Tadeu, P. 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