VITA                                 VIRGINIA McSHANE WARFIELD                                          April, 2009



Born:  Charlottesville, Virginia, September 30, 1942



A. B.   (cum laude, with honors in mathematics) Bryn Mawr College, 1963


M. A.    Brown University, 1965


Ph.D.   Brown University, 1971. 

        Thesis title: A stochastic maximum principle. 

        Advisor:  Wendell Fleming.




Teaching Assistant                  Brown University                   1964-67

Director, Project SEED                        Seattle Public Schools           1970-73

Lecturer                                               Department of Mathematics

                                                            University of Washington      

Part-time                                                                                                     1973-83


Full-time                                                                                                     1983-91

Senior Lecturer                                                                                    1991-2008

Principal Lecturer                                                                                   2008-

Director of Remedial

    Mathematics Program         University of Washington                 1982-2002





1. Invariant extensions of linear functionals, with applications to measures and stochastic processes, (with E. J. McShane and R. B. Warfield, Jr.) Pacific J. Math. 28 (1969), 121-142.


2. Existence and adjoint theorems for linear stochastic differential equations, Pacific J. Math. 52 (1974), 305-320.


3. A stochastic maximum principle, SIAM J. Control  14 (1976), 803-826.


4. "Reflections on Probability" -- the introductory chapter for a WCTM single-topic volume on the teaching of Probability in elementary and secondary schools (1989).


5. "John Holt: Quelle a ete son influence sur l'enseignement des mathematiques aux USA? Pourquoi une telle influence?"  Seminaire de Didactique des Mathematiques et de l'Informatique, Grenoble, 1991-92.


6. "Didactique  through the Back Door", MER Journal,  autumn, 1992.


7. "Discovery Method Algebra" (with Partee, Halsey and Mancer) Ginn Press, 1993.


8.  "Instructor's Manual for Discovery Method Algebra", Ginn Press, 1993.


9.  Mukhopadhyay, S. & Warfield, V.  ( Spring, 1995). Mathematics in the making: An experience in teaching without telling.  Record in Educational Leadership.


Mukhopadhyay, S. & Warfield, V.  (1995).  Mathematics in the making: An experience in teaching without telling. Notices of the Canadian Mathematical Society, volume 27, # 2, March.


10. Co-editor of The Theory of Situations: Didactique des Mathematiques 1970-1990,  the English language version of a collection of the central research articles of Guy Brousseau. Kluwer Press, 1997.


11.  Co-editor of Thˇorie des Situations Didactiques (Didactiques des mathˇmatiques 1970-1990), La Pensˇe Sauvage, 1998


12. Brousseau, G. and Warfield, V., The Case of Ga‘l, The Journal of Mathematical Behavior, Vol. 18, no. 1 (1999) pp. 7-52.


13. Brousseau, G., Brousseau, N. and Warfield, An Experiment on the Teaching of Probability and Statistics, Journal of Mathematical Behavior, volume 20, #3, 2001, pp 363 - 411


14. Brousseau, G., Brousseau, N. and Warfield, Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurement, Journal of Mathematical Behavior, volume 23, #1, 2004, pp 1 Š 20


15. Brousseau, G., Brousseau, N. and Warfield, Rationals and decimals as required in the school curriculum. Part 3: Rationals and decimals as liner functions. Journal of Mathematical Behavior, volume 27, #3, 2008, pp 153-176


16. Invitation to Didactique, Xlibris Press, 2007





1)  "John Holt: Quelle a ete son influence sur l'enseignement des mathematiques aux USA? Pourquoi une telle influence?"  Colloquium at University of Grenoble,  February, 1991.


2)  "L'enseignement constructivist de l'enseignement constructivist" at the Ecole d'ete en didactique, Auvergne, France, August, 1993.


3)  "The constructivist teaching of constructivist teaching", at the meeting of the PME, Asilomar,  October 1993.


4)  "Didactique: What  French Mathematics Educational  Research is up to." MER workshop, Rensselaer Institute, Nov 1993.


5)  "Didactique: Math Education a la Francaise", UW Mathematics Department Colloquium,  March, 1994.


6)  "What possibilities come to hand? Designing a course by inspired opportunism," with Swapna Mukhopadhyay.  MER Workshop, Baton Rouge, Nov. 1994.


7)  "Who's Looking after the Twig-benders?", an invited address on preparation of elementary school teachers, meeting of Texas section of MAA, April 1, 1995.


8)  Workshop on Interactive Teaching (also by invitation) at the same meeting.


9)  Developpement d'un cours pour Instituteurs at the Ecole d'ete en didactique, Auvergne, France, August, 1995.


10)  What's that New York taxicab doing on the U.W. campus?, at the winter meeting of the Puget Sound Council of Teachers of Mathematics, January, 1996.


11)  Workshop on Interactive Teaching at annual meeting of ORAMATYC (Oregon Association of Mathematicians at Two Year Colleges), April 1997.


12) Took part in two panel discussions at the Joint meetings in 2001


13) Introduction to Didactique, at the University of British Columbia and by cyber-connection at Rutgers University, November 2001.


14) A brief introduction to Didactique at a discussion session at the research pre-session of the NCTM, April, 2002.


15) A more substantial introduction to Didactique at the seventh Symposium on Elementary Mathematics Teaching, which took place at the Charles University in Prague. I was responsible for a session introducing the basic notions of Didactique and for serving as a translator for Guy Brousseau, founder of the field.


16) Took part in a panel discussion at a session honoring Guy Brousseau at the annual meeting of the NCTM in Anaheim, April 7, 2005


17)  Collaborated with Guy Brousseau in writing and presenting the opening plenary address at the Congress of the International Psychology of Mathematics Education group, Prague, July, 2006


18) Collaborated with Guy Brousseau in writing and presenting a pair of talks on Misuses of Evaluation, March and April, Seattle and Rutgers.


19) Math Wars and the New Math, Keynote Talk at Everett Community Math Conference, June, 2007


20) Two decades of WashingtonÕs K-12 Mathematics from one PersonÕs Perspective, at the Northwest Math Conference, October, 2007




Grants and conferences:

Received grant from Board of Scholars to design a course with minimal prerequisites aimed at giving non-math majors some insight into the workings and use of mathematics, summer 1983.


Received grant from Center for Instructional Development and Research to translate the above design from the abstract to the classroom-ready.


Received grants from Graduate School for travel to France for purposes of conference and research on Didactique, summers of 1995 and 1996.


Co-PI of a five year NSF grant with Ramesh Gangolli (Mathematics Department), Jack Beal of the College of Education and Gini Stimson of Mercer Island High School, to work with middle and high school teachers from six school districts around Lake Washington. The grant is entitled "Creating a Community of Mathematics Learners."  In connection with that, we ran a one week pilot institute for teachers in the summer of 1995.


Co-PI of a second five year grant entitled "Expanding the Community of Mathematics Learners", working with elementary school teachers in the same six school districts.


Project Director of PFF (Preparing Future Faculty) grant to expand the horizons of graduate students and increase departmental communication with them. This is in many ways an extension of the PFF grant we had before (see item VI below.) (1999-2002)


Co-PI of the GK-12 project funded by NSF and run by Loyce Adams (1999 -  ) This year I have become quite active in the project. In summer of 2003 I helped run a week-long workshop for teachers and graduate students involved in the project, and during autumn quarter I worked with one other person to run a two day workshop for more teachers and graduate students, and have begun a program of regularly spending time at one of the schools, both to support what is going on and explore ideas for what might go on in the future. In summer of 2004 I again helped run a week-long workshop and also a follow-up workshop for graduate students, and since then I have been helping run an ongoing seminar helping to acquaint the graduate students with aspects of K-12 education that might help them and deepen their understanding.


Participant in the 2001 Institute for Teaching Excellence run by the U.W. Teaching Academy.


Participant in the 2002 2nd International Congress on the Teaching of  Mathematics (at the undergraduate level)on the island of Crete


Participant in Spring, 2003 conference in Tucson on Mathematics Education and Mathematics in the 21st Century: The Roles of Outreach, Teacher Preparation, and Research in Teaching and Learning in a University Mathematics Department


Participant in the June, 2003 PMET (Preparing Mathematicians to Educate Teachers)  Workshop sponsored by the MAAÕs Committee on Mathematical Education of Teachers


Since spring of 2004 I have been one of a team of three faculty members running TEAM-OP Š Teaching for the Environment: Active Mathematics on the Olympic Peninsula. The other faculty members are from the College of Forestry and the College of Education. The chief involvement is a two week summer institute in Forks, but there are also some winter planning sessions and de-briefings.


I have been working a little with the Transition Math Project, a state-wide project working to smooth the transition from high school to college. I attended the end of their institute in 2005 and arranged to have a session at WaToToM the following year at which the Project was presented.


I am a member of the steering committee for Project TIME (Transitions in Math Education) being run by Green River Community College.




Services to Department:


I. Course development


        1.      I designed Math 107, Mathematics, a Practical Art, which has been taught since winter, 1985.  It is the only course in the department which is designed to be of interest and use to non-scientist students.  As such, it fulfills the department's need for a way to permit students to fulfill the Quantitative and Symbolic Reasoning requirement without adding to the already drastic overload in Math 120.  I wrote a workbook which serves as the text for the class, and have since done a major revision of it.


        2.      When the trio of professors who had been teaching the courses for future elementary school teachers retired in the mid-eighties, I re-designed both Math 170 (Mathematics for Elementary School Teachers) and Math 171 (Geometry for Elementary School Teachers).  For the former I arranged for a new text and set up a series of classes, worksheets and assignments to go with it.  This set of notes was sufficiently comprehensive and clear to be used either in part or entirely by other instructors of the course (in particular, the instructors for several summer sessions of Math 170 felt very comfortable simply reproducing the course on a shorter time line).  In the course of the nineties, between the changes going on in the world of mathematics education and the increase of my knowledge of it, I have been continually revising the course. As of 2007, I am engaged in trying out a new pair of books for Math 170 and 171


        3.      Math 171 as I envisioned it did not conform to any existing textbook, so I wrote notes and put together many pieces and resources.  My notes have since been used by at least one other instructor. More recently I have been using Sybilla Beckman's textboo


        4.      With Michael Mancer, I revised the Student Workbook for Math 100-102. I also to a large extent rewrote the Instructor's Manual for the same courses.

[Since 1993 both have been published by Ginn Press, now Simon and Schuster.]



II .   Administration


        When I first joined the 100-102 program,  the training of T.A.'s consisted of a weekly seminar on Piaget's theories of learning, which the T.A.'s found bewildering.  I instituted, and still run, a systematic training program, which is well received by most T.A.s and actively sought  after by those interested in pursuing a teaching career as such. Graduate students who have taken part in this program are very much valued by the local Community Colleges.



III.   Committees      


        1.      I was the representative of the Mathematics Department on the admissions committee for Group III E.O.P. students from 1982 until the committee ceased to function. The committee spent many hours discussing not only specific decisions about admitting individual marginal students, but the overall admissions policies for E.O.P. students in general.


        2.      In the spring of 1987 I served on a committee set up by the Vice President for  Minority Affairs  to review the structure and objectives of the Instructional Center.   After many meetings and a good deal of discussion, we sent in a comprehensive report with a number  of suggested changes.  Many of the suggestions were acted upon, with the result that the Instructional Center became appreciably more effective in 1987-88 than it had been for the preceding few years.


        3.      In 1985-88 I was a member of the T.A. Training Committee.


        4.      Since 1986,  I have periodically been a member of the Teaching Majors Committee.  Currently I am serving on that committee.


        5.      In 1993-94, I served on the committee of the College of Education which was designing the reformed program for preparation of elementary school teachers. The following year, I worked on the design of the mathematics courses within the new program, and co-taught the first sequence of them.


6.            In 1998-99, I served on the committee of the College of Education which was revising and fine-tuning the above program for preparation of elementary school teachers


7.            I have been on several doctoral committees for the College of Education, and am currently serving on another.


         8.     I have been on the Math Day committee for several years, and habitually run the origami session, produce games for the teachers' lunch and serve as a go-between for the Math 'n' Stuff session.


IV.    Brown Bags      


        Starting in November, 1993, I have run lunch time "Brown Bag Seminars" at which a variety of issues of teaching and learning are discussed.



V.     Colloquia


         I have arranged for sundry colloquia on issues in education. Speakers have included Leon Henkins, Marjorie Enneking, Guy Brousseau, David Clarke and Nicolas Balacheff.


VI.    PFF


                From summer of 1994 to spring of 1996, I served as one of the faculty coordinators for the department's grant from the Pew Charitable Foundation entitled "Preparing Future Faculty".  Activities on this front have included:


        1.      Arranging for eight of our graduate students to spend time at Seattle University and/or Seattle Central Community College, working with one specific faculty member, observing classes, and absorbing some of the culture of the institution.


        2.      Taking seven graduate students to a conference of the Northwest Council of Teachers of Mathematics in Victoria in November, 1994.


        3.      Taking another seven graduate students to the Washington Community College Mathematics Conference in Wenatchee in April, 1995. While we were there, several of us presented a forum about the PFF.


        4.      Taking five graduate students and one faculty member to the Washington Community College Mathematics Conference in the Columbia Gorge in May, 1996.


        5.      Arranging five "Festive Fora". The first four featured David Clarke (twice), Brian Greer and Susan Pirie, all well known researchers in Mathematics Education. The last featured a dramatized dialogue (in costume, yet) between Gauss and Eisenstein on the subject of the Quadratic Residue Theorem. The parts were played, respectively, by Prof. David Pengelley and myself.


        6.      Arranging a series of small dinners at local restaurants designed to promote conversation among faculty members and graduate students about issues of graduate education. These have since been revived under other funding. Summaries of many of the conversations can be found at


        7.      Serving as the Mathematics Department's representative on the PFF Steering Committee starting in December, 1994.



VII. In 2003 and 2004, I took part in SIMUW (Summer Institute in Mathematics at the University of Washington), teaching probability for two weeks and taking part in sundry social activities.


VIII. Newsletter


        Since October, 1994, I have been producing an asynchronous e-mail newsletter about issues and events on the teaching/learning front within the math department.  I had intended it as simply an in-house item, but at this point there are subscribers in several states and even a few out of the country,  The newsletters can be found at



Service to the University

               Since 2003 I have been a member of the advisory committee of the Pipeline Project. This is an extremely lively and project providing  channel (or pipeline) for university-wide outreach to K-12 schools around the state.


Community Service:


        In spring of 1986, I spoke to the High School Teacher's Network on the subject of some problems which are accessible to and enjoyable by high school students.  I also spoke at the annual meeting of Washington Community College Teachers of Mathematics, on the subject of Math 107.


        In October, 1986, I was part of a panel leading a forum for an Intercollege Relations Commission discussion of the quantitative reasoning requirement.  At the request of a fellow panel member, I repeated the talk at a meeting of the Washington Community College Humanities Association in April.


        For six weeks at the end of winter quarter and the beginning of spring quarter, 1986, Francesco Agostoni, who has a doctorate in the teaching of mathematics from the University of Milan, came to the University of Washington as my mathematical visitor.  He observed the teaching of Math 170, Math 100, 102 and 103, and the training of TAs in Math 100 and 102.


        In May, 1987, I gave a full day of inservice training in the Renton School District on the subject of Probability and the teaching of it to high school students.


        In August, 1987, I gave a full day seminar on group discovery teaching to a class of high school teachers taking a course at Evergreen College.


        In October, 1989, I gave an invited workshop on the Art of Probability at the Northwest Mathematics conference -- a meeting of teachers from kindergarten through college.


        In June, 1990, I gave a two week summer workshop for teachers on Geometry for Elementary and Middle School Students.  The workshop was sponsored by the mathematics department of the University of Virginia.


        In  October, 1992 I gave a three hour mini-course on the Didactique approach to teaching fractions and decimals at the Northwest Mathematics conference.


        In April, 1993,  I  co-taught a three day workshop for in-service teachers in American Samoa.


        In May, 1993, I taught a two day workshop for in-service teachers in El Paso, Texas.


        In June, 1994, I co-taught a two week institute for inservice teachers in Carbondale, Illinois.


        In March, 1995, I taught a two-day workshop on Probability for in-service teachers in  Carruthersville, Missouri.


        In October, 1995,  I taught a two-day workshop on Algebra and Probability for in-service teachers in Madisonville, Kentucky.



Note: The last five workshops listed were all done under the auspices of the National Faculty.


        In October, 1995, I ran a workshop on semi-regular tilings at the annual Northwest Mathematics Conference.


From autumn, 1996, to spring, 2002 I was a member of the Board of Trustees of the Little School.  Serving successively as  chair of its Education and Operations committee,  chair of its Diversity committee and member of the Board Development committee.


On several occasions (whose dates I failed to record) I have gone to local elementary schools, either to take part in a school-wide meet-some-scientists day or to teach a special topic in an individual classroom.


In March, 2002, I presented a session on Probability at an Expanding Your Horizons conference at Shoreline Community College.


In March, 2003, I presented a session on Graph Theory at an Expanding Your Horizons conference at Shoreline Community College.


October, 2007 Š April, 2008, I was a member of the writing team for the Washington State Mathematics Standards, and in particular of the K-2 Editorial Team responsible for writing and reviewing the Standards at the kindergarten through second grade level.


Since October, 2007 I have been member of the Washington State Mathematics Coordinating Council.


Since autumn of 2006, I have been a member of the Steering Committee of Project TIME, a branch of the Transition Math Project.


Since autumn of 2008, I have been a member of the Advisory Council for Explorations in Math, a non-profit organization devoted to changing the mathematics culture at elementary schools.            


WaToToM .  Since 1998, I have run an annual gathering of Washington Teachers of Teachers of Mathematics, at which members of departments of mathematics and mathematics education from all over the state get together for a week-end of conversation and idea-sharing. Over time, we have become a strong community with a desire to serve mathematics education in the state on a wider basis. We have formalized with the creation of an Executive Committee and the sponsorship of a website:


Memberships and positions:


           Mathematical Association of America

               Committee on Professional Development    

               Committee on Mathematical Education of Teachers


        American Women of Mathematics: 

               Chair of the Education Committee

               Member of Association Review Group for studying the revisions the NCTM Standards.

               Education editor of AWM Newsletter

               Member at large of Executive Committee (elected December, 1999)

Member of subcommittee to select a consultant firm to help the AWM strengthen its operations.


English language editor of the web-based International Newsletter on the teaching and learning of Mathematical Proof, found at



        Member of the National Faculty (an elected membership); Sigma Xi; Mathematical Association of America; Association pour Recherche en Didactiques des Mathematiques.




Project SEED is an innovative project which brings professional mathematicians into inner city elementary classrooms to teach topics in high school and college mathematics, using special teaching techniques.  It is a national project which had state-wide programs in California and Michigan and now has a major project in Dallas, Texas and a growing number of projects elsewhere.  During 1970-72, the project had classes in eight schools in the Seattle Central Area, with a budget of $104,000 (for 1971-72), and employed 30 mathematicians, including 7 members of the University of Washington mathematics faculty. The duties of the director included administration, teaching, and training other mathematicians to teach in the project.  Reductions in available federal funds terminated the project in Seattle in 1973.


The University of Washington department of mathematics used Project SEED as its model in setting up its remedial mathematics program, which has been run since its beginning by people trained in Seattle's Project SEED.  Since 1973, I have been working as a teacher and T.A.-trainer in this program.  In 1977 I became one of its administrators.  Since 1982 I have been its director. In the course of that time, I  set up the current program for training T.A.s.  Recently, I have also edited the Student Workbook and drastically revised the Instructors' Manual.  They are currently being published by Ginn Press.


Details of many of the items listed above are attached to my Homepage: