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The aim is to contribute to the research on the conception and development of mathematics textbooks for undergraduate distance education courses (EAD). In particular, we acknowledge the EAD undergraduate courses in Brazil as an important governmental initiative for teacher education. Amongst other specificities of the Brazilian model of distance education, one aspect consists of writing proper material and textbooks, raising a need to investigate the results of their conception and development. We report on a case study in which a chapter in a written textbook developed by a group of professors is analysed according to hermeneutics, describing the tessiture of the text and context of the implemented task. Aware that the task demanded processes different from those used when writing textbooks for face-to-face lecture courses, though at the same time not coinciding with the wordings of the interactions of a classroom lecture, the group of authors agreed on a notion of "lessons on paper." Our analysis faces the challenge of problematising qualitative differences regarding the semiotic means of the mathematics embedded in face-to-face versus distance learning activities, raising questions on the nature of their results and the development of induced thinking in both contexts. Investigating the kind of mathematical knowledge produced for the "lessons on paper" texts, we drew on whether the written lesson for distance education is closer to the pedagogical-content knowledge than to the classical academic knowledge.

The paper departs from research published in an earlier thematic issue published by ZDM Mathematics Education in 2013 on mathematics textbook research and development by presenting a review of the literature in other languages and including books. Overall, the paper provides a brief overview of the more recent development of research in this area since then. The paper argues that mathematics textbooks as a theme of research have continued to receive rapidly growing attention internationally by opening to new developments such as electronic resources, historical reflections and international comparisons.

The evolution of indexing sequences and series has been little studied so far, although this topic presents difficulties for students. This symbolisation signified, however, an important means for operating more generally with finite and infinite series. This paper investigates the first steps during the eighteenth century and then the different processes in France and in Germany. In France, it was Lacroix with his textbooks from the end of the eighteenth and the early nineteenth century who paved the way, while dealing with difference series, for what would be established by Cauchy as a general practice with indexed sequences. In Germany, a pivotal role was played by the combinatorial school since the 1780s in establishing sophisticated indexing notations; the achievements by Dirksen in elaborating "higher-order" indexing notations prove to be decisive.

Argues that the investigation of the life and personality of textbook authors is one approach by which it is possible to analyze school life in the past. The French text author Lacroix is considered. (PK)