id: 06419773
dt: j
an: 2015c.00799
au: De Bock, Dirk; Van Dooren, Wim; Verschaffel, Lieven
ti: Students’ understanding of proportional, inverse proportional, and affine
functions: two studies on the role of external representations.
so: Int. J. Sci. Math. Educ. 13, Suppl. 1, S47-S69 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: I29 C39
ut: affine model; inverse proportional model; multiple representations;
non-linearity; proportional model
ci:
li: doi:10.1007/s10763-013-9475-z
ab: Summary: We investigated students’ understanding of proportional, inverse
proportional, and affine functions and the way this understanding is
affected by various external representations. In a first study, we
focus on students’ ability to model textual descriptions of
situations with different kinds of representations of proportional,
inverse proportional, and affine functions. Results highlight that
students tend to confuse these models and that the representational
mode has an impact on this confusion: Correct reasoning about a
situation with 1 mathematical model can be facilitated in a particular
representation, while the same representation is misleading for
situations with another model. In a second study, we investigate
students’ ability to link representations of proportional, inverse
proportional, and affine functions to other representations of the same
functions. Results indicate that students make most errors for
decreasing functions. The number and nature of the errors also strongly
depend on the kind of representational connection to be made. Both
studies provide evidence for the strong impact of representations in
students’ thinking about these different types of functions.
rv: