:: COLLOQUIUM

April 20, 2007
Problem Solving Reconsidered:
Toward a Theory of Goal-Directed Behavior

11:00 am - 12:00 pm
Room 2121 Benjamin Building
With discussion and complimentary lunch to follow

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Dr. Alan H. Schoenfeld
University of California, Berkeley

My 1985 book Mathematical Problem Solving offered a framework for analyzing how and why people are successful (or not) when they engage in problem solving - but, it didn't offer a theory that explained how and why people made the choices they did. Such a theory is now within reach. Solving a mathematical problem, teaching a lesson (or a year's course), and building a theory of problem solving are all examples of goal-directed behavior. I'll try to make a case that such behavior can be explained on the basis of models of individuals' knowledge, goals, beliefs, and a particular form of decision-making. In addition, this account will be consistent with what is known about learning and development, context and identity, and more.

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March 9, 2007
Understanding the Experiences of High Achieving African-American Mathematics Majors

11:00 am - 12:00 pm
Room 2121 Benjamin Building
With discussion and complimentary lunch to follow

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Dr. Roni Ellington
Morgan State University

Despite increased attention given to African-American students in mathematics, few studies have explored the experiences of African-Americans who excel in mathematics and pursue undergraduate mathematics degrees. Borrowing elements from social, cultural, and personal factors identified in mathematics education research and factors from the college persistence literature relating to African-American students, this research study sought to understand the factors that shaped eight high-achieving African-American mathematics majors' decision to persist and succeed in mathematics. In particular, the study explored the ways in which these students perceived their own role, and the roles of family, educational institutions, and the community in their success. The data suggests that several factors were essential to these students' success in mathematics, including parental social and cultural capital, elementary school tracking, participation in elite academic programs, and participation in college scholarship programs. The participants' evolving social consciousness and spirituality provided a framework underlying their success and persistence in mathematics, particularly in college. In this colloquium, I plan to discuss some of the major findings of this research and their implications for mathematics educators, researchers and policy makers. I will also discuss how the study's findings can be used as a framework to guide future research on high achieving African-American students.

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January 19, 2007
Researching Race in Mathematics Education

11:00 am - 12:00 pm
Room 2121 Benjamin Building
With discussion and complimentary lunch to follow

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Dr. Danny Martin
University of Illinois at Chicago

Within mathematics education research and policy, race remains undertheorized in relation to mathematics learning and participation. While race is characterized in the sociological and critical theory literatures as socially and politically constructed with structural expressions, most studies of differential outcomes in mathematics education begin and end their analyses of race with static racial categories and group labels used for the sole purpose of disaggregating data. One consequence is a widely accepted, and largely uncontested, racial hierarchy of mathematical ability. Rather than challenging and deconstructing this hierarchy, many math educators take, or unwittingly accept, it as a natural starting point in their assumptions about learners, learning, and teaching. Disparities in achievement and persistence are then inadequately framed as reflecting race effects rather than as consequences of the racialized nature of students’ mathematical experiences. This inadequate framing is, itself, reflective of a racialization process that continues to legitimize the social devaluing and stigmatization of students identified as African American, Latino, and Native American and the privileging of students identified as White and Asian American. In this colloquium and paper discussion, I hope to foster a critical conversation and dialogue about how race has been addressed in mathematics education research, policy, and practice. Participants are asked to read the accompanying paper and prepare comments and questions.

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December 1, 2006
Promoting Mathematical Habits in High School: Some Snapshots

11:00 am - 12:00 pm
Room 2121 Benjamin Building
With discussion and complimentary lunch to follow

by

Al Cuoco
Director
Division of the Center for Mathematics Education
Education Development Center, Inc.

For many high school students, the real utility of mathematics lies in a style of work--the habits of mind that allow one to look at the world through a mathematical lens. This stance has implications for curriculum design. One benchmark for the choice of topics and approaches is that they help students develop specific mathematical ways of thinking. I will present a few examples of how this benchmark plays out in activities for high school students. The activities are designed in part because they promote important habits from analysis, algebra, and geometry. More precisely, we will take a look at ways to encourage "reasoning by continuity" and "abstracting regularity from repeated calculations," a form of encapsulation.

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November 10 , 2006
Research, Theory, and Standards: What affects the classroom practice and professional life of one high school teacher

11:00 am - 12:00 pm
Room 2121 Benjamin Building
With discussion and complimentary lunch to follow

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Marty Schnepp
Holt High School
Holt, MI

Marty Schnepp has been teaching for 19 years and has participated in both NSF-funded and other research projects. He and others have written about his teaching in a variety of places, including book chapters, conference proceedings, and national and international journals. In his talk, Marty will share brief episodes of his teaching, using these episodes as a backdrop for discussing how being a producer and consumer of math education literature influences his work with students and colleagues.

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Dr. Lew Romagnano
Metropolitan State College of Denver University

As a central part of their professional work, mathematics and mathematics education faculty (and those who aspire to be) wrestle with these questions: How do mathematics students learn to be mathematics teachers? How can pre-service programs, faced with myriad structural and policy constraints, set informed and conceptually sound, yet realistic and attainable, goals for the mathematical and pedagogical preparation of prospective teachers? This talk will present the elements of a framework for building and enacting programs of study for prospective mathematics teachers that combine mathematics and education courses with field experiences, and then describe some features of one program that is using this framework.

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Dr. Judith Reed
National Council of Teachers of Mathematics

This study used qualitative methods to study the teaching of high school mathematics teachers teaching in tracked schools. Based on the findings of Oakes’s (1985) study on tracking in United States secondary schools, I compared two tracked classes for each of three participants. The research questions were the following: (1) What knowledge of students do teachers in tracked classrooms use to inform their teaching practice? (2) How does this knowledge of students influence their teaching practice? (3) What role does the race or culture of the students have in this knowledge? The findings suggested that in between-participant comparisons, teachers made similar associations between the behavior and the motivation of the students with their track. Differences in pedagogical approaches in the two classes were directly related to these associations.

Room 2121 Benjamin Building
11:00 am – 12:00 pm
with discussion and complimentary lunch to follow


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Dr. Kay McClain
Vanderbilt University

This colloquium will take data from both a classroom design experiment and a teacher development design experiment in which statistical data analysis was the focus.  Episodes from both settings will be used to track the learning of the teachers and the students in a manner consistent with Simon's (1995) realized learning trajectory. This initial analysis will be used to build a case for the importance of theory in undergirding our work in mathematics education.

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Friday, September 22, 2006
The Inquiry-Oriented Differential Equations Project: An Example of Rethinking Undergraduate Mathematics Education

Room 2121 Benjamin Building
11:00 am – 12:00 pm
with discussion and complimentary lunch to follow

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Dr. Chris Rasmussen
San Diego University

This talk provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project as an example of one approach to rethinking the learning and teaching of undergraduate mathematics. In the first part of the talk I highlight the theoretical underpinning for the IO-DE project. In particular, I outline how the project capitalizes on advances within mathematics and on advances within K-12 mathematics education, including the instructional design theory of Realistic Mathematics Education (RME) and the social negotiation of meaning. In the second part of the talk I report on the main results of a study that compared students’ beliefs, skills, and understandings in IO-DE classes to more conventional approaches. In the final part of the talk I address ways in which IO-DE teachers have met the challenge of inquiry-oriented teaching. Specifically, the notion of pedagogical content tool is put forth as a way to capture forms of teacher interventions that use students’ thinking and reasoning as a basis for the development of mathematical ideas. A pedagogical content tool is a device such as a graph, diagram, equation, or verbal statement that a teacher intentionally uses to connect to student thinking while moving the mathematical agenda forward. Two examples of pedagogical content tools are tendered: Transformational record and generative alternative. These two pedagogical content tools are instructional counterparts to the RME design heuristics of emergent models and guided reinvention, respectively.

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