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The aspiration of this paper is to develop a novel approach towards investigating the socio-political history of mathematics teaching in educational systems. Traditionally, historical studies are confined to just one country, the author's country. Broader approaches address international developments by confronting and comparing global and local aspects--revealing general patterns and more specific 'local' structures and characteristics. Yet, already in antiquity and medieval times, the specific characteristic of mathematics teaching, namely to operate at the crossroads of general education and vocational training, proved to be intimately tied to the functioning of the particular political system. In pre-modern times, however, a truly international pattern emerged for the first time: European powers conquered, occupied and colonised overseas regions. Given that educational systems were emerging at the same time within these states, they often transmitted elements of these structures to their colonies. This phenomenon included mathematics, and the history of its teaching is analysed here as a part of coloniality. It is shown that this was not a uniform process, and the differences between the various colonial powers are discussed. The involvement of mathematics in the process of decolonisation is addressed, as well as its role in the tension between continued coloniality and movements of decoloniality. Finally, the general framework provided for studying socio-political processes connected with establishing mathematics teaching within public educational systems is applied, in order to analyse recent coloniality practices effected by international achievement studies.

The life and work of Hermann Günther Graßmann (1809–1877) attract not only ever again the attention of mathematicians, mathematical historians and those interested in the history of mathematics, they constitute also a challenge for the methodology of historiographical research. This challenge persists since Friedrich Engel’s biography of 1911; there, two sources were presented and interpreted in a not legitimate manner which even mislead since then various scholars. This paper faces the intricate task to unravel not only the methodological shortcomings of Engel’s biography, but also to re-assess the misinterpretations – particularly of alleged influences on Graßmann’s approaches – induced by Engel’s misleading claims. Based upon broader historically contextualised analyses of Graßmann’s innovative elements in his theory of extension and upon new primary sources for his student times at the Gymnasium and Berlin University, the paper presents a novel assessment of Graßmann’s approaches. [ABSTRACT FROM AUTHOR]

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 approach of coloniality to analyse the impact of political-cultural power structures on mathematics teaching is currently being discussed in mathematics education, especially in Latin America. In particular, one affirms there a hierarchy between the mathematical knowledge that is to be taught in the different educational levels, and is lamenting the hierarchy: as an effect of coloniality and as an expression of a global, Eurocentric hegemony. However, such relationships between the different content parts of the educational structure have been established in each country in a specific way, that is, according to the forms in which the educational system had emerged in that country. Whether hierarchies are implied has to be investigated for each case separately. The core of the differences is constituted by the structural functions achieved in Modern Times by the former Artes Faculty of Medieval Times. It depended on these functions which requirements were instituted for the transition from secondary level to higher education and which authority had to decide whether the requirements were met. In particular, the paper will discuss how the different paths for the transition from secondary to higher education have also shaped different structures of school mathematics and to what extent power mechanisms and hierarchies can be proven in them. [ABSTRACT FROM AUTHOR]

This comment is analysing the last section of a paper by Piotr Blaszczyk, Mikhail G. Katz, and David Sherry on alleged misconceptions committed by historians of mathematics regarding the history of analysis, published in this journal in the first issue of 2013. Since this section abounds of wrong attributions and denouncing statements regarding my research and a key publication, the comment serves to rectify them and to recall some minimal methodological requirements for historical research., Author(s): Gert Schubring[sup.1] Author Affiliations: Gert Schubring is a retired member of the Institut für Didaktik der Mathematik , a research institute at Bielefeld University, and at present is visiting [...]

PME, the International Group for the Psychology of Mathematics Education, was founded in 1976, at the "Third International Congress on Mathematical Education" in Karlsruhe, organised by the International Commission on Mathematics Instruction (ICMI). While PME is thus beyond coming of age and is reflecting its further orientation--due to the present "social turn"--the origins of investigating psychological aspects of mathematics learning have not yet been systematically studied. I am undertaking here a first such approach, concentrating on Germany, where the first pertinent monographs were published in 1913 and 1916. Different endeavours, focussing in particular on the notion of error, merged into the characteristic approach of "experimental pedagogy". Given the key function of ICMI for founding PME, an additional aspect is whether the forerunner of ICMI: the "Internationale Mathematische Unterrichtskommission" (IMUK), founded in 1908, had an impact upon promoting research into the psychology of mathematics education. The pertinent research was effected by psychology; doing research themselves was still outside the horizon of mathematics educators. Perspectives of future research, in particular comparative ones, are outlined.

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.

There is an over-arching consensus that the use of the history of mathematics should decidedly improve the quality of mathematics teaching. Mathematicians and mathematics educators show here a rare unanimity. One deplores, however, and in a likewise general manner, the scarcity of positive examples of such a use. This paper analyses whether there are shortcomings in the--implicit or explicit--conceptual bases, which might cause the expectations not to be fulfilled. A largely common denominator of various approaches is some connection with the term "genetic." The author discusses such conceptions from the point of view of a historian of mathematics who is keen to contribute to progress in mathematics education. For this aim, he explores methodological aspects of research into the history of mathematics, based on--as one of the reviewers appreciated--his "life long research."

Ewald Fettweis (1881-1967) was the first researcher to develop and establish the term ethnomathematics. This article presents his contribution to ethnomathematics and its development as a scientific theory. We will show that he was the first researcher to realize and practice ethnomathematics in his research and to explain it in his lectures, thus giving a disciplinary status to ethnomathematics. Fettweis's conceptualization of ethnomathematics was developed in the 1930s, much earlier than Ubiratan D'Ambrosio's subsequent, independent introduction of the same term. Based on this work, we argue for the existence of a pre-paradigm period in the development of ethnomathematics.

Presents and analyzes a previously unknown document that reveals controversy within the Brandenburg school authority in 1816 about the Suvern syllabus. Explains that the argument arose between representatives of two opposed conceptions of education and concerned subject matter to be taught and curriculum. Raised questions about the entire organization of teaching and fundamentals of the image of man. (DK)

Critiques studies on the Suvern syllabus of 1810-16, a document on the history of German public education. Provides a historical empirical reconstruction of the syllabus as a process of curriculum reform. Divides the discussion into two parts: (1) the early debates over the syllabus; and (2) its implementation after 1812. (RW)

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)