Resumen

Background: several studies in mathematics education show the use of the physical abacus in the activities of teachers in initial graduation, emphasising, in their manipulation, practices with addition or subtraction operations, or yet, which express a direct translation of the numeral to the physical abacus and, vice versa, without, however, explaining part of the complexity involved the social practice of quantifying physical quantities, which even makes possible the structuring of the numeral. Objective: to show that the use of the abacus by teachers in initial training may not ensure the realisation or mastery of the practice of quantifying physical quantities with discrete units. Design: in this sense, a study and research path (SRP) was carried out based on the training of early years teachers. Environment and participants: 25 students in initial training of a degree course at a public educational institution participated in an activity on decimal number system (DNS), but largely positional number system (PNS), proposed based on a problem in an unusual context (for them), they mobilised to face and answer questions. Data collection and analysis: we present an excerpt from the empirical research forwarded by Ferreira (2020) with teachers in initial training. Results: the data observed in the empirical confirms the hypothesis of the existence of a problem regarding the use of the abacus as a possible facilitator in the structuring of non-decimal numbers through the practice of quantifying physical quantities. Conclusions: the results found with the teachers revealed, in addition to the problem of teacher training on what to teach and how to teach numerals, that using the abacus made it difficult, if not hindered, the practice of quantifying physical quantities with discrete units. We also found changes in the quality of the teachers’ relationships with structuring decimal and non-decimal numbers.