Principles to
Guide the Design and Implementation of
Doctoral
Programs in Mathematics Education
A Task Force
Report for the
Association of
Mathematics Teacher Educators
This report,
in some ways, has been several years in the making. As you will see, the thinking behind Principles to Guide the Design and Implementation of Doctoral Programs
in Mathematics Education began with a national conference on doctoral
programs in mathematics education in 1999.
I know all about this conference, which was organized by Robert Reys and
Jeremy Kilpatrick. You see, the
thinking behind this work actually began before 1998 with a conference proposal
submitted to this then National Science Foundation Program Officer. The conference was important, the work that followed
by Reys and Kilpatrick in the editing and publication of One Field, Many Paths: U.S. Doctoral Programs in Mathematics Education
(CBMS, 2001) may be more important.
This manuscript, completed by a task force representing some of the
finest and most well respected mathematics educators in the country, provides
the Association of Mathematics Teacher Educators (AMTE) with the concluding
effort of this now four-year project.
Principles to Guide the Design and Implementation of
Doctoral Programs in Mathematics Education is not a mandate. This document should serve to drive
discussion and action as institutions of higher education consider reviewing,
revising, or creating doctoral programs in mathematics education. The task force and I believe that this
initial AMTE contribution is best used to help define and discuss the core
elements of doctoral study in mathematics education.
We hope the
dialogue that this publication generates is helpful to institutions and
individuals as we all consider the elements of doctoral study in mathematics
education.
In closing,
allow me sincerely thank the Task Force for this important and initial AMTE
publication.
Francis (Skip) Fennell, President
AMTE
September 23, 2002
Part 1:
Background
The
1999 National Conference on Doctoral Programs in Mathematics Education funded
by the National Science Foundation revealed great diversity in goals,
components, and expectations of mathematics education doctoral programs across
the United States (see Reys & Kilpatrick, 2001). The number of and variation in programs was further documented
with data from the National Research Council’s Annual Survey of Doctoral
Recipients in the United States (NRC, 2000), which reported that from 1980
to 2000, over 120 different institutions awarded doctoral degrees to people
identifying their major discipline as mathematics education. Two related and nontrivial questions
surfaced during the conference: Is there a “core or canon of knowledge” needed
by those earning doctorates in mathematics education? And what are the essential elements of a doctoral program in
mathematics education?
Identifying
a common core of knowledge for recipients of doctorates in mathematics
education is confounded by several factors, including the following:
1.
Mathematics education
is a young field, with most programs having evolved during the last 50 years.
2.
In some universities,
doctoral programs are located in departments of mathematics; in others, they
are in schools or colleges of education.
3.
Careers awaiting
people with doctoral degrees in mathematics education vary greatly.
Jobs include positions as classroom teachers and district or state
mathematics supervisors, as well as employment by textbook publishers, test
development enterprises, research centers, and institutions of higher education.
4.
Positions in
higher education vary greatly in focus and scope.
Nationwide, there is an acute shortage
of people with doctorates in mathematics education to fill positions in
universities granting advanced degrees in the field (Reys, 2000, 2002). That shortage is exacerbated when, as
happens increasingly, new degree recipients take other types of jobs. Over half take faculty positions in higher
education, but these positions are often in junior colleges and four-year
institutions and not just in institutions with doctoral programs (Glasgow,
2000). Others take jobs outside higher
education.
Those taking faculty positions in
higher education may be called upon to teach undergraduate and graduate level
mathematics courses in departments of mathematics. Those in schools or colleges of education typically undertake
some combination of teaching undergraduate methods courses in mathematics
education, supervising student teachers, teaching graduate courses in
mathematics education, and providing professional development activities for
in-service teachers of grades pre-kindergarten to 14. Although teaching expectations vary, positions in higher
education typically require the establishment of an active research agenda.
Regardless
of the job, a knowledge base is central to the work of mathematics
educators. If mathematics education is
to advance its status as an emerging discipline and effectively prepare
graduates for a wide range of positions, it is important to deliberate about
“essential elements of a doctoral program in mathematics education.” A rationale for the mathematics education
community to address this issue was provided in the closing chapter of One Field, Many Paths: U. S. Doctoral
Programs in Mathematics Education:
The
absence of system-wide standards for doctoral programs is perhaps, the most
serious challenge facing systematic improvement efforts. Shared standards have never existed for U.S.
programs in mathematics education. . .
Indeed, participants in the system have grown accustomed to creating
their own standards at each local site.
Developing a consensus on goals or standards is a significant step
because it will require a change of practice.
It will remove some of the isolation and autonomy of individual programs
in favor of a shared commitment to improving the system of doctoral
education. Changing practice in this
way involves changing culture, and cultural changes are neither quick nor easy.
(Hiebert, Kilpatrick, & Lindquist,
2001, p. 155)
Consensus
on the core elements of doctoral programs in mathematics education will be
difficult (some might say impossible), but progress can be made if educators
engage in an iterative process involving thoughtful discussion and
reflection. The process itself has the
potential to improve the quality of doctoral programs in mathematics education,
the preparation of graduates of these programs, and ultimately the profession
of mathematics education.
To
move this process forward, the Association of Mathematics Teacher Educators
(AMTE) appointed a Task Force charged with identifying “core elements of
quality doctoral programs in mathematics education.” AMTE recognizes that the challenge is formidable, but its action
was based on the belief that articulation of core elements would inform
institutions initiating new doctoral programs in mathematics education as well
as institutions with established programs.
This
report is organized into three parts:
Part
1—Background
Part 2—Core Knowledge Expectations for Doctorates
in Mathematics Education. Each
element is identified, together with a brief rationale for its inclusion,
and some means of addressing the elements is briefly described.
Part 3—Institutional Capacity Needed to Support
Quality Doctoral Programs. A list
of institutional components necessary to support high quality doctoral programs
is proposed.
The Task
Force believes that the quality of doctoral programs in mathematics
education is influenced by the availability of opportunities to acquire an
essential knowledge base. By detailing
these components, we hope to serve at least two audiences: faculty and future
doctoral students. Consequently, this
report might be used by faculty to review existing programs in light of these
core elements and to make changes as deemed appropriate.
Students might use the information to make informed choices about which
institution to enter to pursue a doctorate in mathematics education.
This
report builds on discussions of key components of doctoral programs in mathematics
education found in One Field, Many Paths:
U. S. Doctoral Programs in Mathematics Education (Reys & Kilpatrick,
2001). Because of its brevity and focus, the report
can only point toward a direction we believe will lead to an overall improvement
of doctoral programs and their graduates in mathematics education.
The report should encourage faculty involved with the education of
doctoral students to reflect on their program and use this reflection
to improve its quality. We also recognize
that a number of institutions are contemplating the establishment of doctoral
programs in mathematics education. The
report should be useful to that group as they set about developing high-quality doctoral programs.
A goal of
doctoral programs is to develop leaders capable of contributing
to the profession of mathematics education and communicating
knowledgeably about many topics and issues in mathematics and mathematics
education. The following section
outlines “core knowledge” that the Task Force believes is
essential for the work undertaken by most graduates of doctoral programs in
mathematics education. It is organized
around eight areas of inquiry. These
areas should be viewed not as equivalent to courses but rather as the knowledge
base doctoral students should acquire through a range of experiences. Such experiences should include courses as
well as seminars, clinical experiences, internships, assistantships, and independent
study.
Mathematics
educators need broad and deep mathematical knowledge both to identify the
big ideas in the pre-K–14 mathematics curriculum and to examine how those
ideas develop throughout the curriculum.
For
mathematics educators, how one knows mathematics is vital. And how one knows mathematics is a function
of how one comes to know mathematics.
Knowing mathematics as a teacher needs to know it must be attended to within
doctoral programs in mathematics education.
Historical, Social, Political,
and Economic Context of Education
Schools operate
in a social context that is influenced by a variety of historical, social,
political, and economic factors. Mathematics
education is not immune to the forces shaping education in general,
so the mathematics educator needs to
understand those forces and how they work.
For example, knowing the historical evolution of the equity movement
equips the mathematics educator better to understand and respond to current
efforts to address inequities.
Teaching, learning, assessment, technology, research, mathematics, and curriculum all have a history. Knowledge of these histories and their interrelationships provides a valuable lens to interpret, understand, and act upon these areas and to participate in the process of improvement. Studying the history of mathematics education is an integral part of a doctoral program. This knowledge includes, but is not limited to, policies that have influenced and shaped the evolution of mathematics education. Familiarity with reports from major commissions, committees, and professional organizations is a prerequisite to understanding and responding to contemporary debates about the status and progress of mathematics education.
Learning
Fundamental
theories of learning mathematics provide the foundation for thinking about
issues in mathematics education.
Mathematics educators need to understand these theories and the distinctions
among them in terms of both the kind of learning they are trying to explain and
the theoretical constructs that have proven useful over time. A treatment of both historic and
contemporary theories of learning should be a part of all doctoral programs in
mathematics education.
Drawing on
current theories and research, doctoral students should understand how people
of different ages, mathematical backgrounds, and aptitudes learn
mathematics. This understanding may be
accomplished by various means including courses, seminars, or special readings
focusing on theories of learning and the accompanying research evidence. In addition, a doctoral program should
provide opportunities for candidates to link their knowledge to practice in
designing or evaluating curricula, setting learning goals, and creating
cognitively appropriate patterns of instruction.
Teaching and
Teacher Education
Technological
tools are vital to the development of mathematical concepts and processes, and
their availability is changing mathematics at all levels. Consequently mathematics educators need both
knowledge of and an ability to use such tools effectively. Graduates of doctoral programs in
mathematics education should understand and be able to utilize technology as a
tool of inquiry that has implications for teaching and learning
mathematics. Although technology offers
opportunities to present and explore mathematics in new ways, it is critical
that doctoral students understand the potential and limitations of
technology. They should be able to
design learning experiences for students and teachers at various levels that
utilize technology to enable and support mathematics exploration and
learning. Fluency is expected with
technology tools that support teaching, learning, and research. Knowledge of research related to the
interaction of technology and mathematics teaching and learning should be a
specific focus of study within a doctoral program.
Curriculum
The work of mathematics educators
involves designing effective curricula and learning environments to facilitate
the development of deep and connected mathematical understanding. To do such work, doctoral students need
experiences in curriculum analysis, design, and evaluation. For example, they need to understand the
role and influence of local, state, and national curriculum frameworks and
standards on the design and implementation of school programs.
Curriculum
development is informed by knowledge of current theories and research about
human learning, how to connect different areas of mathematics, and how students
come to appreciate mathematics as a discipline. It is also informed by knowledge
of how curricula, technology, and instructional strategies work together to
support mathematics learning. Avenues
to develop a deeper knowledge of curriculum and curricular issues include
studies of different strands of curricula, comparisons of international curricula,
and studies of mathematical concepts across grade levels. Evaluation of curricula should include experiences
in examining topics and making judgments about their relative importance in
the curriculum and their utility in developing other mathematical ideas.
Assessment
Mathematics educators must have knowledge of assessment. Doctoral graduates should know the literature
on assessment, including the major influences assessment practices have on
the intended, implemented, and achieved curricula in mathematics instruction.
More specifically
they should be knowledgeable about the interconnections among learning goals,
assessment and teaching. They
should understand different forms and purposes of assessment, including mathematics
teacher-made student assessments used to inform future
instruction and school-, district-, or state-mandated testing used to evaluate
programs. Doctoral
graduates should have opportunities to analyze
and compare tests, including commercial achievement tests and state-constructed
instruments. They should also know
about national and international efforts to monitor student learning in mathematics
and about the challenges associated with interpreting these results.
Doctoral
programs in mathematics education may be offered by a single institution or
a collaboration of institutions. Regardless of the institutional structure,
a high-quality doctoral program comprises
more than a set of courses and a dissertation. Equally important is the environment created
within an institution where students and faculty learn, work, and interact.
It is critical that students have opportunities to work alongside and
learn from active researchers and experienced collegiate teachers while they
are engaged in their work. Doctoral programs in mathematics education
should have resources of appropriate quality and sufficiency to support preparation
of doctoral students and continual renewal of faculty. These institutional resources include the following:
1.
A critical mass of faculty with expertise in mathematics education
who provide program leadership and model professional behavior.
2.
Faculty, possibly including some from outside mathematics education,
who are engaged in research in mathematics education.
3.
Adequate physical and technological facilities (e.g. computers,
libraries, and meeting rooms) that support an active learning community of
students and faculty.
4.
Print and video resources (research journals in mathematics education; important
reports; resources for teaching methods and content courses, including quality
pre-K–14 mathematics curricula, methodology textbooks, state frameworks; and videos
modeling mathematics teaching and learning) that facilitate professional growth.
5. Resources necessary to provide financial support for a critical mass of full-time resident doctoral students.
6.
Mentored internships focused on acquiring expertise in collegiate
teaching, supervising student teachers, designing and implementing a research
study, designing and facilitating professional development activities for
teachers, preparing grant proposals, and writing papers for publication.
7.
A supportive mathematics department that includes a group of
mathematics faculty with interest in and a commitment to mathematics education.
8.
Services available from all departments across the institution
with appropriate expertise and a willingness to contribute to the program.
9.
An environment that demonstrates respect for cultural, ethnic,
racial, and individual diversity.
In
closing, the Task
Force recognizes that this report is not a definitive road map for doctoral
programs in mathematics education. Neither
complete nor perfect, it should be viewed as a work in progress. Although some in the mathematics education
community may applaud this AMTE initiative and the report, others may be quick
to critique both the effort and the product.
To the former, we encourage you to send AMTE your ideas and suggestions
for further refining the report. To
the latter, we offer this challenge: If after a careful reading and analysis
of the report, you believe a better blueprint exists that would be of greater
use to the wide range of institutions with job opportunities that require
a doctorate in mathematics education, please contact AMTE with your ideas
for an alternate approach. Comments
from all readers are welcome, as the resulting dialogue will serve to energize
the mathematics education community and move the field forward.
Task
Force Members:
F.
Joe Crosswhite, The Ohio State University (Emeritus)
James
Fey, University of Maryland
Susan
Gay, University of Kansas
Jeremy
Kilpatrick, University of Georgia
Glenda
Lappan, Michigan State University
Johnny
Lott, University of Montana
Barbara
Reys, University of Missouri
Robert
Reys, University of Missouri (Chair)
Glasgow,
R. (2000). An investigation of recent graduates of doctoral programs in
mathematics education. Unpublished
doctoral dissertation, University of Missouri-Columbia.
Hiebert, J.,
Kilpatrick, J., & Lindquist, M. (2001).
Improving U. S. doctoral programs in mathematics education. In R. E. Reys & J. Kilpatrick (Eds.), One field, many paths: U. S. doctoral
programs in mathematics education (pp. 153-162). Providence, RI: American Mathematical Society.
National
Research Council. (2000). Summary report 2000: Doctoral recipients
from United States universities.
Washington, DC: National Academy Press.
Reys, R. E. (2000).
Doctorates in mathematics education: An acute shortage. Notices
of the American Mathematical Society, 47(10), 1267-1270.
Reys,
R. E. (2002). Mathematics education
positions in higher education and their applicants: A many to one
correspondence. Notices of the American Mathematical Society, 49(2), 202-207.
Reys,
R. E., & Kilpatrick, J. (Eds.). (2001).
One field, many paths: U. S.
doctoral programs in mathematics education. Providence, RI: American Mathematical Society