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Chapter 3

Spatial Distribution, Growth, Medium of Instruction , Infrastructure and Physical Facilities in Primary Schools by Type of Management - A

Comparative Analysis

3.1 Introduction

This section presents spatial distribution and characteristics of schools in terms of year of

establishment of school, growth and medium of instruction. A comparative analysis of

infrastructure and physical facilities by type of school management has been analysed by two

methods, namely, by the method of composite index and by the method of multivariate statistical

graphics—to be specific by Chernoff Faces – a statistical technique to represent k-dimensional

data graphically.). Further this section provides classification of primary schools by similarity of

infrastructure and physical facilities in each type of school management and to find schools

which were different in infrastructure and physical facilities, if any. That is to identify through

faces the schools which showed phenomenal differences -- (i.e. outliers) in each type of school

management. The secondary data is based on enumeration of all the 121 schools1. in Navi

Mumbai.

3.2 Types of Schools in Navi Mumbai - Spread and Clientele

There are three types of primary schools in Navi Mumbai, namely, ZP, NMMC and Private. The

ZP schools are the oldest schools; majority of NMMC schools came into existence in late

nineties and bulk of private schools was established after 1970. The NMMC schools are located

in Thane Taluka; ZP schools are situated in villages in Raigadh area of Navi Mumbai; whereas

private schools are located in all over the city. A few of the private schools are aided or partly

aided and follow the state government educational norms such as curricula, examination system

to maintain the uniformity in the educational standards.

The Private schools are both owned and run by private management. These schools may be run

by religious institutions, charitable trusts, private societies, education foundations etc.

1 Out of the total 243 primary schools in Navi Mumbai, there were only 121 primary schools which had classes from

1st to 7th standard..

Private schools follow state and central board syllabus. Table 3.1 provides percent of schools

(primary + secondary) functioning by type of management and students’ enrolment in each type

of the school.

As may be seen from the Table 3.1, the largest number (64%) of schools and also bulk (85.4%)

of students’ enrolments belonged to the private schools. ZP schools are primary schools. NMMC

and ZP schools together accounted for about one third (36%) of the total number of schools in

the city. Curiously enough, students’ enrolment (14.6%) in both the public schools, i.e., NMMC

and ZP, was too low as compared to students enrolled in private schools. Data clearly showed

preference of parents for private schools in Navi Mumbai.

Table 3.1 Distributions of Schools and Students’ Enrolments by Type of Management

ZP NMMC Private Total School 22% 14% 64% 100%

Enrolment 5.20% 9.40% 85.40% 100% Source: CIDCO (2010), Primary and Secondary Schools in Navi Mumbai

3.3 Spatial Distribution of Schools by Type of Management

3.3.1 Number and Location of Schools by Node/Area and Type of Management

The schools are located in 14 self-contained nodes including 95 villages, two Municipal

Councils and MIDC area2. Figure 3.1 showed that among the planned nodes, Nerul had the

largest percent ( 12.5%) of schools followed by Uran Taluka (11.6%), Vashi (9.7%) and

Airoli (7.2%). NMMC schools are located in first seven nodes and in MIDC area; whereas,

Zilha Parishad schools are found only in Panvel and Uran Talukas. Among the Private

Schools, again the largest number of schools was in Nerul followed by Vashi. These

observations suggest that by and large, the number of schools conform to the pace of

2 Panvel and Uran Talukas include villages, non-nodal areas and two Municipal Councils of Navi Mumbai. The

schools in the villages of respective nodes were included in that node

development of nodes/areas in time domain. For example, the Panvel Taluka was the oldest

area and thus have the highest number of schools.

Figure 3.1: Number of Schools by Location and Type of Management

3.3.2 Households by Mother Tongue

Mother tongue is a person's native language that is, a language learned from birth. Medium

of instruction is a language used in teaching. It may or may not be the official language of the

country or territory. Where the mother tongue or first language of s

the official language, it may be used as the medium of instruction for part or all of schooling.

Bilingual or multilingual education may involve the use of more than one language of

instruction.

Sanpada

Jui-Kamothe

Kalamboli

CBD-Belapur

Kharghar

New Panvel

Ghansoli

Koperkhairne

MIDC

Airoli

Vashi

Uran Taluka

Nerul

Panvel Taluka


thus have the highest number of schools.


3.3.2 Households by Mother Tongue



country or territory. Where the mother tongue or first language of students is different from



1.9%

2.3%

3.0%

3.2%

3.5%

3.7%

5.6%

6.3%

6.3%

7.2%

9.7%

11.6%

12.5%





tudents is different from



23.2%

Perhaps, only very few cities in the world offer education in as many medium of instructions

as Navi Mumbai does. Schools in Navi Mumbai offer primary education in five different

medium of instructions. This is because Navi Mumbai is mainly composed of migratory

populations from Mumbai, neighbouring states and other parts of the country. More than 14

languages were spoken by residents of Navi Mumbai (Table 3.2). However 67% of residents

speak Marathi, 15% Hindi and rest, few significant categories were, Gujarati

(3.3%),Malayalam and Tamil (2%) each speaking.

Table 3.2 Percent of Households by Mother Tongue in Navi Mumbai

Sr. No. Mother Tongue Percent Sr. No. Mother Tongue Percent

1 Marathi 66.7 8 Malayalam 2.4

2 Hindi 14.4 9 Kannada 1.2

3 Gujarati 3.4 10 Telgu 1.3

4 Punjabi 1.7 11 Oriya 0.5

5 Sindhi 0.5 12 Bengali 1.8

6 Urdu 0.9 13 English 0.6

7 Tamil 2.4 14 Any Other 2.2

Source: CIDCO (2011), Socio Economic Profile of Households in Planned Nodes in Navi Mumbai

3.3.3 Medium of Education by Mother Tongue

Table 3.3 reveals that more than 70% students in Navi Mumbai study in English medium

irrespective of their mother tongue. About 72% of Marathi speaking households prefers to

send their children in English medium schools and 27% households in Marathi medium.

Surprisingly north Indians (5%), south Indians(5%), Guajarati (7%) and other households

send their ward to Marathi medium schools, though their mother tongue may be other than

Marathi , they may be born and brought up in Maharashtra and may be staying from

generations. Many of them may be staying for more than 15 years, hence domicile of

Maharashtra state.

Table 3.3 Medium of Instruction of Students by Mother Tongue

Medium of Education (%)

S. No. Mother tongue Marathi English Others

1 Marathi 27 72 1

2 Hindi 8 82 10

3 South Indian Languages 5 93 2

4 North Indian Language 5 94 1

5 Gujarati 7 91 2

6 East Indian Language 3 95 2

7 English 0 100 0

8 Others 9 87 4 Source: CIDCO (2011), Socio Economic Profile of Households in Planned Nodes in Navi Mumbai

Figure 3.2 presented distribution of schools by medium of instruction. To meet the local

demand, the largest number (58%) schools offered Marathi as medium of instruction. All the

ZP and NMMC schools and few of the private schools had Marathi as medium of Instruction.

One third (33%) schools offered English as medium of instruction. Other medium of

instructions were Hindi (5%), Urdu (4.2%), and Gujarati (0.5%) in the schools of Navi

Mumbai.

Figure 3.2: Distribution of Schools by Medium of Instruction

3.3.4 Year of Establishment of Schools

The information available on the year of establishment of the schools suggested

of schools in Navi Mumbai were set

established only after 1970. Setting

decade, 60 new schools were established in different nodes

new schools from previous decade 1970

21.7% growth of schools was recorded. The period 2000

of new schools. In 9 year the number of

2000-2008. The increase in the number of schools in this period was maximum growth rate ever

recorded during the observation period (Figure 3.3).

Year of Establishment of Schools

The information available on the year of establishment of the schools suggested

of schools in Navi Mumbai were set-up before 1950. The schools in planned nodes were

established only after 1970. Setting-up of new schools got accelerated during 1980

decade, 60 new schools were established in different nodes/area registering 14.3% growth of

new schools from previous decade 1970-79. During the next 10 year period i.e. 1990

21.7% growth of schools was recorded. The period 2000 -2008 witnessed a boom in the increase

of new schools. In 9 year the number of schools rose from 21.7% in 1990

2008. The increase in the number of schools in this period was maximum growth rate ever

recorded during the observation period (Figure 3.3).

Marathi

58%

English

33%

Hindi

5%

Gujarati

0.5%

The information available on the year of establishment of the schools suggested that nearly 9%

up before 1950. The schools in planned nodes were

up of new schools got accelerated during 1980-1989. In this

/area registering 14.3% growth of

79. During the next 10 year period i.e. 1990-1999,

2008 witnessed a boom in the increase

schools rose from 21.7% in 1990-1999 to 32.2% by

2008. The increase in the number of schools in this period was maximum growth rate ever

Urdu

4%

Gujarati

0.5%

Figure 3.3: Year of Establishment of Schools

3.4 Construction of Composite Index for Measuring Infrastructure and Physical Facilities

at Primary Schools

An index for measuring quality of school by taking infrastructure and physical facilities was

formulated with a basic idea to identify the inputs which

level in terms of quality of education. The methodology used for the purpose was that of Morris

(1982), who used this method in finding the quality of life of the people in different states of

India and the same was employ

has been adopted here to construct the composite index for measuring the overall quality of

schools as measured through the infrastructure and physical facilities available in primary

schools of Navi Mumbai.

The present study was based on the primary schools from class 1 to class 7

1-7th standard were considered for infrastructure and physical facilities to maintain the

3Navi Mumbai is planned city and developed to attract the migrated population in Navi Mumbai instead of main city Mumbai. The schools are comparatively new and school authorities add one or more standard to their schools each year depending on the requirement. This is the reason primary to 2nd standard, pre primary to 4

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

Before

1950

1950-1959

9.1%6.9%

Figure 3.3: Year of Establishment of Schools

Construction of Composite Index for Measuring Infrastructure and Physical Facilities


formulated with a basic idea to identify the inputs which may maximize the output at school



India and the same was employed to calculate the human development index. The same approach



The present study was based on the primary schools from class 1 to class 7

standard were considered for infrastructure and physical facilities to maintain the

Navi Mumbai is planned city and developed to attract the migrated population in Navi Mumbai instead of main city Mumbai. The schools are comparatively new and school authorities add one or more standard to their schools each

nt. This is the reason schools in Navi Mumbai have different classes such as pre standard, pre primary to 4th standard, 2-4, 3-10, 1-4, 1-7, 1-6, 5-6, 5-9, 5-10, 5

1959 1960-1969 1970-1979 1980-1989 1990-1999

6.9%

11.7%

4.1%

14.3%

21.7%

Construction of Composite Index for Measuring Infrastructure and Physical Facilities


may maximize the output at school



ed to calculate the human development index. The same approach



The present study was based on the primary schools from class 1 to class 73. The schools having

standard were considered for infrastructure and physical facilities to maintain the

Navi Mumbai is planned city and developed to attract the migrated population in Navi Mumbai instead of main city Mumbai. The schools are comparatively new and school authorities add one or more standard to their schools each

schools in Navi Mumbai have different classes such as pre 10, 5-12.

1999 2000 &

after

21.7%

32.2%

uniformity. As stated earlier out of 243 schools, there were 121 schools having classes from

standard 1 to standard 7 in three types of management. The ZP school management had 50

schools; NMMC management had 34 schools and private management had 37 schools having

standards from 1st to 7th.

For compilation of the composite index, all infrastructure and physical facilities considered in the

study have been listed along with appropriate weights given against them in Table 3.4. The

overall facilities have been classified under four heads, namely infrastructure, health, sports

facilities and extracurricular activities. The infrastructure and physical facilities such as library,

common room, fire fighting equipment, play ground etc were considered for constructing the

composite index. The detail of computation of the index is given below.

Let Xij represent the size or value of the ith indicator in jth school

Where ( i=1,2,……n, j=1,2,…….m).

Y ij = X ij- Min j X ij / Maxj X ij - Min j X ij ;

Where Min j X ij and Maxj X ij are respectively the minimum and maximum of

(X ij = X11, X12, ……………… X1m ).

The scale value Yij varies from zero to one.

From the values of Y [(Yij)], the index of the infrastructure and physical facilities of the jth school

has been computed as Mean Yij = W1 Y1j + W2 Y2j + …………… + Wn Ynj

Where W’s ( 0 < Wi <1 and ∑Wi =1) are arbitrary weights reflecting the relative importance of

the individual variable.

However, a more rational view would be to assume that the weights vary inversely as the

variation in the respective variable of infrastructure and physical facilities i.e. Wi = 1/ s. d. * (1/∑

s. d.), Where s.d. is standard deviation of the ith variable. If data fluctuates much than the

reliability of that indicator becomes less and the importance of that variable decreases

proportionately.

For classification purpose, let (0.0, 0.2), (0.21, 0.4), (0.41, 0.6), (0.61, 0.8), (0.81, 1.0) be linear

intervals such that each interval is to characterize the various types of schools by quality of

infrastructure and physical facilities. The index values have been computed by this method for

each of the school. Also on the basis of the values of the index the overall quality of schools was

measured and schools wre classified into five categories of quality, namely, ‘Very Poor’, ‘Poor’,

‘Moderate’, ‘Good’, ‘Very Good’.

The percentage of classification of schools using composite index was computed which was

given in Table 3.5. It can be revealed from the table that 90% of ZP schools and 41% of NMMC

schools were in the category of ‘very poor’. None of the Private schools were in the category of

‘very poor’ or ‘poor’. About one tenth of ZP schools and 47% of NMMC schools were

classified in ‘poor’ category. Nearly 8% of private school and 12% of NMMC schools were

classified into ‘moderate’ category. Only private schools found into ‘good’ (48%) and ‘very

good’ (44%) categories in terms of the quality of school measured by using various infrastructure

and physical facilities available in schools.

Table 3.4 Weights Assigned to Infrastructure and Physical Facilities Available in Schools

Sr No. Infrastructure Facilities Weights

Availabilile 4

1 Toilets* Yes-1 No-0 2 Drinking Water* Yes-1 No-0 3 Water Supply* Yes-1 No-0 4 Power Supply* Yes-1 No-0 5 Fire Fighting Equipment Yes-1 No-0 6 Health / First Aid Yes-1 No-0 7 Playground Yes-1 No-0 8 Library Yes-1 No-0 9 Laboratory Yes-1 No-0 10 Staff Room Yes-1 No-0 11 Canteen Yes-1 No-0 12 Computer/Internet Yes-1 No-0 13 Auditorium Yes-1 No-0 14 Common Room Yes-1 No-0 15 Parking Facility Yes-1 No-0 16 Telephone Facilities Yes-1 No-0 17 Playground Yes-1 No-0

Physical Facilities

18 Health Facilities Yes-1 No-0

Availability of First Aid box, General Health Check-up , Dental Check-up, Eye Check-up

19 Sport Facility Yes-1 No-0

Cricket, Foot Ball, Volley Ball, Indoor Games, Swimming, Skating, Karate, Kabbadi, Kho- Kho

20 Extracurricular Activities Yes-1 No-0

4* These facilities were available in all the schools, therefore these four facilities (Availability of toilet, drinking

water, water supply and power supply) are not taken into account for computing the composite index.

Drama / Acting, Photography, Elocution/Debate, Community Service and others

Table 3.5 Composite Index of Schools by Type of Management

Score Range of Composite Index

ZP

Schools

NMMC

Schools

PRIVATE

Schools

(Min, Max) N % N % N %

Very Poor-1 (0.00,0.2) 45 90 14 41 0 0

Poor-2 (0.21,0.4) 5 10 16 47 0 0

Moderate-3 (0.41,0.6) 0 0 4 12 3 8

Good-4 (0.61,0.8) 0 0 0 0 18 48

Very Good-5 (0.81,1.0) 0 0 0 0 16 44

Total 50 100 34 100 37 100

Table 3.6 showed average rank given to the index values. The first position was occupied by

private schools and second position was occupied by NMMC management. The last position

was assigned to ZP school management. It was concluded that ZP schools had less number of

infrastructure and physical facilities than that of other two school managements. The private

schools had most of the facilities, may be because these school charge high fees to the students.

Hence they could provide infrastructure and physical facilities required for overall development

of students.

Table 3.6 Average Rank based on Composite Index for Infrastructure and Physical Facilities of

Schools by Type of Management

Type of Management No of schools Sum of Rank Average rank Score

ZP 50 55 1.1 Third

NMMC 34 58 1.71 Second

Private 37 161 4.35 First

3.5 Assessment of Infrastructure and Physical Facilities through Chernoff Faces

3.5.1 Introduction

Graphical methods are well-known for data analysis because of effective means of depiction,

exploration, summarization and communication of data. Graphical methods are helpful in

suggesting suitable analytical procedures, and in explaining conclusions founded upon them.

Chernoff faces, invented by Herman Chernoff in 1972, display multivariate data graphically in the

shape of a human face. The individual parts, called face parameters, such as eyes, ears, mouth

and nose represent values of the variables by their shape, size, placement and orientation all

controlled by well defined mathematical functions. The idea behind using faces is that humans

easily recognize faces and notice small changes without difficulty. Chernoff faces handle each

variable differently. Because the features of the faces vary in perceived importance, the way in

which variables are mapped to the features should therefore be carefully chosen (e.g. eye size

and eyebrow - slant have been found to carry significant weight).

The method consists of vector value data point into geometrically constructed face, features of

which are controlled by the values taken for particular variable. The program variables are X1,

X2 …….. X20, for example X6 , variable may be assigned to the curvature of mouth, the X8 to the

length of the nose and so on. Thus the facial representation has an advantage over techniques of

other graphical methods such a Profile, Stars, Glyphs, Trees and Andrew’s Plots (See Saxena,

1983 and 1985). In Chernoff face programme, it is possible to map paired multivariate

measurements. X1=(x11, x12, …… x1k) and X2=(x21, x22, …… x2k) separately to right hand and left

hand side of the face. A face half which contains 20 parameters is constructed by an array Z= (z1,

z 2, … z20) belongs to (0,1), z1 values are used as construction of face part. The face program

allows the user to define for each variable xi an interval (ai , bi) may either be fixed by user or by

programme as multiples of standard deviations.

To asses overall quality of primary schools by type of management in Navi Mumbai, Chernoff

faces were constructed using software package called ‘STATISTICA’ version 10. This has

enabled us in characterizing quality of schools measured in terms of infrastructure and physical

facilities of different administrative system of primary education. For illustrative purpose, data

on infrastructure and physical facilities of 121 schools of different types of management have

been used. The infrastructure and physical facilities available in the schools were arranged based

on their importance in the respective schools. The vital facilities like drinking water, power

supply, availability of toilet and water supply were available in all the schools, therefore these

facilities were not taken into account while drawing the Chenoff faces. The other important

facilities were used for construction of faces such as library, canteen, computer, staff room, fire

fighting, common room for students, first aid/health, playground, telephone/P.C.O., parking

facility and extracurricular activities. The three types of management were represented by

development in their schools through important infrastructure and physical facilities.

The rationale of using Chernoff face – a technique to represent k-dimensional data graphically is

that simply by seeing the faces it is possible to place similar faces in a group and place altogether

different faces separately i.e. it is easily possible to identify multivariate outliers present in the

data. Saxena and Navneetham (1993) have shown that by seeing the gestalt of the faces,

hierarchical cluster structure of subjects (here primary schools) can be obtained through Chernoff

faces which may make possible to assess and compare the overall quality of schools by type of

management. From the gestalt of the faces, schools were classified according to availability of

infrastructure and physical facilities in each of the three types of management namely ZP,

NMMC and private. This technique has been used to place schools in the hierarchy of

development with respect to availability of infrastructure and physical facilities. The authors

observed that hierarchical cluster structure obtained through Chernoff faces can help in

identifying the variables which put faces at a different level within a group. From this

hierarchical order of the faces, the variation in the characteristics (variables) within a group can

also be studied. Simply, by looking at the faces, all those variables, which have been responsible

to place the faces within a group at different hierarchical levels, can easily be identified. This is

perhaps a unique feature which only faces or some other graphical techniques may reveal (see

Saxena and Navaneetham, 1993).

3.5.2 Faces with Extreme Values

Figure 3.4 illustrates the minimum value of the variables with 0 and maximum value of the

variables with 1 of all the 20 face parameters, which shows a profound effect on the appearance

of face features. The faces we propose contain 20 parameters for each side of the face.

The major difference in the face parameter were size of the face, eye pupils, nose, curvature of

mouth, eyebrows, size or radius of ear etc. We have assigned this variable to face features, the

face with the values 0 looks frown\saddest" and the face with the value 1 looks

smiling\happiest."

Figure 3.4: Chernoff Faces with Extreme Values

3.5.3 Construction of Chernoff Faces

Table 3.7 shows the variables and their assignment to face parameters. All the selected variables

were assigned to face parameters in the order given in Table 3.7. Assignment of the

infrastructure variable was in the same sequence for ZP, NMMC and private school management

to make the comparisons possible.

Table 3.7 : Chernoff Face Parameters and Variables

Sr. no. Facial Features Variables

1 Face width Library

2 Ear level Canteen

3 Half face height Sports Facilities

4 Eccentricity of upper face Play ground

5 Eccentricity of lower face Common room

6 Length of nose Computer

7 Position of center of mouth Fire fighting

8 Curvature of mouth Fire fighting

9 Length of mouth Fire fighting

10 Height of center of eyes Fire fighting

11 Separations of eyes Parking

12 Slant of eyes Telephone

13 Eccentricity of eyes Telephone

14 Half length of eyes Parking

15 Position of pupils Health facilities

16 Height of eyebrows Staff room

17 Angle of eyebrow Parking

18 length of eyebrow Staff room

19 Radius of ear Extra- curricular Activities

20 Nose width Computer

The assignments were chosen according to following considerations: the availability of fire

fighting facilities in the school was depicted by mouth, i.e. the variables number 7- 10 which

represented contour of face, span of mouth, position of centre of mouth and height of the centre

of eyes from mouth respectively. The face width corresponds to the availability of library and

face height corresponds to existence of sports facilities. The eccentricity of upper face was

represented by playground and eccentricity of lower face was controlled by availability of

common room for students. The nose related variables were shown by the facilities related to

computer in the primary schools. Level of ears and radius of ear represented the availability of

canteen facilities and extracurricular activities in the school. Variable 11 to 15 were related to

eyes. The separations or distance between eyes, length of eyebrows and angle of eye brows were

characterized by the availability of parking facility in the school. Eccentricity and slant of eyes

were controlled by the availability of telephone facility in the school. Position of pupils reflected

the availability of first aid or health facility. The height of eyebrows and length of eyebrows

were controlled by the availability of staff room.

3.6 Placement of Schools in the Hierarchy of Development by Type of School Management

using Chernoff Faces

The faces of three types of school management were shown to 21 respondents to identify the

cluster of faces which looked alike and which were unique or present outliers. Based on the

response of respondents the schools were arranged in hierarchy of development by type of school

management. Table 3.8 and Table 3.9 provided the details of availability of infrastructure and

physical facilities in public schools and Table 3.10 gave the details of non-availability of

infrastructure and physical facilities in private schools. The numbers of infrastructure and

physical facilities were listed in ascending order.

ZP School Management

The faces, which look alike in ZP school management (Figure 3.5), were school 13, 15, 22, 36,

38, 41, 48, 49. These schools did not have any infrastructure and physical facilities therefore, the

faces of these schools gave saddest look. Another cluster of schools, which looked similar,

consisted of school numbers 9, 10, 12, 18, 19, 20, 21, 23, 25, 27, 33, 35, 39, 40, 42, 44, 45, 47.

These schools had only playground and were lacking in other facilities. This could be seen from

eccentricity of upper face. A set of school numbers 34 and 37 had only extracurricular activities,

which could be identified from radius of ear. Another set of schools with numbers 30 and 46 had

better face because they had playground (eccentricity of upper face) and extracurricular activities

(radius of ear). School numbers 32 and 43 revealed the impression of having playground

(eccentricity of upper face) and staff room (height and length of eyebrows). The set of schools

with numbers 17 and 24 had playground and parking facilities. These faces looked somewhat

better because of eccentricity of upper face (playground), separations (distance) of eyes, length

of eyes and angle of eyebrow which represented the availability of parking facility. Another set

of school with numbers 4, 16, 28, 31 were identical because all of them had playground, staff

room, extracurricular activities. Schools with numbers 1, 2, 3, 5, 6, 7, 8, 11, 14, 29, 26 and 50

appeared to be unique, because these schools had the combination of facilities, which other ZP

schools did not have.

For example, school no. 26 had only library and school number 5 had playground, parking

facility, extracurricular activities and staff room.

Appendix III showed the data of ZP School Management for construction of Chernoff faces.

Figure 3.5 Chernoff Faces of ZP Schools

Table 3.8 Hierarchy of Development of ZP Schools as per Number of Infrastructure and Physical

Facilities

School no. Total Facilities Facilities Available 4,

13,15,22,36,38,41, 48,49 0 No facilities

9,10,12,18,19,20,21,23,25,27,33,35,39,

40,42,44,45,47 1 Playground 26 1 Library

34,37 1 Extracurricular activities 30,46 2 Playground, extracurricular activities

50 2 Library, playground

6 3 Play ground , health and extracurricular activities

32, 43 3 Play ground, staff room 7 4 Health, extracurricular activities, staff room 8 4 Playground , health Fac., staff room

4,16,28,31 4 Playground, staff room, extracurricular activities 17,24 4 Playground and parking

29 4 Sports facilities, playground and computer

11 5 Parking, playground facilities and extracurricular activities

1 6 Parking, health facilities and staffroom 14 6 Sports facilities, parking and computer

2 7 Playground, parking, health facilities and staffroom

3 8 Fire fighting, extra activities health facilities and staffroom

5 8 Playground, parking, extra activities and staffroom

Figure 3.6 Chernoff Face of NMMC Schools

Table 3.9 Hierarchy of Development of NMMC Schools as per Number of Infrastructure and

Physical Facilities

School no. Total

Facilities Facilities Available 16 2 Library and playground

25,26 2 Playground and extracurricular activities 30 2 Library and sport facilities 14 3 Library and staff room 24 3 Common room and staff room 19 4 Playground, computer and extra activities

21,27 4 Playground and parking 28 4 Library, sports facility and staff room

22, 23,31 5 Playground and fire fighting equipment

1 6 Common room, staff room and sport facilities, health and extra activities

9 6 Library, staff room, computer and playground 13 6 Fire fighting equipment & staff room 17 6 Library, fire fighting and extra activities

32 6 Playground, fire fighting equipment, extracurricular activities

10, 29, 34 7 Playground, staff room and fire fighting equipment

12,20 7 Library, sports facilities and fire fighting equipment

15 7 Library, playground, computer, staff room and extracurricular activities

18 8 Playground and fire fighting equipment, parking 33 8 Library, fire fighting, staffroom

4,8 9 Library, playground, sports facilities, parking health facilities, staff room

11 9 Library, sports facilities, fire fighting, playground, staff room

6 12 sports, common room, fire fighting, staff room, parking, health

2 13 Library, sports, common room, fire fighting, staff room, parking, health

3 13 Computer, sports, common room, fire fighting, staff room, parking, health

7 14 Sports, computer, fire fighting, staff room, parking, health, extracurricular activities

NMMC School Management

From the 34 Chernoff faces of NMMC schools (Figure 3.6), it was found that a set of school

numbers 25 and 26 had playground and extracurricular activities, which could be seen from

peculiarity of upper face and radius of ear. School numbers 21 and 27 of NMMC were at par

with ZP schools of numbers 30 and 46 because they had only playground (eccentricity of upper

face), extracurricular activities (radius of ear). School numbers 1, 2, 3, 5, 6, 7, 9, 13, 14, 15, 16,

17, 18, 19, 24, 30, 32, 33 were distinctive in the sense that each of them had disjoint set

(combination ) of infrastructure and physical facilities. Among these schools, school numbers 14,

16, and 19 had two to four facilities, school numbers 1, 9, 11, 13, 15,17,24, 30, 32, and 33 had

combination of facilities ranging from five to nine and remaining schools with numbers 2,3,7,

and 6 had maximum facilities ranging between 12 to 14. NMMC Schools with numbers 25 and

26 had playground which could be seen from eccentricity of upper face and extracurricular

activities (radius of ear). The set of schools 21 and 27 were looked somewhat better because of

eccentricity of upper face ( playground), separations (distance) of eyes, length of eyes and angle

of eyebrow which represented the availability of parking facility. Schools with number 28 had

library, sports facilities and staff room which could be observed from face width, ear level and

height of eyebrow. Another set of schools with numbers 22, 23 and 31 had playground and fire

fighting facilities. Similarly, school numbers 10, 29 and 34 had playground, staff room and fire

fighting equipment and set of schools with numbers 12 and 20 had library, sports facilities and

fire fighting equipment (Table 3.9).

Appendix IV showed the data of NMMC School Management for construction of Chernoff

faces.

Figure 3.7 Chernoff Face of Private Schools

Table 3.10 Hierarchy of Development of Private Schools as per Number of Infrastructure

and Physical Facilities

School no. Total of Facilities Facilities Lacking (not available) /26 12 Canteen, parking and fire fighting equipment 36 13 Library, canteen, parking, telephone 5 14 Common room, computer and parking 6 14 Fire fighting, computer

27,28,30 14 Canteen, common room and fire fighting equipment

32 14 Canteen, parking, telephone

20 14 Library, common room and fire fighting equipment

9 15 Computer and parking 1,15 15 Common room and fire fighting equipment 18,29 15 Canteen and fire fighting equipment

17 16 Canteen and fire fighting equipment 19 16 Library, parking, health

10,11,23 17 Canteen ,computer 4 17 Sports facilities, computer 14 17 Library, sports, common room

7,8, 16,21 18 Computer 31 18 Canteen and common room

33,37 18 Library and common room 22 19 Common room

24,25 19 Canteen 34,35 19 Library

2,3,12,13 20 -

Private School Management

The faces, which look alike in private school management, were schools with numbers 1 and 15.

These schools required the facilities of common room and fire fighting equipment. This could be

seen from eccentricity of lower face and length, curvature, position of mouth. Similarly, school

with numbers 18 and 29 were identical. These schools were lacking in providing canteen and fire

fighting facilities, which could be seen from the ear level and expression of mouth. School with

numbers 10, 11 and 13 were similar; these schools had all the facilities except canteen and

computer which were represented by ear level and nose (length + width). The schools 33 and 37

look similar; revealing a longish face with other similar facial parameters. In these schools

library and common room were required which could be seen by shape of face, by face width

and eccentricity of lower face. School numbers 27, 28 and 30 look similar. The year level, shape

of mouth and face were different from normal level because these schools needed canteen,

common room and fire fighting equipment. Figure 3.7 revealed that schools with numbers 4, 5,

6, 9, 14, 17, 19, 20, 22, 26, 31, 32, and 36 had different combination of facilities which were not

matching with other schools (due to different faces). For example, school number 4 did not have

sports facilities and canteen; there may not be any school which was lacking only in these two

facilities. A set of schools with numbers 7, 8, 16, 21 were in shortage of computers; whereas the

school with numbers 24 and 25 be deficient in canteen facilities. Similarly, schools with numbers

34 and 35 did not have library. There were 4 schools with numbers 2, 3, 12, and 13 which had all

the infrastructure and physical facilities which could be seen from gestalt of their faces (Table

3.10). Appendix V showed the data of Private School Management for construction of Chernoff

faces.

It could be evident from the facial expressions of the Chernoff faces that private school

management had smiling faces while majority of ZP and NMMC schools gave a frown look.

This implied that the majority of private schools had most of the infrastructure and physical

facilities; whereas public schools were lacking in the infrastructure and physical facilities. The

school faces were placed according to hierarchy of development in each of the three types of

school management. It was found that Chernoff face was easy method to recognise availability

of infrastructure and physical facilities. Since, by simply looking at faces, one can easily

recognise even small change, if any. From the facial expression of the ZP schools, it was found

that fire fighting facility, staff room and common room facilities were not available in any of

these schools. These facilities were represented by seven face parameters namely, contour of

face, span of mouth, position of center of mouth, height of center of eyes, height of eyebrows,

length of eyebrows and eccentricity of lower face. The happy faces of private school revealed

that majority of facilities were available in private management. These schools had funds

available for these facilities since these schools charge high fees; hence the management of

private schools may be able to provide more infrastructure and physical facilities. On the

contrary, the public schools suffer from financial crunch since they provide free education to

primary students and they are depending on government funds.

3.7 Comparison of Classification of Schools through Chernoff Faces Method and

Composite Index Method

Navaneetham (1994) observed that the inherent difficulty with the use of composite index is that

a particular score (value of index) can be obtained by a number combinations of the values of the

variables selected to construct the index. Further, the composite score (index) conceals much

more what it reveals about the data. Chernoff Face method overcomes this problem and helps in

studying in totality the data structure.

From the analysis it was observed that the use of Chernoff faces not only characterize the

availability of infrastructure and physical facilities of schools but also facilitates to find out

which variable(s) is/are responsible for classifying them into various stages of infrastructure and

physical facilities of schools. Such finer analysis may not be possible from the composite index

constructed by formal statistical procedures. Although, the composite index is useful to rank the

type of school management according to the level of infrastructure and physical facilities of

schools, the analysis using Chernoff faces may help to understand the differences with respect to

infrastructure and physical facilities within the management. This section has demonstrated the

efficacy of face analysis to confirm or contrast the findings observed from the composite index.

Further, if there were outliers present in the data, Chernoff faces technique had brought out this

fact in the analysis. Though the development index constructed by using formal statistical

procedures may be used for studying the overall infrastructure and physical facilities available in

the schools, but it may not be sufficient to contemplate the schools by level of infrastructure and

physical facilities of schools. Thus, the use of Chernoff faces along with the composite index

may supplement the information and may ameliorate the researcher’s ability to interpret the data

in a way that may be much more meaningful.

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