NCERT / About the National Curriculum Framework-2005

About the National Curriculum Framework-2005

A discussion on what NCF-2005 is and what it aims for

Chapter -1

Q.1 What does the National Curriculum Framework-2005

deal with?

A.1 Certain broad aims of education have been identified in

the  National Curriculum Framework-2005 (NCF-2005)

seeking guidance from the constitutional vision of India as

a secular, egalitarian and pluralistic society. These include

independence of thought and action, sensitivity to othersí

well-being and feelings, learning to respond to new

situations in a flexible and creative manner,  predisposition

towards participation in democratic processes, and the

ability to work towards and contribute to economic

processes and social change.

NCF-2005  provides a guideline with  which teachers

and schools can choose  and plan experiences that they

think children should have.  It is a reviewed version of

NCF-2000 in the light of the report Learning Without

Burden (1993, Professor Yashpal). To make teaching a

means of harnessing the childís creative nature, the report

recommended a fundamental change in the matter of

o r g a n i s i n g   c u r r i c u l u m   a n d   a l s o   i n   t h e   s y s t e m   o f

e x a m i n a t i o n   w h i c h   f o r c e s   c h i l d r e n   t o   m e m o r i s e

information to reproduce it. The  National Curriculum

Framework emphasises that curriculum, syllabus and

t e x t   b o o k s   s h o u l d   e n a b l e   t h e   t e a c h e r   t o   o r g a n i s e

classroom experiences in consonance with the childís2 Q & A

nature and environment, and provide opportunities to

all children. Significant changes are recommended with

a view to the present day  and future needs in order to

alleviate the stress, children are coping with today. NCF-

2005  sets out the broad conceptual framework and

guidelines regarding school education in India from early

c h i l d h o o d   s t a g e   t o   t h e   h i g h e r   s e c o n d a r y   s t a g e   o f

education in its five chapters (i) Perspective (ii) Learning

and Knowledge (iii) Curriculum Areas, School Stages and

Assessment (iv) School and Classroom Environment (v)

Systemic Reforms.

Q.2 In what way is a ëcurriculum frameworkí different from

a ëcurriculumí?

A.2 A ëcurriculum frameworkí, as the word suggests is a broad

framework of concepts and guidelines that informs the

school education policy of a country. It  is a plan that

interprets educational aims vis-a-vis both individual and

society to arrive at an  understanding of the kind of learning

experiences teachers should provide to children.    Its scope

is wide and it  relates all those who are concerned with

educationñstudents, teachers, parents, teacher educators,

policy makers and the public at large.

A ëcurriculumí is guided by the ëcurriculum frameworkí;

it pertains to learning experiences in and outside the

classroom, and the enabling conditions needed for the

desired teaching-learning process. It includes content,

pedagogy, systemic characteristics and assessment.

Q.3 Is ësyllabusí the same thing as ëcurriculumí?

A.3 ëSyllabusí refers to the content of each subject in  the

curriculum. It outlines  what is to be taught and the

k n o w l e d g e ,   s k i l l s   a n d   a t t i t u d e s   w h i c h   a r e   t o   b e

d e l i b e r a t e l y   f o s t e r e d ,   t o g e t h e r  wi t h   s t a g e - s p e c i f i c

objectives. Syllabus also contains time allotment and

assessment scheme for each subject. Moreover, the current

syllabus developed by the NCERT provides guidelines to

teachers  to connect  school  knowledge wi th chi ldís

experiences.3 Q & A

Q.4 What is the need for bringing out a new ëcurriculum

frameworkí document?  Do we not already have an

education policy underlying school education in

India?

A.4 Indiaës National Policy on Education (NPE), 1986  proposed

a national framework for curriculum as a means of evolving

a national system of education. This system is aimed to be

capable of responding to Indiaís diversity of geographical

and cultural milieus while ensuring  a common core of

values along with academic components. The policy has

also entrusted NCERT with the responsibility of developing

and promoting the National Curriculum Framework and

reviewing the Framework at frequent intervals.

The National System of Education will be based on a national

curricular framework, which contains a common core along

with other components that are flexible. The common core

will include the history of India's freedom movement, the

constitutional obligations and other contents essential to

nurture national identity. These elements will cut across

subject areas and will be designed to promote values such

as India's common cultural heritage, egalitarianism,

democracy and secularism, equality of sexes, protection of

environment, removal of social barriers, observance of small

family norm and inculcation of scientific temper. All

educational programmes will be carried on in a strict

conformity with secular values. India has always worked

for peace and understanding between nations, treating the

whole world as one family. True to this hoary tradition,

education has to strengthen this world-view and motivate the

younger generations for international cooperation and peaceful

co-existence. This aspect cannot be neglected. To promote

equality, it will be necessary to provide equal opportunity

for all, not only in access but also in the condition of success.

Besides, awareness of the inherent equality of all will be

created through the core curriculum. The purpose is to

remove prejudices and complexes transmitted through the

social environment and the accident of birth.

NATIONAL  POLICY ON  EDUCATION, 19864 Q & A

Hence, NCERT has formulated  NCFs in 1975,1988, 2000

and recently in 2005. Further, you would agree without

any doubt that a curriculum framework for   any society

cannot be a static document, ëfrození in time. With the

creation of   new knowledge   all over the world, sociocultural and economic conditions of our society change,

new opportunities of work arise and aspiration of people

grow. This dynamism of the society must be reflected in

school education.

Q.5 I appreciate it. I suppose the new knowledge that you

referred to now  also includes new ideas and insights

on education itself, that is, our steadily evolving views

on teaching-learning process, educational technology,

and so on.

A.5  Y o u   a r e   a b s o l u t e l y   r i g h t .   T h e   p a r a d i g m   ( i . e . ,   t h e

conceptual foundations and broad principles) of school

education itself is being debated and clarified all over the

w o r l d .   F u r t h e r ,   e x p e r i e n c e s   o f   N C E R T   a n d   o t h e r

educational agencies as well as the field work of several

NGOs throw new insights into and ideas on education in

India. NCFñ2005  encapsulates  the emerging insights

into education in India.

NCF-2005 says that we need to pay attention to new

developments and concerns to which our Universal

Elementary Education (UEE) emphasises. There is a need

to broaden the scope of the curriculum to include the rich

inheritance of different traditions of knowledge, work and

crafts.  Some of these traditions today face a serious threat

from market forces and the commodification of knowledge

in the context of globalisation of the economy. The

development of self-esteem and ethics, and the need to

cultivate childrenís creativity, must receive primacy.  In

the context of a fast-changing world and a competitive

global context, it is imperative that we respect childrenís

native wisdom and imagination.5 Q & A

Q.6 Could you   throw   some light on the major concerns

addressed in NCF-2005?

A.6 One major concern is that our school system has, over the

years, become rigid and inflexible. In the process, our

education tends to suppress the natural creativity and

curiosity of children. One of the reasons why this has

happened is the dominating  role of examinations in our

system. The examination that supposedly determines

childís future occupies the centre stage and childís presence

has gone to the background. What is necessary is to give

primacy to childrenís experiences and their voices and  to

encourage their active participation in learning. NCF-2005

points out that every child is talented in some way. We need

to identify and nurture talent of each child.

A n o t h e r  ma j o r   c o n c e r n   i s   t h a t   q u a l i t y   s c h o o l

education has still not reached to a large section of our

population. There is no doubt about some ëislandsí of

excellence, but the large majority of marginalised groups

such as girls, socio-economically disadvantaged children,

etc., do not get meaningful learning experiences in school,

which will give them a sense of dignity and confidence.

Curriculum design must reflect the commitment to

Universal Elementary Education (UEE), not only in

representing cultural diversity, but also by ensuring that

children from different social and economic backgrounds

with variations in physical, psychological and intellectual

characteristics are able to learn and achieve success in

school. In this context, disadvantages in education arising

from inequalities of gender, caste, language, culture or

religion need to be addressed directly, not only through

policies and schemes but also through the design and

selection of learning tasks and pedagogic practices, right

from the period of early childhood. Education must

empower them to overcome the disadvantages of unequal

socialisation and enable them to develop their capabilities

of becoming autonomous and equal citizens.  The National

Curriculum Framework-2005 is focused on providing

quality education to all children.6 Q & A

Q.7 Now I understand that there are major concerns and

problems in the educational scenario of our country.

Does  NCF-2005 address these concerns?

A.7 I am glad you asked this  question. Indeed, NCF-2005  was

formulated mainly in response to the widespread concerns

of teachers and other stakeholders throughout the country.

Addressing these concerns NCF-2005  suggests that school

knowledge needs  to be connected wi th day- to-day

experiences of the child. It also recommends plurality of

text books, continuous and comprehensive evaluation,

flexibility in examination and time schedules of school and

also mother tongue as the medium of instruction.

Q.8 I appreciate these recommendations. Also, I agree

with you on quality of education that you explained.

Indeed all responsible citizens of our country must

be concerned about these two issues: (i) the need to

universalise school education making it accessible

t o   a l l  ma r g i n a l i se d   g r o u p s   a n d   ( i i )   t h e   n e e d   t o

enhance its quality. But, we have been discussing

and debating these matters for years. What is new

in NCF-2005 regarding these long-standing problems?

A.8 The issues are deep and the problems are gigantic.  There

is no magical solution being offered by NCF-2005.  But it

has projected and focused on these issues with greater

clarity and given several practical measures to make

progress with  regard to them.

NCF-2005 has two very significant things to say

about the twin major concerns expressed above. First,

universalisation of education and quality in education are

not to be regarded as two ëopposingí needs.  They are

complementary and  reinforce each  other.  Quality cannot

flourish for long in a society that is not based on equality

and justice for all. Likewise, universalisation can be an

empty slogan unless quality is assured for all. Second,

NCF-2005 interprets the quality dimension holistically,

departing from its narrow connotation of excellence in

particular subject areas.7 Q & A

Q.9  I   w h o l l y   a g r e e   w i t h   w h a t   y o u   s a i d   a b o u t

universalisation.  Quality and universalisation are no

doubt inseparable.  But I did not get exactly what you

have in mind regarding the broad meaning of ëquality

educationí.

A.9 Before I come to that let me understand your own views on

ëqualityí, since it is the teacher who plays a pivotal role in

ensuring quality education for all.

Q.10 In my view, quality education means children should

be involved in joyful and meaningful learning at

schools that leads them to attain the necessary life

skills and become good and useful members of the

society. Am I right?

A.10 Yes, exactly. NCF-2005 says much the same thing.  It

emphasises that school learning should not be confined to

textbooks alone; teaching-learning experiences should be

embedded in the childís life experiences. For this, it is

necessary that learning should be shifted from rote method.

This clearly requires that the school system should be

flexible, allowing innovation and promoting creativity among

children. Overall development of the child should be

emphasised. Thus quality in education includes concern

for quality of life in all its dimensions. This is why a concern

for peace, protection of the environment and predisposition

towards social change must be viewed as core components

of quality, not only as value premises.

Q.11 You mentioned that NCF-2005 interprets ëqualityí very

broadly. What other aspects does ëqualityí refer to?

A.11 We  have already agreed that ëqualityí is inclusive of

universalisation. The document clearly explains that

quality is a systemic characteristic rather than only a feature

of instruction or attainment. The attempt to improve the

quality of education will succeed only if it goes hand in

hand with steps to promote equality and social justice.

Equality in education can be brought by enabling all

learners to claim their rights as well as to contribute to

society and the polity.  Quality education should promote8 Q & A

these social values necessary for a democratic society such

as ours.

Q.12 In  continuation of the same discussion, there has

been much talk of the so-called ëconstructivismí in

NCF-2005.  What does this   term mean?

A.12 ëConstructivismí is not a new mysterious educational

philosophyó it has always been a part of the  good

pedagogical practices. NCF-2005 clarifies and projects

it with emphasis, mainly to promote quality education

that we discussed above. Constructivism holds that

knowledge should not be regarded as ëout thereí to be

emptied into the childís head. Rather, it recognises that

meaningful learning involves the child ëconstructingí

knowledge by himself/herself.  This happens by actively

engaging the learner. School must provide every possible

opportunity to children for this. Active engagement involves

inquiry, exploration, questioning, debates, application and

reflection, leading to meaningful understanding, arriving

at concept and creation of new ideas.

This term can  further  be explained by reproducing

a  part of the text from NCF-2005 (p. 17) as given below:

ìIn the constructivist perspective, learning is a process of

the construction of knowledge. Learners actively construct

their own knowledge by connecting new ideas to existing

ideas on the basis of materials/activities presented to them

(experience). For example, using a text or a set of pictures/

visuals on a transport system coupled with discussions

will allow young learners to be facilitated to construct the

idea of a transport system. Initial  construction (mental

representation) may be based on the idea  of the road

transport system, and a child from a rural setting may form

the idea centred around the bullock cart. Learners construct

me n t a l   r e p r e s e n t a t i o n s   ( ima g e s )   o f   e x t e r n a l   r e a l i t y

( t ranspor t  system)   through a given set  of  ac t ivi t ies

(experiences). The structuring and restructuring of ideas

are essential  features as the learners progress in learning.

For instance, the initial idea of a transport system  built

a r o u n d   r o a d   t r a n s p o r t   w i l l   b e   r e c o n s t r u c t e d   t o9 Q & A

accommodate other types of transport systemsósea and

airóusing appropriate activities. The engagement of

learners, through relevant activities can further facilitate

in the construction of mental images of the relationship

(cause-effect) between a transport system and human life/

e c o n omy .  Howe v e r ,   t h e r e   i s   a   s o c i a l   a s p e c t   i n   t h e

construction process in the sense that knowledge needed

for a complex task can reside in a group situation. In this

context, collaborative learning provides room for negotiation

of meaning, sharing of multiple views and changing the

internal representation of the external reality.î

Q.13 If the child is to ëconstructí knowledge himself/herself

what then is the role of the teacher? Is the teacher

redundant in the process?

A.13 Not at all.  The teacher  plays a  crucial role, by creating

enabling and supporting conditions for the process of

ëKnowledge Constructioní by the child to happen.  In this

context, teacher is a facilitator who encourages learner to

reflect, analyse and interpret in the process of construction

of knowledge. Teacher creates  various situations wherein

students interact with the teacher and understand the

concepts, and then the teacher  refines or revises those

concepts by asking questions, posing contradictions and

engaging them in inquiries. Teacher engages her students in

discussion in a democratic set-up of the classroom to

facilitate them to understand the words and concepts not

understood yet. She makes the children aware that their

experiences and perceptions are important. They are

encouraged to develop the mental skill needed to think and

reason independently and to have the courage to dissent.

Thus the role of the teacher in  the construction of

knowledge of her students is to provide a safe space to

express themselves without fear of being ridiculed and

simultaneously to build  certain forms of interaction.10 Q & A

Q.14 In particular, what are the facilitating conditions for

the childrenís knowledge construction?

A.14 Teacher  should provide an environment conducive to

learning, where children feel  secure, where there is absence

of fear and which is governed by relationships of equality

and equity.  If students feel   that they are valued and

their own knowledge  about their surroundings such as

their homes, communities, languages and cultures are

valuable as resources of experiences to be analysed and

inquired into at school, they get motivated to learn. The

curriculum must enable children to find their voices,

nurture their curiosity, to do things, to ask questions and

to pursue investigations, sharing and integrating their

experiences with school knowledge. Learning should not

be equated with childrenës ability to reproduce textual

knowledge.

Q.15 Would you please give some ideas for integrating childrenís

experiences and local knowledge with their learning?

A.15 Sure, it is studentsí interaction with their environment and

integration of their experiences and local knowledge, that

leads to meaningful learning. NCF-2005 emphasises the

significance of contextualising education, of situating

learning in the context of the childís world, and of making

the boundary between the school and its natural and

social environment porous. This is not only because the

local environment and the childís own experiences are

the best entry points into the study of different disciplines

of knowledge, but more so because the aim of knowledge

is to connect with the world. It is not a means to an end,

but both means and end. This does not require us to

reduce knowledge to the functional and immediately

relevant, but to realise its dynamisms by connecting with

the world through it. The local environment is thus a

natural learning resource, which must be privileged

when making choices regarding what should be included

in the curriculum or what concrete examples should be

cited in planning for their transactions in the classroom.11 Q & A

Q.16 I  r e c o g n i s e   t h a t   k n o w l e d g e   i s   d i f f e r e n t   f r o m

information. What does NCF-2005 say about it?

A.16 Knowledge can be conceived as experiences organised

through language into patterns of thought, thus creating

meaning, which in turn helps us to understand the world

we live in. It is important that all children learn to

participate in the very process of knowledge creation, as

this constitutes the basis for further thinking and for acting

appropriately in the world. Conceiving knowledge in this

broad sense directs us to the significance of dynamic

engagement of the children with the world through

observing, inquiring, experimenting, discussing, listening,

LOCAL  KNOWLEDGE  TRADITIONS

Many communities and individuals in India are a rich

storehouse of knowledge about many aspects of India's

environment, acquired over generations and handed down

a s   t r a d i t i o n a l   k n owl e d g e ,   a s  we l l   a s   t h r o u g h   a n

individual's practical experiences. Such knowledge may

pertain to: naming and categorising plants, or ways of

harvesting and storing water, or of practising sustainable

agriculture. Sometimes these may be different from the

ways in which school knowledge approaches the subject.

At other times, it may not be recognised as something

that is important. In these situations, teachers could help

children develop projects of study based on local traditions

and people's practical ecological knowledge; this may also

involve comparing these with the school approach. In

some cases, as in the case of classifying plants, the two

traditions may be simply parallel and be based on different

criteria considered significant. In other cases, for example

the classification and diagnosis of illnesses, it may also

challenge and contradict local belief systems. However,

all forms of local knowledge must be mediated through

Constitutional values and principles.

NCF-2005 (p. 32)12 Q & A

thinking and reflectingóboth individually and with others.

Here you engage the children actively. If, on the other hand,

knowledge is regarded as a finished product, then it is

organised in the form of information to be ëtransferredí to

the childrenís mind. In this view of knowledge, children are

conceived as passive receivers of knowledge.

Q.17  L e t   u s   r e t u r n   t o   t h e   a l l - imp o r t a n t   q u e s t i o n   o f

universalisation.  What are the recommendations of

NCF-2005 in this regard?

A.17 We have already discussed about it (please refer Q. 6).

Broadly speaking, the recommendations of NCF-2005

regarding universalisation are: (i) inclusion  and  retention

of all children in school through proper design of learning

tasks that reaffirms the value of each child and enables

all children to experience dignity and confidence to learn;

(ii) to ensure  q u a l i t y   a n d   e q u a l i t y   o f   o u t c o m e   f o r

c h i l d r e n   f r o m   d i f f e r e n t   s o c i a l   a n d   e c o n o m i c

backgrounds; and (iii) inclusion of  the rich inheritance of

different   traditions of knowledge, work and craft.

The formal approach, of equality of treatment, in terms of

equal access or equal representation for girls, is inadequate.

Today, there is a need to adopt a substantive approach,

towards equality of outcome, where diversity, difference and

disadvantage are taken into account.

A critical function of education for equality is to enable all

learners to claim their rights as well as to contribute to

society and the policy. We need to recognise that rights and

choices in themselves cannot be exercised until central

human capabilities are fulfilled. Thus, in order to make it

possible for marginalised learners, and especially girls, to

claim their rights as well as play an active role in shaping

collective life, education must empower them to overcome

the disadvantages of unequal socialisation and enable them

to develop their capabilities of becoming autonomous and

equal citizens.

NCF-2005 (p. 6)13 Q & A

Q.18 Universal isat ion  is,  of  course,  a Const i tut ional

requirement.  We must give equal treatment to all,

irrespective of   caste, class, clan, religion, language,

region, etc.  What is new in NCF-2005?

A.18 N C F - 2 0 0 5   g o e s   b e y o n d   e q u a l i t y   o f   t r e a t m e n t .     I t

emphasises that school education should be so geared that

there is equality of outcome. Equality of treatment focuses

only   on parity   across different groups, for example, equal

representation of all  in the curriculum and textbooks.

Equality of outcome emphasises that  the  processes

of education have to be designed to ensure that the

marginalised  groups are able to relate to the curriculum

and teaching practices with their experiences and native

wisdom so that they  can overcome  disadvantages  and  be

able to perform on par with everyone.

Q. 19 I agree that these ideas are good. But they seem rather

idealistic and not practical. How will a   teacher like

me implement these various recommendations in

practice?

A.19 A majority of teachers have a similar feeling. This is because

our education system is textbook and examination centric.

We need to go beyond the textbooks and see connectivity

between childís everyday life experience and the knowledge

school provides.  Once we develop faith in childís abilities,

we will be able to design challenging tasks for her learning

and move towards engaging her in observation,  enquiry

and construction of knowledge. The ideas we have discussed

above may seem impractical in the beginning but that is

because we are not used to them. Experience shows that

once teachers start implementing these ideas they begin to

feel comfortable with them and indeed enjoy interacting

with children with this new approach. Teacher autonomy

is essential for ensuring learning environment that

addresses childrenís diverse needs. It is important to

appreciate that as much as the class room needs to nurture

a democratic, flexible and accepting culture, so also the

school institution and the bureaucratic structure need to

do the same.14 Q & A

Chapter - 2

Science and Mathematics Learning

Key issues and ideas of NCF-2005 pertaining to science and

mathematics;  doubts   resolved

Q.1 NCF-2005 states that ëgood science education is true

to the child, true to life and true to scienceí.  What is

this supposed to mean?

A.1 In the context of NCF- 2005 ëtrue to childí means that the

science we teach should be understandable to the child

and be able to engage the child in meaningful and joyful

learning.

ëTrue to lifeí means that the science we teach should relate

to the environment of the child, prepare her for the world of

work and promote in her concerns  for life and preservation

of the environment.

ëTrue to scienceí means the science we teach should convey

significant aspects of science content at appropriate level

and engage the child in learning the processes of acquiring

and validating scientific knowledge.

Q.2 NCF-2005 refers to six ëvaliditiesí of a good science

curriculum.  What does that mean?

A.2 This is just a way of saying what the essential features of a

good science curriculum are. The six different validities refer

to cognitive, content, process, historical, environmental and

ethical aspects of a science curriculum. They should

provide base for the teaching learning of science. These

validities do not set the limit for the teachers. On the15 Q & A

contrary, they provide freedom to the teacher to plan a

variety of experiences to seek participation of her students

in learning process.

Q.3 Should I understand these in more concrete terms?

A.3 Yes indeed.  Let us see few examples that satisfy the required

validity and alongwith them the counter examples that

illustrate the topics not reflecting the required validity.

Cognitive validity

Cognitive validity implies that the content should be age

appropriate so that children can  understand them.The

way of transaction of the content should be according to

the level of  the child.

Example:

Up to upper primary level, the basic concepts of light are

transacted  qualitatively taking concrete examples from

their surroundings. At the secondary stage, the ability of

l o g i c a l   t h i n k i n g   a n d   a b s t r a c t   r e a s o n i n g   d e v e l o p s .

Therefore, children are introduced to draw ray diagrams

explaining formation of images using different types of

lenses and mirrors. At higher secondary stage, children

are ready to understand the broader concepts of light like

principle of various optical instruments using relevant

formulae and solving problems with appropriate rigour.

ëWave Theory of Lightí at higher secondary stage satisfies

cognitive validity. Based on this reasoning we decide which

topic should be taken up at which stage.

Teaching ëFormation of Shadowsí in class VI, and

ëDifferential Calculusí in class XII also satisfy cognitive

validity.

Counter example:

Teaching  ëWave Theory of Lightí in class VII or ëIrrational

Numbersí in class VI do not satisfy cognitive validity.

Content validity

It requires that curriculum must convey significant and

scientifically correct content. We should not teach grossly

incorrect science in our effort to simplify it. The idea that16 Q & A

electron pairs are equally shared in all covalent bonds

should be reconstructed as electron pairs are not shared

equally in all covalent bonds. In some, one atom attracts

the electron pair more than the other atom (i.e., a difference

in electronegativity) and causes the electron pair to be closer

to it than to the other atom.

Example:

The spontaneous and widespread idea of students at

secondary stage that force is directly proportional to velocity

should be carefully transformed into the correct idea that

force is directly proportional to acceleration. This is

necessary for satisfying content validity.

Counter example:

Explaining ëDarwinian Theory of Natural Selectioní as a

ënatural desireí of species to survive; matter is destroyed

during burning; electric current is used up in lighting the

bulb; do not fulfil the requirement of content validity.

Process validity

It is an important criterion of a good science curriculum. It

helps children in learning to learn science. It implies that

we should not focus only on the content but also ensure

that while teaching, the right pedagogic processes are used

that enable interactive and activity-based learning.

Curriculum should engage the learners in acquiring the

methods and processes of learning science so that they can

generate and validate the scientific knowledge. It should

develop a spirit of enquiry, objectivity, creativity and openmindedness among the learners. In order to satisfy the

process validity, children should be given all possible

opportunities of observation, classification, measurement,

making hypothesis, experimenting, reasoning, arriving at

conclusions and communicating results in teachinglearning situations of science.

Example:

Learning ëFaradayís Law of Electromagnetic Inductioní

through a variety of different  situations in the laboratory:

magnet and coil in relative motion, two current carrying

coils in the vicinity of   each other, etc. and arriving  at the17 Q & A

mathematical law followed by solving problems and critical

conceptual   questions,  satisfy process validity. Similarly,

arriving at the approximate value of π as nearly 3.14 by the

students after finding the ratio of circumference to the

diameter of different circles and then generalising it

themselves meets the requirement of process validity.

Counter example:

V e r b a l   d e s c r i p t i o n   o f   t h e   a r r a n g e m e n t   o f   f l o w e r s

(inflorescence ) in a plant, without exposure to plants in

the environment  does not fulfil the requirement of process

validity. Other counter examples are teaching ëLaws of

Reflection and Refraction of Lightí  or ëMagnetí without

providing the children situations of performing activities

and experiments.

Historical validity

It means that science teaching should not convey a static

image of science. It should be informed by historical

perspective enabling the learner to appreciate how the

concepts of science evolve with time with better and more

reliable theories. Satisfying historical validity helps the

learner to view science as a social enterprise and to

understand how social facts influence the development

of science.

Example:

The ëPeriodic Tableí in Chemistry was earlier based on

atomic  weight, later based on atomic number, and finally

explained by quantum theory. The concept of ëgenesí in

t e r m s   o f   i t s   p h e n o t y p i c   e x p r e s s i o n   o r   m o l e c u l a r

understanding of ëgeneí with reference to structure of DNA

accomplish the requirement of historical validity.

Counter example:

Teaching ëHeliocentric Theory of Solar Systemí without any

reference to the earlier ëGeocentricí model; teaching ëWave

Opticsí without reference to the historical debate between

the wave  and corpuscular pictures of light do not meet the

requirement of historical validity.18 Q & A

Environmental validity

It means that science teaching should be contextualised

and related with the childís environment. Curriculum of

science should enable the learner to appreciate the issues

at the interface of science, technology and society. It should

also equip them with the requisite knowledge and skills to

enter the world of work.

What Biology do students know?

These students donít understand science.  They come from

a ìdeprived background!î We frequently hear such opinions

expressed about children from rural or tribal backgrounds.

Yet consider what these children know from everyday

experience.

Janabai lives in a small hamlet in the Sahyadri hills.  She

helps her parents in their seasonal work of rice and tuar

farming.  She sometimes accompanies her brother in taking

the goats to graze in the bush.  She has helped in bringing

up her younger sister.  Nowadays she walks 8 km every

day to attend the nearest secondary school.

Janabai  maintains  int imate  l inks wi th her  natural

environment.  She has used different plants as sources of

food, medicines, fuelwood, dyes and building materials; she

has observed parts of different plants used for household

purposes, in religious rituals and in celebrating festivals.

She recognizes minute differences between trees, and notices

seasonal changes based on shape, size, distribution of leaves

and flowers, smells and textures.  She can identify about a

hundred different types of plants around heró many times

more than her biology teacher canó the same teacher who

believes Janabai is a poor student.

Can we help Janbai translate her rich understanding into

formal concepts of biology? Can we convince her that school

biology is not about some abstract world coded in long texts

and difficult language: it is about the farm she works on,

the animals she knows and takes care of, the woods that

she walks through every day? Only then will Janabai truly

learn science.

POSITION PAPER ON TEACHING OF SCIENCE (p.14)19 Q & A

Example:

Encouraging   children to build models of windmill, solar

cooker; relating global warming with carbon dioxide

emission from burning of wood and increasing number of

automobiles; relating neutralisation of acid with base with

ways of treatment of soil to decrease alkalinity or acidity

are some examples satisfying environmental validities.

Counter example:

Teaching biodiversity in a school in tribal areas without

any field visit to the surrounding area; teaching concepts

of sound without any sensitisation to noise pollution does

not satisfy environmental validity.

Ethical validity

It means science education should promote values of

honesty, objectivity, cooperation, freedom   from   fear and

prejudices, and concerns for life and the environment.

Example:

Encouraging children to report the experimental and

observational data honestly and critically, enquiring into

the reasons for departure from standard or expected value,

if any, establishes ethical validity.

Counter example:

Being insensitive to water and electricity wastages in

schools and homes, indulging in cutting of trees and cruelty

to animals does not satisfy ethical validity.

Q.4 Knowing NCF-2005 perspective on science, now I am

curious to know  what are the thrusts of NCF-2005

with respect to mathematics education?

A.4 As per NCF-2005,the main goal of mathematics education

is the development of childrenís ability of mathematisation.

Q.5 What does that mean?

A.5 Basically it means that children should learn to think about

any situation using  the language of mathematics so that

the tools and techniques of mathematics can be used. This

typically involvesó drawing pictures (representations),

choosing variables, framing equations and arriving at a

conclusion logically.20 Q & A

Q.6 Would you please explain it with the help of an

example?

A.6 Sure. Let us consider, length of a rectangular field is

two times its width and its area is 400 square metres.

This situation can be expressed (mathematised) as

(2x)(x)=400 choosing x as a variable representing width

of the field.

Q.7  B u t   y o u   t a l k   o f   n a r r o w   a n d   h i g h e r   a i m s   o f

mathematics. Why does one make such a distinction?

A.7 The difference is basically between numeracy-related skills

such as the ability to deal with arithmetic operations, ability

to compute percentage, area, volume, to factor polynomials

etc., and the mathematics required to handle abstraction.

The former is needed to transact oneís daily life business

along with social obligations smoothly. It is of immediate

need. But the later is important to deal with the modern

complex technological world.

Q.8 How do you visualise achieving the higher aim of

mathematics in our education?

A.8 It is possible by developing the childís capability   for logical

and analytical thinking, nurturing a confident attitude to

p r o b l e m   s o l v i n g ,   a n d   a n   a b i l i t y   t o   d e c i d e   w h i c h

mathematical tools are appropriate in which context and

to apply them accordingly.

Q.9 NCF-2005 talks about teaching ambitious, coherent

and important   mathematics. What   does that mean?

A.9 An ambitious mathematics seeks to achieve the higher

aim rather than only the narrower aim. Coherent means

linkages of mathematics with other subjects. Teaching

important mathematics means that it is not merely

textbook material but something both children and

teachers consider worth spending their time and energy

o n ,   a n d   m a t h e m a t i c i a n s   c o n s i d e r   s i g n i f i c a n t   f o r

m a t h e m a t i c s .   A n   i m p o r t a n t   c o n s e q u e n c e   o f   s u c h

requirements is that school mathematics must be activity

oriented.21 Q & A

Q.10 It is appreciable.  Could you next explain the meaning

of nature of mathematics?

A.10 Mathematics reveals hidden patterns that helps us to

understand the world around us. Much more than

arithmetic and geometry, Mathematics today is a  diversified

discipline, which deals with data, measurement and

observations from science; with reference, deduction and

proof, and with mathematical models, natural phenomena,

human behaviour and social systems. As a practical matter,

mathematics is a science   of patterns   and order. Its domain

is not molecules or cells, but numbers, chance, form,

algorithm  and change. As a science of abstract object,

mathematics relies on logic rather than on observation as

its standard of truth, yet employs observation, simulations

and even experimentation as means of discovering the truth.

The result of mathematicsótheorems and theoriesóare

both significant and useful; the best results are also elegant

a n d   d e e p .   I n   a d d i t i o n   t o   t h e o r e m s   a n d   t h e o r i e s ,

mathematics offers distinctive mode of thought which are

both versatile and powerful, including mathematical

modelling, abstraction, optimisation, logical analysis,

inference from data and use of symbols. Due to diverse

application of mathematics, the various mathematical tools

are required which are interlinked with each other. It is the

tall shape of mathematics.

Q.11 What is the meaning of ëthe tall shape of mathematicsí?

A.11 Many concepts are needed to be learnt sequentially in

mathematics. Only after mastering arithmetic, algebra is

learnt, and only when one can factor polynomials, is able

to understand   trigonometry, and so on. Thus, since each

theme is built on another, it results in a tall shape. This

makes it difficult for children; someone who finds one stage

difficult finds it hard to catch up later.

Q.12 B u t ,   a s   I   u n d e r s t a n d ,   t h a t   i s   t h e   n a t u r e   o f

mathematics. What does NCF-05 say about it?

A.12 NCF-2005 says that the tall shape of mathematics can be

de-emphasised in favour of a broad-based curriculum22 Q & A

with more topics that start from the basics. Revisiting the

basics   of mathematics at secondary and higher secondary

stages will help children   make better use of their   time

at school.

 Q.13 We  often face a difficult choice, especially at the

secondary and higher secondary stages, of deciding

whether we  should teach  many topics without much

detail, giving children exposure to those topics, or

should we cover a few themes in depth, giving children

competence. What is the solution to this problem?

A.13 There  are  arguments in favour of either choice. It is

generally not possible to do both, since there are often

conflicting demands of depth versus breadth. There is no

general answer to this question. The teacher is the best

person to find the right balance, in the given local situation

and context.

Q.14 I appreciate that NCF-2005   advocates this flexibility.

I  wo u l d   l i k e   t o   k n ow,  wh e t h e r   t h e  me a n i n g   o f

ë c o n s t r u c t i v i smí   i s   t h e   s ame   i n   t h e   c o n t e x t   o f

mathematics as it is in science?

A.14 It means the same thing; an approach by which children

discover and construct their knowledge, rather than it

being simply given and taken uncritically. In mathematics,

for example, this means that childrenís ability to come up

with a formula is more important than being able to

correctly use well known formulae.

Q.15 I understand. It means that discovering even simple

facts (theorems) on their own, and arguing why they

are true is more important than being able to recall

famous theorems and their proofs. Am I right?

A.15 Absolutely. Children view mathematics as something to

t a l k   a b o u t ,   t o   c o m m u n i c a t e ,   t o   d i s c u s s   a m o n g

themselves, to work together on. Making mathematics a

part of childrenís life experience is the best mathematics

education possible.23 Q & A

Q.16 I  try my best to help  children to discover the formulae

on their own and I have observed that this way they

enjoy mathematics rather than fear it.  I understand

t h a t   m a t h e m a t i c s   i s   m o r e   t h a n   f o r m u l a e   a n d

mechanical procedures.

 A.16 That is great.

Q.17 What is the meaning of the term ëmultiplicity of

approachesí?

A.17 Very often, there are many ways of solving a problem, many

procedures for computing a quantity, many ways of proving

or presenting an argument. Offering such a choice allows

children to work out and use the approach that is most

natural and easy for them.  For some students who learn

more than one approach, this is a technique for selfchecking. Multiplicity of approaches is crucial for liberating

school mathematics from the tyranny of the one right

answer, found by applying the one algorithm taught. When

many ways are available, one can compare them, decide

which is appropriate when, and in the process gains insight.

For instance, to subtract 53 from 100, you could use

the standard algorithm of taking away with borrowing, or

consider how people do this in shops. When someone buys

material for Rs 53 and gives a hundred-rupee note, the

shopkeeper may return as follows: here, four notes of rupees

10, another five rupees and two coins of rupee 1. Here even

the answer, 47, is not mentioned but the operation is

correct. (This is not an argument to say that children need

not learn the standard method, but to say that for children

having difficulties, alternatives may help, until they gain

confidence.)

Q.18 What does it mean to shift focus from content to

process?

A.18 In mathematics, content areas are well established:

arithmetic, algebra, geometry, trigonometry, mensuration,

etc. Our teaching is  content oriented, and while it is

important to teach content, it is even more important to think

of how we teach such content. Here process refers to24 Q & A

pedagogic techniques. For example, many general tactics

of problem solving can be taught progressively during the

different stages of school. Techniques like abstraction,

quantification, analogy, case analysis, reduction to simple

situations, even guess-and-verify, are useful in many

problem contexts. When children learn a variety of

approaches (over a period of time), their tool-kit gets richer

and, as we talked about it above, they also learn which

approach is best suitable in a given situation. Instead of

looking at whether children know something, it is more

important to observe how they acquire such knowledge.

Though the processes cut across several subject areas, these

are central to mathematics. Problem solving, estimation of

quantities, approximating solutions, visualisation and

representation and mathematical communications are some

of the processes of mathematics. As an example, an ability

to convert grams into kilograms is important, but more

important is the capacity to talk in terms of kilograms for

weight of cabbage, and grams for eggs.

Q.19 What is the meaning of mathematical communication?

A.19 Precise and unambiguous use of language and rigour in

formulation are important characteristics of mathematical

treatment. The use of jargon in mathematics is deliberate

and stylised. Discussing with appropriate notations aids

thinking. That is what mathematical communication

means.

Q.20 I ensure that children give as much importance to

setting up the equations as to solving them. Is that

also mathematical communication?

A.20   Yes, you do the right thing.

Q.21 What is the difference between ëword problem and

mathematical modellingí?

A.21 In word problem, we do not care for physical insight of the

problem, but in mathematical modelling, physical insight

of the problem is more important. The term modelling is

typically used at the secondary stage and later, for25 Q & A

situations where students come up with a mathematical

(typically algebraic) formulation to solve them, translating

the answers back into the situation. The model is intended

to be used later on for other similar purposes. Word

problems are similar, but typically used at the elementary

stage, and refer to exercises where the child formalises the

situation into a form where a specific mathematical

technique can be applied. We can think of word problems

as ëdisposableí (or ëuse and throwí) models!

Q.22 D i s t i n g u i s h   b e t w e e n   u s e   o f   c o n c r e t e   m o d e l s ,

mathematical models and mathematical modelling.

A.22 When we talk of using concrete models, we are referring to

models already built by self or others which make it simpler

to comprehend a difficult concept, and to visualise it; for

example, cone, cylinder, frustum of cone, etc. used in

mathematics laboratory. The meaning of mathematical

model is to connect physical situation into mathematics

with the help of symbols, such as calculating simple interest

with the help of the formula  

P R T × ×

100

, where symbols

have their usual meanings.

Mathematical modelling, on the other hand, is a

process of transformation of a physical situation into

mathematical analogies with appropriate conditions. It

may be an iterative process where we start from a crude

model and gradually refine it until it is suitable for solving

the problem and enables us to gain insight  into and

understanding of the original situation. For example,

constructing a mathematical model for the estimation of

number of fish in a pond without accessing the situation,

estimating the number of trees in a dense forest, etc.

Q.23 What is systematic study of space and shapes?

A.23 Space is all around us, and we see shapes all the time.

But  when we see a hal f - f i l led glass of  water ,  only

systematic study opens our eyes to the circular base,

the cylindrical body, an estimate of the volume of water,26 Q & A

etc. Similarly, geometry gives us a sense of symmetry

and stabi l i ty when we  look at  archi tecture.  Thus,

g e o m e t r y ,   i t s   s y s t e m a t i c   u n d e r s t a n d i n g   u s i n g

quantities, and its principles (theorems) altogether can

be considered the beginning of systematic study of

space and shapes.

Q.24 What is tyranny of procedure?

A.24 When we learn to do something only as a procedure: ìdo

this, then that, then thisî, without understanding why, we

not only make mistakes, but also become incapable of

applying this learning in a slightly changed situation. A

good cook knows not merely the recipe, but also the roleplayed by each ingredient, so that she can use a different

one when something is not available. In mathematics,

simply learning formulae without understanding makes

for such tyranny, as a consequence, we stop thinking.

Q.25 What is meaningful problem solving?

A.25 Exercises at the end of a chapter typically involve only

application of a specific skill learnt in a specific situation.

P r o b l e m   s o l v i n g   i s   m o r e   g e n e r a l   a n d   s h o u l d   b e

distinguished. The problem-solving situation is meaningful,

when it interests the child who is then motivated to solve

the problem, the situation is genuine and the solution is

relevant. Meaningfulness is different from interesting

stories. A problem asked: Mother made 120 puris, 5 people

ate 22 each, how many were left over ? This is utterly

meaningless!  Even if one can produce a family with 5 people

eating exactly the same number of  puris, who cares how

many are left over after   each one ate 22 of them? The only

purpose of asking such a question may be to have children

reflect on the atrocity of having their mother (or anyone

else for that matter) to make 120 puris in the first place!

On the other hand, finding the number of bricks required

to make a wall of given dimension is a meaningful problem

as it involves the use of concepts of volume as well as

concepts of division.27 Q & A

Q.26 Why is problem posing as important as problem

solving?

A.26 Problem solving usually means a better understanding of

the concepts involved, which in turn helps in solving the

problem. Problem posing, on the other hand, often requires

original  and diverse thinking and has many a time

resulted in the development of mathematics. For example;

(i) Many attempts were made to prove/disprove Euclidís

fifth postulate. The work done during these attempts

resulted in the development of Non-Euclidean Geometry;

( i i )  Famous seven br idges problem  resul ted  in  the

development of a new branch of  mathematics called Graph

Theory.

Q.27 What is visual learning in mathematics and why is it

important?

A.27 Learning   mathematics by drawing visuals such as number

line, bar graph, line graph, histogram, pie chart, etc., is

called visual learning. It is important because it facilitates

learning, makes it more permanent, and facilitates

communication of ideas or result.28 Q & A

C hapter-3

Towards Implementation

Obstacles in implementing key ideas, issues and concerns in

the context  of  science and mathemat ics;  sof tening  the

boundaries between different subjects and bringing reforms in

evaluation: revisiting vision of NCF-2005

Q.1 NCF-2005 seems  to be  ful l  of  good      ideas and

intentions. But we are all aware of ground realities of

our schools.  How   are we going to implement these

different ideas?

A.1 Though it has been   phrased   in general conceptual

terms, NCF-2005 is deeply rooted in the  ground realities

of the country. It was widely debated throughout the

country involving different stakeholders of education.

Still I appreciate that you are concerned about the

obstacles in its implementation. Let us see what the

possible obstacles are and what we can do about them.

Q.2 The first obstacle is the quality of infrastructure. In

many schools of our country, infrastructure is far from

adequate. Every school must have an ideal laboratory,

space for carrying out activities, and mathematics

laboratory.

A.2 That is perfectly right. NCF-2005   has   recommended

that we must provide access to science experimentation

kits and laboratories in rural areas as one of the important

ways   of equitable  provisioning for science learning. It

should be ensured that   basic infrastructure is available

in all schools of the country. For quality improvement,

every school must have mathematics laboratory.

Q.3 It is sometimes said that even without adequate

infrastructure, activities and experiments can be

carried out, at least up to elementary levels. How can29 Q & A

this be done? I feel that we do need tools and space

to carry out activities.

A.3 What is required is that teachers of a school discuss together

and exchange their ideas to design their own tool kits to

improvise equipments to carry out low-cost activities and

experiments using locally available materials. They can

even meet together at the   district, zonal and regional levels

for this purpose. Even children can participate in the

development of the tool kits. Here, one must try to explore

the possibilities of sharing the resources. Some specific

equipments could be shared among schools if they are

placed in the cluster centre.

Children are constantly interacting with the physical

envi ronment  of   thei r  schools dur ing st ructured or

unstructured time, consciously or unconsciously. We need

to pay attention to it.

Teachers might utilise every conceivable situation for

learning process. For example, on the schoolís ground certain

things are almost always available, such as soil, plants, trees,

insects, birds, sunshine and shadows, bicycles and

automobiles. A range of activities can be organised from these

things, situations and materials. Proper planning is required

to encourage participation of children and make their

learning effective.

Q.4 Is it really possible?

A.4 Certainly. There are examples where this has been possible.

For this, a change in mindset   is needed. This is best

brought out by teachers coming together.

Q.5 But  even  i f  act ivi t ies are possible wi th  l imi ted

infrastructure, my fear is that I would not be able to

complete my syllabus. How should I  deal with this

problem?

A.5 Your fear is natural. But once you start this approach with

a little effort, you will   observe that learning among students

is accelerated.  You will begin to devise your own ways of

conducting activities/experiments, group work, discussion

and brainstorming, and you will be gratified to see the30 Q & A

positive outcomes of the approach. You can also consider

involving children and older learners in planning the class

work. Such a practice can bring tremendous richness in

LEARNING THROUGH THE PHYSICAL SPACE:

Children perceive their world through multiple senses,

especially the tactile and visual senses. A three-dimensional

space can offer a unique setting for a child to learn because

i t  can  int roduce a mul t iple sensory exper ience  to

a c c o m p a n y   t h e   t e x t b o o k   o r   b l a c k b o a r d .   S p a t i a l

dimensions, textures, shapes, angles, movements and

spatial attributes like inside-outside, symmetry, up-down,

can be used to communicate some basic concepts  of

language, science, mathematics and the environment.

These concepts can be applied to existing as well as new,

to-be-built spaces.

! Classroom space: A window security grill can be designed

to help children practise pre-writing skills or understand

fractions; a range of angles can be marked under a door

shutter on the floor to explain the concept of angles; or a

classroom cupboard can be modified to be used as a

library; or a ceiling fan can be painted with a range of colour

wheels for children to enjoy the ever-changing formations.

! Semi-open or outdoor space: The moving shadows of a

flag-pole acting like  a sundial to understand the different

ways of measuring time; planting winter deciduous trees

that shed their leaves in winter and are green in summer

to make a comfortable outdoor learning space; an

adventure playground could be developed here using

discarded tyres; a counter space to simulate a bus/train/

post office/shop counter; an activity space for playing with

mud and sand and making oneís own mountains, rivers

and valleys in an outline map of India; or space exploration

and discovery; space to explore three dimensions; or the

outdoor natural environment with plants and trees that

allow children to explore and create their own learning

materials, colours, discover nooks and corners; grow a

herbal garden; and actually see and practise rainwater

harvesting.

NCF-2005 (p.79)31 Q & A

the classroom. In the beginning, it may appear difficult to

manage the class and the time but with commitment, the

new approach will begin to yield fruit.

Q.6 Performing activity/experiment and carrying out

discussion in the class cause disturbance to adjoining

classes and there is objection from the administration.

How can we overcome this difficulty?

A.6 This is a genuine difficulty. Like the teachers, the

administrators too need a change in mindset.  They should

discuss with the teachers and arrive at practical ways of

LEARNING BY DOING

Maria  invites her  IX standard students to contribute in the

teaching-learning process. In order to involve the whole class

and to create ë who is doing whatí atmosphere, all the students

together form four to five groups and write the name of the

group members preparing and presenting an activity/

experiment to the class. Students willingly arrange for some

materials and apparatus from the school/surroundings.

Maria facilitates them in planning and carrying out the

activities. Presentation of the activities is followed by

discussion on the concepts. Using hands for working leads

to a lot of ëhowí and ëwhyí coming up in the mind of the

students. Maria says ìIt makes my job easier as learning is

retained by the students. Furthermore, I am very pleased to

observe that the students who appear very shy in the class,

work actively as a member of a team.î

Experience of a teacher

THIS CAN BE ALSO DONE

Shabana   is in-charge of the science laboratory of her

school. She makes it a point to display a list of apparatus

and materials available  in  the laboratory on the  school

notice board. It facilitates children and her colleagues

to plan activities and experiments well in advance.

Experience of a teacher32 Q & A

maintaining order and discipline in the school, even when

activities/discussions are going on in different classrooms.

Teachers and administrators both need to be flexible.

Q.7 But, there are not enough resource materials for

guidance.

A.7 A number of activities, exercises, ideas for extended learning

and projects have been incorporated in the NCERT

textbooks to facilitate students to build their knowledge.

NCERT is making further efforts in this direction. Teacherís

Handbooks, Science and Mathematics Exemplar Problems

and Laboratory Manuals in Science and Mathematics have

been/being prepared. Apart from this, a teacher can do a

lot herself   by utilising  resources available in the library,

through Internet and also by interacting with other teachers

and by involving parents.

Q.8 It is difficult to get access to the resource materials.

What can be done?

A.8 With some planning and coordination, access to resources

can be improved. For example, newspaper, magazines and

 LET US DO SCIENCE

Shakti, principal of a government school, has initiated a

project in his school. Once in a week, any student or

group of students can demonstrate any activity in any

subject during recess.  They have conducted the activity

on formation of bubbles, air occupies space, formation of

shadow by different settings of oneís palms, testing

adulterations in food items, etc. Their names are

announced during the morning assembly. Children finish

their lunch fast, to observe, interact and participate in

the activity which is held on the assembly ground. Many

times, students of class VI demonstrate and students of

secondary and higher secondary stages also get actively

involved in it. Lively interaction is observed during

presentation. Though, it is not a mandatory exercise,

almost all the students and teachers look forward to it.

Experience of a principal33 Q & A

electronic media can also be used to supplement classroom

teaching. Good  educational programmes  are aired on

various T.V. channels, especially on Gyan Darshan. For

example, whenever Rohit, a teacher at higher secondary

stage, watches a good educational programme on the T.V.,

he informs two of his students on telephone about it. Those

two students inform two other students and through this

chain of information, the whole class watches the educational

programme in the late evening or early   morning or on

holidays. Later the topic is discussed in the class. Learning

is appreciated as participatory process.

Q.9 We do not have access to innovative curricular

materials and ongoing professional support to meet

the objectives of NCF-2005. What do you say in this

regard?

A.9 NCERT and various state agencies organise training

programmes  from time to time for this purpose. You may

visit our website www.ncert.nic.in. Please refer to List of

Resource Materials on the inner side of back cover page.

Q.10 Our efficiency and competence are evaluated   on the

basis of percentage of marks obtained by our students

in the examinations, not on how well they have learnt.

Why should we follow the constructivist approach to

learning?

A.10 It is true that most activities in the school are examination

driven.  When children are involved in active learning in

this approach, they are able to perform well in the

examinations too, because   they   learn   how to learn.

They get self motivated to learn. Facilitating students in

studying and relating their learning to their everyday life

experiences  make the job of the teacher easier.

Q.11 There is another problem. There is no flexibility in

school calendars. This is a real hurdle to implement

the constructivist approach.

 A.11 You are right.  If   you   feel the need to bring changes in the

school calendar, you should feel empowered to put forth

your point of view to the concerned authority with conviction34 Q & A

and in a persuasive manner. NCF-2005   recommends

flexibility in school calendar as well as in the timetable.

There is a need for providing a few longer periods lasting

an hour, or one and a half hours, in the school timetable

that allow for other kinds of activities, such as laboratory

work, projects, etc. This much length of time is also essential

for undertaking across the subjects integrated learning and

for effective group work.

Q.12  What is the meaning of going beyond the textbook

and the classroom?

A.12 Textbook is only a tool of transaction of contents in teachinglearning process. Learnersí own experiences outside the

classroom and the textbook should be integrated in their

learning. It is through interaction with the environment that

the child construct knowledge and derives meaning.

Therefore, it is necessary to make the boundary between

school  and her  natural  wor ld porous.  Explorat ion,

inventiveness, field visits  and creativity through activities,

exper iments and  technological  modules should be

emphasised. These should be contextualised, as far as

possible, in order to make learning joyful.

Q.13 NCF-2005 says that for any qualitative change from

the present situation, science education in our country

must undergo a paradigm shift. What does it mean?

A13 Any policy of education is based on   contemporary ideas on

how children learn as well as on a certain understanding of the

societal situation around and the need of time. NCF-2005 has

recommended a constructivist approach to learning science

and mathematics and has strongly discouraged rote learning.

It also recommends that schools should give much greater

emphasis on various curricular elements, considering   them

as integral part of curriculum, with an aim to stimulate

investigative and creative abilities of  children. Areas of

knowledge such as heritage crafts, work, the arts, health and

physical education, and peace education have very rich

potential for the development of creativity, resourcefulness,

practical intelligence and   teamwork. These should be

integrated and interrelated with different subjects. Concerns

and issues pertaining to environment should be emphasised

in every subject and through wide range of activities. These

principles are not new, but there is considerable change in

focus and emphasis. This is the   paradigm shift.

Q.14 Traditional method of teaching also allows for dialogue

between the teacher and the learner. What then is

the difference between the traditional method and

the constructivist approach?

A.14 In the traditional method, generally the   teacher explains the

concept, and asks questions having predetermined answers.

If learners reply along that way, the objectives   of teaching are

assumed to be achieved. But in the constructivist approach,

due attention is given to the thought process of the learners.

Children are involved in enquiry and exploration and develop

the concepts by their own experiences. They perform activities

and experiments. They are facilitated to connect new ideas to

the existing ideas on the basis of material/activities presented

to them. The teacher involves the children in all activities of

teaching-learning process in order to facilitate construction of

their knowledge. She   provides them opportunities to express

their ideas in their own words about the concept. Their ideas

are acknowledged and valued.

Q.15 How can we provide them opportunities to construct

their knowledge?

A.15 This can be done by engaging them in activities, experiments,

projects, field visits, library, discussion with peers and

teachers, group work, conducting brain storming sessions,

collecting information from different sources, inquiring,

listening, thinking, etc. Learners should be allowed to share

and explain their ideas, and to ask, raise, pose and frame

questions. Teacher can design her own way of facilitating

the learners in constructing their knowledge depending upon

the situations. For example, they may form different

hypotheses for the conditions of rusting. Their opinion may

be collected and teacher may design experiments to test their

opinions (e.g., iron nailsó kept in water, kept in open space,

kept in an airtight container, kept coated with  some oil,

kept in vinegar, and so on, for the same duration).36 Q & A

Q.16 Can  chi ldren be  t rusted  to const ruct   thei r  own

knowledge?

A.16 Yes, they can be. They are part of teaching-learning system.

Children may be allowed to make mistakes and think

independently, and not be ridiculed. They should be

encouraged to speak in their own words. Textbook wording

need not be repeated. In the beginning, even the incorrect

answers of students may be accepted and respected without

being judgmental. Gradually, they can be facilitated to validate

and construct their knowledge by engaging themselves in

various activities. We need to provide opportunity to children

to realise that learning to learn and the willingness to

unlearn and relearn are important as means of responding

to new situations in a flexible and creative manner.

Processes of science and mathematics and construction of

knowledge should be emphasised at all levels of learning.

Q.17 Conducting activities and experiments, I face a

problem. Only the more vocal students come forward

in the discussion of the activity. How can I ensure

active participation of all the students?

A.17 Yes, this is a problem. NCF-2005 says students need to be

encouraged to speak up what they think, to explain their

answers, to predict if concepts learned earlier are being

applied in new situations. Teacher needs to respond to

studentsí thinking/responses in a neutral rather than in

an evaluative way.  This will encourage students to

participate actively in teaching-learning process and

explore their own ideas.

Q.18 How is an activity different from an experiment?

A.18 Activity is rather a general   term, which encompasses

various meanings. It is usually open ended with broad and

flexibly structured steps. It is carried out in a natural

environment. Its aim is   to develop various process skills

of science, like observation, measurement, making

inferences, communication, etc. With the help of an activity,

students arrive at some conclusion. Activities are part of

learning process. It cannot be taken into isolation.

A c t i v i t y   u n d e r   c o n t r o l l e d   s i t u a t i o n   i s   e x p e r ime n t .

Experiment is more focussed, controlled and   structured.37 Q & A

A few of the variables are controlled and their relationship

with other   variables are explored. There is usually some

hypotheses to be tested in an   experiment. It   often, if not

always, involves some quantitative measurement and it

aims to verify/confirm some principles of science.

Distinction between an activity and an experiment is

not very rigid. At the upper primary and secondary stage,

where science is taught with more interdisciplinary

approach, teaching-learning process is activity driven. But

at the higher secondary level, where different areas of science

are taught as separate disciplines, experiments are

necessary.

Q.19 Class tenth and twelfth students are too busy to be

involved in any type of activity. Why should we

involve them in those activities?

A.19 We need to convince them that doing experiments helps in

learning and retention of scientific concepts   better.  They

need to experience this fact themselves. Once this happens,

students will regard experiments as an aid  and not a hurdle

for their examinations. Further, experimental works are to

be integrated with the theory to make it meaningful.

Q.20 I am not yet convinced. How do activities help to aid

learning?

A.20 Activities aid in learning in many ways. When children

perform any activity, they enquire, explore and do things

on their own, with their peers or in the company of adults,

and use language to express or ask, to listen and to interact

with the environment around. They learn the processes of

science. Therefore, it helps in understanding the concepts

and reduces rote memorisation. At the same time, it

minimises stress of children and helps   them in enhancing

their self-confidence.

Q.21 Now I am convinced of carrying out various  activities

during teaching-learning process. But a major problem

is how to evaluate students in activities/experiments.

How can I do it?

A.21 This is a very relevant question. First of all, evaluation

cannot be separated from learning.  It is to be integrated

with all teaching-learning experiences. There must be space38 Q & A

and time for students and teachers to plan activities and

experiments, discuss ideas and critically record and analyse

observations. Oral testing, evaluation of group work, and

process skills of science should be in-built part of activities/

experiments. How students summarise and record their

observations, interpret the data, draw conclusion, participate

in activities, set up the experiments, improvise simple

apparatus, make models, collect and display specimen of

parts of plants, rocks, etc., and get involved into inquiry are

some of the parameters for evaluation of activities and

experiments. Teachers may also evolve a flexible and

implementable scheme to assess a wide range of performance

parameters of students for this purpose.

Q.22 Will it be correct to evaluate an activity/experiment

only on the basis of the result obtained?

A.22 Science is more than the product of knowledge. The

process of science is equally important. Different process

skills such as observation, classification, measurement,

communication, inquiry, manipulation of apparatus, etc.,

are some of   the parameters  that  can be assessed.

Conducting activities helps teacher to spot unique

strengths and weaknesses of her students. In fact,

activities and experiments provide the basis for ongoing

observation and qualitative assessment of children.

Q.23 This seems to be all idealistic and impractical. My

question is how to give marks/grades to students in

activities/experiments.

A.23 Grades should be given on the basis of continuous

assessment of the childís progress and accomplishment.

The inputs to this assessment may be written reports by

the student, teacherís record of the studentís work,

observation, interviews, etc.

Q.24 But this is impractical for assessment on a large scale,

such as at a Board Examination.

A.24 The Boardís assessment of practical work includes

internal assessment, which is carried out by schools.

Recently, CBSE has also taken important measures to

i n c l u d e   w r i t t e n   q u e s t i o n s   i n   p r a c t i c a l s   f o r   t h e i r

examination papers.39 Q & A

Q.25 NCF talks of diffusing boundaries across different

subjects. Please explain about it.

A.25 T h i s   m e a n s   t h a t   w e   s h o u l d   a v o i d   e x c e s s i v e

compartmentalisation of knowledge. In the elementary

stages of school education especially, we should adopt

integrated approach as much as possible.  Even in later

stages, boundaries between subjects should not be viewed

too rigidly. Natural phenomena do not occur as physics,

chemistry or biology. Nor do social issues separate

themselves into different disciplines.  Every phenomenon

or issue has many interconnected aspects, which draws

on different subjects and disciplines. This is particularly

so in the modern complex technological world.

Q.26 Wh a t   i s   t h e   d i f f e r e n c e   b e twe e n   i n t e g r a t e d   a n d

interdisciplinary approach?

A.26 Integrated approach of curricula facilitates students to

learn the concepts as an interconnected body of knowledge,

not as fragmented piece of knowledge. It helps students to

make connection of concepts across the curricula. Students

develop life long skills that allow them to think critically

and make informed decision about their world. Science upto

secondary stage is dealt with this approach. In the

interdisciplinary approach attempt is made to design

planned learning experiences which provide the learners

with a unified  view of commonly held knowledge. Subjects

are treated with various perspectives cutting across

disciplines and forming a new method for understanding

the problem at hand. It also equips the learners to develop

power to perceive new relationships and create new mental

models. For example, lessons on the themes ëEnergyí,

ëGlobal Warmingí, ëNatural Resourcesí, ëOur Environmentí,

have much scope for dealing with interdisciplinary

approach.

Q.27 What does NCF-2005 say about the integrated and

interdisciplinary approach to science?

A.27 NCF-2005 greatly emphasises both. Upto secondary stage,

integrated approach is especially advocated. A curricular

area like science is not to be seen in terms of individual

discipline, like physics, chemistry or biology. At later stages,40 Q & A

these subjects have to be taught as separate disciplines,

but there again, NCF-2005 lays great emphasis on

interdisciplinary approach.

Q.28 How is diffusing   boundaries across different subjects

useful for learning?

A.28 Knowledge becomes interrelated and integrated to the child

by softening the boundaries between different subjects. She

constructs her knowledge the way she views the world.

Knowledge in the school and outside the school becomes

part of her knowledge framework and she is able to apply

it in her daily life. Areas of knowledge such as crafts and

sports, if integrated, have the potential for development of

v a r i o u s   s k i l l s ,   a n d   p r omo t e   a e s t h e t i c s ,   c r e a t i v i t y ,

resourcefulness and teamwork.

Q.29 Should we allow the students to answer in different  ways?

A.29 Children answer the same question in different ways if  you

have not imposed your answer. There is no issue in allowing

them; the issue here is accepting their answer and analysing

it to see the progress of learning and the direction of

learning.

Q.30 What is continuous and comprehensive assessment?

A.30 Continuous assessment means assessment of learners

in the beginning of instruction, during the instructional

processes and assessment of performance done at the

e n d   o f   u n i t / t e r m   u s i n g   m u l t i p l e   t e c h n i q u e s.

C o m p r e h e n s i v e   a s s e s s m e n t   m e a n s   a l l   a s p e c t s   o f

learning, i.e., curricular areas, personal and social

qualities, interests, attitudes, values need to be assessed

as well. Therefore, each school should evolve a simple

QUESTIONS ASKED IN DIFFERENT WAYS

A question, ëëWhat is the colour of this solutionî can be

better framed as ìTell me about the colour of this

solution.î  Some other form of open-ended questions

may beñ ìWhat do you think will happen if...........î

ìIs there another way to...........î41 Q & A

and suitable scheme that could be developed   by it,

involving its teachers.

Q.31 Why is the need for school-based continuous and

comprehensive evaluation felt?

A . 3 1 Its need is felt to reduce stress among children and

p r o v i d e   s p a c e   f o r   t h e   t e a c h e r   f o r   c r e a t i v e   a n d

diagnostic teaching. Diagnostic teaching helps students

to learn to detect, understand and correct misconceptions

on their own and their fellow studentsí work. As an

experienced teacher, you might always be doing it and

might have observed that it provides opportunity  to

children to develop greater skills. The continuous and

comprehensive scheme should be simple, flexible and

implementable in any type of school from the elite one

to a school located in rural or tribal area.

Q.32 H o w   c a n   w e   b r i n g   a b o u t   f l e x i b i l i t y   i n   t h e

examinations?

A.32 NCF-2005 suggests many ways to bring flexibility in the

e x a m i n a t i o n .   S o m e   o f   t h e s e   a r e   c r e a t i n g   m o r e

opportunities for children to appear in the examination,

change in the typology of question paper and a balance

between internally and externally examinable knowledge

and intellectual skills. There are public as well as internal

examinations in our system. It is true that any radical

change in large-scale public examinations is not easy; it

requires a broad consensus and corresponding policy

changes.  NCERT is making efforts in this direction. But a

lot can be done for the internal examinations within the

school by the teachers. Schools should be given internal

autonomy to   bring about flexibility in assessment in

terms of types of questions, time and tests that cater to

individual differences.

Q.33 In order to shift the focus from memory-based learning

t o   h i g h e r   l e v e l   c o m p e t e n c i e s ,   w h a t   m o d e s   o f

assessment   should be used?

A.33 You have asked a very good question. Oral testing, group-work

evaluation, open-ended questions, open-book examination,42 Q & A

e x a m i n a t i o n   w i t h o u t   a n y   t i m e   l i m i t ,   o n   d e m a n d

examination may be used as various modes of assessment.

Besides, the teacher can design her own innovative methods

of assessment.

Q.34 Will the approach to open book examination and

similar ideas   not  be equivalent to cheating?

A.34 Not at all.  For an open book examination, a different kind

of question paper is to be set. Such measures   would

discourage rote learning, one of the guiding principles of

NCFñ2005, and measure interpretation, analysis and

problem-solving skills of children.

Q.35 Are there any examples of open-ended questions

in mathematics?

A.35 There are plenty. Examples:  finding two polynomials such

that the degree of their product is 5; finding three or four

rational numbers between two given rational numbers say

3/5 and 4/7.

Q.36 What is the meaning of non-detention?

A.36 Non-detention means   a student is not detained in the

same class even if her performance in an examination is

unsat isfactory.  Somet imes nonñdetent ion pol icy  is

confused with no assessment. Assessment is an integral

part of teaching-learning process at all stages of education.

Of course, its form may be different at different stages and

for different components of the curriculum. NCF-2005

says that up to upper primary stage there should be no

detention of students. It recommends taking remedial

measures to improve performance.

Q.37 Will it not dilute the standards?

A.37 Not  necessar i ly.  For   this,  assessment  needs  to be

continuous and comprehensive.  Learner  should be

a s s e s s e d   d u r i n g   t h e   t e a c h i n g - l e a r n i n g   p r o c e s s .

Diagnosis of misconceptions can be done from formative

assessment and accordingly remedial measures can be

taken. Non-performance is the problem of the system, not

of the child. He/she should not be penalised for this.43 Q & A

Q.38 What is the meaning of   the ëthree year windowí?

A.38 It is a time limit suggested to clear the particular public

examination as per the pace of learning of different

students. In a given year, they may appear in only those

subjects for which they are well prepared.

Examination Reforms

For many students the Standard X year is a time of

unremitting stress. Failure in the examination is seen as a

major disaster; among the better students, even failure to get

sufficiently high marks causes grave anxiety and guilt. From

the standpoint of the school, the examination determines the

content and methodology of schooling right down to the upper

primary level.  Thus if we are to conceptualise meaningful

reforms in the educational system as a whole,  it is essential

that we turn a critical eye at this examination and the

associated curriculum, syllabi and textbooks.

Whether one assigns marks or grades, one of the most

fundamental reforms that must be affected is alternatives to

the concept of overall pass or failure in the Standard X

examination. The student who cannot make the grade at

the examination  of Standard X must not have to go through

life with the ignominious label ìtenth standard failî. Schools

must be evaluated on the basis of the number of

children who have continued their study, not on the

basis of their performance in examination. The 15 or

16 year old in Class X are adolescents; the schools must be

ready to engage with them, providing them guidance and

counseling as integral part of education.

POSITION PAPER ON SYSTEMIC REFORMS  FOR CURRICULUM CHANGE

(p.22)

Q.39 NCF-2005 recommends eliminating the term ëfailí from

the marksheet. Why do we need to remove pass/fail

terms?

A.39 As an experienced teacher you must have observed that

the term ëfailí carries a social stigma. It amounts to44 Q & A

victimising a child for systemic deficiencies: inadequate

teaching, unavailability of textbooks, etc. The term ëfailí may

be replaced by ëneeds more work to attain desired standardí

or ëneeds improvementí.

In  the publ ic examinat ion  there may be some

students who do not demonstrate satisfactory completion.

They should be provided a number of chances (within

three or even five- year period) to retake the examination.

Till then they are ëworking towards certificateí. Even after

expiry of this period, they should be free to attempt the

whole examination again. Hence, while it is possible to not

succeed in passing an examination, no one ever definitely

(and permanently) ëfailsí.

Q.40 NCF-2005 says that the focus should shift to framing

good questions rather than mere paper setting. How

can it be done?

A.40 Good   questions need not be generated by experts only.

These can be pooled all year round, from teachers, college

professors, educators from different states, and even

students. These questions, after careful vetting by experts,

could be categorised according to difficulty level, topic,

concept, competency, and   the estimated time to solve. A

record of these questions can be helpful in generating good

questions.45 Q & A

ANNEXURE ñ I

KEY WORDS AND PHRASES

Abstraction

The process of developing concepts. In this process, concrete

experience is generalised and idealised to form a logical

structure. For  example, many experiences with four objects

produce the concept of a number 4. Similarly, many

experiences with boundaries produce the concept of curve

and surface.

Analogy

Considering a similar but slightly different situation. For

example, if a, b and c are positive integers such that c=ab,

then a and b are factors of c. In the same way, for three

polynomials p(x),q(x) and r(x), if

r(x)=p(x). q(x),

then p(x) and q(x) are factors of r(x).

Approximation

Arriving close to a quantity without getting   it  exactly. For

example the square root of 500 is approximately 22. A better

approximation is 22.5. But neither of these is actually equal

to the square root of 500.

Argumentation

A process by which something is claimed to be true or false

and by giving reason why it is so. Then addressing  the

question ìwhat if it is false (or true)?î and giving  reasons

why it cannot be false (or true). Such reasons may again

raise new questions, and so on. It is similar to proof but

more informal.

Case analysis

Break up a problem into different cases: for instance,

providing different proofs for the cases when x < 0, x = 0

and x > 0, thus showing it true   for all values of x.46 Q & A

Children learn to enjoy mathematics

This is based on the premise that mathematics can be both

used and enjoyed lifelong, and hence, that school is best place

to create such a taste for mathematics. Children learn to enjoy

mathematics if activity-based teaching is done in the class.

Conjecture

Making a statement that we strongly believe to be true,

without proving (or disproving) that it is indeed true. For

instance, ìEvery even integer greater than 4 can be

expressed as the sum of two odd primesî(Gold Bach

Conjecture). This statement has not been proved or

disproved so far.

Consolidation

Revisiting a concept that has already been learnt, perhaps

with new ideas (as opposed to learning new things) so that

foundation is strengthened.

Contextualisation

More autonomy and flexibility in textbooks and syllabi at

all stages of school education within the broad guidelines

of the curriculum framework. This is because we need to

reflect on the diversity of our country.

Critical pedagogy

It is an approach of teaching in which children are

encouraged to question, to argue and to debate on the topic

being taught. They are helped in forming their   own

opinions and not accepting theories and practices of the

subjects without reflections.  Critical pedagogies facilitate

collective decision making through open discussion and

by encouraging and recognising multiple views.

Critical thinking

It is a mental process of gathering information from all

sensesóverbal, written, observation, experience, reasoning

and reflection. It enables the children to channelise,

evaluate, explain and reconstruct their thinking.

Curriculum

All the activities which are planned and guided by school

whether it is inside or outside the school. It is a plan for47 Q & A

facilitating learning for the child and coordinating between

the aim of education and the childís capabilities. It is neither

a document nor a sequence of experiences. It consists of a

set of aims in terms of the content of what is to be taught

and the knowledge, skills and attitudes that are to be

deliberately fostered.  It also states criterion for selection of

contents and choices in methods, materials and evaluation.

Curriculum that is ambitious and coherent

Ambitious in the sense that it seeks to achieve the higher aim

of mathematics education, i.e., to develop the childís resources

to think and reason   mathematically, to pursue assumptions

to logical conclusions and to handle abstractions. Coherent

in the sense that different methods and skills acquired

through the study of mathematics, namely, arithmetic,

algebra, geometry, etc. can be applied to solve problems of

daily life and can also be  applied  to other  subject  areas.

Estimation

Determining a quantity without performing detailed

calculation.  For instance, we estimate the wood required

for making doors and windows in a house in terms of

number of logs. We often guess the weight of a gourd as

ìbetween and 1 kiloî   without actually weighing it.

Folk algorithms

Methods employed commonly by people. For instance, the

way people estimate the number of mangoes in a tree for

leasing. These are relevant and can be of use in schools as

well. It exists for not only mentally performing number

operat ions,  but  also  for  measurement ,  est imat ion,

understanding of shapes and aesthetics.

Generalisation

Arriving at a general conclusion through   a large number

o f   e x amp l e s / p a t t e r n s / s i t u a t i o n s .   F o r   e x amp l e ,   b y

measuring angles of different types of triangles and finding

their sum to reach at the general conclusion that the sum

of all angles of a triangle is 180

0.

Good science education is true to science

It implies that children make attempts to learn processes

and facts of science logically, honestly and meaningfully.48 Q & A

Good science education is true to child

The phrase means active involvement of children in

teaching-learning process of science so that she is motivated

for learning to learn.

Good science education is true to life

I t  means  that  chi ld  is equipped wi th  the  requisi te

conceptual understanding of science to apply it in her

everyday life situations.

Heuristic

The term ëHeuristicí is used to describe an approach to

problem solving. It involves ërules of thumbí. Here those

strategies are used which are loosely applicable, which

work often but not always. For instance, when we are

unable to solve a problem in the general case, a good

heuristic is to try a few examples and watch for patterns.

To find a property of some triangle, it is often useful to

first investigate the special case when the triangle is right

angled and then look at the general case afterwards are

examples of heuristics.

Higher aim of mathematics

It stands for providing adequate opportunities and scopes

to students for their intellectual development according to

their inherent potentialities. This calls for clarity of thought

and pursuing assumptions to logical conclusions and to

handle abstractions.

Innovative alternatives

Coming up with new methods to solve existing problems.

Learning environment

Places  where children have an opportunity to learn on

their own, at their own pace, according to their individual

ability and motivation.

Mathematical communication

A specific style and notation is used in mathematics for

making statements, and learning. This is useful for

consolidating oneís knowledge. For example, it is better to

talk of an isosceles triangle rather than a triangle whose

two sides are equal.49 Q & A

 Mathematical modelling

The process of constructing a mathematical model (a

mathematical relation that describes some real-life

si tuat ion)   is cal led mathemat ical  model l ing,   i .e. ,  a

conversion of physical situations into mathematics with

cer tain condi t ions.  The var ious stages  involved  in

mathematical modelling are formulation, assumption,

solution, interpretation and validation. The model is useful

in other similar situations also.

Multigrade classroom

Children of different grades, i.e., I, II, III, etc., sitting together

and learning their own age-appropriate content   by a single

or more teachers.

Multiplicity of approaches

Solving   a problem by different methods. Many times, a

result/problem may be proved/solved in different ways.

For example, Pythagoras Theorem can be proved by using

the concept of similarity of triangles as well as using the

concept of area of parallelograms on the same base and

between the same parallels. A system of linear equations

in two variables can be solved in different ways. The fact

that there are infinitely many rational   numbers between

two given rational numbers can be estimated by different

methods.

Multiplicity of textbooks

In our country, textbook is the only accessible and

affordable curriculum resource.  Therefore, we must use

the textbooks as one of the primary instruments of

universalisation   of good science in the country.  National

agencies make efforts to produce quality textbooks.

Considering pluralistic and diverse nature of Indian society,

different states may also develop multiple versions of the

textbook   reflecting local contexts. If possible, states may

be encouraged to make separate textbooks for different

districts.

Narrow aim of mathematics

It specifies the attainment of minimal mathematical literacy

so that one can transact his daily-life business along with50 Q & A

social obligations smoothly. It means acquiring mastery of

the concepts such as numbers, operation on numbers,

measurement, percentages and their application, ratio and

proportion, etc.

Open-ended questions

Questions which seeks from respondents to answer in their

own words. Here answers are not unique and fixed.  It is a

contrast to closed questions which demand a specific piece

of information or choosing the most suitable choice or

selecting yes/no or true/false.  Open ended questions are

vital for effective teachingñlearning.

Open-book examination

It refers to evaluation on comprehension and application

abilities of the learner rather than on   rote memorisation.

It requires thinking about and evaluating the concept and

applying it to some new situation.  Open-book examination

prepares the learner to enter into the world of work.  People

at work may use reference book or collect information from

various resources to solve a problem. Likewise in open-book

examination learner is expected to come with some

knowledge and understanding.  The answer of a question

is not available even on a single page of the textbook. Learner

is allowed to bring books in the examination hall. Question

paper is set in a very typical way.

Optimisation

Finding the maximum or minimum values of a quantity

subject to some constraints. For instance, the area of a

rectangle with a given parameter of dimensions  a  and  b

is maximum when a = b. In life situations, it also involves

trade off: for instance, route 1 is comparatively longer than

route 2 but has less traffic, so route 1 is preferred.

Paradigm shift

This term refers to a radical change in certain thought

patterns. It is a shift from one way of thinking to  the other.

It does not happen automatically but is driven by some

agent of change, e.g., the transition from  Newtonian

Mechanics to Einstein Theory of  Relativity.51 Q & A

Pedagogy

It is an art as well as science of being a teacher.  It is referred

to as suitable selection and use of teaching strategies

keeping in view the learnerís previous knowledge and

experiences, learning situations and goals set up by the

learner and the teacher.

Quantification

It is fundamental to scientific method.  It tells about the

quantity of something, e.g. ëevery child in the classroom is

attentive to the teacherí; ëthe force of gravitation on the

moon is one sixth of that on the earth.í Here ëeveryí and

ëone sixthí are quantifiers. Thus it means associating

numbers with quantities so that they can be computed.

Compare ëDelhi is far away from Chennaií with ëDelhi is

more than 2000 km from Chennai í.

Reflective teaching practices

A process in which teacher/educator examines her own

method of teaching that whether it is supporting in realising

the specific objectives, whether it is suitable to the given

situations and if not which method will best suit the

learners. This is a lifelong and cyclic process in which

teacher continues to build these theories, adjust her

practices and reflects on her theory and practices.

Scientific method

It is a process of predicting a natural event or phenomenon

on the basis of certain principles. It involves several

interconnected steps: observation, looking for regularities

and patterns, making hypothesis, devising quantitative or

ma t h ema t i c a l  mo d e l s ,   d e d u c i n g   t h e i r  wo r k a b i l i t y ,

verification or falsification of theories through observation

and controlled experiments, thus arriving at the principles,

theories and laws governing the physical world.  The order

of various steps might change according to situations.

Spatial reasoning

Understanding relating   the space. For example, locating

various objects with respect to given shapes; interior,

exterior and boundary of a geometrical shape.52 Q & A

Structuration

The process of structure emerging from patterns (and other

mathematical insight). For instance, in algebra, arriving at

ëmultiplication  of a variable  by a constantí after observing

certain patterns. Different sets of numbers have their own

structures with respect to certain operations such as

addition, multiplication, etc.

Systemic reform

Every system has its own strengths and weaknesses.

Reforms, which help a system to correct its weaknesses,

are termed as systemic reforms. Every system works in

coordination with other systems linked to it, e.g., school

system works in coordination with examination and teacher

education system. So when we talk about bringing change

in our assumption about child, learning, teacher and

teaching-learning process, we need to take into cognizance

the fact that until change or reform takes place in

examination and teacher preparation system, it is difficult

to bring reforms in school system.

Systematic reasoning

Proceeding from assumptions to conclusions in a logical

manner, without extraneous matter. The aim of systematic

reasoning should be to develop arguments, make and

investigate conjectures and understand that there are

various methods of reasoning.

Teaching important mathematics

The phrase implies that whatever mathematics  has to be

taught, should be based on the needs of the students,

society and  the subjects, i.e., need-based mathematics.

Students and teachers must find sufficient reasons and

relevance for the topics to be taught.

Teacher expects to engage every child in class

R e m o v i n g   f e a r   a n d   p h o b i a   r e g a r d i n g   l e a r n i n g   o f

mathematics and science and making these subjects so

interesting that every child is encouraged to participate in

teaching-learning process.53 Q & A

Validation procedure

Validation procedure in mathematics is demonstrations

which are integral to the system.  It is specified by an

appropriate set of axioms and definitions. For example,

different concepts in mathematics are prime numbers,

square roots, fraction integers, function, etc.

Validity

Features in the curriculum which are essential to make it

good and meaningful.

 Visualisation

Drawing a picture to reflect a situation. The number line,

g r a p h s   o f   f u n c t i o n s ,   V e n n   d i a g r a m s ,   g r a p h i c a l

representation of data in the form of pie chart, histogram

and frequency polygons are commonly used examples.54 Q & A

ANNEXURE ñ II

EXAMPLES AND ANECDOTES

Most of the examples and anecdotes given below are from

real-life situations. Teachers had conducted classroom

activities in the following manner and received good

results in terms of learning and performance of the

children. They also observed that their relationship with

c h i l d r e n   g o t   s t r e n g t h e n e d .   T h e s e   e x amp l e s   a n d

anecdotes are suggestive, not prescriptive.

UPPER PRIMARY STAGE

1. Let us Learn about a Cell

The teacher had to start the unit on ëCellí. She introduced the unit

by making the students observe stained slide of onion tissues

through microscopes. She guided her students in taking epidermal

peels from the swollen leaves of onion. During this activity, students

also viewed slides of other plant tissues and animal tissues.

Students were curious to know many things about the cell. Till

then the teacher had not used any technical word like protoplasm,

nucleus, etc., except ëCellí. She instructed the students to observe

the slides and to jot down the questions that they wanted to be

answered. Some of the questions that they came up with wereó

ëëWhat is the dotted dark structure, at the centreíí?  ëëWhy is

stain not uniformly absorbed by the cell? Why is there no gap

between two cells? What is the function of the boundaries around

each cellíí? ëëWhy plant cells need cell wallsíí? ëëDo onion of bigger

size have bigger cells?ííDo bigger fruits and vegetables have

bigger cells? Are all living organisms made up of cell?íí ëëI have

heard the name of gene. What is the function of gene?íí Soon she

found students discussing among themselves and framing

questions that needed to be answered. Stage was set up for learning

from first-hand experience. She started the lesson on the ëCellí with

the queries of children. Students wanted to reinforce their learning

and requested their teacher to let them observe the slides again.55 Q & A

2. Perimeter

The teacher managed for a doll house in the class to make the

lesson on Perimeter interesting to her students. One of the

students had volunteered to bring her doll  house to the class.

She made a number of different figures like rectangles, squares,

triangles from a paper sheet equal to the size of the various

rooms/windows/roof of the doll house and wrote the name of

the room/window/roof like drawing room, bed room, window

no. 1, 2, etc., with the help of students. The teacher asked them

to measure the length and breadth of different figures using a

metre scale, then to find the sum of all sides of that figure.

Students started working in groups. They recorded their

observations in tabular form. Students of different groups

discussed among themselves about the activity and shared their

observations. It emerged from the discussion with the teacher

that distance around a closed figure is named as its perimeter.

Thus the perimeter of different rooms of the doll house was

calculated. One of the students asked, "can we make a figure of

any desired shape from this sum? " Teacher suggested her to

try out on her own with the help of her friends. The teacher

asked them to calculate area of each room of the doll house by

multiplying length with breadth of the given paper sheet. Later,

the class was taken to the school garden which was square in

shape. Students measured its one side as 20 metre. Teacher

asked them to find how many metres of fence would be needed

to enclose the garden. Later, teacher provided rectangle, square

and circle having equal perimeter and asked the students which

shape will have minimum area.

One student asked how can we measure perimeter of a

circle. The other student suggested that length around the circle,

i.e, its circumference is the perimeter of the circle. She made a

circular card and marked a point on its edge. A point was marked

on the table also. She rolled the card starting from the point on

the table along a straight line till the marked point on the circular

card again touched the table. This point on the table was then

marked. Students measured the distance between the two

marked points on the table as circumference of the circle. Another

student suggested that perimeter of the circle is the distance

along the edge of the circular card from the marked point back

to the marked point.56 Q & A

Here students constructed their knowledge on perimeter and

area on their own. Teacher provided the learning environment for it.

3.  Parts of a Plant: Experience of a Teacher

The Class VI Science teacher entered the class with an objective to

interact with children about forms and functions of various parts

of different plants. She initiated the discussion by asking children

to tell something about plants and trees they are aware of.   Peepal,

Banana, Jamun, Rose, Mehndiótens of names reverberated in

the classroom environment. When this buzzing faded out, another

leading question from the teacher initiated thinking among

children. This was about different parts of plants. The teacher

advised children to form small groups and discuss and note down

important points about various parts of the plant and their

functions for group presentations. Children began to work. Soon

the bell rang, indicating the end of the day.

Next day, the teacher began the class with group work and asked

the children to present their work after the discussion was over.

Each group presented a number of points about structures and

functions of different parts of plants. A few of them tried to relate

the structures and functions with their own day-to-day life

experiences.  For example, one child said, ìleaves are the ëkitchení

of plants and the roots are suppliers of basic ingredientsî. The

other child asked, ìHow does a plant get proper nourishment like

water, sunlight, etc., for standing erect and strong?î  Another

child asked, ëëIf we do not eat proper food, we fall sick. Do plants

also fall sick?íí A few of them were eager to share stories about

plants and one child recited a poem. The teacher listened, observed

and facilitated the discussion when and wherever necessary. The

discussion continued about plants with lively participation of the

entire class. Children from tribal backgrounds shared their

knowledge and information about plants with other children.

However ,   the  teacher  not iced  that   two chi ldren were not

concentrating in the class. She went to them and asked for the

reason. She found that one was suffering from fever and the other

had lost her pencil box. She took due care of them and the class

progressed.  The next day the teacher took the help of the textbook.

She raised some questions and gave them a few exercises. All the

children had something to say in response.  Many raised related

and thought-provoking  questions. The teacher was so inspired

that she arranged a period for taking the class to the garden and

also to the library. In the garden, the children themselves observed57 Q & A

and gradually found solutions to their queries. Then children

offered the teacher a suggestion that they will make a drawing of

different plants, structures of its various parts, etc.  The teacher

agreed to assign that as homework. The next day the whole class

was full of colourful charts and posters.  The class was brimming

with the joy of understanding the children had experienced in this

ëlessoní. A ëlessoní?  No, in fact it was an interaction.

 ìWhen will you set a test from this lesson?î a child asked out of

habit.

 ìDo you need time to prepare?î the teacher smilingly asked.

 ìThis time I feel I do not need to cram.î

 ìYou donít need any test. All of you have understood the topic

and have done wellî.

The child also smiled.

Now, let us analyze what has happened in this class?

! The teacher provided space to childrenís experiences,

questions, and queries and tried to relate them with school

knowledge.

! She observed each and every child in the class for her

progress in learning. She evaluated her children during the

course of the study.

! Once learning got connected with childrenís day-to-day life,

they themselves felt no need for rote memorisation.

! The teacher did not stick to a programmed timetable but

showed ample flexibility with regard to time.  She was wise

enough to make extra time for visits to the garden and library

and for detailed discussion. She could successfully convince

the school authorities and her colleagues for doing this.

! Children talked about social issues, listened to stories and

recited poems, thus going beyond the textbook. The concerns

of arts, health, and peace, etc., got integrated in the class

without much effort.

! Every child had the taste of understanding. She learned a

lot about different parts of plants interacting with the teacher

and her peers.

Do you think such a method will help each child learn with

ease and joy?  Now, do you think it is difficult for you to implement

all the five guiding principles of NCF-2005 discussed here in your

class?58 Q & A

SECONDARY STAGE

1. Concept of ð

Mathematics teacher asked her class  to bring  a few colourful

chart papers and thread   for her next period. Students were curious

to know the purpose of it. Next day teacher asked them to cut the

chart papers to get 20 circles of different diameters. Students

measured circumference and diameter  of the different circles with

the help of threads and scales. They were  working in four groups.

Each group was asked to calculate the ratio of circumference of

the circles to its diameter and record the value in an observation

table. The teacher then told them to compare their   findings   with

that of other groups. Students were surprised to observe that   the

value of the ratio was very similar in each group. Students

exchanged their circles and repeated their observations. They

observed that the ratio of circumference of the circle to its diameter

was between 3 and 4, approximately 3.14 irrespective of the size

of the circles. Teacher asked, ëëDo you see any relation between

circumference and diameter of a circle?íí She then discussed

about   π.  Ar r iving at   the constant  value  π as  the  rat io of

circumference to the diameter was   very satisfying, both to her

and her students.

2. A Visit to a Water Supply System

The teacher   took her class to a Municipal Water Supply System

nearby. The class was instructed to observe and take notes and

was encouraged to ask questions. They prepared a worksheet

containing questions written on it and space provided for the

answer.  Some of the questions prepared with the help of students

were ëëHow sedimentation process help in cleaning water?î ëëHow

biological inputs like bacteria, algae, fungi, etc., are removed?íí

ëëHow water is disinfected?î ëëHow much water is used per day

in the nearby locality? î ëëDraw a figure of the pump that you

observed.î They were happy when their queries were satisfied by

the authorities working there. After their return, they prepared a

working model of the water supply system. A poster competition

was held on 'Conservation of Water.í A few students prepared a

report of the various steps involved in the purification of water.

One group   dramatised the process of water purification. Students

of other groups performed a dance wearing dresses attached with59 Q & A

brown paper strips and white paper strips to represent dirty and

clean water. The teacher facilitated her students to organise and

summaries their learning on water supply system.

3. Boiling Point of Water

The teacher helped her class to form six groups to perform an

activity on determining the boiling point of water.  Each group

was provided a beaker and different samples of water (such as

distilled/tap/pond water, water with some salt/sugar/milk added

to it), a thermometer and a gas burner. Students were asked to

heat the water samples and note down the readings in the

thermometer as soon as it started boiling. They were surprised to

observe their results. Each group had found different values of

boiling point! They were happy to discuss among themselves and

with the teacher the possible reasons for this difference. They

observed that boiling point of water (solvent) is increased if solute

is added to it. Children were dynamically engaged with the learning

process through observing, reflecting, enquiring and sharing.

4. An Afternoon on a Sea Beach

One day the teacher took her students to the sea beach. Observing

students moving  in different directions to explore the things around

the sea, she got worried for their safety. She got an idea of utilising

the curiosity of the students. She helped them in forming eight

groups so that they could choose some interesting projects to do

as given below:

Group 1: Calculate mean time of waves reaching on the seashore.

Group 2: Estimate the dimension of the boats; talk about it with

fishermen/fisherwomen and compare with your

estimation.

 Group 3: Talk to the fishermen/fisherwomen about their work;

fishes; their profit and loss; their economy; the season

for which fishes are available in plenty; and the way

they manage their home economy.

Group 4: Watch fishermen/women catching fishes, the tides of

wave, the sky, reflections of the sun in the sea, etc.,

and write poems, essay on the topic of their choice.

Group 5: Collect songs and stories from fishermen/women and

sing with them.

Group 6: Observe crabs, tortoise and other living beings, their

motion and habitat.60 Q & A

Group 7: Make   sketches of the natural beauty of the sea and

its surroundings.

Group 8: Calculate speed of the wave by estimating distance

from the place of observation.

After coming back to school, each group presented their report in

the class. They learnt to share their experiences and in this activity,

everybody enjoyed their learning.

Teacher attempted to dissolve boundaries between different

subjects, i.e., maths, science, literature, arts and aesthetics.

5.  Can You Help Geeta

Geeta's father is a vegetable hawker. One day she went to the

market with her father. They had Rs 1000/- with them. They found

that a variety of vegetables were available. Rates of different

vegetable were:

Potato - Rs 20/kg; Onion - Rs 12/kg; Tomato - Rs 25/kg;

Cauliflower - Rs 40/kg; Carrot - Rs 20/kg; Ladyís finger - Rs 24/

kg; Bitter gourd - Rs 32/kg; Cabbage - Rs 22 kg; Spinach - Rs

15/kg; Gourd - Rs 18/kg.

Can you help her in deciding:

1. What factors should she keep in mind to get maximum

profit?

2. Which vegetables should she purchase to get maximum

profit margin?

3. In which vegetables profit margin is likely to be low? How?

4. In which vegetable profit margin is likely to be highest? How?

5. Which vegetable will occupy largest volume in 2kg?

6. Should she purchase different quantities of different

vegetables for easy   loading and unloading?

7. How much weight would she be able to carry on her head?

This situation may   initiate group discussion in the class. These

open-ended questions may be a challenge for learners at   the

secondary stage.

6.  Electricity and Magnetism

A week before the scheduled   date of the chapter, the teacher

facilitated her   students in   identifying six subtopics in   Electricity

and Magnetism. She helped the class in forming six groups. Each61 Q & A

group selected   subtopics of their choice to work on as a project.

They   had freedom to plan for any activity or experiment; make

models or charts; collect information from encyclopedia; internet

or from the magazines; conduct interviews; solve numerical

problems; write and do one-act play or write a poem. The teacher

negotiated this project with her students in an arrangement period

assigned to her. A week later, the lesson was introduced to the

students by asking leading questions based on various sources

of electric current they were aware of. An activity of glowing a

torch bulb by an electric cell was performed by students with the

help of the teacher. They identified transformation of chemical

energy into electric energy.

Each group then gave presentation on their projects with their

teacher acting as a facilitator. Teacher ensured that all members

of the group participate in the presentation.

Group 1

SubtopicóSource of electric current and its historical

background

Students   made charts   describing construction and working of

voltaic cells, dry cells, button cells, rechargeable cells. Some of the

students collected a few of the above cells, which they demonstrated

in the class. They gathered information about specific uses of these

cells. The group also collected interesting anecdotes about scientists

(Thomas Alva Edison, H. C. Oersted and W. Nicolson) and their

work related with the topic and prepared a historical background

of chemical and magnetic effects of electric current.

Group 2

SubtopicóOhm's law

Students performed experiment for studying Ohm's law with the

help of the teacher.

They drew circuit diagram on the blackboard to show the

symbols of electric components. Students observed and recorded

the ammeter and voltmeter readings. The relationship between

the potential difference across a conductor and the electric current

passing through it was discussed by plotting a graph.

Group 3

SubtopicóJudicious use of electricity

The group prepared a scrapbook, which had clippings from

newspapers and magaz ines highl ight ing  judicious use of62 Q & A

electricity. They also pasted print advertisement of   energy efficient

electric gadgets. The members of the group carried out interviews/

discussion with the elders in their families/ neighbourhood about

the life styles of their childhood without electricity and how their

life changed after supply of electric current started in their localities.

The group, with the help of the teacher conducted a ìspeed

testî on calculation of monthly electricity bill using simple formulaPower consumption

Power in watt × Time in hour

= kW h

1000

1000 kW h =1 unit

Electricity Bill = Power consumption  Rate per unit

The group also enacted a ëplayí during the school assembly on

how to reduce wastage of electricity.

One member of the group composed a poem in Hindi on ëBijli

Bachaoí.

Group 4

SubtopicóMagnetism and electromagnet

The group prepared a working model of an electromagnet using

a long iron screw and enamelled copper wire and identified the

relationship between electricity and magnetism.

A brief reference on magneto-therapy was given by one of the

members.

Group 5

SubtopicóEarth as a magnet

The group located northñsouth direction of their classroom with a

magnetic compass needle. During recess, they went to other classes

in the same corridor and then to the classes at  corridor in

perpendicular direction to establish northñsouth direction there. They

prepared a map of different classrooms indicating northñsouth

STDUENTS ENJOYED PARTICIPATORY LEARNING

The teacher observed that each of the students of her class

had worked on their assignment. When the teacher turned

to leave the class after studentsí group presentation was

over, she heard an otherwise quiet and introvert girl saying,

ìMam, today I really enjoyed learning.î63 Q & A

direction there. Using a magnet, iron filings and a drawing board,

they mapped magnetic field lines under the guidance of their teacher.

They drew a diagram of magnetic field line patterns on a chart paper.

Two members of the group had collected information from library

and the internet about the magnetic properties of the earth.

Group 6

SubtopicóElectromagnetic induction

The group performed an activity to demonstrate how   electric

current is observed when   a magnet is quickly moved through a

coil connected to a galvanometer or the coil is quickly moved

around the magnet held stationary in hand. They repeated the

activity by moving the magnet slowly within the coil. Observing

very little deflection in the galvanometer, they discussed the reason

for it. They prepared a chart to explain the experiment.

Teacher facilitated each group of students to exchange their

assignment with other groups. All students had got an opportunity

to develop a background on the topic to express their ideas about

the concept.

The teacher as well as the class asked many questions in

between the presentation.

7. Air Pollution

The teacher familiarised herself with the knowledge of her students

on   the effect   of air pollution with some introductory questions.

She then guided them to perform  an activity   to observe particulate

matter  (chalk particles) in the classroom by patting the

blackboard duster on the table. She allowed the students to ask

questions on various aspects of air pollution. The teacher felt that

students of her class were quite familiar with this topic. She

discussed with them on the design of their assignment work. She

helped the students in forming five groups to carry out work on

the issues  of pollution. She made it clear to her students that if

they thought of something different related to the topic, they were

welcome to discuss with her.

Group 1

Sources of air pollution

Identify various sources of air pollution that you think might be

reason for it. Suggest ways to minimise it. Prepare and present a

report on it.64 Q & A

Group 2

Acid rain

Visit the library/internet to collect the information about acid rain.

What causes it? Study its effect on aquatic life, soil and historical

monuments. Talk to the monument authorities about the steps

taken to minimise the effect of acid rain. Suggest ways to minimise

its negative effect. Prepare and present a report.

Group 3

Smog

How does smog pollute the air? What causes it?  What is its effect

on various modes of transportation? Why does its formation

increase during winter season? What are the ways to minimise

it? Prepare a report of your own observations and experiences

about smog. You may use newspaper clippings, photographs,

etc., for illustrations.

Group 4

Harmful effects of air pollution

What are the harmful effects of air pollution on health? How does

it affect respiratory and circulatory system of our body? Do

pollutants affect the respiratory system of the animals as well?

Identify various diseases occurring due to air pollution. Conduct

an interview with a doctor regarding this issue. Prepare in advance

THE REPERCUSSION: INCREASING

INTERACTION

S t u d e n t s   s t a r t e d   i n t e r a c t i n g   a m o n g

themselves and with other subject teachers.

Students from other sections came to the

teacher requesting to teach them using the

same approach. Even interaction among

teachers also increased.

the questions that you would like to be answered by the doctor.

Collect information through various sources such as television,

library, internet, newspaper, etc., What steps should be taken to

minimise the ill effects of air pollution on health?65 Q & A

Group 5

Collecting and presenting data

Collect data on various air pollutants in your city. Prepare a pie

graph/bar graph depicting their presence in percentage.

Each group prepared a record collaboratively. The group

leader   presented the report to the class with the help of his team

members. The teacher reviewed the concepts whenever required.

She did not appoint the group leader, the group selected the leader

themselves. Later, one of the students read out a brief report about

their findings in the morning assembly of the school.

HIGHER SECONDARY STAGE

1. Derivatives

The lesson was introduced with some observations from everyday

life situations. Teacher cited an example that people maintaining

a reservoir need to know when will the reservoir overflow knowing

the depth of water at several instances of time. Students realised

that in order to know the time of overflow of a reservoir they needed

to know how one parameter (say height) varies with another

parameter (time). The teacher helped them to evolve the concept of

rate of change of height with respect to time. She discussed the

importance of derivatives of functions and the concepts of functions

and limit with the students.

Definition of derivatives of a real valued function f at a point

in its domain was developed through interaction with students.

First principle of derivatives was also developed through discussion

with students. Derivatives of different functions were explored.

Algebra of derivatives of functions was discussed. Teacher

facilitated the class in forming  small groups and solving the

problems based on derivatives.

Group 1

Discuss motion of a body under free fall. Draw a figure showing

variation of distance with time for an uniformly accelerated motion.

Calculate velocity and the acceleration of the object at different

instants of time graphically. You may refer (pp. 43ñ45) Physics

Textbook for Class XI (NCERT 2006).66 Q & A

Group 2

Collect data regarding population of your state for the last 20

years from the Internet. Plot a graph between time (in years) and

population.

Calculate rate of increase/decrease in population.

Group 3

Visit the website http://earthtrends.wri.org.

(a) Calculate the rate at which landmass is under threat of

submerging under seawater from 1961ñ2000. Record your

observations  at least five times at equal time intervals.

(b) Predict the rate of submergence of the landmass for next

20 years.

Present your results using  graphs.

At the end students solved the problems individually and shared

the methods used by them in solving the problems with each other.

2.  Radioactivity

The teacher talked to the students about the various   resources

of information about   the accidental discovery of radioactivity by

A.H. Becquerel and the works of M.S. Curie. The lesson was started

with a brief description of their work. Students   discussed ëLaw

of Radioactive Decayí with their teacher. The teacher, then

facilitated the class to   form four groups. Students took up the

activity of their interest. Each group chalked out their plan of

action with the help of the teacher.

Group 1

Students   conducted   an analogous experiment   by counting

the number of water drops falling per minute from   a burette

fixed on a stand. Students plotted a graph showing its exponential

nature and calculated decay constant and   half-life time.

Group 2

The group identified  Actinoid elements of the f  block from the

periodic table. They discussed the reason of these nuclei being

unstable,  the process of alpha, beta and gamma decay and their

properties with the help of a chart, the group had made. Various

uses of the three rays were also discussed.

Group 3

The group collected   information from   the internet   about the

medical   uses of different radioactive rays such as in the treatment67 Q & A

of cancer, sterilisation of surgical instruments, preservation of

foods, etc. Two members of the group conducted an interview

with a doctor about the uses of radioactive isotopes in the diagnosis

and treatment of various diseases.

Group 4

The group   gave a   presentation   on the application of radioactivity

in determining age of the rocks, age of historical paintings and

age of fossils.

OUT OR IN THE MIND?

When the lesson was completed and discussion

was over, a student said, ìthe concepts of

Radioactivity are very clear to me, now. They

will not go out of my mind like other chapters

went.î

Group 5

The teacher ensured seeking participation of all students in setting

goals and taking decisions. All students had opportunities for

collaboration. Later, the teacher employed a buzz session of fifteen

minutes to review the concepts. Students were allowed to talk

among themselves about what they had learned. They were then

ready to answer the questions asked by the teacher.

3. Habitats of Different Forms of Life

Teacher initiated the discussion on the habitats of different forms

of life. They began raising questions about how   different forms

of life could survive in extreme conditions. Teacher suggested

them to form six groups and find information from the various

sources about the habitat of different forms of life at different

places. The previous day she had asked them to read books from

the library, visit relevant websites, enquire from their parents and

elders on this issue. Students volunteered themselves to work  in

the area of their choice:

Group I Conditions prevailing in scorching heat in the

deserts of  Rajasthan.

Group II Physico-chemical and biotic conditions in rain- soaked

Meghalaya forest.68 Q & A

Group III Abiotic and biotic components under deep ocean

trenches .

Group IV Resources and life at permafrost polar  regions.

Group V Life existing in thermal springs.

Group VI Microbial forms in stinking compost pit and our

own intestine.

Later the groups shared their findings and requested their teacher

to plan for an excursion  trip to the nearby village. It provided

them an opportunity of very lively interaction among themselves.

After coming back all Groups gave a presentation in the class.

When Group V presented their observations regarding the

existence of life in thermal springs, many queries arose, ìIf

microorganisms can exist  in hot water, is there any chance of

getting  infection from hot springs?î ìWhat happens to organisms

when food items are cooked?î ìIf they are killed, how do they

survive in thermal springs?î This led to a discussion and

understanding about the concept of ëadaptationí.

4. Acids, Bases and Salts (Same Concept, Different Stages)

This topic is dealt with at all the three stages of learning i.e. upper

primary, secondary and higher secondary stages of school

education.

Upper primary stage

At this stage objective is to distinguish between acids, bases

and salts on the basis of colour change of the indicator.

There were two classroom situations to realise the first objective:

Situation (A). Teacher lectured everything  whatever  students

were supposed to  learn. She told   about the

change of colour of  the indicator verbally. She

conducted   an activity taking dilute  acid,  base

and few litmus paper herself. Class silently

observed  it.

Situation (B). Teacher first asked some questions   related to the

taste of some edible items. She then conducted   an

activity taking  lemon juice  and litmus paper.

Observing the change in colour of litmus paper,

students  suggested  use of other substances  such

as vinegar, tomatoes, apples, orange, baking soda,

soap solution and tap water for performing the69 Q & A

activity. Teacher encouraged them to perform the

activities in small groups and present their findings

to the class. Working with different substances,

soon they were able to distinguish between acids

and bases. Teacher helped them in drawing

conclusions  from their observation.

In which of the situation do you think construction of knowledge

was facilitated?

Secondary Stage

At the secondary stage  the objective is to relate acidic and basic

nature of the substance with the molecular structure of the

substance.

The teacher elicited the response from the students about

the role of various acidic and basic substances in human bodies,

agricultural fields, different industries and some other living

beings. Gradually she   introduced   the concept of pH. Learners

performed activities to find out pH of solutions of various

substances of their interest. The teacher then provided different

substances to check their pH. In order   to discuss the concepts of

strong and weak acids, dilute and   concentrated   acids, first the

pH of solutions of different acids of  the same concentration  were

taken  and then after diluting those samples of acids   to some

other concentration, their pH was checked.

Higher Secondary Stage

At the higher secondary stage objective is to solve problems

related to acids, bases and salts. They are aware of the concept

of molarity of solution.

Teacher guided her students  in solving numerical problems.

They were asked to calculate the pH of different concentrations of

a given solution. The class  was given to calculate pH of  9M

solution of hydrochloric acid. Calculating according to definition

of   pH, they got the result as ñ9. They  had  got an anomalous

result. Students  discussed various possible causes of anomalies

with their teacher and modified the formula for calculating  pH.70 Q & A

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