(Download) NCERT Revised syllabus Of Maths (Class 6 to 8 )
]The development of the upper primary syllabus has attempted
to emphasise the development of mathematical understanding and thinking in the
child. It emphasises the need to look at the upper primary stage as the stage of
transition towards greater abstraction, where the child will move from using
concrete materials and experiences to deal with abstract notions. It has been
recognised as the stage wherein the child will learn to use and understand
mathematical language including symbols. The syllabus aims to help the learner
realise that mathematics as a discipline relates to our experiences and is used
in daily life, and also has an abstract basis. All concrete devices that are sed
in the classroom are scaffolds and props which are an intermediate stage of
learning. There is an emphasis in taking the child through the process of
learning to generalize, and also checking the generalization. Helping the child
to develop a better understanding of logic and appreciating the notion of proof
is also stressed.
The syllabus emphasises the need to go from concrete to
abstract, consolidating and expanding the experiences of the child, helping her
generalise and learn to identify patterns. It would also make an effort to give
the child many problems to solve, puzzles and small challenges that would help
her engage with underlying concepts and ideas. The emphasis in the syllabus is
not on teaching how to use known appropriate algorithms, but on helping the
child develop an understanding of mathematics and appreciate the need for and
develop different strategies for solving and posing problems. This is in
addition to giving the child ample exposure to the standard procedures which are
efficient. Children would also be expected to formulate problems and solve them
with their own group and would try to make an effort to make mathematics a part
of the outside classroom activity of the children. The effort is to take
mathematics home as a hobby as well.
The syllabus believes that language is a very important part
of developing mathematical understanding. It is expected that there would be an
opportunity for the child to understand the language of mathematics and the
structure of logic underlying a problem or a description. It is not sufficient
for the ideas to be explained to the child, but the effort should be to help her
evolve her own understanding through engagement with the concepts. Children are
expected to evolve their own definitions and measure them against newer data and
information. This does not mean that no definitions or clear ideas will be
presented to them, but it is to suggest that sufficient scope for their own
thinking would be provided.
Thus, the course would de-emphasise algorithms and
remembering of facts, and would emphasise the ability to follow logical steps,
develop and understand arguments as well. Also, an overload of concepts and
ideas is being avoided. We want to emphasise at this stage fractions, negative
numbers, spatial understanding, data handling and variables as important corner
stones that would formulate the ability of the child to understand abstract
mathematics. There is also an emphasis on developing an understanding of spatial
concepts. This portion would include symmetry as well as representations of 3-D
in 2-D. The syllabus brings in data handling also, as an important component of
mathematical learning. It also includes representations of data and its simple
analysis along with the idea of chance and probability.
The underlying philosophy of the course is to develop the
child as being confident and competent in doing mathematics, having the
foundations to learn more and developing an interest in doing mathematics. The
focus is not on giving complicated arithmetic and numerical calculations, but to
develop a sense of estimation and an understanding of mathematical ideas.
General Points in Designing Textbook for Upper Primary Stage
1. The emphasis in the designing of the material should be on
using a language that the child can and would be expected to understand herself
and would be required to work upon in a group. The teacher to only provide
support and facilitation.
2. The entire material would have to be immersed in and
emerge from contexts of children. There would be expectation that the children
would verbalise their understanding, their generalizations, their formulations
of concepts and propose and improve their definitions.
3. There needs to be space for children to reason and provide
logical arguments for different ideas. They are also expected to follow logical
arguments and identify incorrect and unacceptable generalisations and logical
4. Children would be expected to observe patterns and make
generalisations. Identify exceptions to generalisations and extend the patterns
to new situations and check their validity.
5. Need to be aware of the fact that there are not only many
ways to solve a problem and there may be many alternative algorithms but there
maybe many alternative strategies that maybe used. Some problems need to be
included that have the scope for many different correct solutions.
6. There should be a consciousness about the difference
between verification and proof. Should
be exposed to some simple proofs so that they can become aware of what proof
7. The book should not appear to be dry and should in various
ways be attractive to children. The points that may influence this include; the
language, the nature of descriptions and examples, inclusion or lack of
illustrations, inclusion of comic strips or cartoons to illustrate a point,
inclusion of stories and other interesting texts for children.
8. Mathematics should emerge as a subject of exploration and
creation rather than finding known old answers to old, complicated and often
convoluted problems requiring blind application of un-understood algorithms.
9. The purpose is not that the children would learn known
definitions and therefore never should we begin by definitions and explanations.
Concepts and ideas generally should be arrived at from observing patterns,
exploring them and then trying to define them in their own words. Definitions
should evolve at the end of the discussion, as students develop the clear
understanding of the concept.
10. Children should be expected to formulate and create
problems for their friends and colleagues as well as for themselves.
11. The textbook also must expect that the teachers would
formulate many contextual and contextually needed problems matching the
experience and needs of the children of her class.
12. There should be continuity of the presentation within a
chapter and across the chapters. Opportunities should be taken to give students
the feel for need of a topic, which may follow later.