Background: The study of the history of mathematics teaching can be approached from different perspectives, defining contours from which the researcher performs the analysis focused on a process characterised by continuity, or by adopting periodisation. Objective: In this article, we seek to conduct a study based on the delimitation of periods, according to Le Goff’s (2014) argument, and in the light of the depth hermeneutics, based on Thompson (2011). Design: Given the premises above, we conducted a documentary analysis of two historical processes within the scope of mathematics teaching, one focusing on the municipal public schools of Canoas, and the other on a technical course in chemistry of a school in the city of Novo Hamburgo, both in the state of Rio Grande do Sul. Setting and participants: A timeline with conspicuous events used to periodicise both historical processes analysed by the authors. Data collection and analysis: Analysis of documents relevant to the history of the technical school investigated and education in the municipality of Canoas. Results: In both cases, it was possible to characterise the historical processes in periods based on events and official documents that generate changes in mathematics teaching. Conclusions: The historical processes analysed are characterised by ruptures resulting from changes, especially in the legislation, both in the municipal public network and in the technical education institution researched, enabling the realisation of changes and the characterisation of distinct periods, with their nuances.