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5:00 – 5:30 pm |
Session 6 – Contributed
Reports |
Marquis A |
Ways of understanding and ways of thinking in using the
derivative concept in applied (non-kinematic) contexts Steven Jones Much
research on studentsŐ understanding of derivatives in applied contexts has
been done in kinematics-based contexts (i.e. position, velocity,
acceleration). However, given the wide range of applied derivatives in other
fields of study that are not based on kinematics, this study focuses on how
students interpret and reason about applied derivatives in non-kinematics
contexts. Three main ways of understanding or ways of thinking are described
in this paper, including (1) invoking time, (2) overgeneralization of
implicit differentiation, and (3) confusion between derivative expression and
original formula. 31 |
Marquis B |
Graphs of inequalities in two variables Kyunghee Moon In this
study, I analyze how preservice
secondary teachers represented and explained graphs of three
inequalities—a linear, a circular, and a parabolic—in two
variables. I then suggest new ways to explain graphs of inequalities, i.e.
some alternatives to the solution test, based on the preservice
teachersŐ thought processes and by incorporating the idea of variation. These
alternatives explain graphs of inequalities as collections of rays or curves,
which is similar to graphs of functions as collections of points in one
variable functions and as collections of curves in
two variable functions. I conclude the study by applying the alternatives to
the solving of optimization problems and discussing the implications of these
alternatives for future practice and research. 34 |
Marquis C |
MathematiciansŐ grading of proofs with gaps David Miller, Nicole
Engelke-Infante and Keith Weber In
this study, we presented nine mathematics professors with three proofs
containing gaps and asked the professors to assign the proofs a grade in the
context of a transition-to-proof course. We found that the participants
frequently deducted points from proofs that were correct and assigned grades
based on their perceptions of how well students understood the proofs. The
professors also indicated that they expected lecture proofs in the
transition-to-proof course to have the same rigor as those demanded of
students, but lecture proofs could be less rigorous than the rigor demanded
of students in advanced mathematics courses. This presentation will focus on
participantsŐ rationales for these beliefs. 92 |