id: 06038417
dt: j
an: 2012c.00438
au: Selter, Christoph; Prediger, Susanne; Nührenbörger, Marcus; Hußmann,
Stephan
ti: Taking away and determining the difference - a longitudinal perspective on
two models of subtraction and the inverse relation to addition.
so: Educ. Stud. Math. 79, No. 3, 389-408 (2012).
py: 2012
pu: Springer Netherlands, Dordrecht
la: EN
cc: F32 D52 D42 C32
ut: models of subtraction; inverse relation; arithmetic and algebra; mental
arithmetic; standard algorithms; negative numbers; algebraic equations;
taking away; determining the difference; educational research
ci:
li: doi:10.1007/s10649-011-9305-6
ab: Summary: Subtraction can be understood by two basic models-taking away (ta)
and determining the difference (dd) - and by its inverse relation to
addition. Epistemological analyses and empirical examples show that the
two models are not relevant only in single-digit arithmetic. As
curricula should be developed in a longitudinal perspective on
mathematics learning processes, the article highlights some exemplary
steps in which the inverse relation is discussed in light of the two
models, namely mental subtraction, the standard algorithms for
subtraction, negative numbers and manipulations for solving algebraic
equations. For each step, the article presents educational
considerations for fostering a flexible use of the two models as well
as of the inverse relation between subtraction and addition. In each
section, a mathe-didactical analysis is conducted, empirical results
from literature as well as from our own case studies are presented and
consequences for teaching are sketched.
rv: