Abstract:

This study describes a diagnostic test that helps identify the specialized content knowledge preschool teachers have regarding the development of children’s mathematical thinking. It follows the elaboration process of the diagnostic tool. The diagnosis is part of a phenomenological research design, with the aim of generating a teacher-training proposal; that combines practices for the development of mathematical thinking and visual arts, through a cultural approach to pre-Columbian art and its iconography, which impacts the initial and continuous learning process of the Preschool Education program. The plan is developed between universities of Colombia and Costa Rica through a transdisciplinary approach that involves a teacher training pilot program. For such purpose, the design, construction, and validation of a tool enables being aware of what teachers know about children’s mathematical thinking processes, and the development of learning patterns and regularities. The tool is a questionnaire, which covers four dimensions, with a Likert scale, which was applied to a population of teachers; the analysis and implication of the results are included in this report. The foregoing is a way of consolidating knowledge, since the literature in the area indicates that research on the practices of identifying patterns and regularities at the initial education level is in an early stage, while in the visual arts these identification practices can be a constant.

Worldwide, the training and professionalization of teachers constitute a strategic debate point, as training is not an easy task, reduced and restricted to the transmission of knowledge within an institutionalized context. Both Díaz, Figueroa and Tenorio (2007) and the Organization for Economic Cooperation and Development (OECD, 2005) point out that one of the critical problems presented by educational systems is that of the quality of teacher training programs.

These authors consider the teacher as the key stakeholder in the educational processes that are required for transformation initiatives, so current trends in initial training indicate that the teacher must be formed as an agent of change, a practical-reflective professional that uses research as the means to make decisions and intervene practically on them. This involves issues as diverse as empowering and challenging professional practices throughout initial training, strengthening the teaching approach, or opening the classroom to other perspectives, to expand pedagogical reflection on how to build effective, ethical, and meaningful teaching of social justice.
In the field of mathematics, there are specific lines that inquire about the initial and permanent training of teachers. Camargo (In Press) enriches this discourse, stating that in Mathematics Education some new issues under research.
Integrating art into learning is an opportunity to develop skills concerning the mathematical practice of identifying and using patterns, resorting to elements of the cultural environment. For the purposes of this research, it is necessary to approach mathematics because of a social practice, which underlines its human and collective character, as well as to accept that mathematics has a strong relationship with culture and the worldview.
By proposing the iconography of pre-Columbian art and its symbolism as a valid case for the identification of regularities and patterns, the teacher is offered a spectrum of significant possibilities for the child. Thus, an approach based on pre-Columbian art is chosen. And due to the bond and fascination of infants towards fauna, their simple iconography is examined and combined with complex hybrid figures, where the forms are revealed in a regular order. These allow to identify characteristic elements of the selected icons and to focus on this mathematical practice of identification and use of patterns, transversal in the development of this science.

Keywords:

Specialized content knowledge, patterns and regularities, preschool teachers, pre-columbian iconography.