Archive for the ‘Stochastic resonance’ Category

Feminist Diffractions, Stochastic Resonance, and Education, Revisited

May 25, 2015

Lehrer (2015) offers an insightful commentary on Saxe et al’s (2015) recent article in Human Development that prompts some observations.

Two areas for questions and comments come to mind. The first has to do with construing the development and revision of new ways of understanding as contested, which implicitly aligns with Latour’s (1987, pp. 89, 93) sense of the way new constructs are subjected to tests of strength. Haraway (1996) makes an important point in her critique of what she sees as the overly masculinist metaphors of heroic competition and (perhaps not so) sublimated violence in these contests. Her sense of “feminist diffractions” stops short of what I have in mind, but opens the door to an alternative approach to what Lehrer calls the “close coupling of definitions with the development and revision of new concepts and ways of understanding.”

Galison (1997, pp. 843-844), for instance, seeks a metaphor capable of expressing what happens in the conceptual, practical, and argumentative contests between different communities of scientists (instrumentalist technicians, theoreticians, and experimentalists). He wants a metaphor that does justice to the disunified chaos and disorder one finds in the relationships between these different groups, which paradoxically results in such productive and coherent innovations. He recalls Peirce’s and Wittgenstein’s metaphors of cables and threads that take their strength from being intertwined from smaller wires and bits of fiber but finds these images too mechanical for his purposes. He wants something more akin to amorphous semiconductors or laminated materials that can fail microscopically but hold macroscopically better than more structurally homogenous materials.

Berg and Timmermans (2000, pp. 55-56) make a similar observation in their study of the constitution of universalities in medical fields:

“In order for a statistical logistics to enhance precise decision making, it has to incorporate imprecision; in order to be universal, it has to carefully select its locales. … Paradoxically, then, the increased stability and reach of this network was not due to more (precise) instructions: the protocol’s logistics could thrive only by parasitically drawing upon its own disorder.”

The general problem is taken up by Ricoeur (1992, p. 289), who raises the notion of “universals in context or of potential or inchoate universals” that embody the paradox in which

“on the one hand, one must maintain the universal claim attached to a few values where the universal and the historical intersect, and on the other hand, one must submit this claim to discussion, not on a formal level, but on the level of the convictions incorporated in concrete forms of life.”

To repeat another theme that comes up again and again in this blog, this kind of noise-induced order sounds like the phenomenon of stochastic resonance (Fisher, 1992, 2011). The importance of stochastic resonance is that it opens up a way to connect the phenomena of emergent understanding with measurement, both at the local individual and general systemic levels.

This is the crux of some very important issues in the philosophy of science and in philosophy generally. Haraway (1996, pp. 439-440), for instance, points out that “embedded relationality is the prophylaxis for both relativism and transcendence.” And Golinski (2012, p. 35) similarly says, “Practices of translation, replication, and metrology have taken the place of the universality that used to be assumed as an attribute of singular science.”

A start in the direction of embedded relationality, translation, replication, and metrology in education is apparent, for instance, in work that enables teachers to usefully relate individual student performances to general learning progressions, connecting instructional applications with accountability (Fisher & Wilson, 2015; Lehrer, 2013; Lehrer & Jones, 2014; Wilson, 2004). As Lehrer (2015, p. 49) says about the Saxe et al. work, “Recurrent forms of mathematical practice enabled the authors to create compelling trajectories of collective activity and learning over time while preserving the contributions of individual development.”

The second of the two topics I’d like to address comes up here in the closing paragraph of his short commentary, where Lehrer says a “hoped-for future innovation would make it possible to visualize individual and collective trajectories simultaneously.” Though future improvements can certainlty be expected, visualizations of individual and collective trajectories for growth in reading are already being recognized in both educational and metrological contexts (Stenner, Swartz, Hanlon, & Emerson, 2012; Stenner & Fisher, 2013, p. 4) for their potential to serve as the media of an embedded relationality capable of undercutting both the relativism of uncontrolled local variation and the universalist pretensions often built into accountability programs.

With emerging recognition of the potential Rasch’s stochastic approaches to construct mapping (Bond & Fox, 2007; Wilson, 2005) offer in the way of metrological translation networks (Mari & Wilson, 2013; Pendrill, 2014; Pendrill & Fisher, 2015; Fisher & Wilson, 2015; Stenner & Fisher, 2013; Wilson, 2013; Wilson, Mari, Maul, & Torres Irribarra 2015), there are good reasons to expect significant new kinds of progress in fields that rely on assessments and surveys for outcome measurement and management.

References

Berg, M.,& Timmermans, S. (2000). Order and their others: On the constitution of universalities in medical work. Configurations, 8(1), 31-61.

Bond, T., & Fox, C. (2007). Applying the Rasch model: Fundamental measurement in the human sciences, 2d edition. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Fisher, W. P., Jr. (1992). Stochastic resonance and Rasch measurement. Rasch Measurement Transactions, 5(4), 186-187 [http://www.rasch.org/rmt/rmt54k.htm].

Fisher, W. P., Jr. (2011). Stochastic and historical resonances of the unit in physics and psychometrics. Measurement: Interdisciplinary Research & Perspectives, 9, 46-50.

Fisher, W. P., Jr., & Stenner, A. J. (2015). The role of metrology in mobilizing and mediating the language and culture of scientific facts. Journal of Physics Conference Series, 588(012043).

Fisher, W. P., Jr., & Wilson, M. (2015). Building a productive trading zone in educational assessment research and practice. Pensamiento Educativo, in review.

Galison, P. (1997). Image and logic: A material culture of microphysics. Chicago: University of Chicago Press.

Golinski, J. (2012). Is it time to forget science? Reflections on singular science and its history. Osiris, 27(1), 19-36.

Haraway, D. J. (1996). Modest witness: Feminist diffractions in science studies. In P. Galison & D. J. Stump (Eds.), The disunity of science: Boundaries, contexts, and power (pp. 428-441). Stanford, California: Stanford University Press.

Latour, B. (1987). Science in action: How to follow scientists and engineers through society. New York: Harvard University Press.

Lehrer, R. (2013, April 29). (Chair). In A learning progression emerges in a trading zone of professional community and identity. American Educational Research Association, Division C on Learning and Instruction, Section 2b on Learning and Motivation in Social and Cultural Contexts, San Francisco, CA.

Lehrer, R., & Jones, S. (2014, 2 April). Construct maps as boundary objects in the trading zone. In W. P. Fisher Jr. (Chair), Session 3-A: Rating Scales and Partial Credit, Theory and Applied. International Objective Measurement Workshop, Philadelphia, PA.

Lehrer, R. (2015). Designing for development: Commentary on Saxe, de Kirby, Kang, Le and Schneider. Human Development, 58(1), 45-49.

Mari, L., & Wilson, M. (2013). A gentle introduction to Rasch measurement models for metrologists. Journal of Physics Conference Series, 459(1), http://iopscience.iop.org/1742-6596/459/1/012002/pdf/1742-6596_459_1_012002.pdf.

Pendrill, L. (2014). Man as a measurement instrument [Special Feature]. NCSLi Measure: The Journal of Measurement Science, 9(4), 22-33.

Pendrill, L., & Fisher, W. P., Jr. (2015). Counting and quantification: Comparing psychometric and metrological perspectives on visual perceptions of number. Measurement, 71, 46-55.

Ricoeur, P. (1992). Oneself as another. Chicago, Illinois: University of Chicago Press.

Saxe, G. B., de Kirby, K., Kang, B., Le, M., & Schneider, A. (2015). Studying cognition through time in a classroom community: The interplay between “everyday” and “scientific” concepts. Human Development, 58(1), 5-44.

Stenner, A. J., & Fisher, W. P., Jr. (2013). Metrological traceability in the social sciences: A model from reading measurement. Journal of Physics: Conference Series, 459(012025), http://iopscience.iop.org/1742-6596/459/1/012025.

Stenner, A. J., Swartz, C., Hanlon, S., & Emerson, C. (2012, February). Personalized learning platforms. Presented at the Pearson Global Research Conference, Fremantle, Western Australia.

Wilson, M. (Ed.). (2004). National Society for the Study of Education Yearbooks. Vol. 103, Part II: Towards coherence between classroom assessment and accountability. Chicago, Illinois: University of Chicago Press.

Wilson, M. (2005). Constructing measures: An item response modeling approach. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Wilson, M. R. (2013). Using the concept of a measurement system to characterize measurement models used in psychometrics. Measurement, 46, 3766-3774.

 

Revisiting the “Glocal” integration of universals and historical context

April 11, 2014

Integrated considerations of the universal and the local, the pure ideal parameters and the messy concrete observations, seem ever more ubiquitous in my reading lately. For instance, Ricoeur (1992, p. 289) takes up the problem of human rights imperfectly realized as a product of Western Europe’s cultural history that has nonetheless been adopted by nearly every country in the world. Ricoeur raises the notion of “universals in context or of potential or inchoate universals” that embody the paradox in which

“on the one hand, one must maintain the universal claim attached to a few values where the universal and the historical intersect, and on the other hand, one must submit this claim to discussion, not on a formal level, but on the level of the convictions incorporated in concrete forms of life.”

I could hardly come up with a better description of Rasch measurement theory and practice myself. Any given Rasch model data analysis provides many times more individual-level qualitative statistics on the concrete, substantive observations than on the global quantitative measures. The whole point of graphical displays of measurement information in kidmaps (Chien, Wang, Wang, & Lin, 2009; Masters, 1994), Wright maps (Wilson, 2011), construct maps and self-scoring forms (Best, 2008; Linacre, 1997), etc. is precisely to integrate concrete events as they happened with the abstract ideal of a shared measurement dimension.

It is such a shame that there are so few people thinking about these issues aware of the practical value of the state of the art in measurement, and who include all of the various implications of multifaceted, multilevel, and multi-uni-dimensional modeling, fit assessment, equating, construct mapping, standard setting, etc. in their critiques.

The problem falls squarely in the domain of recent work on the coproduction of social, scientific, and economic orders (such as Hutchins 2010, 2012; Nersessian, 2012). Systems of standards, from languages to metric units to dollars, prethink the world for us and simplify a lot of complex work. But then we’re stuck at the level of conceptual, social, economic, and scientific complexity implied by those standards, unless we can create new forms of social organization integrating more domains. Those who don’t know anything about the available tools can’t get any analytic traction, those who know about the tools but don’t connect with the practitioners can’t get any applied traction (see Wilson’s Psychometric Society Presidential Address on this; Wilson, 2013), analysts and practitioners who form alliances but fail to include accountants or administrators may lack financial or organizational traction, etc. etc.

There’s a real need to focus on the formation of alliances across domains of practice, building out the implications of Callon’s (1995, p. 58) observation that “”translation networks weave a socionature.” In other words, standards are translated into the languages of different levels and kinds of practice to the extent that people become so thoroughly habituated to them that they succumb to the illusion that the objects of interest are inherently natural in self-evident ways. (My 2014 IOMW talk took this up, though there wasn’t a lot of time for details.)

Those who are studying these networks have come to important insights that set the stage for better measurement and metrology for human, social, and natural capital. For instance, in a study of universalities in medicine, Berg and Timmermans (2000, pp. 55, 56) note:

“In order for a statistical logistics to enhance precise decision making, it has to incorporate imprecision; in order to be universal, it has to carefully select its locales. The parasite cannot be killed off slowly by gradually increasing the scope of the Order. Rather, an Order can thrive only when it nourishes its parasite—so that it can be nourished by it.”

“Paradoxically, then, the increased stability and reach of this network was not due to more (precise) instructions: the protocol’s logistics could thrive only by parasitically drawing upon its own disorder.”

Though Berg and Timmermans show no awareness at all of probabilistic and additive conjoint measurement theory and practice, their description of how a statistical logistics has to work to enhance precise decision making is right on target. This phenomenon of noise-induced order is a kind of social stochastic resonance (Fisher, 1992, 2011b) that provides another direction in which explanations of Rasch measurement’s potential role in establishing new metrological standards (Fisher, 2009, 2011a) have to be taken.

Berg, M., & Timmermans, S. (2000). Order and their others: On the constitution of universalities in medical work. Configurations, 8(1), 31-61.

Best, W. R. (2008). A construct map that Ben Wright would relish. Rasch Measurement Transactions, 22(3), 1169-70 [http://www.rasch.org/rmt/rmt223a.htm].

Callon, M. (1995). Four models for the dynamics of science. In S. Jasanoff, G. E. Markle, J. C. Petersen & T. Pinch (Eds.), Handbook of science and technology studies (pp. 29-63). Thousand Oaks, California: Sage Publications.

Chien, T.-W., Wang, W.-C., Wang, H.-Y., & Lin, H.-J. (2009). Online assessment of patients’ views on hospital performances using Rasch model’s KIDMAP diagram. BMC Health Services Research, 9, 135 [10.1186/1472-6963-9-135 or http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2727503/%5D.

Fisher, W. P., Jr. (1992, Spring). Stochastic resonance and Rasch measurement. Rasch Measurement Transactions, 5(4), 186-187 [http://www.rasch.org/rmt/rmt54k.htm].

Fisher, W. P., Jr. (2009, November). Invariance and traceability for measures of human, social, and natural capital: Theory and application. Measurement, 42(9), 1278-1287.

Fisher, W. P., Jr. (2011a). Bringing human, social, and natural capital to life: Practical consequences and opportunities. In N. Brown, B. Duckor, K. Draney & M. Wilson (Eds.), Advances in Rasch Measurement, Vol. 2 (pp. 1-27). Maple Grove, MN: JAM Press.

Fisher, W. P., Jr. (2011b). Stochastic and historical resonances of the unit in physics and psychometrics. Measurement: Interdisciplinary Research & Perspectives, 9, 46-50.

Hutchins, E. (2010). Cognitive ecology. Topics in Cognitive Science, 2, 705-715.

Hutchins, E. (2012). Concepts in practice as sources of order. Mind, Culture, and Activity, 19, 314-323.

Linacre, J. M. (1997). Instantaneous measurement and diagnosis. Physical Medicine and Rehabilitation State of the Art Reviews, 11(2), 315-324 [http://www.rasch.org/memo60.htm].

Masters, G. N. (1994). KIDMAP – a history. Rasch Measurement Transactions, 8(2), 366 [http://www.rasch.org/rmt/rmt82k.htm].

Nersessian, N. J. (2012). Engineering concepts: The interplay between concept formation and modeling practices in bioengineering sciences. Mind, Culture, and Activity, 19, 222-239.

Wilson, M. R. (2011). Some notes on the term: “Wright Map.” Rasch Measurement Transactions, 25(3), 1331 [http://www.rasch.org/rmt/rmt253.pdf].

Wilson, M. (2013, April). Seeking a balance between the statistical and scientific elements in psychometrics. Psychometrika, 78(2), 211-236.