
05264394
j
2008a.00009
Otte, Michael
Mathematical history, philosophy and education.
Educ. Stud. Math. 66, No. 2, 243255 (2007).
2007
Springer Netherlands, Dordrecht
EN
A30
E40
H40
I50
axiomatization
arithmetic
integration
Lebesgue
Grassmann
mathematical generalization
doi:10.1007/s106490079079z
Summary: History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and philosophy require generality and abstraction. The paper offers some methodological reflections about these matters together with two case studies from nineteenth century history of arithmetic and integration theory, respectively, which try to strike a balance between the directly opposed requirements.