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Luvsandorj 04:53, 6 March 2009 (UTC)Luvsandorj Tsogdov

RECONCEPTUALIZING THE NATURE OF CURRICULUM IN THE LIGHT OF AN INVARIANT THEORY AND SYSTEMS THINKING

By Luvsandorj Tsogdov

Introduction

Curriculum has been considered as one of key terms in a field of education that bears some attributes which are taken into account when the relevance and validity of schooling are judged. In fact, school judgment compels us to question whether curricula are reliably and valuably developed, designed, implemented and evaluated in terms of meeting social and individual confrontations. Thus, to develop, design, implement, and evaluate curriculum so that it meets challenges triggered by time temper, are fundamental problems within its nature. To dealing with such fundamental problems, it is, in turn, needed to examine the definitiveness of the nature of curriculum. As a matter of fact, there are diverse definitions of curriculum produced by a great deal of effort that aims to determine its definitiveness. Even though every definition has some contributions to reveal an essential attributes of the nature of curriculum, it is, however, recognized that there is no single definition to determine succinctly the nature of curriculum. In order to reveal the comprehensiveness in the nature of curriculum, it is intended to review the literature addressing the identification of the nature of curriculum.

The characteristics of the nature of curriculum are diverse. Its diversity is manifested itself in various definitions with different perspectives. As a matter of fact, it holds five major characteristics, namely, systematic, documentary, experiential, disciplinary and investigative. Its systematic characteristics are highlighted in systems’ perspective to consider curriculum whereas documentary one is raised in the managerial and behavioral perspectives to describe its nature Likewise, its experiential, disciplinary and investigative properties are recognized in such viewpoints that favor respectively some features of curriculum nature associated with experiences, disciplines and investigations.

Those perspectives are worthwhile in terms of revealing some characteristics of the nature of curriculum. However, it is arguable that the capacities of such perspectives to endeavor to penetrate into the nature of curriculum are limited to reach a succinct and lucid definition of curriculum. Thus, it is needed to seek a new insight and approach which can function compatibly and consistently to identify and define the nature of curriculum. The applications of Invariant theory (Jean & James 1971) and System’s theory and analysis (Checkland 1981) into the nature of curriculum bring considerable implications on defining curriculum itself. In fact, curriculum is systematic. What is more, it is also subjected to change in order to meet new challenges triggered by social-economic and environmental changes. Thus, it is reasonable to question whether any particular curriculum is systematically developed so that it can meet all possible challenges derived from all possible changes. The response to this question generated by both invariant theory and system’s thinking is that such curricula is produced as long as it comprises a complete set of its attributes or characteristics that are invariable during any curriculum changes. Such invariable attributes or characteristics of the nature of curriculum might be called as curriculum invariants of curriculum changes whereas curriculum itself is defined or identified as a science that aims to find curriculum invariants and build up a complete system of them. This is regarded as one possible perspective to put forward debates and discussion regarding the identification of the nature curriculum. The identification of the nature of curriculum underpinned by the theories of invariant and system is compatible to other ones derived from any other perspectives in such extent to which curriculum attributes are judged in terms of invariant of curriculum changes. For instance, it is supported by such approach that highlights that curriculum is a field of study. The reason behind it is that study in a field of curriculum probably seeks invariable attributes in the nature of curriculum. What is more, curriculum-as-experiential perspective might be also agreed upon this identification of the nature of curriculum as long as some experiences are regarded as curriculum invariants of curriculum changes. Therefore, such identification of the nature of curriculum that mainly features invariant attributes or characteristics is likely to be contestable in terms of theoretical and practical contributions towards curriculum development. Its theoretical benefits are likely to be determined by its inclusiveness. It is meant that this definition and identification of the nature of curriculum underpinned by theories of system and invariant includes potentially the rest of curriculum definitions to some extent. At the same time, it might compel curricularists to judge themselves practically by asking whether curricula have been developed so that they contain curriculum invariants during changes.

The Nature of Curriculum and its Comprehensiveness The nature of curriculum bears various characteristics or attributes that can not easily recognized and manifested themselves in one single definition. In referring to The International Encyclopedia of Curriculum, it is pointed out that curriculum is a massive, comprehensive, ill-defined field and  there is no single definition, and so there is no single line of inquiry (Lewy 1991). As a matter of fact, there are various definitions of curriculum that are differed from each other with underpinned particular perspectives. Having taken into account specific points aroused from curriculum definitions, it can be remarkably noted that the nature of curriculum has documentary, disciplinary, experiential, systematic, investigative characteristics. At the same time, it is, however, questionable how to translate such diverse definitions emphasizing different characteristics of the nature of curriculum into developing particular curricula in practice. The response to this question is uncertain because diverse definitions with different perspectives can not simultaneously work together. Thus, it is needed to seek an alternative perspective that can underlie the inclusive identification of the nature of curriculum which takes into account all possible characteristics of the nature of curriculum.

The nature of curriculum bears multiple attributes that ought to be taken into consideration when particular curricula are developed. In reference to the International Encyclopedia of Curriculum (Lewy 1991, p.15), it can be seen that there are nine definitions of curriculum that offer different identifications which are ranged from subject matter through a plan to a system. Those definitions are divided into five major categories in terms of perspectives or basic views such as curriculum as a plan (Tyler & Taba, cited in Orstein & Hunkins 1988); curriculum as subject matter (Webster’s New Twentieth century Dictionary of English language 1978); curriculum as dealing with experiences of learners (Dewey 1938); curriculum as a system (Eash, cited in Lewy 1991); curriculum as a field of study (Orstein & Hunkins 1988). In fact, such five major definitions given to curriculum highlight five different attributes in its nature. The definition stated as curriculum as a plan emphasizes the documentary characteristics of curriculum whereas curriculum-as-subject matter-definition brings its disciplinary attributes. Moreover, the definition that identifies curriculum as dealing with experiences of learners, contributes towards revealing the experiential attributes in the nature of curriculum while other two indicates respectively its systematic and investigative characteristics. Thus, taken together such essences of different viewpoints on curriculum, it is remarkably noted that the nature of curriculum bears documentary, disciplinary, experiential, systematic and investigative characteristics. The recognition of such characteristics of the nature of curriculum is useful to increase our awareness of the nature of curriculum in both theoretical and practical senses. However, the definitions addressing different specifications also bring difficulties and conflicts in terms of their consistencies and compatibilities when curricula are developed, designed, realized and evaluated in practice. Therefore, it is needed to generate an alternative perspective that underlies the holistic and inclusive identification of the nature curriculum.

The Identification of the Nature of Curriculum in the Light of Invariant Theory and System’s Approach System’s theory and thinking seems to be applicable to touch upon the nature of curriculum. It is because it bears systematic characteristics that underlie its some definitions. In fact, recognizing systematic attributes, Eash (1991) argues that curriculum is as system that consists of five widely agreed upon dimensions or components: framework of assumptions about the learner and society; aims and objectives; content or subject matter with its selection, cope, and sequence; modes of transaction, for example, methodology and learning environments; and evaluation. What is more, it is also referred that curriculum can be considered as a system for dealing with people and processes, or organization of personnel and procedures (Orstein & Hunkins 1988, pp.6-9). Thus, as a system, the nature of curriculum is likely to be justified within systems’ theory and thinking. Accordingly, the considerable questions such as how it is  structured (organized), i.e. what its constituent parts (entities, units) connected together which form its whole, are   and  how those  conform  to a set of intrinsic laws, which determine  its nature, and theirs parts, how it is structuring (developing), i.e. how its  no staticness (adaptableness) is recognized,  whereby new material is constantly  processed by  and through it, and how its self – regulating is  constructed,  are  consequently  asked in the light of theories of  structure and system.

Apart from systems’ theory, Invariant theory is likely to be applicable for ensuring the consistency and relevancy of curriculum development. Broadly speaking, it is questioned how best curriculum fits to new challenges led by social changes. Referring that curriculum is a system as indicated above, this question is also formulated as such: Is curriculum system structured or/and structuring so that it contains self-regulating mechanism? The response to this question generated by Invariant theory is that such structuring and structure of curriculum will be constructed as long as it comprises a complete set of its attributes or characteristics that are invariable during any curriculum changes. Such invariable attributes or characteristics of the nature of curriculum might be called as curriculum invariants of curriculum changes whereas curriculum itself is defined or identified as a science that aims to find curriculum invariants and build up a complete system of the curriculum invariants.

Such an identification of the nature of curriculum is underpinned by threefold premise. One is that a set of all curriculum changes including all possible social-economical-technological-cultural innovations, reforms and transformations for a closed action named as a composition of two changes can represent a group structure. In fact, the nature of curriculum in association with the composition of changes contains the properties and relationships between its constituent parts (entities or units or components) which meet the requirement of a formal group in mathematics due to the properties of curriculum changes such as: -	An observer is not able to observe at least two phenomena simultaneously (Lorentz, et al 1952) that is to say, in order to investigate the phenomena ,one uses the cognitive ways which are interpretable by mathematical action generally sounded as like  composition -	A composition of two changes is also a change in a broad sense. -	Aforementioned actions for a set of all possible changes, might meet the properties of formal axioms of group structure at least in a hermeneutic sense. The next premise is that since a set of curriculum changes can shape a group, the nature of curriculum holds particular attributes or characteristics which might be invariable for all possible curriculum changes. The last one is that it is sensitized that there is a science that aims to find out curriculum invariant and build up a complete systems of all curriculum invariants. This might be called as curriculogy or simply just curriculum. Having taken aforementioned ideas together here, it is finally suggested that curriculum is a science that studies curriculum invariants during curriculum change.

The conception towards the identification and definition of the nature of curriculum generated in the light of Invariant theory and Systems’ thinking brings to us an alternative insight and thought to tackle the practical and theoretical issues in a field of curriculum. For instance, let us see how the relevancy and consistency issues of curriculum are alternatively interpreted under this conception. In fact, it is problematic to construct curricula so that it meets the requirements and needs triggered by social development. In practice, curricularists are often challenged to reach and judge the curriculum relevancy and consistency because of its subtlety caused by various understandings about the nature of curriculum. However, in the light of curriculum invariant-orientated conception, the relevancies and consistencies of particular curricula are mostly likely to be measured by the degree of the completeness of its curriculum invariants. That is meant that curriculum relevancies and consistencies might be justified by a number of curriculum invariants. Therefore, it is importantly asked how to find out curriculum invariants.

How curricular invariants are found out. As a matter of fact, there is no single way to indicate curriculum invariants. However, it is suggested that nature of the ways, methods  and procedures  to find out  curricular invariants  is so broad  and varietal as to be  broadly orientated by all cognitive methods, procedures, and  ways  including from  classic cognitive methods - deductive and  inductive; analytic and synthetic; abstract and  empirical, to meta-orientative and descriptive ways  such as systems analysis, structural and  hermeneutic technique and invariant thinking. Now, take a simple example that makes sense out of what invariant is and how it is recognized to some extent. Problem: Many handshakes are exchanged at a big international congress. We call a person an odd person if he has exchanged an odd number of handshakes. Otherwise, he will be called an even person. Show that, at any moment, there is an even number of odd persons (Engel 1998, problem no 32). Solution: We partition the participants into the set E of even persons and the set O of odd persons. We observe, that, during the hand shaking  ceremony , the set  O  can not  change  its  parity. Indeed, if two odd persons shake  hands, O  decreases  by  2,  and ,if  an even  and an odd persons shake hands , O  does not change. In the other words, the parity of the set O is invariant during the action named by handshake. Therefore, since, initially, the number of odd persons is equal zero the parity of the set is even number at any moment. As indicated in an aforementioned example, the procedure to reach curriculum invariants during curriculum changes might be consisted of two major processes, namely, hypothesizing and examining. At a hypothesizing phase, some attributes of curriculum are sorted out and analyzed whereas at the next phase the invariableness of such attributes or characteristics in the nature of curriculum ought to be examined. Using this broad procedure to reach curriculum invariant, it is argued that cognitive processes of human being should be regarded as a curriculum invariant for curriculum changes. Moreover, it is also suggested that cultural values are another curriculum invariants. It is because cognitive processes as well as cultural values are tended to be invariable during curriculum changes caused by time temper. However, their possibilities to be regarded as curriculum invariants are needed to be precisely verified in further research.

As a whole, the reconceptualization of the nature of curriculum in the light of Invariant theory and System’s theory is theoretically and practically worthwhile in terms of increasing our awareness as well as producing criteria to justify the compatibility and consistency to other exiting perspectives. Its theoretical validity is that it brings to us a holistic and broad identification of the nature of curriculum that is somewhat compatible to other existing perspectives. At the same time, it has practical contributions towards ensuring the relevancy and consistency of particular curricula. However, some further research is needed to increase the preciseness of this alternative conception of the nature of curriculum and to find out certain curriculum invariant as well as to set up a set of a complete system of curriculum invariants.

Conclusion The nature of curriculum bears various attributes that can not be simply manifested in one single definition and identification. In fact, its specific attributes are well recognized within a particular perspective whereby often producing an alternative definition of curriculum. As a matter of fact, in the light of a managerial approach, curriculum is seen as a plan or written document whereby revealing its documentary attributes whereas it is seen as a system through system’s perspective whereby recognizing its systematic characteristics. Likewise, it is also regarded as dealing with learners’ experiences that brings in its experiential characteristics to us. What is more, its disciplinary characteristics are seen in the viewpoint which suggests that curriculum is a subject matter whereas curriculum-as-field of study approach brings in its investigative attributes. Thus, the documentary, experiential, systematic, disciplinary and investigative attributes are touched within existing perspectives towards curriculum nature according to the relevant literature. However, there is not any perspective whereby identifying the nature of curriculum that takes into account its diverse attributes. In turn, this ill-defined circumstance causes unwillingness to judge curriculum relevancy and consistency. Therefore, it is needed to seek alternative perspective whereby producing an alternative identification and definition of curriculum.

Since the nature of curriculum bear systematic characteristics that ought to be subjected to adapt to curriculum changes, Invariant theory along with System’s theory is applicable to touch upon its nature. In terms of a theory of invariant, the nature of curriculum as a system ought to comprise a complete set of its attributes or characteristics that are invariable during any curriculum changes. Thus, such invariable attributes or characteristics of the nature of curriculum might be called as curriculum invariants of curriculum changes whereas curriculum itself is defined or identified as a science that aims to find curriculum invariants and build up a complete system of the curriculum invariants. Furthermore, curriculum invariant, as mentioned above is regarded a key term which plays a considerable role in this conception. Having agreed upon that it is complicated to identify procedures to find out curriculum invariant, it is recommended that a procedure to reach any curriculum invariant often consists of two steps, namely, hypothesizing and verifying. Using such common procedure, it is suggested that cognitive processes as well as cultural values are regarded as curriculum invariants.

The curriculum invariant-based conception is worthwhile in terms of increasing awareness to judge curriculum relevancy and consistency. Under this conception, the degree of the relevancies and consistencies of particular curricula are mostly likely to be measured by the degree of the completeness of its curriculum invariants. More specifically speaking, curriculum relevancies and consistencies might be justified by a number of curriculum invariants. However, we are challenged to identify curriculum invariants of curriculum change. Therefore, further research towards this reconceptualization of the nature of curriculum is strongly needed in order to examine its preciseness.

References Checkland, P1981, Systems Thinking,  Systems  Practice,  John Wiley & Sons Ltd, Chichester, New York, Brisbane, Toronto

Dewey, J 1938, Experience and Education, Macmillan, New York.

Hawkins,T, 1984, The Erlander Programme of Felix Klein: Reflection of its place in the historyof mathematics, Historia mathematics , no 11, p 442 –470.

Eash.M.J 1991, Curriculum Components, in Lewy, A (ed) 1991, The International Encyclopedia of Curriculum, Pregamon  Press, Oxford,  New-York,  Beijing, Tokyo, Toronto, p.67.

Engel, A 1998, Problem- solving strategies, Springer, New York, p.3- 5.

Jean, A, D & James,B,C 1971, Invariant theory (old & new), Academic Press, New York and  London.

Lewy, A (ed) 1991, The International Encyclopedia of Curriculum, Pregamon Press, Oxford, New-York, Beijing, Tokyo, Toronto, p.11

Lorentz, H,A, Einstein, Minkowski, A, Weyl, H 1952, The principle of relativity，Dover Publications, Inc, New York, p.38 –41.

Orstein,A,C & Hunkins, F, P 1988, Curriculum: Foundation, Principle and Issues, Prentice Hall, Engleswood Cliffs, New Jersey, p6.

Webster’s New Twentieth century Dictionary of English language( unabridged, second edition - Deluxe color) 1978, Nouh, Webster, William Collins + World,Publishing Co., Inc, p447.

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