ESKO MARJOMAA

HOW TO USE CONCEPTUAL SCHEMATA IN E-LEARNING

Abstract

The theoretical background of e-learning lies in social constructivism. It is assumed that students learn in virtual communities by socially constructing knowledge. What does this actually mean is that students aim at knowledge shared by the virtual community they are involved in. For the scientific community, the best touch stone to make sure that the students have adopted relevant information would be the conceptual models created by students. Conceptual modelling may be characterised as the description of information systems on the meta-level, where conceptual processes, model constructions, and knowledge representations play an essential role. In this context,"information systems" may be any kinds of organism or organisation that handles information. We may say that the function, or even the essence, of social constructivism is conceptual modelling. But the question is: "How is it possible for the students to yield new conceptual models of already existing information systems?

"The answer has to be searched in mental infrastructures which form an intermediate level of organisation between the mental and neural levels.

An extra interesting problem would be to study how the so-called spatial representations are made up of the e-learning material. The solution can be sought by considering the construction of conceptual schemata, or "physical instances of conceptual models", used to reorganise the learning material. It seems that spatial representations form the essence of mental representations that, in turn, are just parts of the conceptual models which can be represented in the form of conceptual schemata.

1. The Research Problem

The basic idea in the conception of knowledge construction is that new knowledge is based onthe previous knowledge. From this it follows that in the evaluation of the adaptation of new knowledge it is difficult to clarify whether the kinds of structural changes have occurred in the learner's conceptual system, that would show that the learner has really adapted to the new knowledge. The interpretation of students' essays is always subjective, and the comparison of different essays is not always reasonable: how can one ever be sure that in the conceptual system of the learner there have happened desirable changes and that the evaluation would be as fair as possible? This question will be elaborated by searching an answer to the proper research problem. How to utilise the construction of conceptual schemata in the evaluation of E-learning?

2. Learning in Virtual Environments

Individual and group learning essentially differ in one respect: individuals learn to know something, but groups of individuals learn to do something together, and more exactly, they learn to form entirely new concepts, or they outline already subsisting concepts that are previously unknown to some of them. The theoretical background of E-learning lies in social constructivism. It is assumed that students learn in virtual communities by socially constructing knowledge. What this actually means is that students aim at knowledge shared by the virtual community they are involved in. For the scientific community, the best touchstone to make sure that the students have adopted relevant information would be the conceptual models created by students. Conceptual modelling may be characterised as the description of information systems on the meta-level, where conceptual processes, model constructions, and knowledge representations play an essential role. In this context, "information systems" may be any kinds of organism or organisation that handles with information. We may say that the function, or even the essence, of social constructivism is conceptual modelling.

But the question is: "How is it possible for the students to yield new conceptual models of already existing information systems?" The answer has to be searched in mental infrastructures which form an intermediate level of organisation between the mental and neural levels.

Another interesting problem would be the study of how the so-called spatial representations occur in E-learning material. This would certainly involve the construction of conceptual schemata, or "physical instances of conceptual models", used to reorganise the learning material. It seems that spatial representations form the essence of mental representations that, in turn, are just parts of the conceptual models which can be represented in the form of conceptual schemata.

The terms "schema" and "schemata" were apparently introduced into psychology by Bartlett(1932), in his study of memory. Bartlett got the term from the neurologist Henry Head who had used it to describe a person's conception of their body or the relation of their body to the world. According to Davis & Tall (2000), Bartlett's notion of schema was picked up by Skemp (1962,1971), and then Rumelhart (1975) also resurrected Bartlett's idea and terminology, once again in the study of memory. Minsky (1975) introduced his idea of "frames" and Schank (1975) the idea of "scripts", both of which are similar to Bartlett's schemata. Davis' (1984) influential book on cognitive science methods in mathematics learning leant heavily on the idea of schemes. As Davis & Tall (2000)notify, it is fair to say that whilst the term scheme has been used in mathematics education (see, for instance, Davis, 1984; Dubinsky, 1992; Cottrill et al., 1996) there have not been many attempts to define more precisely what might constitute a scheme.

3. What are Concepts?

There are myriads of conceptions of what concepts are. In this paper we consider them from a ramified constructivist conceptualist's point of view, i. e., we consider concepts as being productsof human logical thinking. There are two main traditions concerning the existence of concepts, namely, the entity 2 theories of concepts and the dispositional theories of concepts. If they are entities, they are either sensible, mental entities such as innate ideas, images, thoughts, conceptions, etc., or supersensible entities such as universals, meanings, abstract objects, etc. (Palomäki 1994: 53.) We often model the world through language. In natural languages the most central words havebeen classified as nouns, adjectives, pronouns, and verbs. From nouns we can derive proper names, which stand for singular terms and refer to singular things. Out of other nouns, adjectives, and verbs we can form predicates and relations. Pronouns can be seen as variables. Using this strategy, fragments of ordinary language can be translated into second-order logic. (Compare Palomäki 1994: 25.)

Traditionally there have been three general types of attitude towards the problem what concepts are: nominalism, realism, and conceptualism. Roughly, for an example, concerning the existence of "redness", nominalists tend to think that there are red things, such as red balls, red houses, red sunsets, but against realists, they claim that there is no such a thing as "redness". Conceptualists, on the other hand, say that red balls, red houses, red sunsets, and "redness" are just products of the human mind, existing in some 'non-material world'.

Palomäki (1994: 31 ff.) distinguishes three types of conceptualism: constructive conceptualism, ramified constructive conceptualism, and holistic conceptualism. He states that conceptualism is a 3 theory based on socio-biology, dealing with the human capacity for systematic concept-formation. ”As capacities, or cognitive structures based upon capacities, concepts are neither mental images nor ideas in the sense of particular mental occurrences. That is, concepts are not individuals but, rather, unsaturated cognitive structures. The saturation of a concept results in a mental event, and if explicitly expressed, in a speech act as well; but the concept itself is neither the mental nor the speech act (as an event), but rather that which accounts for the predictable or referential nature of that act."The main thing that differentiates the three types of conceptualism is the interpretation of the nature of the human capacity to systematically form concepts. "One important feature of all forms of conceptualism is the assumption that concept-formation proceeds through developmental stages of increasing structural complexity, where the later stages contain reconstructions of the earlier.

These reconstructions are brought about by what Piaget has called'a process of reflective abstraction'. This process consists of the projection of previously constructed concepts onto a new plane of thought, where they are reorganized in accordance with the closure conditions of new laws of concept-formation characteristic of the stage in question."(Palomäki 1994: 36-37.)If, as Peirce (1931-60) says, concepts are just products of logical reflection, the question arises "What is the process of producing concepts like?" Or, "How can one form or create entirely new concepts?" In this respect, it is important to notify the feature most concepts have, namely, "family resemblance" (Familienähnlichkeit, Wittgenstein 1953): "And for instance the kinds of number form a family in the same way.

Why do we call something a "number"? Well, perhaps because ithas a direct relationship with several things that have hitherto been called number; and this can be said to give it an indirect relationship to other things we call the same name. And we extendour concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some single fibre runs through its whole length, but in the overlapping of many fibres.

4. How do concept processing systems create new concepts?

Whewell (1847) discussed the formation and use of new technical terms in science. Accordingto him, scientists should aim at exact, accurate and adequate concepts, but he also says that according to the basic principle concerning scientific terminology, the terms should be constructed and taken into use so that they can help us to simply and clearly express true general sentences. In this principle, there are the following four different goals of scientific concept forming:

(1) simplicity,

(2) clarity,

(3) generality,

and

(4) truth.

On the basis of this we may say that the ultimate criterion of scientific-concept formation is theoretical fruitfulness. What is a meta model? A meta model is a loose collection of different kinds of so-called model concepts that facilitate our construction of conceptual schemata of the objects of our interest, i. e., the UoD's. Some examples of such model concepts are: type, entity, flow, process, event, state.

One useful meta model is the following one (see Figure). The central idea of the figure is to give the reader a hint of a possible answer to the question, what concepts are and where do they subsist: Concepts are private and they are stored in peoples' central nervous systems. What makes them to be in a way common is the fact that peoples' central nervous systems are very similar to each other. Figure.

A sample meta schema of a thing, of a term, and of a concept. In Figure, the processing of concepts is illustrated by an expression "DOG" (and its"connotation" and "denotation"), but the reader may think that many other kinds of expressions also are allowable there, such as, for instance, "HUND", "wuff-wuff" etc. It is also possible to apply the scheme to "sentences", "propositions", and "states of affairs". On the basis of the figure we may say that the proper process of creating a new concept has been inserted between the concept and a set of different mental representations of the concept (or, different mental representations of an expression referring to an individual that belongs to the class of the things the extension of which is the concept).5. What is the Use of this Research? This research will be an essential part of a larger international project on the evaluation of e-learning on the basis of conceptual schemata created by the students. Special attention will be paid to methods that could be used in the exploration of social knowledge construction in e-learning. It seems that to apply mind mapping and conceptual schemata construction techniques in group work would offer best practices within this area. It also seems that the evaluation of conceptual schemata supports the outlining of both aspects of the teaching-learning-process:

(1) Did the teacher manage in teaching how to dissociate relevant from irrelevant things?

(2) Did the student learn how to dissociate relevant from irrelevant things?

Acknowledment

Thanks to G. J. Dalenoort, Pirkko Hyvönen, and Jaana Lahti for thoughtful comments on aprevious version of this paper.

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