please share it to all your friend---क्या आप सरकारी नौकरी की तलाश में हैं तो आप के लिए खुशखबरी। अब एक नया एंड्राइड एप्प बन चुका है जो हर पांच मिनट में आपको नई सरकारी नौकरी की जान कारी देगा। और अधिक जानकारी के लिए एप्प को फ्री डाउनलोड करें। क्लिक करें https://play.google.com/store/apps/details?id=net.andromo.dev312556.app296602

Thursday, 22 December 2011

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
REFERENCES
NCERT .   2 0 0 5 .   Na t i o n a l  Cu r r i c u l um  F r amewo r k ñ 2 0 0 5.  Na t i o n a l
Council of Educational  Research And Training, New Delhi.
. 2006.  Position Paper:  National Focus Group  on Teaching of
S c i e n c e.   N a t i o n a l   C o u n c i l   o f   E d u c a t i o n a l   R e s e a r c h   a n d
Training , New Delhi.
. 2006.  Position Paper: National Focus Group on Teaching of
Mathematics. National Council of Educational Research and
Training, New Delhi.
. 2006.  Position Paper: National Focus Group on Examination
Re f o rms.   N a t i o n a l   C o u n c i l   o f   E d u c a t i o n a l   R e s e a r c h   a n d
Training , New Delhi.
. 2006.   Position Paper: National Focus Group  on Gender Issues
in Education. National Council of Educational Research and
Training, New Delhi.
. 2006.  Position Paper: National Focus Group  on Curriculum,
Syllabus and Text Books. National Council of Educational
Research and Training, New Delhi.
. 2006.  Science Textbook for Class VI. National Council of
Educational Research and Training, New Delhi.
. 2006.  Science Textbook for Class IX. National Council of
Educational Research and Training, New Delhi.
. 2006.  Science Textbook for Class X. National Council of
Educational Research and Training, New Delhi.
. 2006. Physics Part I  Textbook for Class XI. National Council
of Educational Research and Training, New Delhi.
. 2006.  Biology Textbook for Class XII. National Council of
Educational Research and Training, New Delhi.
. 2006. Mathematics Textbook for Class VI. National Council
of Educational Research and  Training,  New Delhi.
. 2006.  Mathematics Textbook for Class XI. National Council
of Educational Research and Training, New Delhi.
. 2007.  Science Textbook for Class VII. National Council of
Educational Research and Training, New Delhi.
. 2007.  Science Textbook for Class VIII. National Council of
Educational Research and Training, New Delhi.
. 2007.  Chemistry Part II  Textbook for Class XII. National
Council of Educational Research and Training, New Delhi.
. 2007. Physics Part II  Textbook for Class XII. National Council
of Educational Research and Training, New Delhi.
. 2007. Mathematics  Textbook for Class IX. National Council
of Educational Research and Training, New Delhi.
. 2007.  Mathematics  Part I  Textbook for Class XII. National
Council of Educational Research and Training, New Delhi.

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