id: 02307401
dt: j
an: 1995c.01667
au: Carraher, D.W.
ti: Lines of thought: a ratio and operator model of rational number.
so: Educ. Stud. Math. 25, No. 4, 281-305 (1994).
py: 1994
pu: Springer Netherlands, Dordrecht
la: EN
cc: F40
ut:
ci:
li: doi:10.1007/BF01273903
ab: A model of rational number is described that exploits the fact that a pair
of line segments can embody a ratio of numbers and that actions upon
segments can embody arithmetical operations. Tasks are described for
bringing out diverse meanings of rational numbers. In the software
under development algebraic equations are used for formulating
descriptions of the relations among segments and for carrying out
operations intended to display geometrically the meaning of the
equations. Incorrect hypotheses produce arithmetic inequalities,
represented in the model as resultant segments of unequal lengths;
correct hypotheses produce resultant segments of equal lengths. None of
the tasks discussed can be solved through rote numerical computation
but require reflecting upon the relations of quantities. This aspect
may be useful in drawing out the relational meaning of rational
numbers. (orig.)
rv: