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What Core Knowledge do Doctoral Students in Mathematics Education Need to Know?. Joan Ferrini-Mundy National Science Foundation. Conference on Doctoral Programs in Mathematics Education Kansas City September 24, 2007. core knowledge for doctoral mathematics education. purposes of

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What Core Knowledge do Doctoral Students in Mathematics Education Need to Know?

Joan Ferrini-Mundy

National Science Foundation

Conference on Doctoral Programs in Mathematics Education

Kansas City

September 24, 2007


knowledge for

doctoral mathematics


purposes of

doctoral education



of doctoral



context and trends

observations on the purposes of doctoral education:

“…to educate and prepare those to whom we can entrust the vigor, quality, and integrity of the field …a scholar first and foremost, who will creatively generate new knowledge, critically conserve valuable and useful ideas, and responsibly transform those understandings through writing, teaching, and application … a ‘steward of the discipline’…”

Chris Golde, 2006, Preparing Stewards of the Discipline, p. 5

“…I believe that a professional field like ours is different from traditional academic disciplines. It requires different talents and different kinds of knowledge, and it makes different kinds of contributions to society. Ours is an appropriately eclectic field. It requires advanced study and skills comparable to those in other professional fields that award doctorate, but a narrow focus on research isn’t the right thing.”

Jim Fey, 2001, Doctoral programs in mathematics education:

Features, options, and challenges, p. 57

“…U.S. Ph.D. scientists and engineers who will pursue careers in research and education, with the interdisciplinary backgrounds, deep knowledge in chosen disciplines, and technical, professional, and personal skills to become, in their own careers, leaders and creative agents for change… understand and integrate scientific, technical, business, social, ethical, and policy issues to confront the challenging problems of the future….”

National Science Foundation, 2007, IntegrativeGraduate Education

And Research Traineeship Program Solicitation

“The PhD program should be designed to prepare scholars who can provide normative as well as epistemic theory, research, and analysis in ways that place discussions about the enterprise in frameworks that are both analytical and morally defensible….a steward who is responsible for both the field of education study and the education enterprise.”

Virginia Richardson, Stewards of a field, stewards of an enterprise: The doctorate in education, pp. 251-2

“Doctoral education is organized around an intensive, real-world research experience that prepares students to be scholars capable of discovering, integrating, and applying knowledge…”

Council of Graduate Schools, 1990, cited in National Science Foundation U.S. Doctorates in the 20th Century, 2006

“…ensure the vitality of intellectual discovery and to promote an environmentthat cultivates rigorous scholarship”

Council of Graduate Schools, Mission Statement, 2007

“My years at Stanford were a time for tearing down and rebuilding my ideas of mathematics education….I think all of us were learning something more fundamental: to be able to adapt high-quality mathematics education practices to whatever context we found.”

Jim Wilson, 2003,Development of a mathematics education community: A personal perspective.

pp. 1793-1794

stewards of the discipline

steward who is responsible for both

the field of education study and the

education enterprise

…confront challenging problems of the future

…leaders and creative agents for change

narrow focus on research isn’t the right thing …

cultivate rigorous scholarship

scholars capable of discovering, integrating, and applying knowledge…





the professional practice of doctoral mathematics educators

What is the “practice” of mathematics education?

  • research

  • teaching

  • service

  • curriculum design

  • teacher education

September 21, 2007—With lawmakers and school leaders alike stressing the importance of math, science, and technology (MST) education in preparing students for 21st-century jobs and careers, one might assume that parents and students would agree these subjects are crucial to their future success. But a new report challenges this assumption. According to the report, titled "Important, But Not for Me: Parents and Students in Kansas and Missouri Talk About Math, Science, and Technology Education," parents and students say they understand the importance of MST skills in general--but they don't see these as important for themselves.

What is the “practice” of mathematics education?

  • critique

  • make an argument

  • explain

  • write

  • trim

  • synthesize

  • learn

  • collaborate

  • mentor

  • lead

  • research

  • teaching

  • service

  • curriculum design

  • teacher education

Where do mathematics educators work?

  • Higher education (doctoral, masters, bachelors, community colleges)

  • K-12 (schools, districts)

  • Government (state, federal)

  • Business and industry (training, publishing, assessment)

  • R&D, think tanks, consulting, development firms

Developing Leadership for Mathematics and Science Education

Joan Ferrini-Mundy

Robert Floden

James Gallagher

Charles Anderson

Scott Ashmann

Gail Burrill

Marco Meneketti

Michigan State University

A Report on NSF ESIE 0101110

Research Questions

1.Characteristics of current leaders in mathematics and science education?

2.What led to their leadership and influence?

3.What has been their role as leaders?

4.Where will the next generation of leaders come from?

Study Components

  • Review of literature  

  • Examine national data bases

  • Interview study of leaders  

  • Study of doctoral programs in market perspective

Leadership Development

  • Background

  • Ability

  • Opportunity

  • Context

  • Responsibility

  • Influence

Arenas of Leadership

  • Undergraduate education

  • Teacher preparation

  •  Professional development

  • Research

  • K-12 curriculum/instructional programs

  • Assessment

  • Standards

  • Policy making

Interview Study of 71 Leaders

  • Characteristics of current leaders?

  • What led to their leadership and influence?

  • What has been their role in mathematics and science education?

Interview Study

  • Method of selection

    - national & state leaders; recent graduates

    - wanted to span the variability of the field

    - 8 arenas of leadership

  • Interview procedures and questions

    - early influences & graduate education

    - 3 career “episodes”

Findings:Early Experiences

  • Develop interest in mathematics or science education

  • Influence of parent or teacher

  • Sometimes a negative experience built commitment to change

Findings: Doctoral Work as a Launchpad for Leadership

  • Mentors

  • Apprenticeships

    • Research assistantships

    • Teaching assistantships

  • Connections

    • Faculty

    • Students

    • Others in the field

Findings: Influence of Formal Coursework

  • Few mentioned contributions to leadership

  • Mixed reports of the salience of content preparation

  • There is a sentiment, though, that strong math background adds credibility

Findings: Reported Leadership Knowledge, Skills, and Dispositions

  • Vision

    • Salesmanship

    • Commitment to long-term goals

  • Good citizenship (willingness to assume leadership)

  • Interpersonal skills and importance of collaboration

  • Readiness to learn

  • Results-oriented approach

Reported Leadership Knowledge, Skills, and Dispositions (continued)

  • Risk tolerance

  • Leaders don’t report starting out planning to be leaders

  • Important to be able to deal with controversy

  • Vision for improvement and belief they can make a difference

Reported Sources of Opportunities

  • Serendipity

  • Engagement with current leaders

  • Promotion by mentors

  • More than one route to leadership; backgrounds are varied

  • Participation in big efforts puts people in places where their leadership can be seen and recognized

The Role of External Funding

  • NSF Summer Institutes

    • Interest in pursuing higher study

    • Personal connections

  • Funded projects

    • Incentive for selecting doctoral program

    • Site for work with mentor

    • Connections to others in the field

context and trends

US PhDs awarded between 1920 and 1999: 1,354,873

  • Science and engineering: 835,221

  • Non-science and engineering: 519,652

    • Education: 256,014

      • Mathematics education 3,084

NSF, US Doctorates in the 20th Century, 2006

NSF Centers for Learning and Teaching (2000-2005):

  • Tackle complex problems through collaboration among researchers and STEM educators from different traditions and communities

  • Offer graduate students the broad range of knowledge, skills, and tools they will need to become leaders in the field

  • Focus research and training on pressing issues facing STEM education in K-12 schools

  • 14 centers: 58 new graduate courses

  • As of May, 2006, support for more than 350 doctoral students

Society for Research on Educational Effectiveness

to advance and disseminate research on the causal effects of education interventions, practices, programs, and policies

  • increase the capacity to design and conduct investigations that have a strong base for causal inference

  • bring together people investigating cause-and-effect relations in education

  • promote the understanding and use of scientific evidence to improve education decisions and outcomes.

Trends: NSF

  • integration of research and education

  • potentially transformative research

  • innovation and discovery

  • definition of “rigorous” research

More trends:

  • Public engagement with controversial issues about mathematics curriculum and teaching

  • Heightened accountability at all levels; metrics, measures, impact, causality

  • Local, state, and national policy debates and activities affecting mathematics education

  • “nearby” fields: science education, technology education

and more…

  • mathematics teaching and learning across the K-20 spectrum

  • learning mathematics outside of school

  • globalization, interest in international practices and benchmarking

  • building the STEM workforce, building STEM literacy

core knowledge for doctoral mathematics education


Reys, Teuscher, Nevels, & Glasgow, 2007, p. 10

Reys, Teuscher, Nevels, & Glasgow, 2007, p. 10

  • Mathematics content

  • Research

  • Educational contexts

  • Learning

  • Teaching and teacher education

  • Technology

  • Curriculum and assessment

  • mathematics and its applications

  • how people learn

  • experience as a teacher

  • broader educational and social context

  • teacher candidates, in-service teachers, and schools

  • research basis for practices

  • scholarly skills to contribute to the improvement of mathematics education

Jim Fey, 2001. Doctoral programs in mathematics education: Features, options, and challenges, pp. 56-57

This conference…

  • Mathematics

  • Curriculum

  • Policy

  • Teaching

  • Diversity

  • Technology

Richardson: preparing stewards requires addressing

  • Formal knowledge

  • Practical knowledge

  • Beliefs and misconceptions

David Berliner, 2006, Toward a future as rich as our past.

Views from educational psychology:

  • Rethink the methods course

  • Consider the rationale for presenting big ideas

  • Introduce doctoral students to the sites where students live and learn

  • Design a research internship in a complex environment

  • Develop an understanding of educational policy

Core for all? Maybe not ….

  • Institutional capacity

  • Character of the program

  • Past as prologue

Questions: Institutional Capacity

  • What is the nature of your intellectual community?

  • What is your institutional capacity to mentor well?

  • What are your hiring plans/potential shifts in your faculty in the next 5-10 years?

  • What resources/allies do you have outside of mathematics education?

Questions: Character of the Program

  • How dynamic and responsive to changing context do you want your program be?

  • Are you trying to prepare a particular type of scholar?

  • Where are you on the stewardship-discovery-leadership-application terrain?

Questions: Past as Prologue

  • What kind of students are attracted to your program?

  • Do you have a large contingent of international students?

  • What do you know about the graduates of your program?

  • Can you describe the portfolio of dissertations your program has produced?

Core knowledge for doctoral students?




Expanded core knowledge for doctoral students?

resources for





and equity











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