
06439639
j
2015d.00779
Flores, Alfinio
Park, Jungeun
Sherman, Milan
Derivatives at several points: an important step between derivative at a point and derivative function.
Ohio J. Sch. Math. 70, 3439 (2014).
2014
Ohio Council of Teachers of Mathematics (OCTM), Columbus, Oxford, OH
EN
I44
U74
derivatives
mathematical concepts
derivative at a point
derivatives at several points
derivative of a function
differential calculus
differentiation
concept formation
misconceptions
trigonometric functions
student activities
slope of a tangent line
mathematical software
visualization
graphical representations
graph of a function
Summary: We present activities, with an interactive computer program, that serve to bridge two related but different concepts, derivative at a point and derivative function, and to help students understand better the relationships between the two. First, students work with tangent lines to the graph of the sine function at several points and then tabulate and graph the values of the slopes of these lines for the corresponding values of $x$. Then, students extend the function to an interval tracing the values of the slopes as the values of $x$ change. Finally, students graph simultaneously the values of quotients of increments for several values of $x$ to make more explicit the relation between the formal definitions of derivative at a point and derivative function.