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plications. While the reformers were set on pushing the everyday practical
applications as far as possible from instruction, they considered the theoreti-
cal applications to be a necessary component of instruction, which was not at
odds with their own emphasis on pure mathematics. A closer look at the real
development of mathematics instruction shows that the opposite occurred:
Pressure by parents and students ensured that the everyday practical applica-

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HANS NIELS JAHNKE
tions attained a well-established position in instruction, while the theoretical
applications hardly mattered at all.
That ordinary arithmetic and everyday practical applications could prevail
against the intentions of the reformers within the mathematical syllabus was a
consequence of the social stratification of the student body in the Prussian
Gymnasium of the time. As D. K. Müller has shown, the Gymnasium was
attended not only by those seeking the Abitur and university studies but also
by young people preparing for a job in commerce, industry, or trade. The lat-
ter left after the lower or upper Tertia (4th or 5th grade) of the Gymnasium as
so-called "early graduates," a fact that permits us to consider the Gymnasium
until the 1830s as some kind of "comprehensive school" for the town and city
population subject to compulsory instruction (Müller, 1977). For these early
graduates, however, an introduction to ordinary arithmetic and everyday
practical applications was indispensable; all the more so as the complicated
and variable relations in contemporary weights, money, and measures
actually required such special training.
How strong the contrasts between the reformers' intentions and the social
facts of the Prussian educational systems actually were becomes visible from
an episode found in the records of the Prussian ministry of the interior (cf.
Jahnke, 1990b, pp. 364-368). In 1815, the ministry's department of educa-
tion tried to implement the mathematical part of the Süvern Syllabus at one of
the leading Prussian schools, the Joachimsthalsche Gymnasium in Berlin.
The number of mathematics lessons per week was increased in accordance
with Süvern's recommendations, partly even at the cost of the classical lan-
guages. To make the reform work, additional mathematics teachers were sent
to this school. Soon after, however, strong opposition arose. Eventually, one
of the mathematics teachers proposed the compromise of dividing the mathe-
matics course into two parallel ones of different character, which were to be
optional for the students. One of these was to be scientific, the other oriented
toward practical requirements. This suggestion was strongly rejected by the
ministry who insisted on maintaining the unity of mathematics instruction,
stressing that the spirit and essence of the Gymnasium were determined by its
scientific character. Most notable is the ministry's assessment stated at this
occasion that presumably all of the students would vote for the practical
course if given the option, thereby driving the reform on the rocks. A similar
pessimistic evaluation was given by F. Kries, author of a then widely used
textbook. Mathematics was regarded as a study yielding no bread, not re-
warding the diligence shown by the students in their own eyes. It had to be
admitted, Kries said, that most of the positions in the state to which the
young people aspired did not permit an immediate application of mathematics.
Thus, the entire episode shows that the insertion of pure mathematics into the
syllabus of the Prussian Gymnasium did not correspond to the demands of
parents and students in their own views, but rather was a consequence of a
pedagogical program that stood in contrast to these.
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The entire conflict between a scientific and practical orientation was settled
by a decree issued by the Prussian administration of education in 1826. The
ministry prescribed that "the real teaching of mathematics will begin in Quarta