AMS-MAA-MER Special Sessions on Mathematics and Education Reform
Joint Annual Meeting, San Diego January 6-7. 2002
Title: International Aspects of Mathematics Education
Presenter: Deborah Hughes Hallett, University of Arizona
Abstract: In this talk, we offer some reasons for exploring aspects of mathematics education in other countries: to broaden our thinking, to consider alternative approaches, and to see what is distinctive about practices in the US. The talk will serve as an introduction to the presentations by Gail Burrill, Curtis McKnight, and Kazuko Ito West that follow this talk.
Title: Japanese High Schools
Presenter: Kazuko I West
Abstract: The TIMSS study concluded that "whole-class instruction,...after school activities,...and collegial interactions among students and teachers motivate student learning in Japanese schools." Though this observation would impress Japanese teachers with its accuracy, it is an observation from an American perspective in which each student and teacher is regarded primarily as an individual, not a Japanese perspective in which each student is regarded as a member of a class and each teacher as a member of the group of teachers. In Japanese high schools, a strong sense of community is basic. Teachers, most are graduates of well known universities majoring in the subject they teach, form a scholastic community. Students are tested and placed in ranked high schools so that none will unable to succeed. Teachers follow the same group of students for three years. Students spend their day with their classmates in homeroom where teachers come to conduct scheduled classes. Teachers of the same class work together next to each other in the faculty room. Teachers have weekly meetings in which they decide the daily academic, social and disciplinary activities of their students. Student/teaching issues are not decided in a top-down manner by administrators.
Title: A Cross-National Comparison of Curriculum Variables in School Mathematics Achievement
Presenter: Curtis C McKnight, University of Oklahoma
Abstract: While many take it as obvious that schooling matters to student achievement in mathematics, this is a complex subject empirically. The relationship between curriculum variables that shape student opportunities to learn and what students actually learned can be demonstrated statistically by appropriate analyses. However, these relationships are far from simple. When viewed in the context of the educational practices of several countries these variables show surprising differences in how they have an impact on student learning. Those from the US can gain important insight into these factors by examining them in a cross-national context. This paper presents an overview of such analyses both across countries from the Third International Mathematics and Science Study and also differences within the US.
Title: Mathematics Education Around the World: Bridging Policy and Practice
Presenter: Gail Burrill, Michigan State University and Joan Ferrini-Mundy, Michigan State University
Abstract: The Institute for Advanced Study brought together mathematics educators involved in policy and practice from Egypt, India, Kenya, Sweden, France, Brazil, Japan and the United States at the 2001 Summer Park City Mathematics Institute to discuss collective issues and challenges in mathematics teaching and mathematics education policy. The group considered the question: How do your very diverse mathematics educational systems function, both in theory and practice? Seven issues framed the conversation:
o the relationship of national standards and curriculum to teaching practice,
o the system of teacher education and its relationship to teaching practice,
o the role of algebra in the secondary mathematics curriculum,
o the balance between tradition and reform,
o the balance between depth and breadth,
o the challenges of excellence and accessibility, and
o the roles of mathematics education as a profession and of mathematics education
research.
One secondary teacher and one policy or higher education representative from each country came eager to learn from practices in the United States as well as from each other. This session will explore common concerns, emerging trends, and some interesting differences in their views and in the practice of mathematics education.
Title: Mathematical Content Preparation for High School Teachers
Presenter: Patrick Callahan
Abstract: This presentation will introduce the themes that will be developed in the four presentations that follow and in the concluding panel discussion. General goals of the session are to examine answers to the following questions: (1) What does it mean for high school teachers to have a "deep understanding" of the mathematics they teach? (2) What can and should be done by mathematicians and mathematics departments to foster this sort of deep understanding in the pre-service and in-service programs they offer for high school teachers?
Title: The Surprising Mathematical Depth in High School Problems
Presenter: Dick Stanley, Professional Development Program, University of California, Berkeley
Abstract: The problems and concepts of high school mathematics have a mathematical depth and richness that is typically not recognized. The simple step of taking high school mathematics seriously as a mathematical field of study can lead to an important and helpful perspective on preparation programs for teachers. We will illustrate these remarks by focusing on an ordinary high school problem: What line through the point (5,2) cuts off the least area in the first quadrant? In the "extended analysis" of this problem that we present, we will indicate how it can be opened up mathematically in ways that students seldom if ever see. The analysis reveals important features of mathematical content that somehow slip through the cracks in what students are exposed to in their university mathematics and mathematics education courses.
Title: High School Mathematics as Part of a Larger Mathematical Landscape
Presenter: Al Cuoco, Education Development Center, Inc.
Abstract: Recommendations for teacher preparation and professional development (the CBMS report "The Mathematical Preparation of Teachers,'' for example) call for courses that make increased connections between topics in undergraduate and precollege curricula. This talk will describe several ways that viewing high school topics through the lens of advanced mathematics can enhance high school teaching and high school mathematics. More precisely, I'll describe examples where the habit of taking a broader perspective on high school topics can help teachers:
o make connections among topics in the high school curriculum,
o develop high school topics in a way that emphasizes general mathematical principles,
o introduce classical mathematical topics into high school in meaningful ways, and
o develop interesting problems for their students.
Title: Some Reflections on Career-long Professional Development for Secondary Math Teachers
Presenter: C Herbert Clemens, University of Utah
Abstract: Since primary and secondary mathematics education is, at least in part, about mathematics, the university mathematical community has a role to play in school mathematics teaching and a profound self-interest in its outcome. Just as was the case with the "reading wars," the "math wars" are not the most productive context for mathematicians' involvement. Furthermore we can safely assume that the math wars, just like the reading wars, will end or stalemate on some middle ground superior to the stated goals of either of the warring parties. A productive posture for the university mathematics community is to anticipate this outcome. This talk will reflect on future roles for the university mathematics community in one fundamental component of career-long professional development for school math teachers.
Title: Teaching Mathematics Horizontally and Vertically
Presenter: Paul J. Sally, University of Chicago
Abstract: In any mathematics course that we teach at any level, the subject matter under discussion should be extended beyond the boundaries usually found in textbooks, but more or less at the same level. In addition, concepts, ideas, and problems which evolve from this discussion should be introduced to the students so that they can engage in more advanced mathematical ideas, whose foundation is based in their current studies. In fact, much of the teaching in mathematics should be done by starting with simple problems in the early grades and building these simple problems into a rich mathematical experience. This process will be illustrated by the Pythagorean Theorem.
Title: Panel on Interpretations of Deep Understanding of High School Mathematics: Implications for Mathematics Departments.
Moderator: Naomi D Fisher, University of Illinois at Chicago
Panelists: Duane A Cooper, University of Maryland and Margaret B Cozzens, Colorado Institute of Technology
Abstract: The panelists will consider the interpretations of the previous speakers of the idea of deep understanding of high school mathematics and how it plays out in their work with preservice and practicing high school teachers. Cooper and Cozzens will reflect on the implications of these ideas and related work for mathematics departments in developing or modifying courses for preservice and inservice high school teachers. The previous speakers, Al Cuoco, Patrick Callahan, C. Herbert Clemens, Paul J. Sally, Jr., and Dick Stanley, will contribute to the discussion.
Title: Contemporary College Algebra, Base Course for a Quantitative Literacy Program
Presenter: Don B. Small, US Military Academy, Westpoint
Abstract: Contemporary College Algebra, a data-driven modeling course, is an example of a reformed college algebra course that serves as a base course for a QL program. The course focuses on problem solving in the modeling sense rather than the exercise sense. Communications (reading, writing, presenting), use of technology, small group interdisciplinary projects, analysis of real data sets, graphical analysis, and recursive sequence models are all strongly emphasized. The course is designed to prepare students to be mathematically literate in today's information society. The focus is on preparing students for the future rather than training them for the past.
Title: Contemporary College Algebra - Inclusion of Collaborative Learning and Technology
Presenter: Laurette B Foster, Prairie View A&M University
Abstract: College Algebra has served a two-fold purpose to many institutions. The first of those is that College Algebra is a prerequisite course. The second is that those students in curriculums that are not mathematically intensive may use the course as the only mathematics requirement - a terminal course. Contemporary College Algebra - a reform approach attempts to address the concerns and needs of these students. One focus that is attempted in the Contemporary College Algebra course is to expose the student to collaborative learning. The student is required to participate as a member of in class group activities as well as out of class small group projects. The Contemporary College Algebra course also includes a required technology component. Each student enrolled in the Contemporary College Algebra course must have access to some form of technology. The technology reinforces concepts that have been presented in the course. Contemporary College Algebra attempts to make an impact on students who need to satisfy a mathematics requirement at this level. It also changes the attitude of students toward mathematics and in some cases recruits new students who have untapped potential in this discipline.
Title: Tracking Students through Algebra, Pre-Calculus and Calculus Courses
Presenter: Steven R Dunbar, University of Nebraska, Lincoln
Abstract: In discussions about curriculum change, two questions naturally arise: What mathematics courses will the students take after completing these courses? and What have students studied before these courses, and how recent is their knowledge?
This report answers these two questions for students at a large state university by tracking the enrollment of students in college algebra, precalculus, calculus, and non-calculus based mathematics courses over 18 successive semesters. Using data from the course enrollments we can answer these questions and note trends in the answers over time. Particular emphasis will be given to students in college algebra: who they are, what they study before taking college algebra, and where they go after completing the course.
Title: The Challenges of Revitalizing College Algebra
Presenter: Judy Clark, University of Massachusetts, Boston
Abstract: This session will seek to address the question of "how" to revitalize college algebra by examining the research on how people learn. The implications of such research for how we teach, how we design learning environments, how we assess student learning, and how we prepare instructors to meet the many challenges of revitalizing college algebra will be explored.
Title: Improving College Algebra by Developing Alternative Courses
Presenter: Bruce C. Crauder, Oklahoma State University
Abstract: College Algebra frequently serves simultaneously as a universal general education course, a terminal math skills course for students who will use mathematics in other disciplines, and a part of a precalculus sequence. Since this last use of College Algebra requires the most intensive use of algebra, the course content emphasizes precalculus preparation over the other uses of the course. On the other hand, the vast majority of the College Algebra students will not go on to take calculus. By moving those students into math courses that are more closely linked to the students' mathematical needs, we have found improved student attitudes and performance in both the alternative courses and in the College Algebra courses.
Panel: Discussion on "Revitalizing College Algebra: Why? And How?"
Moderator: William Barker, Bowdoin College
Abstract: The speakers in the CRAFTY/MER session "Revitalizing College Algebra: Why? And How?" will comment on each others' presentations and engage the audience in a discussion of the issues raised during the morning talks. Suggestions for appropriate action, both individual and organizational, will be particularly welcomed. The panelists will be Judy Clark (U. Mass, Boston), Bruce Crauder (Oklahoma State), Steve Dunbar (Nebraska), Laurette Foster (Prairie View A&M), and Don Small (USMA, West Point). The moderator will be William Barker (Bowdoin College).
Panel: Connecting Mathematics Education Research and Teaching Practice
Moderator: Jerry L Bona, University of Texas at Austin
Panelists: Deborah Ball, University of Michigan; Phil Daro, University of California, Office of the President; Chris Rasmussen, Purdue University Calumet; Rina Zazkis, Simon Fraser University
Abstract: This panel discussion will focus on connecting mathematics education research with teaching practice. There is a growing body of investigation into the process of knowing and learning mathematics. However, many (possibly most) curricular development projects and classroom practices remain uninformed about this research. The usual outlets for reporting mathematics education research are journals that are primarily read by other researchers in the field. It is to the issue of making the connection between research and practice in this area that the panel will be devoted. The panelists will each present a short overview of what they perceive to be the major issues and the current limitations to bridging the gap between research and practice. This will be followed by the moderator posing prepared questions and accepting audience questions and both panelist and audience discussion.