Abstract: This paper draws upon Paulo Freire's concept of "viable-unknowns" and examines how they are built by educators who teach mathematics in the early grades of elementary education from the continued on-the-job training perspective. Viable-unknowns, is a concept that favours explaining mathematical learning processes, concern for materialization, and the mathematical production of educators in youth and adult education. Based on participant research, we carried out formative research circles in a public school, where we developed theoretical studies and practices concerning mathematical knowledge. Among the results are the production of meanings in the learning-teaching processes, the expansion of mathematical concepts, the valuing of mathematics formative role in the individual's political, ethical and moral education, and the educators' adoption of an emancipatory praxis. We therefore conclude that viable-unknowns were built when the collective used actions (limit acts) to overcome hurdles (limit situations) in the formative sessions, thus allowing concepts to be expanded in mathematics education.
Keywords:
Mathematics teaching; Youth and adult education; Viable-unknowns; Teachers' continuous training