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The Mathematics Education colloquia at the University of Georgia are organized by the Mathematics Education Student Association [MESA].


2006-2007 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
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 DNR-based 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 Tunc-Pekkan, University of Georgia
Moderator: Jeremy Kilpatrick, University of Georgia
Pros and Cons of a National Curriculum
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: Please come prepared to discuss this paper.

February 2007

Sarah Ledford, Kennesaw State University
Teachers Making Sense of a Mathematical Professional Development Experience
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
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
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
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 note-taking
3. Take the hassle out of styling your in-text 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
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!
• Non-traditional 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
George Polya (1887-1985) 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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2005-2006 Colloquia

April 2006

Danny Bernard Martin, University of Illinois at Chicago
Race, Identity, and Mathematics Literacy
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 2001-2004. Dr. Martin has a broad interest in mathematics teaching and learning in K-16 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
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 KwaZulu-Natal, South Africa
Some Research Issues on how Technology has Changed the Roles of Proof and Experimentation in Mathematics
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, inter-related 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 Open-Ended Problems in the Mathematics Classroom
Open-ended problems can provide students with a way of seeing mathematics as a creative and powerful endeavor. Based upon simple premises, open-ended problems are rich in mathematical content and can engage students of varying ability levels. When used properly, open-ended problems provide a medium for students to develop problem-solving 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 open-ended problems. Audience members will be introduced, through participation, to examples of open-ended problems. In addition, audience members will learn about issues that teachers should consider when using open-ended problems. The speaker will provide suggestions for implementing open-ended 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, calculus-level, integrated minority support program). Issues arose in this program that have led to two types of mathematics-education 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 8-12 and six universities; comments and suggestions will be appreciated.
2. Developing a capstone course for future math high school math teachers, team-taught by a mathematician and a mathematics educator. Among other things, the results show sophomore-senior 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
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 note-taking;
3. Take the hassle out of styling your in-text 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
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 culturally-centered 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.
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.
A Penn State team working in the context of the Mid-Atlantic 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.
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.
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.
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 well-being, in student-teacher 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
In this colloquium we will present and discuss the BRIDGE, a new educator-generated 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 Garrett-Anthony, 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
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, student-centered instruction, and technology integration in the mathematics classroom when benchmark and end-of-course 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
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
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
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
I observed and interviewed one eighth-grade teacher and one ninth-grade 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
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 sixth-grade students, in the context of solving fractions tasks.

Zelha Tunç-Pekkan and Paola Sztajn, University of Georgia
Views of Curriculum, Students and Teaching Goals in a Graduate-Level Mathematics Education Course
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 Tunç-Pekkan, 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 Illinois-Chicago
And That’s Just How It Starts: Teaching Mathematics and Developing Student Agency

Yung Hwan Kim, Kong-Ju National University, Korea
Improving Teachers’ Proficiency in Statistics Education

Ethel Masihleho, National Research Foundation, South Africa
Educational Reform in Post-Apartheid 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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2002-2003 Colloquia