Abstract:

This inter-institutional project is focused on teacher training. For this purpose, we considered a research design with a phenomenological perspective; qualitative data were processed with an interpretive descriptive analysis. Using mathematics education with a different approach to the traditional one, the artistic context is determined as a wide and diverse space, which favors interdisciplinary study between and with teachers. Mathematics education research establishes that generalization and patterns are fundamental in the development of mathematical thinking; this determines the mathematical practices of identification and use of patterns, which in the visual arts are elements considered as a constant; analysis is developed through-Columbian iconography and supported by studies from archeology and anthropology, with an emphasis in pre-Columbian fauna.

It is based on the theoretical perspective of the Knowledge Quartet (KQ). This is a theoretical framework developed by Rowland (2013) to describe classroom situations, specifically, when the teacher's mathematical knowledge is relevant.

This paper presents one of the construction processes of the research project, which has as one of its objectives to identify the specialized knowledge of the content that the preschool teachers of Costa Rica and Colombia have regarding children's mathematical thinking. For this purpose, the process of design, construction and validation of an instrument was carried out in order to become aware of what teachers know regarding children's mathematical thinking; specially the development of learning patterns and regularities. Based on the results obtained, we proceed to propose a training, to build knowledge that enriches the teaching of these mathematical practices in the preschool classroom using studio arts and pre-Columbian culture. The foregoing is a way of consolidating knowledge, since the literature in the area indicates that research on identifying patterns and regularities at the initial education level is at an initial stage, while in the visual arts these identification practices can be a constant.

The construction of this instrument resulted in a questionnaire with a Likert scale for teachers, validated by experts, and subdivided into four categories: Common development elements in students between 5-6 years of age, artistic skills, mathematical skills, knowledge of regularities and patterns.
The process for preparing the Likert-type questionnaire included 6 phases:
1) Review and analysis of research and literature related to three areas: human development of infants from 5 to 6 years old; Mathematics education - patterns and regularities; Visual arts; fauna in pre-Columbian art;
2) Construction of categories of analysis called dimensions in the instrument;
3) Creation of descriptors for the analysis categories: human development, artistic ability, mathematical skills knowledge of patterns;
4) Triangulation of the information for the selection of items or descriptors according to the proposed dimensions;
5) Preparation of the pilot version of the instrument;
6) Review of the validation instrument for peers;
7) Assessment through expert judgment;
8) construction of the final version of the instrument.

Phases 1 to 4 considered the literature review and research that allowed the instrument to be designed, while phases 4 to 8 were related to the construction and validation of the instrument.

Keywords:

teacher training, regularities and patterns, pre-Columbian, specialized knowledge, mathematical thinking, preschool.