Schema knowledge

A second point has to do with the focus or theme of a schema. Notice the emphasis on actions. This, of course, concurs with the theory developed by Piaget, and again, it is an important observation. Many examples in early works about schemas (or their counterparts, frames and scripts) use objects such as a room (Minsky, 1975) or a story such as a fairy tale (Rumelhart, 1975) or a particular setting such as a restaurant (Schank, 1975). The restriction to these examples suggests incorrectly that actions are not essential to schema knowledge and, in some instances, implies a strict temporal sequence and relatively rigid format. 

Still another thread is experience. Schemas arise from experience. The particular details of any single experience may or may not be part of schema knowledge. Certainly there is the implication that many of the details will fade over time, leaving only broad generalizations to characterize the schema. 

To study the acquisition and use of schema knowledge, we must have a working definition that allows us to observe when such knowledge is present and when it is not. I propose the following ... 

Most structural representations of schemas display them as networks of connected elements, which, of course, opens a wide door of possibilities for the actual form of the elements, the connections, and the networks themselves. Although researchers disagree about some of these issues, they are generally of one mind in adopting the network as the fundamental representation for schema knowledge. 

In constructing a schema, an individual will perforce have available more information than he or she can comfortably process. Consequently, some of the information will receive attention and some will not. That which does will become part of the individual s schema knowledge. That which does not will be ignored. 

A key corollary of the problem-solving requirement for schema development and use is that the individual necessarily does something with schema knowledge. A new schema will not be created or an existing schema will not be activated unless some action is needed. Action does not necessarily mean physical movement. It may just as easily be mental activity. 

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. 

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. 

Two characteristics of the schema have far-reaching effects on instruction. One is the componential nature of knowledge associated with it, and the other is its network structure. The impact of the four components of schema knowledge is that we may create sequences of instructional material to focus on each of them. The influence of the network structure is that we will tend to make many more explicit connections between topics of instruction than we might otherwise. Schema-based instruction looks very different from instruction based on other principles. 

It is useful to consider how schema-based instruction differs from other approaches. One important difference is that schema-based instruction de-emphasizes the quantity of factual bits of information that the student acquires. More is not always better. Factual detail is important, but it is incidental in the development of schema knowledge. It will accrue steadily as part of identification and elaboration knowledge, but it is never the central focus of instruction and learning. The focus is on integrating those facts that are essential rather than on acquiring more and more facts. 

The second example involves a course in chemistry. The professor in this case invites her students to challenge her by finding problems outside class. The students bring the problems to class, and she solves them with no advance preparation. Sometimes she is wrong, sometimes she makes mistakes and has to backtrack, and sometimes she solves the problems easily. The point is that her students learn that problem solving is not a 10-sec affair, that one utilizes all of one s schema knowledge, that one makes plans about how to solve the problem, and that one carries out the plan. 

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. 

Schema knowledge. The first lesson in SPS focuses almost exclusively on identification knowledge. Its purpose is to establish the boundaries of the domain. The student is expected to learn that there are five basic situations, and he or she should acquire some...

Schema knowledge. Most of the second phase of instruction focuses on elaboration knowledge and attempts to tie it to the newly learned identification knowledge. There are important verbal and visual details to be learned, and it is imperative at this point that students acquire both of these aspects of elaboration knowledge.

Schema knowledge. The instruction in this set of lessons assists the student in developing essential planning knowledge. Given the presence of more than one situation in a single problem, the student must acquire the necessary knowledge for selecting which one...

SPS spends quite a bit of time on the introduction of combination stories and problems. The initial example alone fills six screenfuls of display. Students are unfamiliar with looking at problems as combinations of multiple simple situations, and this explicit instruction is needed if they are to acquire appropriate schema knowledge. 

Schema knowledge. As I have elsewhere noted, we were not very concerned with students acquisition of execution knowledge with respect to computational skills, chiefly because students already have very well developed algorithms for the arithmetic operations. We opted instead to focus our attention on developing students understanding of when and why to select the different operations.

The exercises are designed to allow explicit evaluation of the four components of schema knowledge as described earlier. Some of them require only a single choice from one menu, some contain multiple menus and hence multiple selections, and still others necessitate moving elements around on the screen. 

Of special interest also are the types of knowledge that become incorporated into different schema components. Three salient types that are abundant in most instructional materials are examples, abstract characterizations, and graphic representations. It is worthwhile ascertaining when these are acquired as a result of instruction and how they fit together as part of schema knowledge. 

There are two ways to study connections that individuals develop as part of their schema knowledge. First, we can evaluate these linkages by examining students own statements. Second, we can make predictions about an individual s performance in the presence or absence of specific connections and then compare our predictions with observed performance. Both methods yield valuable information, as I will show. 

In several different ways, we can look at competency. On the one hand, we might try to evaluate the competency with which an individual applies any one of the four schema knowledge components. Thus, we might focus on rapid and accurate recognition, efficient use of mental models, and suitable goal setting. On the... 

An important consideration in an investigation of schema development is the nature of the first pieces of information relevant to the schema that an individual acquires. Judging from the structure of many textbooks and the outlines of many class lessons, we should pay special attention to two kinds of information available in instruction, namely, examples and definitions. It is these types of information that are typically used in instruction, and it is from them that students will begin to develop their schema knowledge. 

Poor understanding and weak schema knowledge are demonstrated in the first episode of Table 8.3. This student evidently felt it necessary to carry out some computation using two values available from the problem, but he obviously did not know which calculation to make - so he tried several variations, presumably hoping to recognize a sensible solution if it appeared. Failing that, he finally opted for help (i.e., the call to ShowMe). 

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