Thursday

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.

Paper

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.

Paper

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.

Paper

92