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SYLLABUS
Epistemological Foundations of Mathematics and Sciences:
How does disciplinary knowledge develop and what are the implications for the
design of instruction in math and science?
Richard Lehrer, Peabody College, and Keivan Stassun, College of Arts and Sciences
Mondays, 1:10-4:00, WC 101
Overview
Epistemological Foundations of Mathematics and Sciences examines the social,
cognitive, and material arrangements and mechanisms that contribute to how we know
what we know in mathematics and in sciences. Knowing how we know is the domain of
epistemology, and assembling the means to create disciplinary-distinct ways of knowing
creates what Knorr Cetina (1999) calls an epistemic culture. It is this culture within a
discipline that sustains and regulates core assumptions about knowing within that
discipline.
The focus on epistemology is intended as counterpoint to more traditional approaches to
education, which take the content to be taught as fixed and the aim of pedagogy as being
to develop effective methods (e.g., “best practices”) for delivery of this knowledge.
Epistemological Foundations of Mathematics and Sciences focuses instead on
considering what makes knowing challenging in these disciplines, because such a
perspective offers alternative framings of the problem of teaching. Questions about
teaching science—what should be taught, to whom, and when—are all potentially revised
by considering carefully how we come to know. How well do current instructional
designs help students understand the nature of knowing in sciences and in mathematics?
How might alternative instructional designs be informed by analysis of forms of
knowledge and ways of knowing (i.e., practices) in math and science?
Although epistemology is traditionally the province of philosophy, we aim to adopt a
developmental perspective. A developmental perspective traces the influence of earlier
forms of knowledge making on later forms, and it orients analysis to the history and
progression of ideas. History and progression occur at different scales, and we propose to
examine two senses of development. The first is historic, with a scale measured in
decades, perhaps centuries. Accordingly, one strand of the course will trace the trajectory
of important ideas in the disciplines, such as force, field, or experiment, across social and
historic contexts. For example, although experiment now enjoys an unquestioned status
in the sciences, historically it was hotly contested, primarily because it involved rearrangement and disruption of everyday observation, along with attendant uncertainties
about the machines employed and related material circumstances of observation
(Gooding, 1990; Shapin and Schaffer, 1985). Experiment also demanded a change in
rhetoric: The research article, a form so familiar to us that it appears to have the status of
a naturally occurring event, was the product of a radical shift in written communication
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introduced by Newton (Bazerman, 1988). To complement historic analysis, we will also
consider learning and developmental transitions in how individuals come to understand
disciplinary practices, such as experiment, or how concepts are generated and
transformed by individuals. These studies of individual learning are often conducted in
settings designed to support conceptual change, with explicit attention to reconfiguring
learning environments so that the grounds for knowing—such as proof and proving in
mathematics, or experiment in science—are made more accessible to participants. By
participating in classrooms structured in this way, students presumably are in a position
to know how scientists and mathematicians generate knowledge. We will critically
examine this emerging literature and seek to contribute toward its further progress.
References
Bazerman, C. (1988). Shaping written knowledge. The genre and activity of the
experimental article in science. Madison: University of Wisconsin Press.
Gooding, D. C. (1990). Experiment and the making of meaning. Dordrecht: Kluwer.
Knorr Cetina, K. D. (1999). Epistemic cultures: How the sciences make knowledge.
Cambridge: Harvard University Press.
Shapin. S., & Schaffer, S. (1985). Leviathan and the air-pump: Hobbes, Boyle, and the
experimental life. Princeton: Princeton University Press.
Course Requirements
A typical course follows a trajectory outlined by the instructor(s). This course
does not follow that mold. Instead, instructors suggest resources and prospective
directions, but we expect that the path taken will emerge from the collective activity and
interests of the participants. We are asking each participant to lead one class session. The
leader suggests readings, posts readings on OAK and generates at least one question to
guide further discussion.

We propose to meet weekly to discuss readings and will employ OAK to post
readings, questions for discussion, and threads of conversation before convening
the face-to-face interaction of the seminar. Each participant is responsible for
generating and posting one response to the reading that can prospectively be
elaborated during class discussion.
Each participant will formulate an approach toward pedagogy for an important/puzzling
epistemic idea in math or science. The approach should be informed by analysis of the
history of the idea and by what is known (or could in principle be found out through
research) about how students in math/science classes typically think about that idea. The
goal is to use epistemic analysis to design which knowledge is to be taught, rather than
taking it as given by textbooks and other authorities. Participants may work in
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interdisciplinary teams (but this is not required). The particular form of each project is
determined by the question. Some may wish to design instruction, others may wish to
investigate more closely the history of a particular practice or idea.
 We will engage distinguished scholars in the field to speak about their work in
this area. The talk will be aimed at a general audience that we anticipate will span
Peabody College and the College of Arts and Sciences. Each speaker-scholar will
also consult with participants in the seminar on their projects described above.
o Professor Andrea diSessa is a learning scientist at the University of
California-Berkeley. His work includes careful attention to the nature of
knowledge and especially to relations between everyday and scientific
knowledge in the design of learning environments.
o Associate Professor David Cohen, of the Physics and Astronomy
Department at Swarthmore College, is a practicing astronomer with an
interest in the history of science. We expect that Professor Cohen will
provide a working scientist’s view of prospective relations between
pedagogy and epistemology.
o Assistant Professor Dahlia Porter, Vanderbilt Department of English,
studies the historical development of scientific narratives including the
earliest written descriptions of experimentation and the role of analogy in
scientific narratives.
o Assistant Professor Ole Molvig, Vanderbilt Department of History and
Department of Physics & Astronomy.
o Professor Nancy Nercessian is a cognitive scientist at the Georgia Institute
of Technology. Her work focuses on historic and cognitive analysis of
model-based reasoning in the sciences.

Each week, we anticipate devoting about half of the class time to discussion of
reading and about half to collaborative work aimed at developing an epistemic
project.
Prospective Resources
Why Epistemology Matters for Science (and Math) Education
Duschl, R. (2008). Science education in 3 part harmony: Balancing conceptual,
epistemic and social learning goals. In. J. Green, A. Luke, & G. Kelly, Eds,
Review of Research in Education, V32. (pp Washington, DC: AERA.
Hodson, D. (2008). Towards scientific literacy. A teachers’ guide to the history,
philosophy and sociology of science. Rotterdam: Sense Publishers.
Kelly, G. (2008). Inquiry, activity and epistemic practice. In R. A. Duschl & R. E. Gandy
(Eds.), Teaching scientific inquiry. (pp 97-117). Rotterdam: Sense Publishers.
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Epistemic-Developmental Psychology (Studies of conceptual change)
Chandler, M. (1988). Constructive evolution. Cambridge: Cambridge University Press.
Clement, J. (2006). Thought experiments and imagery in expert protocols. In L.
Magnani, ed., Model-based reasoning in science and engineering. (pp.1-16).
London: King's College Publications.
Clement, J. (1988). Observed methods for generating analogies in scientific problem
solving. Cognitive Science, 12, 563-586.
Clement, J. and Steinberg, M. (2002) Step-wise evolution of models of electric circuits:
A "learning-aloud" case study. Journal of the Learning Sciences 11(4), 389-452.
Piaget, J. (1970). Genetic epistemology. New York: W. W. Norton.
Sandoval, W. A. (2005). Understanding students’ practical epistemologies and their
influence on learning through inquiry. Science Education, 89, 634-656.
Smith, J. P., diSessa, A. A., & Roschelle, J. (1993). Misconceptions reconceived: A
constructivist analysis of knowledge in transition. Journal of the Learning
Sciences, 3(2), 115-163.
Wagner, J. F. (2006). Transfer in pieces. Cognition and Instruction, 24, 1-71.
Designing/Analyzing Epistemically Oriented Instruction
Danish, J. and Enyedy, N. (2007). Remember, We Have to do all the Parts of the Rose:
Negotiated Representational Mediators in a K-1 Science Classroom. Science
Education, 91, 1-35.
Clement, J. and Steinberg, M. (2002) Step-wise evolution of models of electric circuits:
A "learning-aloud" case study. Journal of the Learning Sciences 11(4), 389-452.
diSessa, A. A. (1993). Toward an epistemology of physics. Cognition and Instruction,
10(2&3), 105-225.
Hestenes, D. (1992). Modeling games in the Newtonian world. American Journal of
Physics, 60, 440-454.
Jurow, S., Hall, R., & Ma, J. (2008). Expanding disciplinary expertise of a middle school
mathematics classroom: Re-contextualizing student models in conversations with
visiting specialists. Journal of the Learning Sciences, 17 (3), 338-380.
Lehrer, R., Schauble, L., & Lucas, D. (2008). Supporting development of the
epistemology of inquiry. Cognitive Development, 24, 512-529.
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Lunsford, E., Melear, C. T., Roth, W. M., Perkins, M., & Hickok, L. G. (2007).
Proliferation of inscriptions and transformations among preservice science
teachers engaged in authentic science. Journal of Research in Science Teaching,
44 (4), 538-564.
Lynch, M., & Macbeth, D. (1998). Demonstrating physics lessons. In J. G. Greeno & S.
V. Goldman (eds.), Thinking practices in mathematics and science learning. (pp
269-297). Mahwah, NJ: Lawrence Erlbaum Associates.
Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. New York:
Basic Books.
Sandoval, W. A., & Millwood, K. (2005). The quality of students’ use of evidence in
written scientific explanations. Cognition & Instruction, 23(1), 23-55.
Stevens, R., O’Connor, K., Garrison, L., Jocuns, A., Amos, D. M. (2008). Becoming an
engineer: Toward a three dimensional view of engineering learning. Journal of
Engineering Education, 97 (3),355-368.
Epistemology of Mathematics
Lakatos, I. Proofs and refutations. The logic of mathematical discovery. Cambridge:
Cambridge University Press.
Lakoff, G., & Nunez, R. E. (2000). Where mathematics comes from. How the embodied
mind brings mathematics into being. New York: Basic Books.
Rotman, B. (2000). Mathematics as sign. Writing, imagining, counting. Stanford, CA:
Stanford University Press.
Social Studies of (Scientific) Practice
Giere, R. N. (1988). Explaining science. A cognitive approach. [Chpt 7, Models and
Experiments].
Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606-633.
Goodwin, C. (2000). Practices of color classification. Mind, Culture, and Activity, 7(1 &
2), 19-36.
Knorr Cetina, K. (1999). Epistemic cultures. How the sciences make knowledge.
Cambridge, MA: Harvard University Press.
Latour, B. (1999). Pandora’s hope. Essays on the reality of science studies. Cambridge,
MA: Harvard University Press.
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Philosophy of Science (Historic Analysis)
Bazerman, C. (1988). Shaping written knowledge. The genre and activity of the
experimental article in science. Madison: University of Wisconsin Press.
Brush, S. G. (1989). Prediction and theory evaluation. The case of light bending.
Science, 246, 1124-29.
Daston, L., & Galison, P. (2007). Objectivity. New York: Zone Books.
Dear, P. (2006). The intelligibility of nature. How science makes sense of the world.
Chicago: University of Chicago Press.
Gooding, D. (1990). Experiment and the making of meaning. Human agency in scientific
observation and experiment. Dordrecht: Kluwer Academic Publishers.
Kaiser, D. (2000). Stick-figure realism: Conventions, reification, and the persistence of
Feynman diagrams, 1948-1964. Representations, 70, 49-86.
Kuhn, T. (1996). The structure of scientific revolutions (4th ed.). Chicago: University of
Chicago Press. (1st ed., 1962)
Nersessian, N. J. (2008). Creating scientific concepts. Cambridge, MA: Cambridge
University Press. [Note: A blend of historic and cognitive analyses of modeling]
Pickering, A. (1995). The mangle of practice. Time, agency, and science. Chicago:
University of Chicago Press.
Porter, T. M. (1995). Trust in numbers. The pursuit of objectivity in science and public
life. Princeton, NJ: Princeton University Press.
Shapin, S., & Schaffer, S. (1985). Leviathan and the air-pump. Hobbes, Boyle, and the
experimental life. Princeton, NJ: Princeton University Press.