Theoretical issues for instruction

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. 

A point to be highlighted is that students will develop schemas about the subject matter whether instruction takes a schema-based approach or not. Learners will search for structure and relationships. Thus, the questions to be asked about schema-based instruction do not center on whether or not students create schemas. They do. The questions focus instead on the nature of the schemas that are developed. We ask whether the instruction itself can promote more cohesive and better structured schemas than would instruction having another foundation. It is here that the basis set of schemas becomes important, because these lay the groundwork for the instructional design. 

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. 

Much of today s instruction, either explicitly or implicitly, has its organizational roots in learning hierarchies, as put forth many years ago by Robert Gagne (1970). Learning hierarchies have been extraordinarily valuable to us as researchers and teachers because they help us to understand at a very detailed level the many subordinate skills and prerequisites of a task. However, they have less value as models of learning, and they often fail when used as guides for instructional development. 

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Some final comments are needed to qualify the previous analysis. For the experimental observations, it has already been stated that care must be taken to ensure that like materials are compared (although the term like materials is not quite clear). It is also instructive to remember that the different techniques probe the materials over different length scales, and are sensitive to the different properties of the material. The theoretical techniques also differ in their strengths and weaknesses to simulate these complex lattices, and will be more successful in their description of one aspect ofthe problem. However, the most problematic issue is the comparability of even the most identical samples. 

It is often said that group 432 is too symmetric to allow piezoelectricity, in spite of the fact that it lacks a center of inversion. It is instructive to see how this comes about. In 1934 Neumann s principle was complemented by a powerful theorem proven by Hermann (1898-1961), an outstanding theoretical physicist with a passionate interest for symmetry, whose name is today mostly connected with the Hermann-Mau-guin crystallographic notation, internationally adopted since 1930. In the special issue on liquid crystals by ZeitschriftfUr Kristal-lographie in 1931 he also derived the 18 symmetrically different possible states for liquid crystals, which could exist between three-dimensional crystals and isotropic liquids [100]. His theorem from 1934 states [101] that if there is a rotation axis C (of order n), then every tensor of rank rcubic crystals, this means that second rank tensors like the thermal expansion coefficient a, the electrical conductivity Gjj, or the dielectric constant e,y, will be isotropic perpendicular to all four space diagonals that have threefold symme-... 

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