Learning from Frontier Experiences
Occasionally people can solve problems that on prior reflection they would have judged beyond their capacity. Such are frontier problems, and solving them provides frontier experiences. We propose to investigate learning from frontier experiences by studies in cognitive modelling and machine learning. A priori, the three primary types of frontier experiences are those derived from solutions depending on boundary conditions (accidental solutions), on the interaction of multiple agencies contributing simultaneously to a solution (interactive solutions), and on shifts of the problem representation (frame-shifting solutions). Our proposed research will try to distinguish between these three types of solutions and focus on learning through mechanisms involved in the latter two. In earlier work (Lawler and Selfridge, 1985; Lawler, 1987), we developed an alternative to this classical compositional model, one based on the elaboration and refinement of imitated actions.
Multi-Schema Modelling
We will use for guidance both compositional and imitated action models in constructing a system for multi-schema modelling (MSM). The principle to govern MSM is that significant learning can occur when a secondary scheme of representation provides internal explanations for the unanticipated success of a primary representation in a frontier experience (Lawler '87); this secondary scheme can then be invoked to achieve a new level of performance on problems of the same class. Such a principle appears effective in human learning. Our research will explore the extent to which it can prove productive in cognitive modelling and machine learning also.
Related Work
If our attempt to understand and model ways in which knowledge, embodied externally in people and artifacts, becomes internalized, the work has affinity for Vygotsky's central concerns. To the extent that significant learning takes place from internalized reflection, the work is Piagetian at the core. With the modelling community, the work derives from the classical tradition of compositional modelling (through Selfridge), but moves through imitated action models in a direction similar to exhaustive state-space exploration more nearly in the CMU paradigm. In contrast with SOAR, whose single learning mechanism is chunking within a simple but monolithic memory organization, multi-schema modelling depends on variety in basic representations of knowledge and their interactions as a primary component of learning. Given that the primary motor of significant learning is a surprising success in problem solving, the work derives directly from Lawler's psychological studies. But it does so in a control framework inspired by Sussman's HACKER model (Sussman 1972) which dependsd on bug manifestations, a kind of surprise, to initiate learning. It also works within an epistemological framework that is indebted to Mitchell's establishing the power of interior explanations as a mechanism for generating learning.
Value
Learning through interaction is a primary means of internalizing knowledge that exists as part of the physical world or the culture. We need to develop comprehensible mechanistic models of such processes that are complex enough not to demean that very human intelligence they are meant to represent. If people learn from frontier experiences, we should strive to build fully comprehensible models with similar capability. Modelling learning with small and simple systems of multiple agents, among which are embodied complementary schemes of representation, is a sensible and achievable effort which will advance this grander goal. The importance to education of interacting multiple representations is beginning to gain recognition within the Mathematics Education community (Kaput, 1988; Lawler 1989). Functioning multi-schema models would clarify that discussion.
To the extent that groups of these simple models share schemes of representation, they could be taken to model families of knowledge structures developed in a common mode of sensory perception and motor activity. Lawler (1987) argued that such internal organizations of modally related knowledge provide a system which could permit the cycle of cognitive development we often observe in human behavior. Such a notion of the modal specificity of experience-memories though still not widely popular, is now even being used to interpret particular deficit patterns in the behavior of brain damaged patients (observation on current work of McCarthy and Warrington, see Rosenfeld, 1989). We expect the results of this research to be more of general scientific value than of immediate engineering application. But it would be strange indeed if better success at modeling and simulating humnan learning did not have very broad and significantly useful consequences in the long run. It is possible to imagine, for example, that interacting systems of learning models will be better able to improve user modelling in intelligent tutoring systems or might even lead to smarter software, but the possibility does not represent any claim we would wish to try to establish within the scope of this effort. Such results do, however, represent a long term objective of this line of research.
References:
Kaput, J. (1988) The Role of Reasoning with Intensive Quantities: Preliminary Analyses. Educational Technology Center, Harvard School of Education.
Lawler, R. W. (1981) The Progressive Construction of Mind. Cognitive Science, Vol 5, pp 1-30.
Lawler, R. W. (1985) Cognitive Organization. Chapter 5 in Computer Experience and Cognitive Development, R. W. Lawler, John Wiley.
Lawler, R. W. and Selfridge, O. G. (1985) Strategy Learning Through Interaction. In Proceedings of the 7th Annual Conference of the Cognitive Science Society.
Lawler, R. W. (1987) Coadaptation and the Development of Cognitive Structures. In Advances in Artificial intelligence, DuBoulay, Hoog, and Steels, (Eds.) North Holland. (Reprinted papers from the 1986 European Conference on Artificial Intelligence.)
Mitchell, T. M, P. Utgoff, and R. Banerji (1983) Learning by Experimentation: Acquiring andf Refining Problem Solving Heuristics. In Machine Learning, Michaelski, Mitchell, and Carbonell (eds). Tioga Press. Palo Alto.
Rosenfeld, A. (1989) p.26 in the March issue of Psychology Today.
Selfridge, O.G. and Selfridge, M. (1984) How Children Learn to Count: A Computer Model. Unpublished to date.
Sussman, G. (1972) Skill Acquisition: A Computational Model. Elsevier.
Vygotsky, L.S. (1978) Mind in Society. Eds M. Cole et al. Harvard Press, Cambridge, MA.
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