Curriculum Analysis of "Real Analysis "Math Ed 322 In Nepal

1. Introduction

1.1 Background of Study

Curriculum Analysis means unpacks a curriculum into its component parts (e.g. learning, teaching, knowledge, society, resources); evaluates how the parts fit together, say in terms of focus and coherence; checks underlying beliefs and assumptions; and seeks justification for curriculum choices and assumptions. The extent to which education will be able support the process of national strengths of educational planners, managers, teachers, educators, evaluates etc hoping that the program evaluation facilitates all the students, teachers, researchers and interested person to study the Curriculum analysis. It's also helps to analyze the objectives, course content, evaluation system and point out the strong and weak points of the program. Curriculum analysis is not, student assessment, although student data could inform curriculum decisions; teacher appraisal, although teacher performance data could impact on curriculum decisions.

Evaluation is the structured interpretation and giving of meaning to predict or actual impacts of proposals or results. It looks at original objectives, and at what is either predicted or what was accomplished and how it was accomplished. So evaluation can be formative that is taking place during the development of a concept or proposal, project or organization, with the intention of improving the value or effectiveness of the proposal, project, or organization. It can also be assumptive, drawing lessons from a completed action or project or an organization at a later point in time or circumstance.

Curriculum evaluation is especially difficult for two reasons. The first concerns the nature of curriculum. A curriculum is not an object that can be easily seen to exit. It is an abstraction that can only be glimpsed through the analysis of statement of aims, The observation of content actually taught and the assessment of what pupils have learned. two classroom in which the same curriculum is supposedly being implemented may be quite dissimilar when one looked at the what at the teachers and children are doing what is being taught and what is being learned. Any attempt to evaluate a curriculum must somehow deals with its situation in specific nature. The Curriculum is manifested differently at different times and in different places. How can one capture it for evaluation?

The Second reason is, different arises from the social-political content in which educational decisions are made. Curriculum evaluations are ordinary not undertaken out of dispassionate intellectual curiosity; rather they are undertaken because decision must be made. Should this curriculum development project continue government fund to supports its work?

Each Participant in the evaluation process has his perspective on it and each influences the other participant. Curriculum evaluation as to what shall be psychological process because it effects decisions as to what shall be taught to whom. In democratic in the sense that those affective by decisions about and making the decisions.

Any Curriculums evaluation efforts should be preceded by an attempt to clarify the purpose to be served by the evaluation that one should identify the decisions to be made and actions to be taken on the basis of evaluation. A curriculum of the evaluations should not be undertaken simply to legitimate a decision that has already been made on other hand.

In the classroom one sees the uniqueness of the situation and the many factors that can influence teaching and learning. Further one can respect the individual pupil's right to development in the unique way under the influence of a curriculum. In the Ministry of Education or the local authority's offices, however one sees that society requires certain levels of mathematical competences without denying teachers, their right to tailor the curriculum to fit particular circumstances. The right to individual and society must respect and brought in to balance. The effective evaluator is one who sees the multiple respective of the participants in the evaluation process and who is able to reconcile the concern of teachers and administrators.

In this work is directly to the programmer Evaluations of collage level of School Program in particular mathematics curriculum of that level designed by Tribhuvan University, Nepal, on the basis of relevancy of the course, major strikes, challenges and the significant suggestions as well.

Through every people cannot evaluate a programmer from all aspects, I am doing so as the formal students of the perspective courses. In particular, I am intended to the "Real Analysis" (Math Ed. 322) of three year B.Ed. Program, held under T.U. Nepal.

I intended to evaluation this course on the basis of CIPP (Context, Input, Process, and Product) Model of Curriculum evaluation.

In the course Structure of B.Ed. program, it is 800 marks mathematics out of 1500 marks at this level only 600 marks mathematics is compulsory to all the mathematics students and the remaining 200 marks is given elective course in the third pars of this program. Minimum requirement of the level is 35% in theory and 40% in practical course while 33% respectively in proficiency level.

Out of 800 marks 300 marks of math course is in the second parts of three years B.Ed. math program. Teaching Mathematics (Math Ed 391), Real Analysis (Math Ed. 322) and Geometry (Math Ed. 321) are included in this year.  Teaching Mathematics Education in secondary school consists practical and theoretical course and remaining two are theoretical only.

1.2 Objective of the Study

Each and every study has its own objective. The Study is incomplete without objective. It is said that a study having no objectives is a boat without Rudder. The general Objective of this course is to enable the trains to put into practices the theories principles, methods, and techniques, which they have learned in their specialization area.

The intensive study provides the simple way to study, compare and give the suggestion for improvement of the course. It helps to know the scope and limitation of the area.

The main objectives of the intensive study are listed below:

Ø To understand the course of three year B.Ed.

Ø To describe the objective of the mathematics educational program of Bachelor level.

Ø To identify the Strong and Weak Points of the new program.

Ø To comment on the course and give significant suggestions.

Ø By the support of this program evaluation, educational institutes will be able to predict about the achievement of the student so that education institute will be able to construct the future plan

1.3 Scope and limitation of the study

Program evaluation is one of the most important parts of the educational institutes especially in Master Degree level in education because master level education helps to produce one of the qualified, trained, higher level manpower for the country. So the students of M.Ed. Should be able to guide to this level. But it is difficult to Structure and Objective

2. Structure and Objective

2.1 Course Structure of B.Ed. (Mathematics) program.

Academic Year	Course No.	Course Title	Value of Course	Full Marks	Pass Marks	Remarks
First Year	Math Ed. 316	Foundation of Mathematics	Theory	100	35
	Math Ed. 317	Calculus	Theory	100	35
Second Year	Math Ed. 391	Teaching Mathematics	Theory + Practical	80+20	28+8
	Math Ed. 322	Real Analysis	Theory	100	35
	Math Ed. 321	Geometry	Theory	100	35
Third Year	Math Ed. 331	Algebra, Vectors Analysis &  Graphs Theory	Theory	100	35
	Math Ed. 333	Advance Calculus	Theory	100	35	Elective
	Math Ed 334	Inferential Statistics	Theory	100	35	Elective

2.2 National Objective of B.Ed. Program

Ø To produce qualitative higher manpower in education

Ø The Level-wise objective of this level is to produce trained and qualified teacher for secondary level.

Ø To prepare professionally trained and qualified manpower in the field of educational management and supervision.

Ø To ensure optimum quality of the program so that they came opto the students previlicy in the SAARC countries.

Ø  To provided appropriate knowledge skill and attitudes in they are the specialization.

3. Math Ed. 322: Real Analysis

3.1 Introduction

In the nineteenth century the calculus continues to grow through generalizations of its method and consolidation of its foundations. Both of these directions contributed to the development of calculus into what is now called analysis, a large set of topics grouped around two canters called Real Analysis 

and Complex Analysis. It has turned out that the process of calculus-differentiation, integration, Sequence and series.  Real Analysis is branch of mathematics which deals the theory of real number. This also deals  with the problems with their closely connected with their nation of limit and other notions. It an important place in the course in the Bachelor's Degree (Second Year) mathematics Education of Tribhuvan University in Nepal. I am trying any level best to evaluate "Real Analysis" from different angles. Students read this subject in second year of B.Ed. Level. The nature of course is theoretical. It carries 100 marks in the final examination in which students require to secure 35 to be passed.

This course is designed to provide students with the fundamental concepts of real analysis. Its deals rigorously with the a development of the subject which includes the background knowledge of differential and integral calculus. The course focuses the case of real line only. It covers the axiomatic foundation of real numbers, topological framework of real numbers, real sequence, and infinite series of real numbers, limits, continuity, derivability, and Riemann inerrability of real function.

3.2 Objectives

The main objectives of this course are as follows:

Ø To acquaint the students with the axiomatic structure of real number system.

Ø To familiarize the students with the feathers of real sequences and their convergence.

Ø  To enable to the students in understanding the convergence of series.

Ø To help the students develop a deeper understanding of the properties of limits and continuity of functions.

Ø To make the students able in describing the (C, 1) summability of sequence their properties.

Ø To help the students understand the properties of infinite series with arbitrary term, infinite product and the properties of (C. 1) summability of infinite series.

Ø To make the Students able in understanding the properties of continuous functions define on intervals.

Ø To make the students able in understanding the properties of uniform continuity of a function and non-uniform continuity criterion and monotone function.

Ø To acquaint the students with students with the properties of Riemann integrability of function.

3.3 Contents

Objective cannot be obtained without some specific contents. For fulfillment of above objectives following contents are selected.

Unit I: Axiomatic Foundations of Real Numbers

Algebraic Properties of IR, Oder Properties of IR, Supremum and infimum, Archimedean Property, Completeness axiom, Rational and irrational density theorem, Absolute value of real number and its properties.

Unit II: Point Set Topology of Real Line

Neighbourhoods, Open Sets, Interior Points and interior of a set, Limit point of a set, Limit point of a set, Bolzano Weierstrass theorem, Closed sets and closure of a set, Heine-Borel Theorem for compact sets, Contor set; connected sets and their properties.

Unit III: Real Sequence

Convergence of Real sequence, Squeze theorem, Cauchy's First & Cauchy's Second theorem on limit, Theorem of divergence of sequence, Monotones Convergence theorem, Limit superior and limit inferior of a sequence and their results, Bolzano-Weiwrstrass theorem for convergent sequence, Cauchy Convergence criterian for sequence, Summability of Sequence and its result.

Unit IV: Infinite Series and Infinite Products

Infinite series and its convergence, Conditions for its convergence, Cauchy's Criterion, Dirichelet Theorem, Able's Lemma, Different test of convergence of series and their properties, Alternating series, Absoluate convergence and its covergeance, Rearrangement of infinite series, Riemann theorem, Cauchy's conditions for infinite products, Summability of series.

Unit V: Limits and Continuity

Example of Limit of functions, Properties of limits functions, One sides limits, Infinite limits and limit infinity, Theorem of Continuity theorem, Different type of Discontinuity of functions, Combinations of continuous function and composite functions, Bolzano's theorem, Uniform Continuity, Lipschitz condition, Monotone functions.

Unit VI: Derivability

Derivatives, One sides derivatives of a functions a point an examples, Derivability and continuity properties of derivatives, Chain rule, Darboux theorem, Rolle's Theorem, Lagerange's Mean value Theorem, Cauchy's Mean value theorem, Taylor's Theorem and Maclaurin's theorems,, Extreme value theorem necessary condition for local exterma, First derivatives test for extrema, Taylor's Polynomials and its examples, Remainder in Taylor's series, L'Hospotal Rule and other indeterminate form.

Unit VII: Riemann Integral

Lower Darboux sum and upper Darboux sum and relates results, Darboux theorem, Condition of Riemann integrabity, Integrability criterian in term of Riemann sums, Properties of Riemann integral, Properties of integral, Bonnet's mean value theorem, Indefinite integral theorem, Second fundamental theorem of integral calculus, Integration by parts, Change of Variable.

4. Evaluation of course:

This is important job carried out by students teacher. It is not 'easy' and 'hard and fast' method to evaluate/analysis of the course. To evaluate the course I have followed CIIP model.

4.1 Content Evaluation

The course has a good capacity to give the pure mathematical knowledge. It is seemed that the course have been selected to develop the mathematical abstract knowledge. So in the context of Bachelor level student, the course is capable to achieve its objectives.

4.2 Input Evaluation

Evaluation institute can be compared as engineering process. In this metaphor, the school/collage is a factory and education is a production process of pupils and others physical materials enter as raw materials. Among may inputs pupils, physical facilities, curriculum, teachers are the main. Students are from 10+2 of from Proficiency certificate level passed with major math of mathematics education that they are able to admit Bachelor level. About physical falilities, being underdeveloped country, physical facilities may not be adequate in all the institutes.

Our Curriculum has referred two reference books

1. Gupta, S.L. and Nisha Rani(1993), Fundamental Real Analysis: Bikash       Publishing House,Delhi

2. Malik, S.C.(1992), Mathematical Analysis, New Age International,

          Publishers', New Dehhi

So the books are not sufficient. Mainly Nisha Rani's Book is used which is not prescribed. Nowadays some other reference materials have been published by U.N. Panday(Real analysis), S.M. Maskey (Real Analysis) And Bupal Shrestha and Bolanath Bhattarai (Real analysis) in which the trends of selecting the questions of exam is prevalent that they do not have sufficient materials in Real Analysis, however they have tried well. So it must be prescribed a book as note book in Analysis B.Ed. second year.

4.3 Process Evaluation

It is said that "Process is more important than product". Generally in classroom activities, the talk and chalk is used. Most of the students are reguraly attending the class in this course.

Real Analysis consists of total 150 credit hours. Most of teachers complete the course in the limited period. But in some cases the course is not completed because of different things like morning and evening classes, political strikes etc. In brief the process is less satisfactory in the teaching of real analysis (Math Ed322).

4.4 Product Evaluation

In analysis course the evaluation technique of students in their annual examination taken of controller of examination held every year at the end of the session. Within three hours the given questions of this course should be solved, since it is the theoretical course. so it has increased the rotten study then the understanding.

In brief, the result of Real Analysis is not as poor as other math's student's achievement, but it should evaluate the validity and reliability of outputs.

5. Strong Points

The Strong Points of the Real Analysis are as follows:

Ø Analysis the nature of real sequence.

Ø Explain the axiomatic structure of number system.

Ø The sating of the course is based on rigorous development of the Real Analysis.

Ø The content of the course determines the cases of the real line.

Ø The sequential order of the content is applicable.

Ø The contents, sub topics under the contents are specified.

Ø Comparing with two years B.Ed. course it has covered as wide range and depths in subject matter.

Ø It is fully supportable subjects for to the calculus.

Ø The Riemann integral has considered tendencies on it, which can help to make the vision for developing idea about it.

Ø Every topic tries to provide the mathematical proof.

6. Weak Points

Nothing is free from its negative aspect so that Real Analysis is also affected by weakness. The following weakness I have got after analyzing the course.

Ø Time scheme should be revised consulting with subject teacher.

Ø The derivative topic is not scientifically improves then the old two years B.Ed. course.

Ø In the course plan, the prescribed textbook is not given as well as reference books are not sufficient to cover the whole course.

Ø Mainly misprints are in given reference books as well as it is high costly.

Ø Evaluation system of real analysis is very poor.

7. Recommendations

I have suggested the following points here to development better course in the coming year which is as follows:

Ø Time scheme should be revised consulting with subject teacher.

Ø The derivatives topic should be introduced in practical portion of mentioned theorems.

Ø We have to determine prescribed textbooks by the discussion of subject exports and introduce applicable, simple, practicable reference books.

Ø Misprints in the reference book should be removed.

Ø Evaluating system must be semester system, reliable and valid.

Ø Course must be revised time to time.

8. Conclusion

Education is backbone of the country for each and every development sector. To fulfillment the national objectives only the productions is not sufficient without quality. So for the qualified production, teaching without academic calendar, scarcity of textbooks, expensive textbooks and administration should be improved slowly.

Students are going on parroting to get higher number and feet top level officer. So, qualitative education is going downward. The government has made national policies for jog to the unemployed educated with more investment. But only more investment cannot produce more production without fair process. So, far qualitative production the process of the program should fair.

For good production, physical facilities play an important role. Now world is changing in to the computer age but in the context of Nepal students of University level don't know to make data entry. There are no any good books on the library, no comfortable classroom, no laboratory; no enough furniture, no multimedia, which are indispensable to the university in order to reach to goal.

Even the academic calendar is not fixed. There is not any teaching regulation. The teacher and the students both should be forced to obey the rules and regulation. University should not be a political yield and higher education should not be looked as a fashion but a producer of knowledge and obtain citizen of the country. Recommended books should be available in the library ant the university must not be seller of certificate only. It must be the seller of good knowledge. So for the improvement the government, Ministry of education and concerned authorities should think heartily and should pay attention on their above problems and the department administrators should also work as administrator.

Reference

Panday, U.N. (2014): Real Analysis, Cambridge Publication Pvt.Ltd., Kalimati,                      Kathmandu

Guputa S.L. and Rani, Nisa(1993):Fundamental Real Analysis, Vikas     Publishing             House Pvt.Ltd., New Delhi

Bachelor of Education (B.Ed.) in Mathematics Education Curriculum, Faculty                      of Education, T.U

Cooke, R.B.(1997):The History of Mathematics: A Brief Course. New work:     John          Wiley & Sons Inc.