Thursday

3:45 – 4:15 pm

Session 4 – Contributed Reports

Marquis A

A Study of Common Student Practices for Determining the Domain and Range of Graphs

Peter Cho, Benjamin Norris and Deborah Moore-Russo

This study focuses on how students in different postsecondary mathematics courses perform on domain and range tasks regarding graphs of functions. Students often focus on notable aspects of a graph and fail to see the graph in its entirety. Many students struggle with piecewise functions, especially those involving horizontal segments. Findings indicate that Calculus I students performed better on domain tasks than students in lower math course students; however, they did not outperform students in lower math courses on range tasks. In general, student performance did not provide evidence of a deep understanding of domain and range.

Paper

5

Marquis B

On symbols, reciprocals and inverse functions

Rina Zazkis and Igor Kontorovich

In mathematics the same symbol – superscript (-1) – is used to indicate an inverse of a function and a reciprocal of a rational number. Is there a reason for using the same symbol in both cases? We analyze the responses to this question of prospective secondary school teachers presented in a form of a dialogue between a teacher and a student. The data show that the majority of participants treat the symbol ☐-1 as a homonym, that is, the symbol is assigned different and unrelated meanings depending on a context. We exemplify how knowledge of advanced mathematics can guide instructional interaction

Paper

39

Marquis C

Interpreting proof feedback: Do our students know what weÕre saying?

Robert C. Moore, Martha Byrne, Timothy Fukawa-Connelly and Sarah Hanusch

Instructors often write feedback on studentsÕ proofs even if there is no expectation for the students to revise and resubmit the work. However, it is not known what students do with that feedback or if they understand the professorÕs intentions. To this end, we asked eight advanced mathematics undergraduates to respond to professor comments on four written proofs by interpreting and implementing the comments. We analyzed the studentÕs responses through the lenses of communities of practice and legitimate peripheral participation. This paper presents the analysis of the responses from one proof.

Paper

87

Grand Ballroom 5

Student responses to instruction in rational trigonometry

James Fanning

I discuss an investigation on studentsÕ responses to lessons in WildbergerÕs (2005a) rational trigonometry. First I detail background information on studentsÕ struggles with trigonometry and its roots in the history of trigonometry. After detailing what rational trigonometry is and what other mathematicians think of it I describe a pre-interview, intervention, post interview experiment. In this study two students go through clinical interview pertaining to solving triangles before and after instruction in rational trigonometry. The findings of this study show potential benefits of students studying rational trigonometry but also highlight potential detriments to the material.

Paper

6