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Axiomatic Nature of Mathematics – A Contemporary approach based on intuition . Introduction. Intuition is the Key to guide us from Imperfection to perfection Factors stimulating intuition are intrinsic and extrinsic by nature Axioms: Its meaning & concept in relation with intuition.
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Axiomatic Nature of Mathematics – A Contemporary approach based on intuition .
Introduction • Intuition is the Key to guide us from Imperfection to perfection • Factors stimulating intuition are intrinsic and extrinsic by nature • Axioms: Its meaning & concept in relation with intuition
Challenges & Responsibilities of Modern teacher To make the smart classes smarter • Fundamental mathematical reasoning lies in its axiomatic nature • Set theory as an example: a logically defined pattern of ideas that can be extended to limitless possibilities
Implementation of axioms in class room teaching • The descriptive nature of axioms is extremely beneficial in teaching. • Axiomatic structure relies on independency, completeness and consistency • Intuition leads to rationalization.
Effective use of axioms • Puts the focus on linking the unrelated concepts and turns them into logically related concepts. • Stimulation of learners to think beyond the defined structure and to move from concrete to abstract. • Innovation of a new prospective which gives rise to innumerable possibilities.
Class room scenario today Fault lies in the excessive stress on content rather than process. Puzzled Child
Change in the mindset of the teachers. To look for hidden possibilities within the mistakes
Desired class room To develop a conducive learning environment, the teacher acts as a facilitator
Universe – infinite possibilities The Universe is a set of objects beyond formalised pattern
The philosophy behind the use of axioms is to develop appreciation for mathematics, besides developing an aesthetic value of the subject. This results in a PASSIONATE LEARNER.
Happy Learner Learning environment Using philosophy of axioms passionate learner
Thanks Dr. UshaPathak Associate Professor D.A.V.(P.G.) College, Dehradun & Dr. ChetnaThapa (T.G.T.), Department of School Education Uttarakhand