id: 06440090
dt: j
an: 2015d.00776
au: Park, Jungeun
ti: Is the derivative a function? If so, how do we teach it?
so: Educ. Stud. Math. 89, No. 2, 233-250 (2015); erratum ibid. 90, No. 2, 231
(2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: I40
ut: derivative; commognition; function; calculus; instructor discourse;
classroom
ci:
li: doi:10.1007/s10649-015-9601-7
ab: Summary: This study investigated features of instructors’ classroom
discourse on the derivative with the commognitive lens. The analysis
focused on how three calculus instructors addressed the derivative as a
point-specific value and as a function in the beginning lessons about
the derivative. The results show that (a) the instructors frequently
used secant lines and the tangent line on the graph of a curve to
illustrate the symbolic notation for the derivative at a point without
making explicit connections between the graphical illustration and the
symbolic notations, (b) they made a transition from the point-specific
view of the derivative to the interval view mainly by changing the
literal symbol for a point to a variable rather than addressing how the
quantity that the derivative shows, changes over an interval, (c) they
quantified the derivative as a number using functions with limited
graphical features, and (d) they often justified the property of the
derivative function with the slope of the tangent line at a point as an
indication of the universality of the property. These results show that
the aspects of the derivative that the past mathematicians and
today’s students have difficulties with are not explicitly addressed
in these three classrooms. They also suggest that making explicit these
aspects of the derivative through word use and visual mediators, and
making clear connections between the ways that the quantities and
properties of the derivative are visually mediated with symbolic,
graphical, and algebraic notations would help students to understand
why and how the limit component for the derivative are illustrated on
graphs and expressed symbolically, and the derivative is expanded from
a point to an interval, and properties of the derivative are
investigated over an interval. More explicit discussions on these ideas
perhaps make them more accessible to students.
rv: