# January 2010 Archives

## Math Problem Solving Contest: Spring 10, Question 1

A unit circle is placed against a right angle.

What is the radius of the smaller circle?

Answers due to Dr. Rutter (Benson 87) by 5:00, Friday, Feb 12.

## Math Department Seminar, Feb 2, 3:30PM

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.

The talk will be accessible to undergraduates!

## Math Education Seminar, Jan 27th

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

## CANCELED: Math Ed Candidate Seminar, Jan. 25, 10:00AM

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

## Faculty Math Education Seminar, January 22

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

## Math Club Meeting: January 26th (Free Pizza!)

The next Math Club meeting will take place Tuesday, January 26th at 6:00 PM in the math lounge (Benson 78, now with stapler!).  Pizza will be provided.

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.

## Cornell Summer Math Institute

The 2010 Summer Math Institute (SMI) at Cornell will run from June 5 to July 31, 2010.  The SMI Program's primary purpose is to better prepare undergraduates, particularly women and underrepresented minorities, for the rigors of beginning courses in Ph.D. programs in the mathematical sciences.  The main component of SMI in 2010 is an analysis course at a level comparable to Cornell's honors undergraduate analysis course.  There is also a project component to SMI.  Detailed information is available at

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.

December 2009 is the previous archive.

February 2010 is the next archive.

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