Schema theory

The typical effect of mutate and crossover on the progress of the current best candidate structure using a GA is shown in Fig. 4a, whereas Fig. 4b shows the typical progress of the diversity which is defined as the number of bits along the simulated DNA where 0 and 1 both exist in the current population, and therefore has a value from 0 to 3 (where NG=23m ). Notice that the diversity drops unless the mutation move class is used. By using schema theory [30,31] (where candidates with certain sequences of 0 s and l s in a particular section are associated with a so-called schema) it can be shown how the GA can initially improve the quality of the candidate structures so rapidly [ 19]. Interestingly, if one of the bits within the simulated DNA of the entire current population does not correspond to that of the observed structure then it is impossible for the GA using only crossover as its move class to predict the observed structure. If, for example, the first bit for... 

Chapter 2 contains the basics of schema theory as I see it. The definition of a schema is more complex here than in the earlier research described in chapter 1, although as I point out, the current framework encompasses many of the existing usages already described. Chapter 2 is a foundational chapter, because all the experimental studies and modeling that follow in subsequent chapters derive from the theory laid out here. This chapter paints a broad picture of the schema. It has become the norm in psycholog-... 

Together, Bartlett s and Piaget s ideas provide the skeleton of schema theory. It begins to be understandable but does not yet have sufficient substance. Several recent researchers have sought that substance by performing more-detailed empirical investigations about the nature of a schema and by developing sophisticated computer models that simulate schema instantiation. 

In the history of schema research, 1975 was a very good year. A number of schema-related papers appeared in a fairly short period of time, and they have had strong and lasting influence. Three individuals are frequently cited as primary instigators of the resurgence of schema theory Marvin Minsky, Roger Schank, and David Rumelhart. Each represents a unique viewpoint, uses differ-... 

Minsky s theory articulates the components of the frame. An important contribution to the development of schema theory as we understand it today is Minsky s (1975) recognition of anticipatory knowledge in the knowledge structure. Attached to each frame are several kinds of information. Some of this information is about how to use the frame. Some is about what one can expect to happen next. Some is about what to do if these expectations are not confirmed (p. 212). Not only is there a component dealing with anticipation, but there is also knowledge about how to take action, reminiscent of Piaget s theory. 

Minsky approached schema theory from the field of artificial intelligence. A second and somewhat different perspective from the same field comes from Roger Schank. Schank reached his theory about scripts by way of studying how computers can engage in... 

Of the three researchers influencing schema theory in 1975 -Minsky, Schank, and Rumelhart - David Rumelhart has probably contributed the most to our current understanding of schemas. He has written a number of important articles about the nature of schemas, beginning with the one in 1975 and culminating with his work on parallel distributed processing (PDP) in 1986. Whereas Minsky introduced the frame and Schank the script, Rumelhart retained the word schema in his research. However, it takes on a substantially different meaning from that in earlier schema studies. 

Work on educational applications of schema theory is even more sparse than the research on learning. Nonetheless, some important papers have addressed this issue. 

As I pointed out in chapter 1, Marvin Minsky set forth five issues that a schema theory should address (Minsky, 1975). If we construe them as questions, we can ask how the theory outlined here would answer them. 

These five issues provide a useful yardstick against which the theory can be measured repeatedly as it continues to evolve. At this juncture, of course, neither schema theory nor any other cognitive theory is yet sufficiently developed to explicate them fully. However, schema theory does have something to contribute to each of them, and more importantly, it generates hypotheses about these issues that may be empirically tested and that have the potential of contributing to further theoretical advances. 

Then comes theoretical verification. This stage requires both the elaboration of the hypothetical schema structures and the corroboration that they conform to the strictures of general schema theory. One wants to establish that the chunks of knowledge hypothesized to be potential schemas are capable of functioning in the multiple and complex ways that are expected. Here, it is necessary to consider the four components of schema knowledge and how they may be manifested in the newly identified schemas. 

Adopting schema theory as the basis of instruction almost certainly necessitates a complete restructuring of the curriculum. It also raises questions about the nature of learning. In this part and the next, I address these two issues. 

First, I present the theoretical linkages between schema theory and instruction. Chapter 4 contains an extension of schema theory... 

Chapter 5 shows how schema theory can be practically implemented. It gives a detailed description of one example of schema-based instruction, the Story Problem Solver (SPS). SPS is a computer-based system of instruction constructed around schema theory, using the basis set of schemas developed in chapter 3. It provides fundamental instruction enabling students to build schemas. A second computer program, the Problem Solving Environment (PSE), is also described in chapter 5. PSE provides an exploratory environment in which students can practice and utilize their schema knowledge about story problems. 

A key aspect of schema theory, insofar as instruction is concerned, is that schemas organize knowledge stored in memory. Thus, they provide the necessary scaffolding for a domain, and, as such, they will serve as supports for future instruction and learning. It is useful to consider a simplified overview of instruction to see how this works. Essentially, in an instructional situation, stu-... 

An objective of this chapter, and indeed of much of this book, is to illustrate the importance of linking instructional practice and assessment to a theoretical approach. Schema theory provides a new conceptual foundation for the organization of instruction and the subsequent assessment of students learning from it. In this chapter, I discuss some of the theoretical and practical issues involved in using schema-based instruction. In Chapter 5, I describe a functioning instructional system that is schema driven. 

Finally, the structure of the hierarchy itself is at odds with schema theory. The schema is a network of related knowledge, not a branching tree with distinct levels. A great deal more connectivity exists in the schema than in the learning hierarchy, and instruction based on schemas focuses directly on these connections. 

Imagine what instruction looks like under schema theory. First, it is crucial that students get some overall notion of what is in the domain so that they can develop an ability to distinguish the main situations that occur within it. This requires the teacher to intro-... 

An important aspect of Schoenfeld s approach is his demand that strategies be well articulated. If students are to acquire them, the instructor must present them in sufficient detail to allow discrimination and characterization. Again, I would argue that schema theory is being invoked. What Schoenfeld calls for is the creation of schemas based on the situations or events of using each heuristic. 

The Story Problem Solver (SPS) is a computer-implemented program of instruction about arithmetic story problems.1 My research group and I developed SPS as an explicit instructional test of schema theory.2 Its companion, the Problem Solving Environment (PSE), is also a computer-based system, one that provides no additional instruction but that serves instead as a practice arena in which we can evaluate students acquisition of schema knowledge. Both SPS and PSE are written in Lisp and run on Xerox 1186 computer workstations equipped with 19-inch display monitors and three-button optical mice. In this chapter, I first describe SPS and its instructional objectives and then explain the contributions of PSE. 

The schema theory behind the instruction is invisible to the student interacting with SPS. At no time does SPS cite schema formation or use in fact, the word schema never occurs at all. Instead, the instruction focuses on situations as vignettes of daily life and emphasizes the need for the solver to use his or her own understanding of them to solve problems. 

In any system of instruction - particularly if it is computer-based -the critical issues are often the decisions that must be made prior to or in the early stages of development. In the following description of SPS s instruction, I focus on two types of decisions that influenced the shape of the instructional system those having to do with the mechanics of presenting information or recording responses and those having to do with the way that schema theory is incorporated. Whenever possible, both types of decisions were made on the basis of experimental investigations, either research done in my laboratory or published studies by other researchers. 

Part III begins with an overview of some of the important issues in learning, especially with respect to schema theory. Three areas of study are most relevant the type of information that individuals acquire from learning, the way in which the information is retained, and the strength and reliability with which it is used again. Chapter 6 focuses on recent developments in these three areas. 

A second broad question of interest in learning research is how new information becomes intertwined with existing knowledge. Again, a number of research areas have emerged. The one most relevant to schema theory has to do with the organization of longterm memory. 

The scope of schema theory embraces all three of the areas just described. Schemas have a natural place in each of them contexture, memory, and competency. Moreover, schema theory provides the relationships that tie all three together. The research in the following chapters illustrates this point. 

Given the schema theory developed in part I, specific questions about how schemas develop may be constructively addressed. One critical issue about schema formation is the determination of specific knowledge that individuals acquire from schema-based instruction. Typically, instruction will offer several different kinds of information, including visual aids, examples, formulas, general principles, and definitions. To study schema creation and development, we will need to know which pieces of information are encoded by students and in what relation. It is particularly import-... 

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