id: 05219502
dt: j
an: 2007e.00265
au: Capraro, Mary Margaret; Ding, Meixia; Matteson, Shirley; Capraro, Robert
M.; Li, Xiaobao
ti: Representational implications for understanding equivalence.
so: Sch. Sci. Math. 107, No. 3, 86 (2007).
py: 2007
pu: Wiley (Wiley-Blackwell), Hoboken, NJ; School Science and Mathematics
Association (SSMA), Stillwater, OK
la: EN
cc: E43 D73
ut: equal sign; equivalence; misconceptions; mathematical symbols; mathematical
concepts; textbooks; elementary education; grade 6; USA; China
ci:
li: doi:10.1111/j.1949-8594.2007.tb17773.x
ab: Summary: Teachers and researchers have long recognized that students tend
to misunderstand the equal sign as an operator; that is, a signal for
"doing something" rather than a relational symbol of equivalence or
quantity sameness. Studentsâ€™ equal sign misconception has been
researched for more than thirty years (Weaver, 1971, 1973) with little
refinement in the theory. It was popularly believed that younger
students were not developmentally ready to work variations of open
numbers sentences, such as missing addend problems (Thompson \&
Babcock, 1978). In fact, misconceptions about the equal sign were
identified in kindergarten students even before formal instruction
(Falkner, Levi, \& Carpenter, 1999). However, it is clear that with
specific instructional guidance, elementary students can understand
that the equal sign expresses a relation (Baroody \& Ginsburg, 1983;
Carpenter, Levi, \& Farnsworth, 2000; Saenz-Ludlow \& Walgamuth, 1998).
In this article, the authors examine variables that could contribute to
studentâ€™s equivalence misconception and whether the equal sign
misconception is still manifest in a U.S. sample and present in a
Chinese sample. Findings indicate that misconceptions are still
manifest in the U.S., and textbooks do little to mitigate the problem
in the United States, while in China students are able to interpret the
equal sign as a relational symbol of equivalence. The authors also
found that the inclusion of multiple representations for equivalence in
textbooks and guidebooks in China make a difference in assisting
students to correctly interpret the equal sign. (ERIC)
rv: