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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. 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 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. 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. 6 |