This need for establishing a system of categories led Kagan (1985) to make an analysis of the cooperative learning methods most applied and studied. He identified 25 dimensions, which he grouped into six categories:

1) Philosophy of education;
2) Nature of learning;
3) Nature of cooperation;
4) Role played by the students and types of communication;
5) Role played by the teacher;
6) Evaluation.

Based on the identification of these categories, almost all training programs are beginning to develop under the supposition that a broad command of these categories on the part of teachers allows for the proper application of cooperative methodology in the classroom. In this sense, the general objectives of a teacher-training process in cooperative-learning methods are determined by three basic elements of the constructivist approach:

1. The student’s constructive activity, which gives access to a set of processes (such as Piagetian explanations of the construction of knowledge through processes of increasing equilibration or the socio-conflict hypothesis of the Geneva School) which are today considered as key elements for understanding the interactive processes established between the teacher, the student and the educational content;
   
2. The scaffolding processes—introduced by Bruner, and based, on the one hand on Vygotsky’s law of double formation of the higher psychological processes, and on the other, as a direct consequence of this, on considering education as a creative and driving force of development,—which refer to the need for and “adjustment” of the teacher’s action toward the difficulties the students encounter during the resolution of educational tasks, so that in the interactive process there becomes possible the creation of “Zones of Proximal Development which allow a coherent interiorization of notions;
   
3. The sociolinguistic contexts—based on the work on ethnographic communication, ethno-methodology applied to education, educational discourse analysis and the analysis of communication in the classroom—which allow a response, not only to the question of how language is learned, but also to that of how people learn through the use of language, i.e. knowing how language works in the interactions between the teacher and student, and between peers.

However, our experience in training teachers in methods of cooperative learning (Calvo Serrano, Gonzalez-Herrero and Ato, 1996) allows us to say that the greatest deficit is related to the role of the teacher. In the teacher’s specific activity throughout the development of a cooperative-learning method, we can find a wide range of behaviors that will depend on the role of the cooperative group, and therefore will be different for each of the methods. In this type of methodology, the students take roles that traditionally were reserved for the teacher; therefore, teachers who use cooperative learning must also take on new roles. In some methods, the teacher is available to work individually with students or with groups, while the rest of the class maintains tutoring relationships. In those methods in which there are “groups of experts” or “learning groups”, the teacher has time for these groups to consult with him/her, and in this way, facilitates learning the material. In the methods where the students assume the responsibility of what and how they are going to carry out the teaching/learning process, the teacher is even more “liberated”, and normally speaks with the groups, suggests ideas and study possibilities, thereby assuring an equitable and rational division of labor within the groups.

All these activities should be conducted within the three-dimensional framework mentioned above: respecting and taking advantage of the student’s constructive activity, ensuring the scaffolding process, and knowing and making known the basic educational rules for classroom talk, with the goal of intervening and organizing activities, while facilitating and promoting the process of negotiating meanings around what is being done and said. But it must be always borne in mind that the contexts of interaction are constructed by the people involved in educational activity, and that communicative exchanges cannot be produced under the principle of “all or nothing”, or that they are either produced under an absolute respect for the rules, or not at all. The reality of the classroom is much more complex, and it would be an error to contemplate the interaction between teacher and students as the “dramatization” of a script with previously-established roles.

This change in roles adapted to a new system of rules requires the training of teachers in the methods of cooperative learning. Moreover, educators themselves need this training, because despite the intrinsic and extrinsic value they attach to these techniques, they do not seem to be well informed, and are less well prepared to implement the required effectiveness. In this regard, coming from the teachers themselves there have been proposals, in which they specify the need to bear in mind that in the programs of initial and ongoing training, at least two points should be addressed.

First, and related with ongoing training, there should be work done on three types of classroom structure, while at the same time giving information on which of these types is the most desirable in certain circumstances. Also, emphasis should be placed on the structure of cooperative rewards; the following three issues should be made very clear: how to group students, how to create positive interdependence among them, and finally, what the teacher’s function and behavior should be.
Second, and in relation to the initial training, cooperation should be modeled in the classes of future teachers. This can be easily done, since it is as powerful a way of learning with young people as with adults. The modeling of cooperation will not only offer the future teacher a deeper knowledge of the use of these strategies, but will also help to apply them to their work with staff peers. In addition, this situation should be applied to the case of ongoing training; i.e., teachers should be trained in methods of cooperative learning on the basis of a cooperative-training organization.

Along this same line, the need for generalizing teacher-to-teacher cooperative learning has been pointed out. If teachers desire to learn from one another, they should interact in a cooperative context, since this has been shown to be equally effective with adults. In one of the meta-analyses carried out by the Minnesota School (Johnson and Johnson, 1990), 30% of the empirical studies (133) used sample groups of adults for research on performance. This, in addition, makes possible more positive interpersonal relationships, and generates higher levels of self-esteem. It should not be surprising, then, that very concrete learning experiences among teachers are being experienced (as in the Collegial Support Group), and could easily be incorporated without substantial changes, into teaching programs (primary, junior high and high school), and into university departments and centers.

Figure 1. Actions in the evaluation of programs

The manifest difference between the component parts of a program requires that the evaluation of each of the segments be constructed on two well-differentiated axes: the substantive and the methodological.

The substantive axis is the differentiating axis of the programs and their evaluations.

The substantive axis is composed of five elements that allow one to answer the questions, “Why? How? When? For what?” and “For whom?” The first two elements of this substantive axis make reference to what and how, that is to say, to the content previously established in the program, its viability and the strategies it uses. The third elements refers to the for what—which means, to the reason for this program. The fourth elements refers to the moment of performance, or the when. Finally, the last element to have in mind is the audience, i.e., the for whom.

Once the foundations of the evaluation process have been laid, based on the determination of the substantive axis, it is possible to construct the framework of the evaluation program, which will feature many free alternatives, but will be highly influenced by the second axis of the methodology. This axis allows us to answer the questions of who, how, and with what.

The methodological axis has, therefore, three distinct elements. The first concerns who should be evaluated, i.e. whether the evaluation should be external, internal, or mixed. The second element is whether the evaluation should be free, should be centered on the objectives, or should have descriptive or experimental character; this second element, therefore is about how to evaluate. Finally, the third element of this axis refers to what technology should be used (documentary analysis, observation, scales, etc.), and of course, attempts to answer the question of with what.

The methodological axis is the axis of conflict and controversy because, as Munici puts it (1992, p. 376), its elements are the cornerstones of all program evaluation. In the present paper we seek to give an answer to the proposals emanating from the methodological axis, in the concrete case of the evaluation of a teacher-training program on methods of cooperative learning.

1) Needs. This variable will be understood both in the sense of needs assessment, and of needs evaluation. In it will be considered the analysis of the objectives of the needs search, the obstacles encountered, the conditions accepted, the risk components, and the management of the identification and selection of the needs. Its measurement, as mentioned in the introduction, will be effected based on three components:

a) Design, collection and treatment of the information (sources, procedures, instruments, techniques, management);

b) Identification of needs (issues raised, organization and structuring of information, results desired by the participating teachers, primary needs covering the training program, and needs not covered; secondary needs covering the training program; criteria established by the program developers for evaluating explicit and implicit proposals, establishment of priorities based on the proposals outlined by the teachers in training);

c) Valoration and selection of the needs (criteria and system for valorizing the needs identified; determining which are significant and which are not, and what consequences would result from not covering the needs; defining the system used to establish the criteria of importance and contrast of the needs and determining which will be included in the training program and which not).

2) Context. For the valoration of the context, we will start out from the general theory of systems and focus on an analysis of the system:

a) Physical (delimitation of physical variables that may influence the generation of problems detected, and that create the need for training).

b) Social (all the aspects that influence the socioeducational needs which produce the training program will be included).

c) Organizational (the proximal dimension of organization, focused on the institution or institutions that develop the project; and the distance dimension of organization, composed of the network of organizations that interact on the training program.).

d) Interpersonal relations (Considered here are all the loosely-structured and disconnected transactions that do not fit within the previous systems).

3) Viability. The evaluation of viability is an ex ante, and in the measurement model there will be analyzed:

a) Technical viability (valoration of compatibility between media to be used, teacher’s needs, program objectives and context problems. This has as much to do with the availability of physical and technological resources for developing the training program, as with the availability of a team of trainers who have mastered the technology for training teachers in methods of cooperative learning, and who are identified with the philosophy of change, and the existence of professionals from different educational levels who are willing to make a professional effort, leading to the acquisition of new skills and the modification of their work habits).

b) Social viability (is an affirmative answer to most of the following questions: “Does it meet real social needs? Is it a positive change for the program users, and for their students? Can social impacts be derived from the application of the program?” And so forth...)

c) Economic viability (determines the existence of a reliable general budget and a cash-flow adjusted to the available resources).

d) Management viability (valorizes whether the development of the training program is guaranteed from its beginning to its end, through the valoration of external relations, internal organization, management capability; it is, in short, an evaluation of the team of trainers).

3.1.2 Design
1) Strategy: The strategy is the course or organized action that the training program will use for achieving its objectives. In this variable, there will be valorized the process of creation and selection (rate of innovation of the institutions involved in the project, levels of instability and turbulence of the environment in which the program is developed, and which can affect the variables predicted by the designers and authors of the project, teamwork, etc.), and the type of focus (satisfying, optimizing or adaptive). In this variable, in spite of its being less commonly used in social science, we have opted for the adaptive focus because, in this case, what is most important is not the previously-determined product, but the process established using our training strategy. Given the level of uncertainty as to what may be the knowledge level of the teachers who will take part in the training process, we must evaluate their ability to react to a certain type of developments that could arise during the training process.

2) Activities: The structure of the activities will be measured taking into account the assignments, significant relations, assignment of their possibility of execution, products, time for carrying out activities, and appropriateness of the design.

3) Means: The evaluation of the means of support will be performed through the analysis of their consistency and compatibility; their appropriateness, availability and utilization. It distinguishes between physical, organizational, technological, human, cultural and regulatory environments.

4) Evaluability: To measure this aspect, the criteria of Berk and Rossi (1990) will be used: objectives, structure, components, recourses and prognosis regarding the consequences of not applying it.

3.1.3 Use
Three variables were used to configure the measurements:

1) Tasks and relationships: Evaluates the activities performed by the teachers to achieve the objectives and the manner of sequencing, determining hierarchy and connecting the tasks, by means of the persons implicated in the project.

2) Process: The evaluation of the process will focus on the human aspects, both of the tasks, and of the relations. Determined as indicators of behaviors will be those behaviors that that help or interfere in the manner of addressing and resolving the conflicts that inevitably occur in the process, etc.

3) Management: This variable will take in account five factors: the activation of the means of support, the activation of positive interpersonal relationships, the activation of the information and coordination of the project (internal and external); the help provided a team of specialists by the institutions involved and the integration of project components.

3.1.4 Conclusion
Regarding the last of the independent latent variables, two were observed:

1) Completion: Measures the operations for proving the proposals of the program, according to their accomplishment and the changes introduced.

2) Effects: Categorizes the products, the results, the impacts and the collateral effects.

3.2 Endogenous variables

3.2.1 Results
This construct is the latent variable, and there are five observable variables underlying it:

1) Efficacy: Degree to which objectives have been achieved in the population of teachers of different educational levels, measured in terms of a correct implementation of cooperative methodology in the classroom.

2) Effectivity: Degree to which the effects achieved differ from those achieved without the application of the training program, as compared with those obtained in classrooms of the same scholastic level where the program has not been developed because the faculty has not participated in the training program (equivalent control groups).

3) Efficiency: Evaluation of the cost/benefit and cost/effectiveness relationships (cost expressed as hours dedicated to the program and hours of preparation and planning by the teaching staff based on cooperative methodology).

4) Productivity: Set of relationships between the products and the inputs and means of support used (performance yield).

5) Appropriateness: Relationship between the elements of the project in which the human component (faculty of the participating institutions, teacher of the various levels of education involved in the training activity, etc.) constitutes the key to achieving these objectives.

It is clear that the greater part of these variables report categorical data; therefore, the model we propose is a causal model with categorical data (Hagenaars, 2002).

Figure 2. Pathway diagram

As previously mentioned, this model specifies the hypothetical relationships existing among our five constructs or latent variables (symbolized by ellipses): Definition (F1), Design (F2), Execution (F3), Conclusion (F4) and Results (F5). As indicated by the arrows F1, F2, F3, and F4 (exogenous variables) we may assume that they affect F5 (endogenous variable).

Because they are independent elements of the program, orthogonality between the exogenous variables is assumed; therefore, correlations between these variables have no causal connotations and can be estimated as 0

The magnitude of the causal relationships are expressed by the structural coefficients and in the model.

Furthermore, there has been represented the residual D5 (), which is part of the variance of the endogenous latent variable that cannot be attributed to the constructs of the model.

This group of relationships make up the structural model we have established, and which has already been previously and sufficiently justified. But in addition, the structural model contains a measurement model composed of nine observable variables represented by two vectors (which we will designate as x and y, and which will be found symbolized by squares).

This set of relationships configure the structural model we have established and which has already been previously and amply justified. However, the structural model contains a measurement model consisting of nine observable variables represented by two vectors (which we will designate by x and y, and which are symbolized by squares).

The vector y (v13, v14, v15, v16 and v17) is a vector of measurements for the dependent variables (endogenous), and the vector x (v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11 and v12) is a vector of measurements for the independent variables (exogenous). The errors of measurement are represented, respectively, by the vectors (E13, E14, E15, E16 y E17) y (E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11 and E12).

Where is a scalar which defines the latent endogenous variable, and is a vector (4 x 1) of latent exogenous variables, is a vector (1 x 4) of coefficients of the effects of the exogenous variables on the endogenous variables; finally, is a scalar which specifies the residual (or error) of the general equation (I).

The development of this general equation would be as detailed in Figure 3.

Figure 3. Matricial development of the general equation

Where y is a vector (5 x 1) of measurements for the endogenous variable, is a vector (5 x 1) of coefficients (factorial saturations) of y over the latent variables , and is a vector (5 x 1) of errors of measurements of y (Equation III); x is a vector (12 x 1) of measurements for the exogenous variables, is a matrix (12 x 4) of coefficients (factorial saturations) of x over the latent variables , and is a vector (12 x 1) of errors of measurement of x (Equation IV).
The matricial development of the equations (III and IV) will be as shown in Figures 4 and 5.

Figure 4. Matricial development of the measurement model of the dependent variable

Figure 5. Matricial development of the measurement model of the independent variables

The development we have just proposed complies with all the conditions established by Jöreskog and Sörbom (1978) for the matrix of covariance of the observed variables (always of the assumptions of LISREL).1 Indeed, our model will postulate seven matrices in function of which this matrix of covariance is structured:

1. The matrix of coefficients () or saturations linking indicators of endogenous variables to endogenous latent variables (in our case a vector);

2. The matrix of coefficients () or factorial saturations linking the indicators of exogenous variables with the latent exogenous variables;

3. The matrix () of the effects of the latent exogenous variables on the latent endogenous variables (in our case a vector);

4. The matrix of variance-covariance () of the latent exogenous variables (in our case a scalar);

5. The matrix of variance-covariance () of the residuals (in our case a scalar);

6. The matrix of variance-covariance of the measurement errors of the indicators ;

7. The matrix of variance-covariance of the measurement errors of the indicators .

This design has been chosen while bearing in mind the interests of the work situated in the verification or confirmation of the worth of a training program, and as we have previously stated, the structural models appear to be, from the epistemological point of view, a suitable method for dealing with this and for trying it out (Vega, 1985).

The analysis of the model was conducted with the program EQS Version 13 of the BMDP Statistical Software, and the estimate of the parameters was made using the maximum plausibility estimator of Maximum Likelihood (ML) because this estimator minimizes the function defined as:

Table I. Structural model

b) Components of the measurement model of covariance structures (see Table II)

Table II. Measurement model

Due to the planetarization of politics, economics and, above all, of culture, this situation has led to a rethinking of the dialectical relation between the particular and the universal, a rethinking that pursues a multicultural universalism which can give, simultaneously, a response to the identical and to the different. This brings into question the rationality of an educational system that is entrenched in poverty and a narrow sliver of sameness, while ignoring the enormous wealth in otherness and what is different. Therefore, if our leaders desire stability (global, national or regional), they should be aware of the Hegelian principle that “the identities that are not recognized by those who share life and destinations, are inherently unstable”. They must also be aware that if you want a policy leading to the achievement of these principles of integration without absorption, you must start with the basic element of any transformation: education.

In this sense, starting with the early work of Dewey, passing through the studies of Lewin and the substantive bases emanating from the theories of Piaget and Vygotsky, the process of peer interaction has become the most promising element on which should rest the organization of some classrooms which, increasingly, present a broad cognitive, social, ethnic and cultural heterogeneity.

Under the conditions of this process, beginning with the decade of the 70s, there have been developed methodologies based on a positive interdependence between the individual goals of the students, and the achievement of these, which depends on the quality of this interaction process. These methods of teaching are grouped under the common nomenclature of methods of cooperative learning.

Clearly, the application of a cooperative methodology in the classroom means training the teachers who have to develop it. For this reason, it is necessary to train a body of teachers from different levels of education in the skills needed for dealing successfully with this task.

The preparation of training programs for the teaching force—both the initial training (Dyson, 2001; Serrano Pons and Calvo, 2008) and the ongoing training (Emmer and Stough, 2001; Hawkes, 2000; and Pons Serrano, 2007 Serrano, Calvo, Pons, Lara and Moreno, 2008; Serrano Pons, Lara and Moreno, 2008; Solomon, 2000)—in the use of methodologies that allow the process of peer interaction is a promising line of research in the attempt at cooperative classroom organization (Hoy and Tschannen-Moran, 1999), which enables the development of integrated teacher-training projects such as SELA2 (Almog and Hertz-Lazarowitz, 1999).

Second, we propose here here a segmented preparation for teacher-training programs, because this type of formulation allows for a better evaluation of the effects of the program and its capability of providing:

A greater wealth of the elements that constitute the conceptual keys of the program, attempting to answer questions about what needs it is trying to meet, how can it meet the needs from a highly-contextualized perspective, and how it can be formulated in a way that will guarantee a priori its possibilities of being carried out;

A holistic procedural system, which needs to describe the strategic action that will make possible the achievement of the desired competencies, and that can be reached only through a highly-organized structure among activities, means and products, within a specific time frame;

A prognosis system regarding application vs. non-application, a sine qua non for its evaluability, which necessitates a classification of the products, the results, the impacts, and the collateral effects.

Third, and since they work with categorical variables,3 we propose here that the most appropriate structure for such evaluation is determined by the application of causal models. Moreover, we know that non-experimental research can approximate the experimental based on the use of structural equation models, by introducing into these the variables necessary to refute the relations between variables not derived from the theory.4 We also know that the models of structural equations constitute one of the most powerful tools for the study of causal relationships with non-quantitative data (Batista and Coenders, 2000). This has made it possible for these models to attain great popularity in the last three decades, and for eight important reasons:

1) One works with constructs that are measured through indicators, after which the quality of the measurement is evaluated;

2) Phenomena are seen in their true complexity (incorporating multiple endogenous and exogenous variables) and therefore, from a more realistic perspective and with a high level of ecological validity;

3) Measurement and prediction, analysis and factorial analysis of trajectories are considered together, which is to say that the effects of the latent variables on one another are evaluated without contamination due to the error of measurement;

4) Confirmatory perspective is introduced in the statistical model because the researcher must enter his/her theoretical knowledge into the model’s specifications before making the estimate;

5) The covariances observed (and not only the variances) are decomposed within a perspective of an analysis of the interdependence.

6) The quality of the measurement, the reliability and the validity of every indicator are evaluated;

7) The best indicators, including the modality of optimal response, are chosen;

8) The error of measurement and that of prediction are evaluated separately.

All this shows that, given the purpose of this work, models of structural equations become one of the best tools the trainer of trainers can use for evaluating his/her action/intervention.

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