id: 05595689
dt: j
an: 2009e.00470
au: Ellis, Amy B.; Grinstead, Paul
ti: Hidden lessons: how a focus on slope-like properties of quadratic functions
encouraged unexpected generalizations.
so: J. Math. Behav. 27, No. 4, 277-296 (2008).
py: 2008
pu: Elsevier, New York, NY
la: EN
cc: H23 E43 I23
ut: generalization; quadratic functions; elementary algebra; learning; modes of
representation
ci:
li: doi:10.1016/j.jmathb.2008.11.002
ab: Summary: This article presents secondary students’ generalizations about
the connections between algebraic and graphical representations of
quadratic functions, focusing specifically on the roles of the
parameters $a,b$, and $c$ in the general form of a quadratic function,
$y=ax^2+bx+c$. Students’ generalizations about these connections led
to a surprising finding: two-thirds of the students interviewed
identified the parameter a as the “slope” of the parabola. Analysis
of qualitative data from interviews and classroom observations led to
the development of three focusing phenomena in the classroom
environment that inadvertently supported a focus on slope-like
properties of quadratic functions: (a) the use of linear analogies, (b)
the rise over run method, and (c) viewing a as dynamic rather than
static.
rv: