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From Karnataka Open Educational Resources
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'''Nature of Mathematics:'''
 
'''Nature of Mathematics:'''
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   1. ಗಣಿತವು ನಿಖರವಾದ ವಿಜ್ಞಾನವಾಗಿದೆ. 2 + 3 = 5
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# Own languages. e.g. Mathematical concepts terms, symbols, formulae and principles
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# Its knowledge remains the same in the whole universe everywhere and every time.
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# It is an exact science. Its knowledge is always clear, logical and systematic and that may be understood easily (ಗಣಿತವು ನಿಖರವಾದ ವಿಜ್ಞಾನವಾಗಿದೆ. 2 + 3 = 5).
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# It involves inductive and deductive reasoning and can generalize any proposition universally.
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# It involves the conversion of abstract concepts into the concrete form. Its knowledge is applied in the study of science and its different branches.
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   2. ದೈನಂದಿನ ಜೀವನದ ಒಂದು ಭಾಗವಾಗಿದೆ. (ಆಕಾರಗಳು, ಸಂಖ್ಯೆಗಳು )
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'''Vision for School Mathematics (NCF-2005)'''
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* Children learn to enjoy mathematics rather than fear it.
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* Children learn important mathematics — Mathematics is more than formula and mechanical procedures.
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* Children see mathematics as something to talk about, to communicate through, to discuss among themselves, to work together on.
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* Children pose and solve meaningful problems.
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* Children use abstractions to perceive relation-ships, to see structures, to reason out things, to argue the truth or falsity of statements.
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* Children understand the basic structure of Mathematics — Arithmetic, algebra, geometry and trigonometry, the basic content areas of school Mathematics, all offer a methodology for abstraction, structuration and generalisation.
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* Teachers engage every child in class with the conviction that everyone can learn mathematics
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   (ದೈನಂದಿನ ಜೀವನದ ಒಂದು ಭಾಗವಾಗಿದೆ. (ಆಕಾರಗಳು, ಸಂಖ್ಯೆಗಳು) and ದೈನಂದಿನ ಜೀವನದ ಸಮಸ್ಯೆಗಳನ್ನು ಪರಿಹರಿಸಲಾಗುತ್ತದೆ)
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   3. ದೈನಂದಿನ ಜೀವನದ ಸಮಸ್ಯೆಗಳನ್ನು ಪರಿಹರಿಸಲಾಗುತ್ತದೆ