id: 06006152
dt: j
an: 2012a.00170
au: Van Dooren, Wim; De Bock, Dirk; Verschaffel, Lieven
ti: From addition to multiplication $\dots$ and back: The development of
students’ additive and multiplicative reasoning skills.
so: Cogn. Instr. 28, No. 3, 360-381 (2010).
py: 2010
pu: Taylor \& Francis (Routledge), Philadelphia, PA
la: EN
cc: C30 F90 D70
ut: numbers; word problems (mathematics); mathematical logic; problem solving;
arithmetic; elementary school mathematics; age differences; mathematics
skills; thinking skills; research; primary education; lower secondary;
transfer of training; student errors; learning
ci:
li: doi:10.1080/07370008.2010.488306
ab: Summary: This study builds on two lines of research that have so far
developed largely separately: the use of additive methods to solve
proportional word problems and the use of proportional methods to solve
additive word problems. We investigated the development with age of
both kinds of erroneous solution methods. We gave a test containing
missing-value problems to 325 third, fourth, fifth, and sixth graders.
Half of the problems had an additive structure and half had a
proportional structure. Moreover, in half of the problems the internal
and external ratios between the given numbers were integer, while in
the other cases numbers were chosen so that these ratios were
noninteger. The results indicate a development from applying additive
methods “anywhere” in the early years of primary school to applying
proportional methods “anywhere” in the later years. Between these
two stages many students went through an intermediate stage where they
simultaneously applied additive methods to proportional problems and
proportional methods to additive problems, switching between them based
on the numbers given in the problem.
rv: