The Possibilities and Ways to Improve the Culture Sensitiveness

The Possibilities and Ways to Improve the Culture Sensitiveness

Of the Quality Standards of School Education in Mongolia

Abstract

Referring to the relevant literature, it is known that the dimensionality of the quality of education is more culturally and contextually recognized. Thus, it compels us to question how many dimensions it has in Mongolian contexts and how to identify its cultural dimensions that can function to measure student’s culture acquisition.  In fact, the question regarding a number of the dimensions of education quality has been investigated to some extent especially in international arena whereas the second one has been, however, neglected so far because of its complexity and complicatedness.  As a matter of fact, we have been practically challenged by measuring the degree of students’ culture acquisition and socialization as well as their morality.  The reason behind it is that such educational standards that are able to judge the quality of teaching and learning in terms of measuring students’ culture acquisition, yet measuring their students’ academic performance,  have not been designed yet. Consequently, it is reasonably questioned how to improve the degree of culture sensitiveness of the quality standards of education in Mongolia.

In response to this question, this study aims to examine the possibilities and ways to improve the culture sensitiveness of the quality standards of school education in Mongolia.  Under this purpose, it is intended to identify the set of properties or characters of cultural aspects of school education which can shape cultural measurements into the quality standards of school education whereby measuring students’ culture acquisition.  In accordance with the research aim, this study is also intended to examine whether cultural contents and values in school education hold such characters or properties that can shape cultural constituencies and dimensions of the quality of education and whether the quality of school education in Mongolia be standardized so that students’ culture acquisitions are sensitively measured.

Using mainly qualitative research methods, namely survey with open-ended questions, interviewing and document analysis as well as system’s approach, it will set up cultural measurements into the quality standards of school education in Mongolia whereby measuring students’ culture acquisition, especially social and moral culture acquisition. In doing so, the degree of culture sensitiveness of the quality standards of school education in Mongolia in both theoretical and practical senses will be advanced.

 This research is worthwhile in terms of increasing school effectiveness and efficiency in Mongolia through running the quality standards with culture sensitiveness that will affect tremendously to judge students’ culture acquisition.  In addition, it is also  theoretically vital in terms of bringing in ideas and procedures to set up cultural dimensions into educational evaluation and assessment whereby measuring students’ culture acquisition rather than their academic performances.

Introduction

It is mostly acceptable that a primary goal of schooling is to prepare students to work and live in a future society that might be pictured by uncertain features caused by constant changes. Thus, school effectiveness ought to be judged by the degree of the preparedness of students for engaging in future adult life in future society with uncertainties.  As for Mongolia, it is, however, considered controversially. Its controversy is that among some other countries, Mongolia is placed at the top in terms of quantitative indicators of educational performance, namely enrolment rate, the ratio of boys and girls in schools and literacy rate whereas it is ranged at the end in terms of qualitative indicators such as employment rate, quality life, a human development index.  As a matter of fact, the development index of Mongolia in terms of Educational for All is 0.916 whereby listing at the 67th place out of 127 countries (EFA report 2007).  On the other hand, a recent study indicates that there is no big difference between the poor peoples and the non-poor ones in terms of being satisfied with life quality. In fact, a number of people holding higher degree in education constitute more 10 percent of the whole poor population (National Statistics Office 2002).  Those figures prove that school effectiveness and the quality of education are unsatisfactory and irrelevant to our society wherein we have practised the values of democracy and free economic market for the last two decades.  Therefore, it is undoubtedly reasonable to question how to make sure how well our students are prepared for future uncertainties triggered by constant changes. In turn, it leads us to reconsider measurements of the quality of education in the terms of measuring students’ culture acquisition.

In accordance with research findings appeared in relevant literature, it is evidenced that the dimensionality of the quality of education is more culturally and contextually recognized rather than globally and internationally. In fact, it is known that there are the deficiencies of knowledge and experience as well as evidence in setting up cultural measurements into the quality standards of school education whereby measuring students’ culture acquisition.  Under this circumstance, it is consequently, questioned how to determine a cultural dimension of education quality which can function as measurements and/or norms to define, measure and assure the quality of educational services whereby judging the extent to which students are subjected to acquire appropriate cultures by schooling in Mongolia. The need to find the answer to the challenging question within Mongolian contextual reality compels us to conduct this research.

The Statement of the Problem

The study aims to reexamine the possibilities and ways to regard cultural values and contents as measurements or norms of the quality standards of school education in Mongolia.  Accordingly, this research is intended to find answer to such two questions:

1.      Do cultural contents and values in school education hold such characters or properties that can shape cultural constituencies and dimensions of the quality of education?

2.      Does the quality of school education in Mongolia be standardized so that students’ culture acquisitions are sensitively measured?

To respond to the questions, the following tasks will be realized:

1.      Review cultural contents in existing curricula and identify cultural identities and values that are regarded as underpinnings of student preparation for living and working effectively and efficiently in future society with uncertainties

2.      Generate criteria and indicators that are used to select cultural identities and values so that they can encompass cultural constituencies and dimensions of the quality of school education,

3.      Identify such cultural constituencies and dimensions of the quality of education using the indicators and criteria

4.      Set up cultural measurements into the quality standards of school education in Mongolia so that they can function to measure the degree of students’ culture acquisition?

   Theoretical Background

The nature of the quality of education remains debatable yet in terms its constituencies and dimensions. In fact, no single identification that can determine the number of the dimensions of education quality has been founded yet.  However, the quality of education tends to embody the multiple constituencies and dimensions that are highly likely to be recognized culturally and contextually rather than internationally and globally with reference to research findings displayed in current relevant literature.

As far as the research papers focused on the nature of education quality are concerned, it is notable that the quality of education tends to have multi-dimensions. In fact, a number of the dimensions range from 5 to 10 in accordance with current relevant literature.  As Cheng & Tam (1997) pointed out, the quality of school education, to large extent, comprises three broad constituencies, namely, input, process and output ones. Moreover, Taken together diverse definitions recommended by UNESCO (2005) that varied from time to time, it is highly likely to be noted that notions such as lifelong learning, relevance, accessibility and respectfulness to learner’s right, might be weighted up in determining the constituent parts of education quality as well as its dimensionality. At the same time, UNICEF stresses the child-centered approach founded upon child rights to the quality of education that emphasizes equity and relevance to school education (Wilson, cited in EFA Global Monitoring Report, 2005).

As a whole, it is remarkably noted again that the quality of education centers round such culturally-contextually-understood–notions such as lifelong learning, relevance, accessibility and respectfulness of child rights and equity in terms of the sights of the international education bodies and the existing literature. Therefore, it might embrace multiple constituencies and dimensions that are likely to be culturally and contextually determined.

With respect to aforementioned research findings, it is hypothesized that cultural measurement of the quality standard of school education in Mongolia that can function as norms or criteria to judge students’ culture acquisition are likely be culturally and contextually established.

   Delimitations and Limitations

School normative culture as Halliman (2005) pointed out, covers three components such as academics achievements, social culture and moral culture. As a matter of fact, there has been much effort to measure students’ academic achievements at both the national and international levels. Due to such effort, a variety of norms and criteria as well as indicators to assess student performances and evaluate school effectiveness is displayed in different reports. For instance, at the international level, PISA and TIMSS as well as OECD studies brought diverse indicators and criteria that potentially serve norms and criteria in measuring students’ academic achievements. Moreover, at the national level, many countries, for instance, Mongolia, have created a bank of tests that serves as a tool to measure student academic skills in school subjects, namely mathematics and science. However, there are great deficiencies of both effort and evidence towards taking into account student’s culture acquisition as judging the quality of education as well as school effectiveness. For this reason, this research will focus only on the possibilities and ways to measure students’ acquisition of social and moral culture in school education in Mongolia.

Methods and Procedures

In this research, we will utilize mainly qualitative research methods such as surveys with open-ended questions, interviewing and document analysis as well as systematic approach.

In order to review cultural contents in existing curricula and to identify cultural identities and values that ought to deliver students so that they underpin to prepare them for further society in terms of living and working effectively and efficiently, we will conduct two different cross-sectional surveys. One will be a survey with open-ended questions that aims to reveal attitudes and opinions of parents, employers and policy makers towards the interrelationships between students’ culture acquisition and quality measurement of educational services. A number of survey participants of three targeted personnel such as parents, employers and policy makers will be limited by 40 percents of the whole population (approximately 1200 schools). That is to say,    the survey will site approximately 300 out of 1200 schools. For one particular school, 40 percentages of the whole parents of students (on average, 320 parents per school) will comprise a parent sample whereas 40 percentages of employers and policy makers (approximately 40 employers, 10 policy makers) engaging business in the same province or area where the selected schools run educational services, will be regarded as an employer sample. Therefore, 64000 parents, 1200 employers, 400 policy makers will take part in this survey.  

Apart from collecting individual attitudes and opinions about the interdependence between students’ culture and quality of education, we will conduct one-on one interviewing with school principals and methodologists in order to review social and moral norms existing into school education practice. The interviewee will be the principals and methodologists who work at the same schools sited by the previous survey. A number of interviewee will be estimated at about 600-700 personnel.

In addition, we will review and analyze policy documents that bear cultural values and contents in formal school education. Texts reviewed by document analysis will vary from the constitution through governmental regulations to school moral rules and orders in Mongolia.

Data Analysis and Interpretation

After collecting information and text data regarding the interrelationship and interdependence between students’ cultural acquisition and quality measurement through three major channels open-ended question surveys and interviewing as well as document analysis, the  research will utilize the systematic approach and analysis in order to analyze and interpret them whereby identifying the set of characters of cultural constituencies of the quality of education which can shape cultural measurement in quality standards of education whereby measuring the degree of students’ culture acquisition. This analysis and interpretation will be carried out through three phases such as open coding, axial coding and selective coding in accordance with grounded theory research design.

At the phase known as open-coding, we will analyze and group information and data collected by the afore-mentioned three methods into categories using criteria and indicators for being cultural constituencies of the quality of education. As a result, relevant themes bearing the characters or properties of cultural contents and values in school education so that can comprise cultural components of the quality of education will be identified.

At the second phase referred as axial coding, we will identify the main categories or the set of properties of cultural contents and values which will indicate the strong interdependence between students’ culture acquisition and quality measurement in comparison to the rest of the categories. At the end of this identification, we will generate the core properties of cultural values and contents in school education that might underpin cultural dimensions and norms to measure students’ culture acquisition into quality standards of school education. In this phase, we will identify the features that can function as criteria to distinguish cultural measurements from cultural components in terms of setting up new measurements into the quality standards of school education in Mongolia.

In the third phase named as selective coding with reference to the research design of the grounded theory, we will set up cultural measurements or norms into quality standards which functions to measure students’ culture acquisition.

  Expected Outcomes and Discussion

At the end of this research, we will reach following outcomes:

·         Cultural constituencies of the quality of school education embedded into Mongolian contextual reality.

·         Cultural measurements made into the quality standards of school education which functions as norms to measure students’ culture acquisition.

·         Report on current circumstance of cultural contents and values in school education in Mongolia.

The research findings, namely cultural constituencies of the quality of school education along with cultural measurements of the quality standards of school education in Mongolia will be discussed as follows:

 At the end of this research, we will organize the national conference where the representatives of all stakeholders and organizations such teachers, parents, employers, policy makers will be invited to discuss the research findings and its compatibleness as well as consistency.  

Beyond the research conference, we will send the research report along with its findings to the research site where surveys and interviewing has conducted so that research findings will be critically reviewed and discussed by the participants of the research.

After discussing nationwide, we will reflect on the cultural constituencies of the quality of education as well as cultural measurements of the quality standards with regard to critical points and arguments extended by relevant organizations and personnel. As a result of this modification, the research findings will be extended to the policy makers who are in charge of improving the quality standards of school education in Mongolia.

The Significance of the Study

This research will provide the theoretical orientations and practical ways for making cultural measurement into the quality standards of school education in Mongolia whereby measuring students’ culture acquisition. Thus, it will bring a great deal of contributions to improving culture sensitiveness of the quality standards of school education in Mongolia in a practical sense.  Moreover, in a theoretical sense, the expected findings and techniques used to identify and set up cultural measurements in the quality measurements of educational services will be mostly likely to be exchanged at an international arena in terms of assessing students’ culture acquisition.

Further Conclusion and Recommendation

The dimensionality of the quality of education will be recognized culturally and locally. Thus, the establishment of the measurements of the quality standards is highly likely to be tackled in particular context.  Thus, the task to improve the culture sensitiveness of the quality standards of school education in Mongolia will be realized in our contextual features.  One way to improve the degree of culture sensitiveness of the quality standards is to set up cultural measurements into the quality standards of school education. Since culture as many scholars pointed out, is a complicated term the essence of which is not easily expressed in one single definition, studies on both determining cultural constituencies in the quality of education and establishing cultural measurements into the quality standards of school education is mostly related to the real life and practices of schooling in Mongolia. Therefore, the research data collection and analysis as well as interpretation will favor to utilize the qualitative methods such as open-ended question surveys, one-one interviewing and document analysis along with system approach. 

The determination of the cultural constituencies of the quality of education and setting up the cultural measurements into the quality standards of school education in Mongolia will contribute to defining, assuring and measuring not only students’ academic performance but also their culture acquisition and development of sociality and morality. Moreover, the measurement of students’ culture acquisition will facilitate the judgment of school effectiveness and efficiency in terms of how well students are prepared to live and work in future society.

As long as students’ culture acquisition is taken into consideration in terms of the quality measurement of education, it might be recommended that the allocation policy of government budget for running educational system should be reconsidered in terms of providing different, but necessary conditions under which students can acquire different cultures that are equally considered.  It is meant that per-child funding of educational budget should be advanced in terms of its culture sensitiveness with regard to the new requirements of the quality standards bearing cultural measurements.

REFERENCES

Cheng, Y.C. & Tam, W.M 1997, Multi-models of quality in education, Quality Assurance in Education, vol.5, no.1, pp.22-31.

Halliman, T, M 2005 The normative culture of school and student socialization,  cited in Hedge, V, L &Scheneider, B (ed.) The social organization of schooling, Russell Sage Foundation, New York.

Ministry of Education, Culture and Science 2007, EFA Report (draft), Ulaanbaatar, p.6.

National Statistics Office of Mongolia, the World Bank, UNDP 2004, Household Income and Expenditure, Living Standards Measurement Survey: Main Report, 2002-2003, Ulaanbaatar, p.41.

Pigozzi, M 2004, The 10 dimensions of quality in education, research paper presented at the meeting of Resource pack of curriculum development, Tokyo, UNESCO.

UNESCO 2005, EFA Global Monitoring Report, Paris, pp.27-31.   htt://portal.unesco.org/education/en/ev.php-URL_ID.

RECONCEPTUALIZING THE NATURE OF CURRICULUM

RECONCEPTUALIZING THE NATURE OF CURRICULUM

IN THE LIGHT OF AN INVARIANT THEORY AND SYSTEM’S THINKING

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 a 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 which reflects its characteristics holistically and lucidly. Consequently, it is needed to examine what extent the nature of curriculum has been holistically, but intrinsically researched so far.

The characteristics of the nature of curriculum are diverse. Its diversity is manifested itself in various definitions with different perspectives. According to the perspectives towards the nature of curriculum whereby in fact, producing various definitions, it holds five major characteristics, namely, systematic, documentary, experiential, disciplinary and investigative.  Its systematic characteristics are highlighted in systems’ perspective whereas documentary one is raised in managerial and behavioral perspectives. Likewise, 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.  As mentioned before, curriculum is systematic. At the same time, 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 curriculum invariants.  It is likely to be regarded as one possible perspective to put forward debates and discussion regarding the identification of the nature curriculum in a holistic and intrinsic way.

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 consistent to perspectives behind existing definitions.

Curriculum invariant-based identification of curriculum is contestable and/or beneficiary 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 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, in fact, systematic characteristics that underlie its some definitions.  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 also 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  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 curriculum invariants 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 a 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 to some extent 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 simultaneously and holistically.  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 bears 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 the 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.

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.

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

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.

                             

A ‘Tetrahedron Model of the Content of Teacher Education

 A ‘Tetrahedron Model of the Content of Teacher Education and Its Implications for Mathematics Teacher Preparation in Mongolia

Abstract

The aims of this paper are twofold. The first is to build a model of the content of teacher education through such four step procedure: (1) identifying the key attributes of teacher quality while reviewing relevant literature, (2) generating the perceived attributes of an ideal teacher through generalizing and idealizing the key attributes of teacher quality and its properties and (3) dimensionating the content of teacher education through the  perceived underlying attributes of an ideal teacher and  (4) configuring the dimensionated content of teacher education  to a tetrahedron, a three dimensional configuration which embodies  four same boundaries, each of which is identified as an equal lateral triangle. The second is to reconsider the programme of mathematics teacher preparation in the light of the tetrahedron model of the content of teacher education.  

Using a tetrahedron model of the content of teacher education, it can be proposed that there are at least 24 variants to design and restructure the content of teacher education and to organize teacher preparation. One of them presents the current practice of mathematics teacher preparation in Mongolia while the rest of them provide alternative possibilities to redesign and restructure the programmes of mathematics teacher preparation. Based on the findings from a tetrahedron model, some implications emanated from the tetrahedron model- based analysis were provided to improve mathematics teacher education and teacher preparation in Mongolia.

Key words: teacher quality, the attributes of teacher quality, an ideal teacher, an ideal teacher attributes, the content of teacher education, tetrahedron configuration, tetrahedron model of the content of teacher education

Introduction:

Mathematics teacher quality has a great deal of contributions towards improving the quality of mathematics education that in turn affects tremendously education quality. In fact, as for Mongolia, the quality of education is irrelevant.  As a matter of fact, Mongolia is placed at the top in terms of quantitative indicators of educational performance, namely enrolment rate, the ratio of boys and girls in schools and literacy rate whereas it is ranged at the end in terms of qualitative indicators such as employment rate, quality life, a human development index. Moreover, the development index of Mongolia in terms of Educational for All is 0.916 whereby listing at the 67th place out of 127 countries (EFA report 2007). On the other hand, a recent study indicates that there is no big difference between the poor peoples and the non-poor ones in terms of being satisfied with life quality. In fact, a number of people holding higher degree in education constitute more 10 percent of the whole poor (National Statistics Office 2002).  Those figure proved that the quality of education, is unsatisfactory and irrelevant to our society wherein we have practised the values of democracy and free economic market for the last two decades. Thus, we are challenged by improving education quality. By the same token, as a major component of general education, the quality of mathematics education will be judged.

In order to enhancing mathematics teaching quality, we need to examine how accurate teacher candidates are prepared. Stated differently, it is needed to ensure whether teacher candidates are prepared so that they bear such attributes that meet the characteristics of teacher quality. In respond to this question, this paper aims to build an abstract model of the content of teacher education through generalizing and idealizing the main attributes of teacher quality and dimensionating it and then to discuss the possibilities to apply it for enhancing the design and structure of the programs of teacher preparation. 

 In according with such purpose, this paper will be outlined as follows:

What attributes feature teacher quality?

             The key attributes of an ideal teacher generalized the nature of the attributes of  teacher quality

The dimensionality of the content of teacher education

A tetrahedron configuration and its compatibility with the content of teacher education

A tetrahedron model of teacher education and its contributions to increasing our awareness of teacher education and teacher preparation

The Tetrahedron Model of the Content of Teacher Education and its some Implications on Improving Mathematics Teacher Preparation in Mongolia

As a result, this paper will bring up a tetrahedron model of the content of teacher education along with its four major variants to use it in a practice whereby restructuring and redesigning the programs of teacher preparation. In addition, some interpretations and implication emanated from this model into mathematics teacher preparation in Mongolia were discussed.

What attributes feature teacher quality?

Teacher quality is an underlying concept that encompasses comprehensive and dynamic characters and attributes. The nature of comprehensiveness is manifested itself in diverse insights, attempts and understandings proposed by different scholars and agencies, each of which aims, to some extent, to recognize the constituencies of teacher quality. In fact, the multiple and dynamic constituencies of teacher quality tends to be categorized into two groups, namely, personal qualities and professional qualities. As the name suggests, the personal qualities of teacher quality tend to be personal or subjective and therefore, it is highly likely to belong to disposition of a teacher candidate. Yet, the professional ones are highly likely to cover the qualities possibly possessed by teacher candidates through teacher education services, namely teacher in-service and pre-service training. Accordingly, the latter one tends to cover teacher attributes or competencies of pedagogy, didactics and content knowledge. Taken together the various ideas and perspectives on teacher quality appeared in recent papers, it is likely to be generalized that teacher quality are characterized by teacher attributes  in pedagogy, didactics and content knowledge and his or her disposition as well.

According to Hargreaves (1988, cited in Meg 1991), teaching quality is the blend of personality attributes, sound pedagogy and a secure subject match. At the same time, Lamn (1972, 2000, cited in Arnons & Reichel 2007) proposes four aspects of work of good teacher such acculturation, socialization, individualization and disciplinary expertise. Here, personal and social aspects are emphasized in a broad sense.  What is more, a comparative study of policies in ten countries that aimed at improving teacher quality highlighted that teacher quality bears six key characteristics, namely, commitment, love of children, mastery of subject didactics and multiple models of teaching, ability to collaborate with teachers and a capacity of reflection (Hopkin & Stren 1996). The study highlighted the mastery of subject didactics along with other attributes.

 Moreover, with reference to the OECD report of Quality in Teaching (1994, cited in Fredriksson 2004), it is known that teacher quality has five dimensions such as knowledge of substantive areas and content, pedagogic skills, reflection, empathy and managerial competence.  In addition, Arnons & Reichel (2007) categorized the qualities of ideal teacher into two main categories: teacher personality and professional knowledge. Referring to the authors, teacher personality covers teacher general personal qualities such as having a sense of humor, being kind-hearted, calm, fair, optimistic, humane, stubborn and principled and empathetic and loving children whereas professional knowledge consists of subject knowledge, didactic knowledge about both educational methodology and individual pupil.  Hence, it is referentially ascertained that teacher attributes such as loving children, empathy, humor, being kind-hearted and commitment comprises particular constituencies of teacher quality which, are, apparently more personal rather than professional.

Taken together the ideas and arguments focusing on teacher quality and its constituencies, it can be seen that teacher quality embodies two major components, namely personal qualities and professional qualities. The professional qualities tend to cover teacher attributes in pedagogy, didactics and content knowledge whereas the personal qualities pertain to his or her disposition.

The key attributes of an ideal teacher generalized the nature of the attributes of teacher quality

A challenging question emanated from teaching in practice when its quality is judged is whether   teacher candidates are well prepared so that their attributes and competencies meet the features in teacher quality.  Responding to this question is, practically, controversial because the degree of such preparedness of teacher candidates depends upon candidates’ disposition albeit the sameness in programs of teacher education and its implementation. However, this question is ideally answerable as long as the following ideal conditions are provided: (1) all teacher candidates bear satisfactory dispositions that are compatible with possessing teaching profession; (2) the programs of teacher education are designed and implemented so that all teacher candidates possess the key attributes of teacher quality. In turn, such idealization of teacher education and preparation help us perceive the characteristics of a good teacher. 

Under such idealization of teacher education and preparation mentioned above, it can be seen that any teacher candidate after completing the programs of teacher education will become an ideal teacher. In other words, it is perceived that an ideal teacher is characterized by the same attributes that teacher quality is featured.  Hence, it is generalized that an ideal teacher ought to be featured by the four major attributes compatible with teaching profession such as pedagogical competence, didactical competence, content knowledge and teacher disposition.

In order to prepare teacher candidates as good as ideal, the content of teacher education ought to be designed as an amalgam of the key attributes of ideal teachers. In turn, it prompts us to dimensionate the content of teacher education so that the nature of teacher attributes is holistically represented.  This task will be considered in the next portion of this writing.

The dimensionality of the content of teacher education

In mathematics, the dimensionality of any space is dependent upon whether its properties satisfy with the criteria of dimensions. Generally speaking, the main criterion of space dimensionality can be broadly stated that a space will be dimensionated if only it contains a set of special elements in itself whereby any other element can be expressed for its particular operation. If such a particular set contains finite members, a space is labeled as a space with finite dimensions.  For instance, Euclidean plane is a two-dimensional space because there exits a set of two special vectors whereby any other vector is expressed by their linear combinations. What is more, as far as advantages to dimensionate a space are concerned, it is also known that any attributes of a dimensionated space can be perceived as a certain combination of dimensional elements. Returning to Euclidean plane, it can be said that any vector in this space is perceived as a linear combination of two dimension vectors. Keeping in mind a brief description about the dimensionality of a mathematical space and its advantages, we can examine the degree of dimensionality of the content of teacher education in an interpretative sense at least.

The constituencies of the content of teacher education are, practically, diverse, yet theoretically controversial. In fact, its diversity can be seen in different programs that function differently to prepare teachers in different contexts whereas its controversy can be also appeared in contestable views on defining the nature of teacher and teacher education. However, with regards to a challenging question posed as whether teacher candidates are well prepared so that their attributes and competencies meet the features of teacher quality, the content of teacher education might be perceived as a closed configuration that covers key attributes of an ideal teacher and other potential attributes generated by their combinations. In other words, the content of teacher education is regarded as a set of teacher attributes that are, in turn, composed of the key attributes of an ideal teacher and other potential attributes generated by their integrations and combinations. Indeed, this perception about the content of teacher education gives us to sensitize out that if the nature of the content of teacher education encompasses a set of the key attributes in the content of teacher education whereby it’s any attribute can be expressed to certain degree, it can be dimensionated. Accordingly, whether such a set exists is also an important question.  Such two questions will be dealt with below.

As perceived as a closed configuration of a set of teacher attributes, the content of teacher education contains the key attributes of an ideal teacher whereby its other potential attributes might be generated to some extent in terms of dependence or association or implication at least.  At the same, referring to the main criteria of dimensionality of an abstract space, it is proposed that the key attributes of an ideal teacher might be identified as dimensions of the perceived content of teacher education.  Thus, it is implicitly clarified that the content of teacher education has the four main dimensions such as pedagogical competence, didactical competence, content knowledge and teacher disposition.  Hence, it is importantly asked as how configure the content of teacher education through its four dimensions. The next portion will answer this question.

 A tetrahedron configuration and its compatibility with the content of teacher education

As discussed so far, the content of teacher education is perceived as a closed configuration which might be filled with a set of teacher attributes that are generated by its four dimensions such as pedagogical competence, didactical competence, content knowledge and teacher disposition.  In addition, there is no hierarchical rank among such four dimensions. That is to say, each of four dimensions must be equally considered in configuring the content of teacher education.  Taken into consideration aforementioned properties of the content of teacher education and its dimensions, it is conceived that a tetrahedron and its properties can present best the nature of content of teacher education. This conception will be justified as follows.

Now, let us see how the nature of the content of teacher education is configured to a tetrahedron.  If we suppose that one of the four boundaries of a tetrahedron represents one of the four dimensions of the content of teacher education, the tetrahedron itself in terms of its volume depicts the holistic nature of the content of teacher education. Besides, the edges of the tetrahedron represent the partial associations among four dimensions whereas its every vertex indicates a point at which any three of the four attributes intersect.  What is more, the spirit of the ideal teacher that is in turn determined by the dynamic of teacher competence acquisition might be resembled as a central point of a tetrahedron at which its four medians are intersected. 

The contributions of the tetrahedron model of the content of teacher education towards increasing our awareness of teacher education and teacher preparation will discussed in the next portion of this writing.

A tetrahedron model of teacher education and its contributions to increasing our awareness of teacher education and teacher preparation

According to a tetrahedron model of the content of teacher education, it can be seen that there are at least 24 variants or ways (mathematically, 4*3*2=24) to design and restructure the teacher education content and preparation that is in turn categorized into four major models, namely, a pedagogical competence-based tetrahedron, a didactical competence-based tetrahedron, a content knowledge based tetrahedron, and a teacher disposition based tetrahedron.

As far as the pedagogical competence-based tetrahedron model is concerned, it can be expounded that teacher candidates are initially subjected to be trained by the courses that are intended to enable teacher candidates to acquire pedagogical competence. Followed by the pedagogical courses, they will be delicately provided by other courses that are designated to provide them with the rest of teacher competences. The advantage of this kind of teacher preparation should be recognized that teacher candidates will be aware of pedagogical or managerial knowledge and skills priory to acquiring the rest of teacher competences whereas teacher candidates might be disadvantaged by not making known early how much they are challenged by acquiring the content knowledge and didactical competencies.

Apart from the pedagogical competence-based tetrahedron model, the didactical competence -based tetrahedron model will provide us with a different insight into designing the programme for teacher preparation. According to this model, teacher candidates are subjected to acquire firstly particular didactical knowledge and skills. After that, they will possess the rest of the three major competences. The advantage of this model might be recognized that teacher candidates will be acquired particular didactical approaches, theories and best practices so that they will apply them for own teaching and learning. At the same time, they will be disadvantaged by being subjected to tackle with didactical theories and practices priory to acquiring the rest of the teacher competences, in particular, appropriate content knowledge.

With regard to a content knowledge based tetrahedron model, it can be seen that teacher candidates are subjected to possess firstly the content knowledge concerning a particular teaching subject and then they will proceed with handling the rest of the teacher competencies. Seemingly, it will facilitate teacher candidates to handle teacher’s didactical competences whereas it is likely to have some drawbacks to deal with pedagogical competencies because of their attitudes embedded in one particular area.  In fact, this model seems to be a prevailing one in teacher preparation practices.

In according with a teacher disposition-based model, it can be noted that teacher candidates’ attributes will be observed and examined by the criteria of teacher disposition. Then, teacher candidates whose attributes meet teacher disposition criteria will delicately proceed with acquiring the rest of the teaching competencies. The advantages of this model is that the fitness of the attributes of teacher candidates to teaching profession is early examined whereas it might be biased against individuals who has strong interests to become teacher albeit that she or he does bear appropriate attributes of teaching profession.

To sum up, it can be noted that tetrahedron model of the content of teacher education will bring four major insights into designing and restructuring the programme for teacher preparation such as a pedagogical competence-based tetrahedron, a didactical competence-based tetrahedron, a content knowledge based tetrahedron, and a teacher disposition based tetrahedron. Each of them has disadvantages and disadvantages in teacher preparation in practice. However,   at the end of the teacher preparation processes governed by the tetrahedron model, teacher candidates will be ideally perceived to be a teacher who can bear four major teaching competencies that are in turn generalized by teacher quality attributes.

The Tetrahedron Model of the Content of Teacher Education and its some Implications on Improving Mathematics Teacher Preparation in Mongolia

As a result of analyzing the programme of teacher preparation in Mongolia in the light of the tetrahedron model, it can be exposed out that the content for teacher preparation and its designing tends be expounded by a model that is represented as a tetrahedron with the content knowledge base. Referring to the current programs for mathematics teacher preparation in Mongolia (School of Mathematics and Statistics 2000), it is known that teacher candidates are subjected to handle firstly mathematics courses in four terms that are quite separated from mathematics didactics. In fact, at an initial stage of the teacher preparation, there is no difference between student who is intended to be a mathematician and students who become mathematics teachers. In the last terms, teacher candidates are subjected to take courses dealing with didactical issues in mathematics teaching along with managerial matters related with maintaining mathematics classroom. Hence, reminding the characteristics of a content knowledge-based tetrahedron model, we can point out that the mathematics teacher preparation in Mongolia is likely to facilitate teacher candidates to handle the teacher competences of mathematics didactics whereas it is likely to neglect the equal importance of other competencies of mathematics teachers, namely, teaching competence in mathematics didactics, teaching competence in mathematics classroom management or pedagogical competence and teacher disposition in mathematics teaching.

 Keeping the tetrahedron model and its variants in mind, we will bring forth that there will be three other main variants to redesign and restructure the teacher preparation programs in Mongolia, namely, pedagogical competence-based design, didactical competence-based design, content knowledge based design, and teacher disposition based design.

Conclusion

The attributes of teacher quality will be regarded as key factors that we will take into account designing and restructuring the programs of teacher preparation. As a matter of fact, teacher quality comprises multiple constituencies that are divided into personal attributes, professional ones. Indeed, the personal qualities of teacher quality tend to be personal or subjective and therefore, it is highly likely to belong to disposition of a teacher candidate whereas the professional one tends to cover teacher attributes or competencies of pedagogy, didactics and content knowledge. Taken together, it is likely to be generalized that teacher quality are characterized by teacher attributes  in pedagogy, didactics and content knowledge and his or her disposition as well.

Someone who bears the same attributes that teacher quality is characterized, will be called here as an ideal teacher. Accordingly, it is generalized that an ideal teacher ought to be featured by the four major attributes compatible with teaching profession such as pedagogical competence, didactical competence, content knowledge and teacher disposition. In order to prepare teacher candidates as good as ideal, the content of teacher education ought to be designed as an amalgam of the key attributes of ideal teachers.

The content of teacher education is perceived as a closed configuration that might be filled with a set of teacher attributes that are in turn built upon by its four dimensions such as pedagogical competence, didactical competence, content knowledge and teacher disposition.  In addition, there is no hierarchical rank among such four dimensions. That is to say, each of four dimensions must be equally considered in configuring the content of teacher education. Taken into consideration aforementioned properties of the content of teacher education and its dimensions, it is conceived that a tetrahedron and its properties can present best the nature of content of teacher education.

 A tetrahedron model of the content of teacher education suggests at least 24 variants or ways to design and restructure the teacher education content and preparation that is in turn categorized into four major models, namely, a pedagogical competence-based tetrahedron, a didactical competence-based tetrahedron, a content knowledge based tetrahedron, and a teacher disposition based tetrahedron.  Each of such model has own advantages and disadvantages.

The significance of this is model of the content of teacher education is that it represents all possible ways and orientations to design and restructure teacher education content and preparation to meet teacher competences. In this sense, it can be implied to examine and enhance the existing programs for teacher preparation. However, the justification of building this model is needed to examine in the future study.

References

Arnons, S & Reichel, N 2007, ‘Who is the ideal teacher? Am I? Similarity and difference in perception of students of education regarding the qualities of a good teacher and of their own qualities as teachers’, Teachers and Teaching: theory and practice, vol.13, no.5 October 2007, pp.441-464.

Fredricksson,U 2004,  ‘Quality Education: The key role of Teachers’,  Education International Working Paper, no.14, September 2004. 

Hopkins, D & Stern, D 1996, ‘Quality teachers, quality schools: International perspectives and policy implications’, Teaching & Teacher Education, vol.12, pp.501-517, 1996.

Meg, M 1991, ‘Quality in teacher education’, Assessment & Evaluation in Higher Education, vol.16, no.1, April 1991.

Ministry of Education,Culture and Science 2007, EFA Report (draft), Ulaanbaatar, p.6.

National Statistics Office of Mongolia, the World Bank, UNDP 2004, Household Income and Expenditure, Living Standards Measurement Survey: Main Report, 2002-2003, Ulaanbaatar, p.41.

 School of Mathematics and Statistics, The programmes for mathematics teacher preparation, 2000, The University of Education, Ulaabaatar.