Prioritizing Purposes: Two American History Teachers' Choices Among Subject Matter and Classroom-Related Purposes

This study explores how two American history teachers - one novice and one experienced – make in-the-moment choices among their history subject matter and classroom-related purposes during the teaching of an American history unit. Using classroom observations, lesson artifacts, student work products, and deep, retrospective interviews with the teachers as they watched videos of their teaching, this study maps out in detail the teachers’ purposes, both within and across different lesson activity structures. This study finds that the novice and the experienced teacher navigated among their purposes differently from each other, and that the characteristics of each teacher’s purposes navigation aligned with student outcomes in that teacher’s class. The novice teacher acted more like a juggler, with visible, reactive navigation among each purpose operational throughout his teaching; student outcomes in his class were similarly fragmented and discrete. The experienced teacher presented more like an orchestra conductor, interweaving his purposes and anticipating the navigation decisions that would create a more seamless whole; student outcomes in his class were aligned with his holistic navigation of purposes. Findings from this study have important implications for education research and teacher practice, including the relationship between teachers’ navigation among purposes and desired student outcomes, the integral role of classroom-related purposes interwoven with history subject matter purposes in teachers’ decision-making, and the differences in purposes navigation between a novice and an experienced history teacher.

Self-Organizing Map Neural Architectures Based on Limit Cycle Attractors

Recent efforts to develop large-scale neural architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason is that most conventional SOMs use a static encoding representation: Each input is typically represented by the fixed activation of a single node in the map layer. This not only carries information in an inefficient and unreliable way that impedes building robust multi-SOM neural architectures, but it is also inconsistent with rhythmic oscillations in biological neural networks. Here I develop and study an alternative encoding scheme that instead uses limit cycle attractors of multi-focal activity patterns to represent input patterns/sequences. Such a fundamental change in representation raises several questions: Can this be done effectively and reliably? If so, will map formation still occur? What properties would limit cycle SOMs exhibit? Could multiple such SOMs interact effectively? Could robust architectures based on such SOMs be built for practical applications? The principal results of examining these questions are as follows. First, conditions are established for limit cycle attractors to emerge in a SOM through self-organization when encoding both static and temporal sequence inputs. It is found that under appropriate conditions a set of learned limit cycles are stable, unique, and preserve input relationships. In spite of the continually changing activity in a limit cycle SOM, map formation continues to occur reliably. Next, associations between limit cycles in different SOMs are learned. It is shown that limit cycles in one SOM can be successfully retrieved by another SOM’s limit cycle activity. Control timings can be set quite arbitrarily during both training and activation. Importantly, the learned associations generalize to new inputs that have never been seen during training. Finally, a complete neural architecture based on multiple limit cycle SOMs is presented for robotic arm control. This architecture combines open-loop and closed-loop methods to achieve high accuracy and fast movements through smooth trajectories. The architecture is robust in that disrupting or damaging the system in a variety of ways does not completely destroy the system. I conclude that limit cycle SOMs have great potentials for use in constructing robust neural architectures.