id: 05824048
dt: a
an: 2011f.00408
au: Lengnink, Katja; Schlimm, Dirk
ti: Learning and understanding numeral systems: semantic aspects of number
representations from an educational perspective.
so: Löwe, Benedikt (ed.) et al., PhiMSAMP. Philosophy of Mathematics:
Sociological aspects and mathematical practice. Including selected
papers of the 3rd PhiMSAMP conference ‘Is mathematics special?’,
Vienna, Austria, 2008. London: College Publications (ISBN
978-1-904987-95-6/pbk). Texts in Philosophy 11, 235-264 (2010).
py: 2010
pu: London: College Publications
la: EN
cc: F30 C30 D40
ut: Roman numeral arithmetic; semantic content
ci:
li:
ab: The authors’ stated aim is to “. . . look at the basic arithmetic
operations of addition, subtraction, and multiplication. For each of
these we first describe the main difficulties that students reveal by
making systematic errors in their computations in the decimal
place-value system. Then, we discuss semantic tools that have been
proposed in the didactical literature and are used in schoolbooks to
develop a better semantic understanding of the basic written algorithms
for these operations. Finally, we present how the computations could be
carried out with Roman numerals, which is a purely additive system of
numerals.” The familiar Roman numeral “subtractive conventions,”
e.g. using IX for nine, are excluded, as these were introduced in the
Middle Ages and violate the semantics of a purely additive system.
Their method of Roman numeral multiplication is essentially lattice
multiplication.
rv: Steven C. Althoen (Holly)