Catálogo de publicaciones - libros

As described in Chapter 5, a finite automaton specifies a system by means of a set of states and a transition function. The arguments of the transition function are the state and event. We can speak about an actual state. The transition function assigns a state to an actual state. The assigned state is a next state while the actual state can be called the active present state. By repeating the assignments, a sequence of actual states is obtained. In the finite automaton there is always only one state active.

A system can often be broken down into subsystems. If it is required to describe activities of subsystems and their mutual relations, a finite automaton model can be cumbrous because each combination of subsystem states needs a separate state of the finite automaton. Another model known as a Petri net removes that inadequacy. Petri nets are named after a German mathematician C. A. Petri who first proposed a model of that kind (C. A. Petri, 1962). With Petri nets the main idea is to represent states of subsystems separately. Then, the distributed activities of a system can be represented very effectively. Many properties of the DEDS, , synchronization, concurrency, and choices can be well presented and analyzed using Petri nets. They can be used not only for the specification of the DEDS behavior but also the control design. However, Petri nets have various other uses.

The range of terminology used in the field of ‘visualization’ is reviewed and, in the light of evidence that it plays a central role in the conduct of science, it is argued that it should play a correspondingly important role in science education. As all visualization is of, and produces, models, an epistemology and ontology for models as a class of entities is presented. Models can be placed in the public arena by means of a series of ‘modes and sub-modes of representation’. Visualization is central to learning, especially in the sciences, for students have to learn to navigate within and between the modes of representation. It is therefore argued that students -science students’ especially - must become metacognitive in respect of visualization, that they must show what I term ‘metavisual capability’. Without a metavisual capability, students find great difficulty in being able to undertake these demanding tasks. The development of metavisual capability is discussed in both theory and practice. Finally, some approaches to identifying students’ metavisual status are outlined and evaluated. It is concluded that much more research and development is needed in respect of visualization in science education if its importance is to be recognised and its potential realised.

Visualizations are central to many tasks, including instruction, comprehension, and discovery in science. They serve to externalise thought, facilitating memory, information processing, collaboration and other human activities. They use external elements and spatial relations to convey spatial and metaphorically spatial elements and relations. The design of effective visualizations can be improved by insuring that the content and structure of the visualization corresponds to the content and structure of the desired mental representation (Principle of Congruity) and the content and structure of the visualization are readily and correctly perceived and understood (Principle of Apprehension). Visualizations easily convey structure; conveying process or function is more difficult. For conveying process, visualizations are enriched with diagrammatic elements such as lines, bars, and arrows, whose mathematical or abstract properties suggests meanings that are often understood in context. Although animated graphics are widely used to convey process, they are rarely if ever superior to informationally equivalent static graphics. Although animations use change in time to convey change in time, they frequently are too complex to be apprehended. Moreover, because people think of events over time as sequences of discrete steps, animations are not congruent with mental representations. Visualizations, animated or still, should explain, not merely show. Effective visualizations schematize scientific concepts to fit human perception and cognition.

Mental models have been outlined as internal representations of concepts and ideas. They are memory structures that can be used to extrapolate beyond a surface understanding of presented information, to build deeper comprehension of a conceptual domain. Thus, these constructs align with the explicit objectives of science education; instructors want students to understand the underlying principles of scientific theories, to reason logically about those principles, and to be able to apply them in novel settings with new problem sets. In this chapter, I review cognitive and educational psychological research on mental models. Specific attention is given to factors that may facilitate students’ construction of mental models for scientific information. In addition, these factors are related directly to the use (and potential) of visualizations as educational methodologies. The chapter concludes with several challenges for future work on visualizations in science education.

We argue that molecular visualization is a process that includes constructing a mental model. Current qualitative research has shown that participants working on a mental molecular visualization/rotation task invoke components of a mental model. Four of the components are static representations: referents, relations, results, and rules/syntax. The fifth component is dynamic: operation. Two examples of operation are visualization and rotation. Participants used the constructed mental models as mental tools to complete the task. This conceptualization of mental model construction constitutes a theory of learning.

This chapter defines visualization as it is used in psychology and education. It delineates the role of visualization research in science education as being primarily concerned with external representations and how to best support students’ while learning with visualizations. In doing so, relevant literature from Cognitive Science is reviewed. Two science education projects, namely, Making Thinking Visible and Modeling Across the Curriculum are then described as exemplars of projects that leverage cognitive theory and technology to support students’ science learning and scientific literacy.

Computer-based visualizations play a profoundly important role in chemistry instruction. In this chapter, we review the role of visualization tools and possible ways in which they may influence thinking about chemistry. There are now several visualization systems available that allow students to manipulate important variables in obtain a solution to a scientific problem. We discuss the fundamental differences between these tools, and we emphasize the use of each within the context of constructivist curricula and pedagogies. We also consider the impact such tools may have on visuo-spatial thinking. We suggest that although visuo-spatial ability may be important in visualization use, its role has at times been overemphasized. We argue for a more nuanced, richer understanding of the many ways in which visuo-spatial reasoning is used in solving chemistry problems. This discussion leads to a set of design principles for the use of visualization tools in teaching chemistry. Finally, we present our work on the Kinemage Authorship Project, a program designed to assist students in understanding spatial structures in complex, biochemical molecules. The Kinemage Authorship Project allows students to construct their own molecular visualizations, and we discuss how this may lead to greater understanding of the spatial properties of molecules. This constructivist program embodies many of the design principles that we present earlier in the chapter.

This chapter examines the role that representations and visualizations can play in the chemical curriculum. Two types of curricular goals are examined: students’ acquisition of important chemical concepts and principles and students’ participation in the investigative practices of chemistry—“students becoming chemists.” Literature in learning theory and research support these two goals and this literature is reviewed. The first goal relates to cognitive theory and the way that representations and visualizations can support student understanding of concepts related to molecular entities and processes that are not otherwise available for direct perception. The second goal relates to situative theory and the role that representations and visualizations play in development of representational competence and the social and physical processes of collaboratively constructing an understanding of chemical processes in the laboratory. We analyze research on computer-based molecular modeling, simulations, and animations from these two perspectives and make recommendations for instruction and future research.

The main issue in this chapter is imagery in physics learning. Three epistemological resources are used to address this issue: Imagery in the history of physics, cognitive science aspects of imagery, and educational research on physics learning with pictorial representations. A double analysis is used. The first analysis is focused on imagery in classical test cases in the history of physics, such as Faraday’s work on magnetism and Einstein’s thought experiments described in the 1905 papers. The categories identified in the first analysis were used for the second: analysis of imagery in naive students’ reasoning. In particular we describe a learning experiment, which examined naive students’ representations of magnetic phenomena, during hands-on activities in the physics laboratory. We show that naive students use imagery in making sense of the physical phenomena; that modes of naive students’ imagery resemble, on several levels cognitive mechanisms identified in physicists’ imagery strategies; and that the product of imagery, pictorial representations, mirror processes of changes in conceptual understanding. We conclude with suggestions and implications for physics learning.

In this chapter we review three studies done at the University of Massachusetts which have implications for the role of visualizations in learning. We then identify common themes in these studies and their implications for instructional design. We describe two studies of model-based and imagerybased strategies for teaching conceptual understanding in science. To investigate these issues we have conducted learning studies where students are asked to think aloud while learning from innovative science lessons. The goal of these studies is to describe learning processes and teaching strategies that lead to the construction of visualizable models in science. A third study examines similar processes in scientists thinking aloud about an explanation problem. The studies develop observable indicators for the presence of imagery and use them to support a theory of how imagery is being used. A common theme across the studies is that dynamic imagery from one context could be transferred to a new model being constructed for a new context. In some cases new models can be grounded on runnable prior knowledge schemas (e.g. physical intuitions) that can generate dynamic imagery. We suspect that developing students’ runnable mental models in this way provides a deeper level of conceptual understanding. Describing expert novice similarities in terms of hidden nonformal reasoning processes and the use of intuitive knowledge structures allows us to build a map of the conceptual terrain in students that should have important implications for instructional design.