Summary
In the present work, a Didactic Strategy for the Dynamics of the Professional Contextualization of the Contents of the Higher Mathematics I subject is based on the Profile of Administration and Economics of the Health Technology Career. Its characteristics are explained and reflects its structuring by stages and actions.
This research has the following scientific categories: problem: Insufficient appropriation of the contents required for the solution of problems related to the professional profile, to be defined as the object: The educational teaching process of the Higher Mathematics I subject, for the administration profile and economy in the Health Technologies career, as objective: To elaborate a didactic Strategy for the dynamics of the professional contextualization of the contents of Mathematical Subject I to the profile of Administration and Economics of the Health Technologies career, field of Action: Dynamics of the professional contextualization of the contents of the Mathematical Subject I to the profile of Administration and Economics of the Health Technologies career and as hypotheses:If a Didactic Strategy for the dynamics of the professional contextualization of the contents of Mathematical Subject I is applied to the profile of Administration and Economics of the Health Technologies career, it can contribute to the appropriation of the contents required for the solution of mathematical problems related to the professional profile. In other works developed by the authors, the contribution made is subject to expert judgment, and the strategy is partially introduced, confirming its validity.You can contribute to the appropriation of the contents required for solving mathematical problems related to the professional profile. In other works developed by the authors, the contribution made is subject to expert judgment, and the strategy is partially introduced, confirming its validity.You can contribute to the appropriation of the contents required for solving mathematical problems related to the professional profile. In other works developed by the authors, the contribution made is subject to expert judgment, and the strategy is partially introduced, confirming its validity.
1. Theoretical foundations of the didactic strategy for the dynamics of the professional contextualization of the contents of the mathematical subject I, to the profile of administration and economics of the career of health technologies
For the elaboration of the strategy, the structural systemic approach developed by Álvarez de Zayas is taken into account, according to which a system is a set of elements or components, which behave according to certain internal laws, which establish their relationships and which offer a qualitatively new result.
The concept of the contextualized problem developed by Campistrous, L. (1998) and taken up by Diéguez, R. (2001), is adopted, in the sense that the work with this type of problem can be achieved in the classroom, through an approach of object of study to the object of the profession, but with it it is intended to achieve a didactic orientation for the development of the solution of the problem, The concept of contextualization developed by Pérez, G. (2001) and systematized by (Numa, 2011: 15) is assumed, which expresses that “when speaking of professional contextualization of content, reference is made to a conception of the dynamics of the training process that focuses the development of the knowledge, skills, values and valuations system, in the approach and solution of possible problems of presenting in centers related to the profession, by applying the methods of a subject ”
The concepts of independent work and teaching tasks developed by are adopted, according to which "It is the method in which the student alone develops the process with less or greater degrees of participation." And the teaching task is “The teaching task is the elementary teaching process that, despite containing all the components of the process, refers to a single cognitive action, which attends more to the conditions in which the process is developed than to the objective itself., The concept of problem teaching developed by Majmutov, M. (1983) and systematized by (Torres, 1993: 5) is assumed, according to which this is defined as “one where students are systematically placed before problems, whose resolution must be carried out with their active participation, and in which the objective is not only to obtain the result but also to provide them with independent training for solving problems in general ”; the concept of meaningful learning developed by Ausubel, P. D, (Valdez, J., 2004) and systematized by (Escaño, 1992), who expresses that: “Meaningful learning is usually called the one carried out by the student building new knowledge based on their own mental schemas,after having experienced the absence of knowledge to resolve situations related to practical life or other previous knowledge that they already possess. »
The conception of interdisciplinarity argued by (Busquet, 1997: 26) is adopted, who enunciates it as: “the confirmation of a new theoretical object between two or more previous sciences, which lead to a new particular discipline or when application is achieved, to the same practical object, of theoretical elements of different subjects ”. The concept of mathematical reasoning developed by (Castellano, 1997) and systematized by (Numa, 2011: 23) who defines it as “the action and effect of thinking or reflecting and applying intelligence, ordering ideas about mathematical concepts and their application argued in a certain context, taking into account the interconnection between them, to reach a conclusion or make a judgment, expression of the mathematical results, and to fully interpret these results ".
The concept of developer learning enunciated by (Castellanos, 2000: 12) is assumed, who expresses that “it is one that guarantees the individual the active and creative appropriation of culture, promoting the development of its constant self-improvement, its autonomy and self-determination, in close connection with the necessary processes of socialization, commitment and social responsibility ”.
The strategy is oriented to achieve the development of a dynamic that has as:
Beginning
Treatment of content contextualized to the profession.
Contextualizing problem approach
Linking the Academic, Labor and Research components
Independent work as a manager of meaningful learning and developer.
Organization of situations that favor the development of learning.
Interdisciplinary relationship
Construction of knowledge bearing individualized methods and procedures
The dynamics for whose execution the Strategy is elaborated have two essential qualities: The Appropriation of the integrating logic of the mathematical contents and those inherent to the professional profile; and The Systematization of skills in solving mathematical problems contextualized to the professional profile.
The Appropriation of the integrative logic of the mathematical contents and those inherent to the professional profile is an expression of the apprehension of a mathematical culture carrying the forms of thought in accordance with the processes of solving mathematical problems contextualized to the profile of Administration and Economics, and systematized through a didactic mediation that favors the application of mathematical reasoning in the search for ways to solve these problems.
This quality is reached from the establishment of interdisciplinary relationships through the treatment of the contents, which favors the understanding of the mathematical content of the mathematical problem contextualized to the profile achieved in its relationship with the attribution of a mathematical meaning of the contents, conditions and demands given in the problem, from this relation the appropriation of the logic of the solution of the mathematical problems contextualized to the profile of Administration and Economy is reached. Figure 1
To achieve such appropriation, the method used for the transmission of the knowledge system must be centered on a problem approach, through the exemplification of: procedures for solving such problems, economic concepts that are represented through mathematical expressions like this as mathematical expressions that have an economic meaning; and oriented to the link with the labor practice, by means of the conception of an investigative scientific student work that leads to the identification of situations that occur in the labor practice, leading to the solution of mathematical problems.This methodological approach is made feasible through the projection of an independent work promoting the development of mental actions that enrich cognitive structures and is consolidated by carrying out a contextualizing evaluation.
Appropriation of the integrative logic of the mathematical contents and those inherent in the professional profile.
Figure 1. Appropriation of the integrative logic of the mathematical contents and those inherent in the professional profile.
The systematization of skills in the solution of mathematical problems contextualized to the professional profile is the quality that expresses the development of skills for the interpretation of the problem through the integration of the mathematical and the economic, the search for ways and procedures of solution, the application of such procedures and the attribution of an economic meaning to the result obtained.
This quality is manifested in the dynamics in the need to systematically confront students in solving mathematical problems contextualized to the profile of Administration and Economics, which leads to an appropriation of the logic of solving such problems that is focuses on the search for the solution, preceded by the interpretation of the problem and consisting of several steps: Identification of the type of problem: recognition of the mathematical expressions that make up the contents, conditions and demands, inherent to the economic context, given in the problem, delimitation of the procedures and methods of solving the problem, application of mathematical procedures to the calculation of economic measures and functions and the attribution of an economic meaning to the result obtained in mathematical terms.
Achieving such a purpose in the development of dynamics requires taking advantage of the potential offered by the guidance and control of independent work, for the systematization of individualized methods, as an expression of the development of significant and developer learning; and the integrative evaluation of the academic, labor and research components. Such didactic orientation is made possible through the execution of a class typology that fosters creativity within the framework of carrying out developing educational tasks, and an orientation and development of a scientific student work related to work practice. Figure 2
The systematization of skills in solving mathematical problems contextualized to the professional profile
Figure 2. Systematization of skills in solving mathematical problems contextualized to the professional profile
2. Essential characteristics of the didactic strategy for the dynamics of the professional contextualization of the contents of the subject Higher Mathematics I, to the profile of administration and economics of the health technologies career.
The strategy presented is didactic, since it aims, from its actions, to transform the dynamics of the educational teaching process of Higher Mathematics I, in order to achieve the formative relevance of the professional of the administration and economics profile of the career of technologies of health.
It takes into account, taking into account the particularities of the process of the dynamics of the professional contextualization of the contents of the mathematical subject, the profile of administration and economics of the career of health technologies, based on the previous heading and the contributions of Weapons, N. (2003) on the structuring of strategies.
This strategy is recognized as an open system, as it is subject to multiple influences on its implementation. Its recursion is manifested in the subordination relationship between the stages and subsystems, as well as between its components. It is subject to constant improvements from the results of its instrumentation and readjustments from the diagnosis, as well as to the feedback of its actions, that is, to autopoiesis. It is also subject to entropy, which can be evidenced in:
Resistance to change by the teachers involved in its implementation.
Preparation of teachers and workers of labor entities for their understanding and implementation.
Availability of work entities to attend to students and make possible the required information on contextualized mathematical problems to be solved.
As homeostasis it can be foreseen:
Preparation of exercise brochures and problems that correspond to the demands of the planned actions.
Didactic-methodological orientation suitable for the instrumentation of statistical-professional dynamics in careers with a humanistic profile.
The synergy of the strategy is given in that the system of actions contributes, in an integrated way, to the formative relevance of the appropriation of the mathematical contents required for the solution of the mathematical problems contextualized to the professional profile, in the dynamics of professional contextualization of the contents of the Mathematical Subject I, to the profile of Administration and Economics of the Health Technologies career
This strategy is aimed at developing a dynamic of the professional contextualization of the contents of the Mathematical Subject I, to the profile of Administration and Economics of the Health Technologies career in correspondence with the integrative logic of mathematical reasoning and interpretive contextualized professional, based on the relationships established between the qualities of dynamics, and which are an expression of its regularity.
2. Structuring of the didactic strategy for the dynamics of the professional contextualization of the contents of the mathematical subject I, to the profile of administration and economics of the health technologies career.
The strategy is structured in five stages. Figure 3. Stage III of Strategic Planning is divided into two moments: Planning resources and methods to make the execution of the dynamics feasible and the execution of the dynamics, which is subdivided into two threads, defined as starting from the qualities acquired by the dynamics conceived in its epistemological characterization. At each stage the corresponding objectives and actions are defined.
Teaching strategy
Figure 3. Teaching strategy
STAGE I-. Diagnosis of the level reached in previous knowledge that affects the appropriation of the contents of the Higher Mathematical Subject I.
Before applying the actions of the Didactic Strategy for the dynamics of the solution of contextualized mathematical problems to the professional profile in the mathematical subject I, it is suggested to characterize the students in terms of the cognitive development achieved by them in the Mathematical subject during General Education, identifying the contents that influence the appropriation of the contents of the Higher Mathematics Subject I and its application in solving problems related to the profile of administration and economics of the health technology career.
This characterization allows taking into account the individualities of the students in terms of mastering the preconditions necessary for the study of Higher Mathematics I and its application in solving problems linked to the professional profile, which makes it possible to conceive of carrying out the activities. teachers in correspondence with the elaborated strategy and the characteristics of the group of students.
Taking into account that the student has to carry out, according to the hypothesis raised, the student has to apply the interpretation, to be able to recognize in the context of the problem the meaning of each information that is offered, to look for the way of solution by determining the typology of the problem and the sequence of mathematical procedures to be applied, establish the relationship between the concepts related to the professional profile and the mathematical contents and apply solution procedures, which involve, in addition to the contents of the Higher Mathematics I subject, previous contents such as: problem solving, working with variables, numerical calculation, solution of equations and substitution in formulas,For which a mathematical logic integrated with the logic of the profession and an orientation towards the integration of the mathematical contents that are received in the subject and the preceding ones are required as a first approach to the desired dynamics, it is important to have some information about of its level reached in the solution of problems, and the preceding contents mentioned above.
To solve the mathematical problems linked to the professional profile, students must achieve the systematization of the skills of Mathematics I, including infinitesimal calculus, the development of algorithms for the calculation of derivatives and algebraic and numerical procedures., contemplated in the Mathematics of General Education, and in that sense it is necessary to have knowledge of the level of mastery that they possess prior to the study of Higher Mathematics, since this affects the peculiarity that they attribute to the training process and the delimitation of the general and individual characteristics of the group of students.
The characterization carried out in this sense enables the teacher to adapt the actions of the strategy for the development of the dynamics of solving mathematical problems contextualized to the professional profile in the mathematical subject I, in the administration and economics profile of the health, in function of which the students can carry out the processes of interpretation, search of the solution routes and application of the solution procedures, from an integrative logic of the mathematical thought and the understanding of the own knowledge of the profession.
In general, a diagnosis is required that includes: logical reasoning, problem solving, working with a variable, solving equations, substituting formulas. This diagnosis can be made by applying an exam where the student, according to the specified aspects, solves exercises and problems that reveal the levels reached.
Course objective: To determine the level of previous knowledge of the students, that influence the development of skills to solve problems related to the professional profile.
Specific actions:
To determine skills to measure in the diagnosis of the necessary preconditions for the development of the dynamics of solving mathematical problems contextualized to the professional profile in the mathematical subject I, in the profile of administration and economics of the career of health technologies.
Prepare an exam to measure the level that students have in the development of the preconditions, which includes the following:
Troubleshooting: Formulating a simple percent and proportion problem.
The substitution of formulas. Using a question in which an algebraic expression containing several variables appears, with medium degree of difficulty, and they are instructed to substitute specific values for the variables.
I work with variables. An algebraic expression is written and you are asked to perform operations such as factoring, simplifying, and performing addition, subtraction, and multiplication of terms, allowing you to measure the level achieved in working with variables.
The development of algorithms. Using a question that includes values of two variables with subscripts, after which they are asked to perform addition, product, and both operations, for certain subscripts.
Note: Other aspects considered important may be included in the execution of the subsection action.
Apply the elaborated questionnaire. (Annex 6)
Evaluate the result obtained from the application of the questionnaire.
Organize the information obtained.
Characterize the group of students in terms of mastering the preconditions assessed.
STAGE II. Statement of the general objective
Objective: Achieve higher levels in the appropriation of the contents required for the solution of mathematical problems related to the professional profile.
STAGE III -Strategic planning
It is structured in two sub-stages
SUPETAPA III.1: Planning of resources and methods to make feasible the execution of the dynamics
Objective: Manage the necessary conditions for the execution of the dynamics of the professional contextualization of the contents of the mathematical subject I, to the profile of administration and economics of the Health Technologies career in the Medical Sciences Branch of Morón.
Actions:
Determine the potentialities and existing conditions to achieve the contextualization of the contents through interdisciplinary relationships.
- Identify the contents of the profile that are related to the mathematical contents, Identify the functions and economic measures that are calculated with the use of the contents of Higher Mathematics II Identify situations that manifest in professional practice that are solved with the contents of Mathematics higher
a) Guarantee the means and materials necessary to apply the necessary methods for the development of the dynamics conceived.
To elaborate a system of exercises and mathematical problems contextualized to the profile of administration and economics of the career of health technologies.
b) Perfect the preparation of the subject in terms of:
- The typology of classes The treatment of the contents The orientation of independent work The conception of the evaluation system
c) Management of the methodological preparation of teachers for the execution of the dynamics
- Hold a Methodological Meeting to make the teachers of the group know the characterization of the dynamics to be developed, highlighting their essential qualities. Give a methodological instructional class to instruct the teachers on how to execute the dynamics, emphasizing the methods to be applied. and the use of exemplification through a theme. Hold workshops to socialize ideas and experiences about how to develop the dynamics in correspondence with the elaborated strategy.
SUPETAPA III.2: Execution of the dynamics of the professional contextualization of
contents of the mathematical subject I, to the profile of administration and economics of the Health Technologies career at the Morón Medical Sciences Branch
In order to establish a logical order in the actions of this stage, based on the recognition of the qualities of the characterized dynamics and its movement, two sub-processes are defined:
SUBPROCESS 1. APPROPRIATION OF THE INTEGRATING LOGIC OF MATHEMATICAL CONTENTS AND THOSE INHERENT TO PROFESSIONAL PROFILE.
The actions that are conceived in this sub-process are aimed at encouraging the student to interact with the process of attributing a mathematical meaning to the contents, conditions and demands given in a mathematical problem contextualized to the professional profile, which will allow him to determine the ways and procedures solution to apply to solve the problem.
Objective: To guide the required reasoning processes required to determine the ways and procedures for solving a contextualized mathematical problem to the professional profile, from understanding its mathematical content through an integrative logic of mathematics and economics
Specific actions to be carried out by the teacher:
Illustrate the usefulness of the study of Higher Mathematics I for their professional performance, through the professional contextualization of the content or the interrelation with an institution related to the profile.
Explain the way in which the mathematical content is manifested in the calculation of economic or accounting measures, using examples.
Explain the process of determining the type of problem to be solved, and the interrelation between the mathematical and economic contents.
Explain the process of delimiting the mathematical content of problems contextualized to the professional profile.
Illustrate by means of exemplification the interrelation that exists between some concepts of the professional profile and the mathematical contents studied.
Exemplify the process of searching for the way to solve a mathematical problem contextualized to the professional profile applying the contents of the subject.
Exemplify the complete process of solving a mathematical problem contextualized to the professional profile.
Specific actions to be carried out by students:
Recognize the interrelation between some economic accounting concepts and the mathematical concepts studied
Attribute a mathematical meaning of a professional situation given by the teacher, through interpretation, through a sufficient approach to the interrelation of economic and mathematical knowledge.
Identify the mathematical expression of economic measures and functions.
Identify the mathematical content of a mathematical problem contextualized to the profile.
Identify the conditions of the contextualized mathematical problem, from the initial information about the context and the circumstances in which it develops, envisioning its possible solution from Mathematics.
Identify the demands of the problem, given in the professional field as the final objective to be achieved.
Recognize the types of problems to present and the possible solutions.
Recognize the mathematical procedures to be applied, in correspondence with the type of problem.
SUBPROCESS 2. SYSTEMATIZATION OF SKILLS IN THE SOLUTION OF MATHEMATICAL PROBLEMS CONTEXTUALIZED TO THE PROFESSIONAL PROFILE
The actions that are conceived in this sub-process are aimed at the student systematically solving mathematical problems contextualized to the profile, through the identification of the mathematical expression that represents the economic or accounting measure to calculate, the type of mathematical content to apply, find the way to solution, properly apply the required mathematical content and interpret the value of the result obtained in the context of the economic profile.
These actions can be developed from the educational process of Higher Mathematics I for the profile of Administration and Economics in the Health Technology career, in its interrelation with other subjects of the profession, through the orientation of independent work oriented to the solution of problems, reaching higher levels of systematization if that interaction is achieved through the orientation of investigative tasks, from other subjects according to their needs, in investigative work practice or in carrying out student scientific work
The systematic manner in which these actions are carried out constitutes an indispensable condition in the process of systematizing the sociocultural statistical-professional logic.
Course objective: Systematize the methods of solving mathematical problems linked to the professional profile, from an integrative logic of mathematics and economics.
Specific actions to be carried out by the teacher:
Solve with students exercises not contextualized to the professional profile and contextualized to the professional profile.
Guide the study of the subject through texts and materials prepared by the teacher, with mathematical problems contextualized to the professional profile with problems solved and proposed.
Guide students to solve mathematical problems related to professional profile
Control independent work oriented in practical classes and through frequent and partial evaluations.
Promote the development of an integrative logic of mathematics and economics.
Facilitate learning situations situations that facilitate the development of individualized methods for solving mathematical problems contextualized to the professional profile.
Structure the contents in such a way that they are oriented towards the development of the mathematical problem solving procedures contextualized the professional profile
Systematically require students to argue the steps taken in the process of finding ways to solve and explain the interpretation of the problem and its solution, as a way for them to reach a deeper understanding of the mathematical content- professional.
Induce, throughout the training process, the systematization of methods that in turn constitute a system of mathematical procedures, articulated by a logic of economic reasoning, expression of the inherent thought to the solution of the mathematical problem contextualized to said profile.
Propose to students problem situations related to their work environment that are solved by applying the mathematical content.
Guide students towards investigating situations in the profession that lead to the planning and calculation of economic measures or work with economic functions, through student scientific work.
Specific actions to be carried out by students:
Carry out the independent work oriented by the teacher, aimed at deepening the content and developing skills in solving mathematical problems contextualized to the professional profile.
Identify ways and apply resources for solving mathematical problems contextualized to the professional profile
Develop skills in solving mathematical problems contextualized to the professional profile, by systematically confronting this teaching task.
Establish relationships with the work object of your profession, from interdisciplinary integration, and visits to labor institutions where the professional and social activity that you aspire to develop is developed.
Carry out a mathematical interpretative analysis of the professionalized contextual reality.
Inquire about the economic measures that are calculated applying the studied mathematical contents.
To argue the steps carried out in the process of searching for the solution routes and the explanation of the interpretation of the problem and its solution, as an expression of having reached the deepening of the mathematical-economic content.
To argue the identification and solution of problems identified in institutions related to the professional profile, through teamwork, and the collaboration of workers from these centers and the teacher who teaches the integrative discipline that is related to the sphere of work in which carries out investigative work practice, as a way to achieve contextualized mathematical-economic construction.
Explain the economic problems that are identified and solved using mathematical methods, by integrating and generalizing the knowledge, skills and values of Mathematics required to solve such problems.
Solve real problems existing in institutions related to the professional profile, with the purpose of deepening the interpretation of the contextual situations manifested from a mathematical reasoning that allows us to verify in the context the validity of the obtained mathematical solution.
IV. Instrumentation
- It will be applied in the development of the educational teaching process of Mathematical Subject I, in the Health Technologies career in the profile of administration and economy, of the Medical Sciences Branch of Morón. It will be developed within the framework of the planning usually conceived, of the teaching process of the subject. It will be taught by an experienced teacher. The results will be measured at the end of three stages of the semester, each of which will take place in a time that represents a third of the total time assigned to the subject. (hours) The preparation of the improved subject will be taken into account. Consultations and socialization workshops will be held with the students.The auxiliary materials prepared will be used The person in charge is the head of the group of the Subject and the participants are the members of the group who will participate in open classes, taught in the process where the Strategy is applied and will debate the way in which the activities are developed and will value the level of effectiveness of the implementation of the Strategy through the observation of student activity.
V. Determination of the evaluation criteria of the effectiveness of the didactic strategy for the dynamics of the professional contextualization of the contents of the mathematical subject I, to the profile of administration and economy of the career of health technologies
Course objective: Evaluate the effectiveness of the application of the didactic strategy for the dynamics of the professional contextualization of the contents of the mathematical subject I, to the profile of administration and economics of the career of health technologies
Specific actions:
Select the indicators to evaluate the effectiveness of the application of the actions included in the strategy.
Establish the scale of values to evaluate the selected indicators.
Prepare instruments taking into account the established indicators.
Apply the instruments.
Coding the results obtained.
Interpret the results obtained.
Assess the existence or not of significant progress in the development of the educational teaching process.
Dimensions and indicators are established for evaluating the effectiveness of the actions carried out in the previous stages.
Dimension Interpretation of the problem
ID
Understanding
Integration
Identification dimension of the solution routes
- Contextual analysis Algebraic analysis Numerical analysis
Dimension Application of settlement procedures
Algebraic work
Infinitesimal calculation
Mathematical integration profession
To evaluate, in correspondence with the selected indicators, it is proposed that each indicator be measured on an ordinal scale from 1 to 3, considering 3 as the highest value, and consequently each dimension is measured on an ordinal scale from 3 to 9, considering values 3 and 4 as low, means from 5 to 7, and high as 8 and 9.
This evaluation can be carried out by means of a review guide of the product of the activity of the students in the development of practical activities, at different stages of the semester, and by reviewing the product of their activity, reflected in the solution of the oriented tasks. by the teacher.
Conclusions
The didactic structuring of the strategy is based on the relationship between the appropriation of the integrative logic of the mathematical contents and those inherent in the professional profile and the systematization of the skills for the solution of contextualized mathematical problems, essential qualities of the dynamics of problems. mathematicians contextualized to the profile of Administration and Economics in the Health Technology career.
To solve the identified problem, the strategy is proposed, with which it is hoped to contribute to the students achieving a higher level of appropriation of the mathematical content required for the solution of problems related to the professional profile.
The strategy foresees the preparation of a system of problems related to the professional profile that makes it possible to guide and carry out an independent work that contributes to the students systematically facing the resolution of this type of problem.
recommendations
- From the results of the investigation, promote other investigations that reveal the essence of the strategy elaborated in other profiles of the Health Technology career based on the specificities of each profession Continue working on the integration of Basic Mathematics for the different profiles of the Health Technology career, with other disciplines for the improvement and expansion of the topic covered, that value the possibilities of its improvement, also as an important element that contributes to achieving greater solidity in the application of mathematical methods and the development of skills and alternative procedures by the students in relation to the exit profile of the future health technologist.
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