Lehrer (2009)

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Designing to Develop Disciplinary Dispositions: Modeling Natural Systems

The article Designing to Develop Disciplinary Dispositions: Modeling Natural Systems was written by Richard Lehrer and published in American Psychologist in 2009. The article is available from PubMed at http://www.ncbi.nlm.nih.gov/pubmed/19899886.


This article addresses the problem of designing classroom settings where students have the opportunity to generate knowledge in a manner consistent with the epistemic foundations of a discipline. Because classroom settings are complex ecologies, successful design requires a working model of how components of the design—including tasks, inscriptions, material means, and forms of argument—function to promote epistemic development. These ideas are illustrated in an extended program of design research oriented toward introducing children to modeling, a form of knowing characteristic of the natural sciences. The example highlights the considerations that informed the guiding epistemology, the elements of design and their orchestration, and the forms of student learning that resulted.

Outline of Headings

  • Designing for Disciplinary Learning
    • Tasks
    • Inscriptions
    • Material Means
    • Modes and Means of Argument
    • Identity
    • Orchestrating Elements of Pedagogical Design
    • Design Experiments
  • Designing a Science Education
    • Images of Science
      • Science as logic
      • Science as modeling
      • Representational models
    • Designing to Support Children's Modeling
      • Analogical reasoning
      • Teacher professional development
    • Forms of Modeling and Representation That Bootstrap Conceptual Change
      • Entrée to modeling through physical microcosms
  • Discussion


Lehrer begins this article by arguing that supporting valued forms of learning is a design problem (Simon, 1969) and in education the goal is to create an epistemic culture (Knorr Cetina, 1999), or "an arrangement of social, cognitive, and material mechanisms that support disciplinary-distinct ways of knowing" (p. 760). Lehrer proposes a "designer's toolkit" containing basic elements of design and a form of investigation, the design experiment, as means to express and produce "epistemologically oriented learning ecologies" (p. 760).

Disciplinary knowing can be separated into content knowledge and an understanding of how that knowledge is produced, although ways of knowing are associated with forms of practice. Lehrer also acknowledges constructivism (Piaget, 1970) and a "commitment that the structures, forms, and possibly the content of knowledge are determined in major respects by its developmental history" (diSessa, 1995, p. 23). Lehrer suggests that a design approach should be used to support students' encounters with disciplinary knowledge, rather than assume a relationship between a child's capabilities and "affordances or constraints of any pedagogical context" (p. 760). These supports include design elements such as tasks, inscriptions, material means, modes of argument, and student identity in relation to the discipline.

Tasks embody a discipline's goals and frame how students encounter them. Tasks can be long or short, routine practice or inquiry-based, and are shaped by the setting of enactment, including a teacher's transformation of a demanding task to a less demanding one (Stein, Grover, & Henningsen, 1996). Tasks can be judged for the student strategies they are likely to elicit and sequenced to develop particular skills (Rittle-Johnson & Koedinger, 2005). Because disciplinary thinking is distributed over space and material (Goodwin, 1994), we must also consider thinking as mediated by representations (Wertsch, 1998) and situated (Greeno, 1998).
Inscriptions refer to writing and the marks we make (Latour, 1990) to mobilize cognitive and social resources. Inscriptions are scalable and reproducible that preserve as well as edit change by reducing and enhancing information (Lehrer & Schauble, 2002b; Lynch, 1990). The knowledge of a discipline gets expressed through inscriptions and involves disciplined perception (Stevens & Hall, 1998), and some inscriptions, like mathematical notation, allow for new conceptual objects (Goodman, 1976; Thompson, 1992). Learning involves choices between inscriptions and the appropriate contexts for using them (diSessa, 2004).
Material Means
Material means play a larger role in some disciplines, particularly in science where there is a history of debate between knowledge via reasoning versus through experiments and instruments. Lehrer's concern for school science is that "materiality is obscured by providing students with questions to answer, apparatus, and prescribed routines, exemplified by labs. Students are seldom asked to struggle with the material problem of developing conditions or instruments for investigation. Yet, these struggles with the natural world define, constrain, and enhance scientific ways of knowing" (p. 762).
Modes and Means of Argument
Disciplines rely on unique rhetoric (Bazerman, 1988). Mathematical proof, for example, is a form of argument essential to the disciplined but used with difficulty students and, frequently, their teachers (e.g., Hanna, 1995). Sometimes "what counts" as an explanation is a negotiated norm (e.g., Yackel & Cobb, 1996), a condition that supports greater conceptual understanding (Boaler, 2002).
Gee (1999) argued that learning goes beyond content and performance to include "a particular type of who (identity) engaged in a particular type of what (activity)" (Gee, 1999, p. 18). The design of learning environments should consider what it means to participate in the discipline (Gresalfi, 2009) and how to author disciplinary knowledge (Lehrer, 1993).

Using their pedagogical content knowledge (Shulman, 1987), teachers can use the above elements to coordinate the relationship between disciplines and learners (e.g., Lampert, 2001; Seymour & Lehrer, 2006). In some disciplines, such as math (Hill, Rowan, & Ball, 2005) and science (Hammer & van Zee, 2006), pedagogical content knowledge is specialized to the discipline, and an increasing focus is given to the facilitation of disciplinary arguments (Forman, Larreamendy-Joerns, Stein, & Brown, 1998; Staples, 2007) and the value of student responses in that facilitation (O'Connor & Michaels, 1996).

Design experiments (or design studies) are a combination of intervention and investigation coordinated to research development and learning (Brown, 1992; Collins, 1992). Design experiments take an engineering approach "in which there is a serious epistemic analysis of the grounds for knowing in a discipline, along with development of possible genetic pathways for incubating the formation of these ways of knowing" (p. 762). The usefulness of design experiments is debatable (Sloane & Gorard, 2003), but, done well, they can yield information about how the development of knowledge interacts with elements used in design. Instead of being driven by grand theories of learning, design experiments are generally driven by choices made by the designer over multiple iterations of a design cycle, where knowledge gained from one cycle informs the design choices made in the next cycle.

Designing a Science Education

Lehrer describes a design for science education that attempts to base children's education "in the invention and revision of models" (p. 763) of natural systems. This work includes design at two levels: the level of the student, and the level of the teacher who engages students in modeling. To define modeling, Lehrer differentiates between science as logic and science as modeling (Lehrer & Schauble, 2006b), where science as logic reflects a more traditional view such as Inhelder & Piaget's (1958) description of science as skills and heuristics for hypothetical-deductive reasoning. Rooted in logical positivism (Carnap, 1967; Hempel, 1952; Mach, 1898/1942), this logical view of science is believed to be generalizable (Schunn & Anderson, 1999) and is recommended by some to be taught via direct instruction (Klahr & Nigam, 2004) or in experiments focused on maintaining control of variables (Dean & Kuhn, 2007).

Science as modeling is rooted in refutations of positivism (Duschl & Grandy, 2008; Kuhn, 1962) and proposes that scientists invent and revise models to connect theory and the world (Giere, 1988; Hesse, 1962). Modeling may be central to laboratory tasks (e.g., Clement, 1988; Gentner & Gentner, 1983), historical studies (Gooding, 1990; Nersessian, 2008), or ethnography (Dunbar, 1998; Nersessian, Kurz-Milcke, Newsletter, & Davies, 2003) that generates idealizations of a working system in context.

While model-based approaches to science education existed (e.g. Hestenes, 1992; Lesh & Doerr, 1998; White & Frederiksen, 1998), Lehrer wished to focus on modeling practices with younger learners whose scientific participation was just emerging. Because modeling involves comparisons of representations to the world, Lehrer leveraged research on childrens' analogial reasoning (Gentner & Toupin, 1986), thinking not only about models might be accessible to children, but which may best be generated and revised by the children themselves. Lehrer's professional development around modeling (Lehrer & Schauble, 2000, 2005) focused on (a) arranging activity and opportunities for students to question and model a natural system and (b) the investigation of student thinking as students proposed, tested, and revised their models. The products of this professional development (e.g., Lehrer & Curtis, 2000; Lehrer & Schauble, 2002a; Lucas, Broderick, Lehrer, & Bohanan, 2005), combined with cooperation with school administrators, fostered a professional community (Gamoran, Anderson, Quiroz, Secada, Williams, & Ashmann, 2003) to support students' use of models.

Lehrer's use of modeling with students initially focused on models that had some literal similarity (Grosslight, Unger, Jay, & Smith, 1991) to the natural system, then transitioned towards models that focused more on the relations to the system and reflected the function of a phenomena instead of extraneous features (Lehrer, Carpenter, Schauble, & Putz, 2000; Penner, Giles, Lehrer, & Schauble, 1997). Other models attempt to recreate an environment on a smaller scale (Lehrer, Schauble, & Lucas, 2008). Modeling often includes both individual and collective student work, with attempts to associate models to inquiry in the context of experience, centering epistemology in practice (Sandoval, 2005). When students represent natural phenomena with models, the model is not just a recording, but also a representation of selections and interpretations. Students' use of mathematical inscriptions were particularly useful, as they transport across systems and enlarge the conceptual field in what Latour (1999) called circulating reference.

For example, students modeling plant growth (Lehrer, Schauble, Carpenter, & Penner, 2000) initially drew simple sketches of the plants, while later plant sketches were annotated with labels indicating height at various points in time. A later model illustrated plant growth with a graph, with different rates of growth identified between various points in time. Students measuring a bacteria population fit an exponential curve to model growth, then had to revise their model as the bacteria population slowed due to limited resources. The mathematical structure allowed for conjecturing and experimenting (by increasing the nutrient level to the bacteria, for example), and supported students' thinking about both the organisms and population of organisms. Students also considered matters of distribution and chance in relation to population growth (Lehrer & Schauble, 2004) and made inquiries not only about the natural system, but about factors that cause change seen in their models.

The example Lehrer provides shows a different kind of science, one that studies natural systems using different methods of investigation (Lehrer & Schauble, 2006a) using both physical and representation models. Physical models can amplify certain phenomena and draws attention to why things observed and measured, unlike traditional science lab experiments (Schauble, Glaser, Duschl, Schulze, & John, 1995). Representational models encourage students to redescribe natural phenomena and promote conceptual growth. Representational models inscribe phenomena in ways that can be transported to other contexts, with mathematical inscriptions being particularly powerful. Together, physical models and representational models compliment each other (Nersessian, 2008), and teachers can use them to give students opportunities to engage in disciplinary learning.


Lehrer, R. (2009). Designing to develop disciplinary dispositions: Modeling natural systems. American Psychologist, 64(8), 759–71. doi:10.1037/0003-066X.64.8.759
author = {Lehrer, Richard},
doi = {10.1037/0003-066X.64.8.759},
journal = {American Psychologist},
keywords = {epistemology,inscription,instructional design,learning ecology,modeling},
month = nov,
number = {8},
pages = {759--71},
pmid = {19899886},
title = {{Designing to develop disciplinary dispositions: Modeling natural systems}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19899886},
volume = {64},
year = {2009}