# January 2010 Archives

*School of Science: Math
Seminar*

Dr. Daniel J. Galiffa

Assistant
Professor of Mathematics

Tuesday, February 2, 2010

3:30 pm

168 Nick

*Some
Insights Into the Sheffer B-Type 1
Orthogonal Polynomial Sequences*

In this talk we first
discuss the
importance of *characterizing*
orthogonal polynomial sequences (OPS); namely, extracting OPS from *generating functions*. We then discuss
some of the key elements involved in the characterization process and
supplement this discussion with classical examples. From there, we
briefly
explain that in 1939, I.M. Sheffer proved that every polynomial
sequence
belongs to one and only one *type,* and
extensively developed properties of the *B-Type
0* polynomial sequences determining which sets are also orthogonal.
Sheffer
subsequently generalized his classification method to the case of
arbitrary *B-Type k, k=1,2,3,..., *by constructing a *generalized generating function*.
Although extensive research has been done on characterizing polynomial
sequences,
no analysis has yet been published on higher-order Sheffer classes (*k*>0). The crux of this talk is to
present an overview of a preliminary analysis of a special case of the *B- Type 1* (*k*=1) class, which is an
extension of the *B-Type 0* class, in order to determine
which sets, if any, are also
orthogonal. We conclude with a conjecture based on this work and a
brief
discussion of extensions and future research.

Cookies provided!

The talk will be accessible to undergraduates!

School of Science Faculty

Candidate Seminar

*Sarah Hicks*

University
of Missouri

Wednesday, January 27,
2010

3:00 - OBS 123

*A
Study of Teacher Knowledge as Secondary Mathematics
Teachers Use A New Technology*

During this research
presentation, I will describe the background, theoretical framework,
methodology, and preliminary findings of my dissertation research project. Effective use of technology to teach
mathematics requires a teacher who is knowledgeable about the
technology
as well as how to integrate it during mathematics instruction (Kaput,
1992;
Laborde, 2001; Mitchell, Bailey, & Monroe, 2007; Ruthven &
Hennessy,
2002). I qualitatively investigate the following research
questions: (1) What pedagogical content knowledge (PCK) do secondary
teachers
draw from when they begin to implement a new technology in their
mathematics
instruction? and (2) What orientations do teachers hold about teaching
mathematics with a new technology?

**Assistant
Professor of Math Education**

**Due to a flight issue, this event is canceled!**

School of Science Faculty

Candidate Seminar

*Corey Webel*

University of Delaware

Tuesday, January 26, 2010

10:00 am - Nick 169

*Student
Perspectives on Collaboration in their
High School Mathematics Class*

Recommendations from high school mathematics
reform
documents and curricula often include the use of collaborative
approaches to
learning, where students work together to generate solutions to tasks
that are
posed to the group rather than individuals.
However, teachers often
struggle
to implement these recommendations, resulting in situations where
students
merely copy each others' answers, fail to make mathematical progress
while
working together, or continue to depend on the teacher as the sole
provider of
mathematical knowledge. In this
presentation, I will describe a qualitative research project which
investigates
students perspectives on working collaboratively in one mathematics
class,
revealing some of their beliefs about mathematics, their goals for
working
together, and some of their reasons for assuming various roles during
collaborative activity. I will also
share some conjectures about how the teachers strategies for
structuring
collaboration may have influenced their perspectives.

**Assistant Professor of Math Education**

School of Science Faculty

Candidate Seminar

*Vanessa Pitts-Bannister*

Virginia Polytechnic Institute and
State University

Friday, January 22, 2010

10:00 am - Nick 165

*NAEP:
Do Pre-Service Teachers Measure Up?*

In
acknowledging the importance of translating among mathematical
representations,
Romberg, Fennema and Carpenter (1993) emphasize the need for research
that
accentuates students and teachers' understandings of translations among
multiple representations of functions. In fact,
it is suggested that competence of
translations consists of being able to operate within two perspectives: process and
object. The process perspective
entails viewing a line (or an equation) as a set of individual points
that are
related in a fixed way (ordered pairs).
Object perspective entails viewing a line (or an equation) as
an object
that can be manipulated as a whole (Moschkovich, Arcavi &
Schoenfeld,
1993). Research regarding students' knowledge and or illustrations of
process
and object perspectives (e.g., Schoenfeld, Smith & Arcavi, 1993 and
Knuth,
2000) provide insight into how students view algebraic and
graphical representations and how such ways
of thinking may promote or inhibit their attempts in making
translations among representations. While this
information is considered
important, such information concerning teachers' knowledge is limited. Accordingly, in this presentation, we will
discuss solution methods of pre-service
mathematics teachers as they attempt problems that call for
translations.

**Assistant Professor of Math Education**

We will be discusing our plans for the upcoming semester, including the annual trip to the sectional MAA meeting, bowling night, math week, and what ever else we can come up with.

Hope to see you there.

http://www.math.cornell.edu/~smi/

Please circulate this information to interested students in your department. It is expected that applicants have taken a standard sophomore-level multivariable calculus course. A further course in analysis, complex analysis, differential equations, or a related topic would also be helpful. Students who will graduate during the 2009-2010 academic year are eligible to apply. Applicants must be US citizens or permanent residents.