The Mathematics Education colloquia at the University of Georgia are organized by the Mathematics Education Student Association [MESA].
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20062007 Colloquia
April 2007
Guershon Harel, University of California, San Diego
A Definition of “Mathematics” and Its Pedagogical Consequences;
Focus on the Transition between the Empirical Proof Schemes to the
Deductive Proof Schemes
Abstract:
Current teaching practices tend to view mathematics in terms of subject matter, such as definitions, theorems, proofs, problems and their solutions, not in terms of the conceptual tools that are necessary to construct such mathematical objects. This talk has two main goals: The first goal is to define these two categories of knowledge and explain why both categories are needed. The definitions and explanations are oriented within a theoretical perspective called DNRbased instruction in mathematics. Central to DNR is the distinction between way of understanding and way of thinking and the definition of “mathematics” in terms of these two constructs. The second goal is to discuss curricular and instructional implications of this definition to the learning and teaching of proof, more specifically, to the transition from empirical proof schemes to deductive proof schemes.
March 2007
Presenters: Brian Lawler, Na Young Kwon, and Zelha TuncPekkan, University of Georgia
Moderator: Jeremy Kilpatrick, University of Georgia
Pros and Cons of a National Curriculum
Abstract:
A few weeks ago there was a national conference on mathematics curriculum in Washington DC. The lead plenary speaker was Jere Confrey, and her talk was essentially about the pros and cons of a national curriculum. The goal of this colloquium is to bring together the mathematics education community – national and international – at UGA to discuss this talk and pros and cons of a national curriculum. Confrey’s paper is online at: http://cltnet.org/cltnet/misc/csmcmath07/agenda.html
Please come prepared to discuss this paper.
February 2007
Sarah Ledford, Kennesaw State University
Teachers Making Sense of a Mathematical Professional Development
Experience
Abstract:
The purpose of this study was to understand how teachers make sense
of their professional development experience for their own learning,
their students’ learning, and their teaching. Three teachers were
observed and interviewed during a professional development course
where the goal of the course was for the teachers to develop their
mathematical content knowledge. The mathematics instruction of the
course was similar to how these teachers are expected to teach in
their classrooms with a course emphasis on using technology to explore
mathematics. The participants’ experiences were broken into their
making sense of the mathematics, technology, and problem solving,
and their making sense was observed as assimilation (content was
not problematic) or perturbation (content was problematic) and how
they dealt with each.
About the author:
Sarah Ledford is a recent graduate of the PhD
program in Mathematics Education from the University of Georgia.
She will be talking about her dissertation research and will happily
answer any questions about the process of dissertation writing.
January 2007
AnnaMarie Conner, Penn State University
Student Teachers' Conceptions of Proof and Facilitation
of Argumentation in Secondary Mathematics Classrooms: Focus on the
Case of Karis
Abstract:
Drawing on the work of Krummheuer and others in argumentation as
well as research on proof and proving, my research considers relationships
between three student teachers' conceptions of proof and their support
of claims, data, warrants, and backings as elements of argumentation
in secondary mathematics classrooms. In this talk, I will give an
overview of the larger study and then focus on one student teacher's
conceptions of proof and how these relate to her facilitation of
argumentation in a calculus class she taught as part of her student
teaching experience.
November 2006
Dr. Tad Watanabe, Department of Mathematics, Kennesaw State University
Pictorial Representations of Quantities in Japanese Elementary
Mathematics Textbooks: A Content Analysis
Abstract:
Representing quantitative relations mathematically is an important
goal of mathematics education. Moreover, representations may also
support students’ learning of mathematics. Japanese elementary mathematics
textbooks often utilize sophisticated, and often unfamiliar to US
students and teachers, diagrams to support students’ learning. In
this presentation, I will discuss the results from a content analysis
of two most widely used elementary mathematics textbook series in
Japan.
Virginia Benjamin, University of Georgia Libraries
Endnote Bibliography Software: An Introduction
Abstract:
An overview of how Endnote bibliography software can be used to:
1. Help you exploit the GALILEO scholarly databases by easy transfer of pertinent references, including keywords and abstracts
2. Organize your readings and expedite your notetaking
3. Take the hassle out of styling your intext citations and bibliography
as you write
October 2006
Heather Robinson, Commerce High School
A Discussion of the Deconstruction and Reconstruction of
Teaching Methods in a Mathematics Classroom
Abstract:
Topics to be discussed will include...
• Teacher centered vs. student centered instruction: What's good
for the Goose is not always good for the Gosling!
• Nontraditional assessments: How to measure student learning "differently"
• Effectively using research in the mathematics classroom.
September 2006
Dr. Jeremy Kilpatrick, University of Georgia
A Conversation About George Polya
Abstract:
George Polya (18871985) was a fine mathematician, influential mathematics educator, and delightful human being. I will try to give you some sense of his teaching and his ideas about mathematics education. Then I'll be happy to answer questions you might have about him and his work.
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20052006 Colloquia
April 2006
Danny Bernard Martin, University of Illinois at Chicago
Race, Identity, and Mathematics Literacy
Abstract:
This presentation draws on findings from three interrelated studies
of the mathematical experiences, identities, and advocacy practices
of African American parents and caregivers. Extant research has
shown that African American parents express the same folk beliefs
about mathematics as other parents—stressing it as an important
school subject for their children and important for basic literacy.
However, I argue that as they frame mathematical literacy within
the larger contexts of African American, socioeconomic, and educational
struggle, these parents and caregivers reveal that mathematics learning
and participation can be conceptualized as racialized forms of experience.
Moreover, as they attempt to become doers of mathematics, negotiate
their identities as such, and advocate for their children’s mathematics
learning, a host of discriminatory forces—fueled mainly by socially
constructed meanings for race—continue to challenge the agency of
African American parents. Those who resist subjugation and exercise
their individual and collective agency often do so based on the
belief that mathematics knowledge can be used as a tool of liberation.
I suggest ways to leverage the positive agency of African American
parents to better support mathematics learning for African American
children. I discuss the implications of this work for teacher education.
Finally, I will discuss how these studies have led to a new paper
in which I am examining the ways in which the concept of race has
been addressed in mathematics education research and policy.
About the speaker:
Danny Martin is an associate professor of mathematics education and mathematics and faculty affiliate of the African American Studies Department at the University of Illinois at Chicago. Prior to coming to the University ofIllinois in 2004, Dr. Martin was Instructor and Professor in the Department of Mathematics at Contra Costa College for 14 years, where he served as Chair from 20012004. Dr. Martin has a broad interest in mathematics teaching and learning in K16 contexts. However, his primary research interest is equity issues in mathematics education, with a specific focus on mathematics socialization and the construction of mathematics identities among African American adults and children in classroom and community contexts.
February 2006
Thomas Banchoff, Brown University
Slicing Solid Shapes: The GPS and the Internet
Abstract:
Georgia Performance Standards for seventh
grade mathematics include describing and sketching solid figures.
This also includes cross sections. How can we unpack that topic
for students at all levels from K through graduate school? How can
the Internet help?
November 2005
Michael de Villiers, University of KwaZuluNatal, South Africa
Some Research Issues on how Technology has Changed the Roles of Proof and Experimentation in Mathematics
Abstract:
This talk will provide a brief overview of a theoretical framework regarding the role of proof and experimentation in mathematics in the light of the general availability of powerful modern computing technologies in order to provide a conceptual frame of reference and researchers in mathematics education is to develop meaningful activities which not only illustrate these functions of experimentation and proof within the context of technologies such as dynamic geometry and computer algebra systems, but to also accurately reflect an authentic view of the complex, interrelated nature of experimentation and deductive reasoning. A brief report will also be given of some completed research projects involving dynamic geometry from this theoretical framework, and further research directions and issues that need to be considered.
October 2005
Kyle Schultz, University of Georgia
Power and Creativity in Mathematics: Using OpenEnded Problems
in the Mathematics Classroom
Abstract:
Openended problems can provide students with a
way of seeing mathematics as a creative and powerful endeavor. Based
upon simple premises, openended problems are rich in mathematical
content and can engage students of varying ability levels. When
used properly, openended problems provide a medium for students
to develop problemsolving skills, communicate mathematically, use
technology, and see connections between seemingly unrelated mathematical
ideas. In this presentation, the speaker reflects on his experiences
in implementing projects based on openended problems. Audience
members will be introduced, through participation, to examples of
openended problems. In addition, audience members will learn about
issues that teachers should consider when using openended problems.
The speaker will provide suggestions for implementing openended
problems in a secondary classroom and show examples of his students'
work.
Richard Hill, Michigan State University
Some Mathematics Education Issues Arising in a Mathematics Department
Richard Hill is a professor of mathematics at Michigan State University. He has written research papers in algebraic topology and numerical linear algebra. Since 1992, he has directed an Emerging Scholars Program (an Uri Treisman style, calculuslevel, integrated minority support program). Issues arose in this program that have led to two types of mathematicseducation research which will be of interest to both mathematics and mathematics education faculty:
1. The transition in mathematics from high school to college. We are writing up the results of a study involving about 3000 students from 34 high schools, the students’ senior year math courses and their grades, standardized test scores, and MSU math courses and grades. The results have been interesting, many surprising. This study is being expanded to grades 812 and six universities; comments and suggestions will be appreciated.
2. Developing a capstone course for future math high school math teachers, teamtaught by a mathematician and a mathematics educator. Among other things, the results show sophomoresenior mathematics courses often miss opportunities to draw connections between the mathematics in these courses and school mathematics. Various issues will be presented.
September 2005
Virginia Benjamin, University of Georgia Libraries
Endnote Bibliography Software: An Introduction
Abstract:
An overview of how Endnote bibliography software can be used to:
1. Help you exploit the GALILEO scholarly databases by easy transfer
of pertinent references, including keywords and abstracts;
2. Organize your readings and expedite your notetaking;
3. Take the hassle out of styling your intext citations and bibliography
as you write.
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2004  2005 Colloquia
April 2005
Lou Edward Matthews, University of South Carolina Upstate
Examining and Reforming Mathematics Teaching Through a Culturally Relevant Pedagogical Lens
Abstract:
Emerging in the early nineties, research on culturally
relevant pedagogy to teaching have illuminated the work of successful teachers whose pedagogy is committed to the intellectual, political, cultural and social aspirations of the student groups they teach. This promise has arisen from studies of teachers who redefine teaching as a culturallycentered practice which seeks deliberately and creatively to realize high academic achievement while centering instruction around students’ cultural and community identities, challenging curriculum and schooling limitations, and preparing students to challenge inequitable school and society norms. This redefining of "good" teaching gives rise to important implications for achievement and equity aims espoused in mathematics reform. How do teachers become culturally relevant, and can viewing mathematics teaching through the lens of culturally relevant pedagogy aid current reform efforts? This presentation will explore the components of culturally relevant pedagogy, and the implications for teaching mathematics, reform, and mathematics education research.
Beatriz D'Ambrosio, Indiana University
The Role of Mathematical Conversations in Supporting Student Learning.
Abstract:
In this presentation I will discuss the development of classroom conversations and the different types of listening that support student learning. The study that will be described occurred in a large urban school district at the middle grades level. I will share a particular teaching episode in which the children engaged in a large group conversation and wrote journal entries after the conversation. The analysis of the journals provides evidence of how the children’s reasoning was influenced by their understanding of their peer’s ways of thinking about the problem.
March 2005
M. Kathleen Heid, Penn State University
Understanding the mathematical understandings of prospective
secondary mathematics teachers: Some results and observations.
Abstract:
A Penn State team working in the context of the MidAtlantic Center
for Mathematics Teaching and Learning has created courses to help
secondary mathematics teachers think about mathematics related to
the curricular demands of "reform" high school mathematics.
In that context, the team is investigating the mathematical understandings
of prospective secondary mathematics teachers. This session will
describe some of our initial observations of these students' mathematical
understandings and ways of thinking.
David Wayne Stinson, Georgia State University
African American Male Students and School Mathematics.
Abstract:
Dr. Stinson discusses his dissertation study entitled African American
Male Students and Achievement in School Mathematics: A Critical
Postmodern Analysis of Agency (The University of Georgia, Department
of Mathematics Education, August 2004). The purpose of his study
was to shed light on the schooling experiences of African American
male students who embraced school, academics, and mathematics. In
particular, the study examined the influence of sociocultural discourses
on the agency of 4 African American men in their early 20s who had
demonstrated achievement and persistence in school mathematics.
Agency in this context was defined as the participants’ ability
to accommodate, resist, or reconfigure the available sociocultural
discourses that surround African American males in order for them
to effectively negotiate these discourses in their pursuit of success.
February 2005
Herbert Khuzwayo, University of Zuzuland, South Africa
A Study of Mathematics Teachers' Constraints in Changing
Practices in South Africa: Some Lessons from Countries Participating
in the Learner's Perspective Study.
Abstract:
My presentation would report on my current involvement in studying
constraints and struggles experienced by mathematics teachers as
they attempt to take on new curricular and pedagogies in South Africa.
Some of the obstacles, tensions and contradictions that arise as
teachers make attempts to transform fundamentally their mathematics
teaching from an apartheid to post apartheid curriculum are not
unique to South Africa alone. This has become evident from an attempt
to analyze teacher data collected as part of an international research
project, The Learner’s Perspective Study.
Amy Hackenberg, University of Georgia
Kernels of Algebraic Reasoning: A Study of Sixth Grade Students'
Mathematical Learning in the Context of Mathematical Caring Relations.
Abstract:
The purpose of this study was to understand how sixth graders reason
quantitatively as a basis for beginning to reason algebraically
in interaction with a teacher who endeavors to enact mathematical
caring relations (MCR) with them. From a teacher’s perspective,
MCR is an orientation to balance stimulation and depletion, or increases
and decreases in levels of energy and feelings of wellbeing, in
studentteacher interactions aimed toward mathematical learning.
From a student’s perspective, MCR involves willingly engaging with
the teacher in mathematical activity and pursuing questions of interest.
To this end, the researcher taught two pairs of sixth graders from
a rural middle school in Georgia in a constructivist teaching experiment
from October 2003 to May 2004. Teaching practices included posing
situations that involved multiplicative reasoning in fractional
contexts to build toward solving problems that underlie basic linear
equations (of the form ax = b), adapting problem situations to harmonize
with and challenge students’ current ways of operating, and tracking
students’ engagement with and affective responses to this interactive
activity. Retrospective analysis entailed creating chronologies
for each pair of students that mapped changes in their ways of operating
and in their engagement in mathematical activity with the researcher.
The results of the study highlighted the construction of multiplicative
structures as a significant factor in students’ construction of
schemes for reversing multiplicative relationships among quantities,
the difficulty students had in constructing reciprocity and operating
on unknowns, and the influence of MCR on the construction of self
as an able doer of mathematics.
Paola Sztajn & Amy Sanford, University of Georgia
Real Answers to Real Math Teachers' Questions: An Introduction
to the BRIDGE
Abstract:
In this colloquium we will present and discuss the BRIDGE, a new
educatorgenerated website designed as a peer reviewed resource
for beginning as well as experienced teachers. Particular attention
will be given to the mathematics component of the BRIDGE and to
ways in which mathematics education students can publish in or serve
as reviewers for the BRIDGE.
January 2005
Holly GarrettAnthony, University of Georgia
When Am I Ever Going To Use This? Teachers' Instructional Practices With Contextual Problems
December 2004
Torian White, Salem High School, Rockdale County, Georgia
The Real Deal: A Conversation with a New Teacher in Mathematics
Education
Abstract:
As an undergraduate, I can recall just wanting to question a fresh
teacher in the field to find out the real deal. Informally, I would
like to share with undergraduates the effectiveness and usefulness
of pedagogical techniques given by the Mathematics Education faculty.
Also, I will discuss how my teaching philosophy was influenced by
what I learned at UGA. For example, I will share the freedoms and
restraints of using investigation, studentcentered instruction,
and technology integration in the mathematics classroom when benchmark
and endofcourse assessments and standards are becoming more restrictive
and significant. Moreover, I will also discuss the importance of
administrative and mentoring support for the success of a beginning
teacher as well as other challenges such as special education accommodations
and raising student motivation and morale.
November 2004
Godfrey Sethole, Tshwane University of Technology, South Africa
Making Sense of the Everyday in Mathematics
Abstract:
The new South African Curriculum, Curriculum 2005 places emphasis
on the need for teachers to recruit contexts that are meaningful
to their learners’ realities in the teaching of mathematics. The
main aim of the paper is twofold: Firstly, it looks at the way in
which two teachers, located in different racial settings handle
the expectation of recruiting the everyday context into mathematics.
In particular the teachers’ movements from authentic to inauthentic
context will be teased out. Secondly, it highlights different ways
in which learners at these two schools view the value and significance
of the everyday in mathematics lessons. Bernstein’s theory on recognition
rules and Skovsmose’s notion of exemplarity will be summoned to
make sense of learners’ arguments regarding the value of context
in mathematics.
October 2004
Mark Hoover Thames, University of Michigan
Defaulting on Equity in the Teaching of Elementary School Mathematics
Paola Sztajn, University of Georgia
Brazilian Mathematics Teachers: How They are Prepared and
How They Teach
Abstract:
In this colloquium I will present information about teacher education
in Brazil, using data from the SAE large scale educational assessment
used in the country that resembles the American NAEP in many ways.
I will discuss how mathematics teachers are educated in the country
and talk about some results from SAEB concerning teachers’ classroom
practices.
September 2004
Holly Anthony, Denise S. Mewborn, John Olive, University of Georgia
The Research School and Other Conversations about South
Africa
Abstract:
The three presenters each spent a month or more in South Africa
in the summer of 2004. All attended the Research School for doctoral
students in mathematics and science education. Each also spent time
at various universities and schools around the country. They will
discuss their shared experiences at the Research School and their
individual experiences with various aspects of mathematics education
in South Africa.
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2003  2004 Colloquia
July 2004
Ayhan Kursat Erbas, University of Georgia
Teachers’ Knowledge of Student Thinking and Their Instructional
Practices in Algebra
Abstract:
I observed and interviewed one eighthgrade teacher and one ninthgrade
teacher of Algebra 1 to investigate and understand their knowledge
of student thinking and instructional practices in algebra. The
following research questions guided the study: What is the nature
of teachers’ professional knowledge about student thinking in Algebra
1? How is this knowledge grounded? How does student thinking and
knowledge of it inform teachers’ instructional practices?
What are teachers’ beliefs about student thinking in Algebra 1?
Andy Norton, University of Georgia
Students' Conjectural Operations
Abstract:
What are conjectures? How are they formed? How do they contribute
to learning? How might teachers foster conjecturing activity? This
presentation focuses on answers to those questions based on teaching
experiments with four sixthgrade students, in the context of solving
fractions tasks.
Zelha TunçPekkan and Paola Sztajn, University of Georgia
Views of Curriculum, Students and Teaching Goals in a GraduateLevel Mathematics Education Course
Abstract:
We will talk about university professors’ views about mathematics curriculum, goals for a graduate level curriculum course and how they see their graduate students’ contributions to the classroom atmosphere. We will also discuss how these views play a role in the professors planning.We will talk about university professors’ views about mathematics curriculum, goals for a graduate level curriculum course and how they see their graduate students’ contributions to the classroom atmosphere. We will also discuss how these views play a role in the professors planning.
April 2004
Tracey Smith, Charles Sturt University, Australia
Using Narrative Inquiry to Learn in Mathematics Teacher Education
Andreas Ryve, University of Malardalen, Sweden
What Is a Mathematically Productive Discourse?
Sergei Abramovich, State University of New York at Potsdam
Hidden Mathematics Curriculum’ as a Conceptual Framework for Mathematical Preparation of Prospective Elementary Teachers
Andrew Izsák, Erik Tillema, and Zelha TunçPekkan, University of
Georgia
Teaching and Learning Fraction Addition on the Number Line
Steve Sigur, Teacher, Paideia School, Atlanta
The Many Dimensions of Teaching SketchPad
Panel: Jeri Benson, Jeremy Kilpatrick, Judith Preissle, Elizabeth
St. Pierre, University of Georgia
How Do We Define Scientific Research in Education?”
March 2004
Eric Gutstein, University of IllinoisChicago And That’s Just How It Starts: Teaching Mathematics and Developing
Student Agency
Yung Hwan Kim, KongJu National University, Korea
Improving Teachers’ Proficiency in Statistics Education
Ethel Masihleho, National Research Foundation, South Africa
Educational Reform in PostApartheid South Africa
Ben Blount,Department of Anthropology, UGA
Cultural Models and Representation of Local Knowledge
January 2004
Lu Pien Cheng, Mathematics Education, UGA
Overview of Singapore’s Education System
November 2003
Patricio Herbst, University of Michigan
Asking Epistemological Questions About Educational Practice: The
Place of Proof in Geometry Instruction
Shelly Harkness, Miami University, Oxford, OH
The ‘Rewards’ of Listening to Students’ Mathematical Constructions
October 2003
Mamokgethi Setati, University
of the Witswatersrand, South Africa
Learning and Teaching Mathematics in a Primary MultilingualClassroom
Carlos Gomez and Victor Brunaud, Universidad Catolica Cardenal Raul Silva Henriquez Santiago de Chile
Mathematics Education of Teachers in Chile
Pam Smith, Executive Director for Curriculum, Assessment, and Accountability, Clarke County School District, GA,
The No Child Left Behind Act and Adequate Yearly Progress in Georgia
Ed Azoff, Department of Mathematics,UGA
What Is Mathematics?
Anna Kristjansdottir, Agdar University College and Iceland University of Education
Supporting the Professional Development of Teachers: A View from Iceland and Norway
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20022003 Colloquia
