
06038417
j
2012c.00438
Selter, Christoph
Prediger, Susanne
N\"uhrenb\"orger, Marcus
Hu{\ss}mann, Stephan
Taking away and determining the difference  a longitudinal perspective on two models of subtraction and the inverse relation to addition.
Educ. Stud. Math. 79, No. 3, 389408 (2012).
2012
Springer Netherlands, Dordrecht
EN
F32
D52
D42
C32
models of subtraction
inverse relation
arithmetic and algebra
mental arithmetic
standard algorithms
negative numbers
algebraic equations
taking away
determining the difference
educational research
doi:10.1007/s1064901193056
Summary: Subtraction can be understood by two basic modelstaking 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 singledigit 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 mathedidactical analysis is conducted, empirical results from literature as well as from our own case studies are presented and consequences for teaching are sketched.