id: 05495520
dt: j
an: 2009f.00490
au: Carraher, David W.; Martinez, Mara V.; Schliemann, Analúcia D.
ti: Early algebra and mathematical generalization.
so: ZDM, Int. J. Math. Educ. 40, No. 1, 3-22 (2008).
py: 2008
pu: Springer, Berlin/Heidelberg
la: EN
cc: H22 C32
ut: elementary algebra; algebraic thinking; cognitive development; linear
functions; concept formation; grade 3; primary education; generalizing
patterns
ci:
li: doi:10.1007/s11858-007-0067-7
ab: Summary: We examine issues that arise in students’ making of
generalizations about geometrical figures as they are introduced to
linear functions. We focus on the concepts of patterns, function, and
generalization in mathematics education in examining how 15 third grade
students (9 years old) come to produce and represent generalizations
during the implementation of two lessons from a longitudinal study of
early algebra. Many students scan output values of $f(n)$ as n
increases, conceptualizing the function as a recursive sequence. If
this instructional route is pursued, educators need to recognize how
students’ conceptualizations of functions depart from the closed form
expressions ultimately aimed for. Even more fundamentally, it is
important to nurture a transition from empirical generalizations, based
on conjectures regarding cases at hand, to theoretical generalizations
that follow from operations on explicit statements about mathematical
relations.
rv: