## Stäckel's contribution to Mathematics Teaching

As well as his involvement in mathematical research, another of Stäckel's interests lay in the teaching of mathematics. Having grown up seeing his father involved in education, this early exposure to pedagogy must surely have influenced his initial decision to enter teaching. Even after he turned his back on this career path, Stäckel retained an active interest in how mathematics was taught both in schools and universities and became heavily involved in moves to reform mathematical teaching.

The turn of the nineteenth century saw the beginning of much educational reform in Germany, particularly in secondary schools. This was largely down to a scholar from Berlin named Wilhelm von Humboldt. Among his reforms were a requirement for secondary school teachers to be trained to degree level in their subject and the introduction of the

*Abitur*, roughly the equivalent of the English A-Levels. He also introduced three principles for university education which influenced German universities until as late as the 1960s, namely those of:-

It was against this background that Paul Stäckel pursued, with his characteristic energy and enthusiasm, his goals of improving the profile of mathematics in schools and universities and of making the subject more accessible to non-specialists.... academic freedom, the unity of teaching and research, and self-government by the professor.

Following his membership of the Deutsche Mathematiker-Vereinigung (German Mathematical Society), Stäckel was commissioned in 1899 to prepare a report for the society on the state of applied mathematics teaching in German universities

*Über die Entwicklung des Unterrichtsbetriebes in der angewandten Mathematik and den deutschen Universitäten.*This was a chance for Stäckel to demonstrate his competence to the Society and he did this to great effect. Over the years, he had numerous other papers published on the subject, for which he received international acclaim.

Around the beginning of the twentieth century, discussions were initiated by the mathematician Felix Klein about a reorganisation of mathematics teaching in Germany, mainly focussing on trying to look beyond the rigidity of both geometry (which was based solely on Euclid's

*Elements)*and of algebra as it was then. A similar reform movement was taking place in France at around the same time, largely due to Émile Borel, who had written several books in French on the subject. Having, as he did, a good command of French, Stäckel read, and was impressed by, Borel's books and wanted to make [2]:-

available in his own country. He was, however, not content simply to translate Borel's work into German and instead set about reworking the French version into a textbook suitable for a German-speaking audience and for the German education system. The resulting publication was reprinted for the last time in 1968, sixty years after it was first produced -- proof indeed of its value and importance. According to the literary press at the time, the book, produced in two volumes [2]:-... this modern approach to arithmetic, algebra and geometry ...

Hellpach, in his obituary of Stäckel, is even more lavish in his praise, saying:-... helped not only teachers, but also non-specialists who needed mathematics for the study of other sciences and medicine.

In another obituary, Stäckel is praised by Perron for his ability to put across complex ideas and concepts in an understandable way [3]:-[Stäckel]has handed down to German education a model ... which is in many respects unsurpassable.

Perron is not alone in his admiration of Stäckel's teaching ability, an area in which he possessed an undoubted gift.How highly Stäckel rated the interaction between practice and theory, and how able he was to make this interaction clear to non-mathematicians and in doing so to teach an understanding of seemingly quite abstract mathematical concepts ...

Stäckel continued to pursue his goal of educational reform right up until his death. In 1908, he was selected by the German Mathematical Society to represent them on the newly-formed

*Deutscher Ausschuss für den mathematischen und naturwissenschaftlichen Unterricht,*a commission set up by the German Society of Natural Scientists to report on teaching and make recommendations. Stäckel's role was to lead a sub-committee whose aim was to ascertain the needs and demands of trade and industry with regard to the education of the future workforce and to make recommendations based on this.

Stäckel's contribution to education was by no means unnoticed, even in wider circles and he also became involved in the International Mathematics Education Committee which was overseeing educational reforms not only in Germany, but also in France, Austria-Hungary, Italy and Great Britain. His reputation was such that the education ministry in the state of Baden was keen to tap into his vast knowledge and experience. In 1910, he became an extraordinary member of their schools inspectorate.

Stäckel certainly made a large contribution to mathematical education in Germany and other European countries, making use of his considerable pedagogical talents as well as his mathematical knowledge to make recommendations on the way in which mathematics teaching could be reformed. He was in fact asked to join the Ministry of Culture in Germany to advise on education, an honour he chose to decline because of home commitments and perhaps also because he felt he was better suited to a role as an academic and educator, rather than of a bureaucrat.

**References**

- Biography in
*Dictionary of Scientific Biography*(New York 1970-1990).

- T Bohnet,
*Leben und Werk des Mathematikers Paul Stäckel*(Staatsexamensarbeit, Karlsruhe University, 1993).

- O Perron, Paul Stäckel,
*Sitzungsberichte der Heidelberger Akademie der Wissenschaften*(1920), 3-20.

Article by: Vicky Ryan (University of St Andrews)