This research project describes the results of applying two pedagogical methodologies: problem-based learning and the use of new information technologies through GeoGebra in the development of the theme of functions for students of public accounting. The research was developed from a positivist paradigm, quantitative approach of quasi-experimental type of pretest and posttest with control and experimental group. In order to determine the development of competencies, a diagnostic test was initially applied to evaluate the mathematical knowledge with which the students enter; then pretest and posttest tests were applied to the control and experimental groups, in which by means of an intervention plan to the experimental group in the posttest stage, favorable results were evidenced by improving the proportion of correct answers and the development of competencies in geometric algebraic reasoning compared to the pretest stage. One of the conclusions reached in the research is that applying other methodologies in class such as problem-based learning with the support of GeoGebra software encourages the process of teaching learning and students find applicability to the topics treated by associating them with situations of practical life.

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Geometric thinking is a process in which competences are developed to understand three-dimensional space. The experience arises from the need to implement teaching methodologies that allow to optimize both the potential of teachable that has the geometry as the potential of learnability of the student with the purpose of deepening in the learnings so that, by means of the construction of models and the mathematical principle of reconstruction and invention of mathematics, emphasizing spatial thinking and leading the student to recognize geometric objects, geometric spaces and associated transformations to develop mathematical skills while strengthening their geometric thinking.

Scientific communication and diffusion is one of the challenges of higher education institutions, related to the implementation of strategies of free access to the scientific and technological productivity of the teachers and researchers of the institutions, which allow to increase the visibility and impact of the research, for which a model of information architecture of the technological platform for the management of the investigative production of teachers and researchers was designed, under an environment focused on satisfying the information needs of the users that allows to organize, to group and to visualize the information by means of metadata. The research is of exploratory-descriptive type, through which the products of science, technology and innovation that should be visible in the technological platform were identified, generating as a result an architecture model-view-controller, with data storage in a relational database, which has access through a RESTful API made in Java, the views and controllers were made in HyperText markup language and JavaServer pages respectively. MySQL was used as a relational database engine to store information and MYSQL Workbench as a platform for the construction of the relationship model between entities, tables and columns; which will be used as a framework for the design, planning and implementation of the technological platform.