Abstract
In mathematics, an Irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals. Since we know less about Irrational numbers, this research aims to determine the geometrical representation of Irrational numbers. Textbooks do not contain any physical or geometrical representation of irrational numbers except ‘Spiral of Theodorus’ and ‘Semi Circle Method’, it seems difficult for a teacher to make a learner explain or visualize irrational numbers or operating on them. This paper proposes a methodology by which representation of addition and subtraction of some irrational numbers i.e. (√x + √y , (√x - √y ) and representation of further irrational numbers such as (x)^1/4 , (x)^1/8 , (x)^1/16 , ……… , can be visualized.
Due to lack of proper understanding of concepts, and limited textbook approach, students do not explore the various concepts further. Many students face difficulties when it comes to irrational numbers in spite of having keen interest in knowing numbers. Learners do not try to discover any new methods which can help them to achieve meaningful education. This leads them to quite limited information about any topic. Geometrical approach to learn about any concept is effective. Geometry lesson or representation can help individuals to develop their mathematical thinking and interest in mathematics. This research is a pedagogical guide for making number mathematics more relevant to learners through geometrical representation.
The approach can help students to learn more effectively about ‘numbers’ which is the basis of mathematics. And by this method students can also compare irrational numbers without any estimation, such as comparing (√13 + √17 or √11 + √19 , which one is greater? The ideas presented in the paper can be used as an effective pedagogical tool to integrate mathematics with visualization and conceptualization and allowing students to view mathematics as a more doable stream.
*the paper was presented in NCERT's National Conference on Mathematics Teaching –
Approaches and Challenges in RIE Mysuru 2015 by the author Jahangir and Sourabh Garg
In mathematics, an Irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals. Since we know less about Irrational numbers, this research aims to determine the geometrical representation of Irrational numbers. Textbooks do not contain any physical or geometrical representation of irrational numbers except ‘Spiral of Theodorus’ and ‘Semi Circle Method’, it seems difficult for a teacher to make a learner explain or visualize irrational numbers or operating on them. This paper proposes a methodology by which representation of addition and subtraction of some irrational numbers i.e. (√x + √y , (√x - √y ) and representation of further irrational numbers such as (x)^1/4 , (x)^1/8 , (x)^1/16 , ……… , can be visualized.
Due to lack of proper understanding of concepts, and limited textbook approach, students do not explore the various concepts further. Many students face difficulties when it comes to irrational numbers in spite of having keen interest in knowing numbers. Learners do not try to discover any new methods which can help them to achieve meaningful education. This leads them to quite limited information about any topic. Geometrical approach to learn about any concept is effective. Geometry lesson or representation can help individuals to develop their mathematical thinking and interest in mathematics. This research is a pedagogical guide for making number mathematics more relevant to learners through geometrical representation.
The approach can help students to learn more effectively about ‘numbers’ which is the basis of mathematics. And by this method students can also compare irrational numbers without any estimation, such as comparing (√13 + √17 or √11 + √19 , which one is greater? The ideas presented in the paper can be used as an effective pedagogical tool to integrate mathematics with visualization and conceptualization and allowing students to view mathematics as a more doable stream.
*the paper was presented in NCERT's National Conference on Mathematics Teaching –
Approaches and Challenges in RIE Mysuru 2015 by the author Jahangir and Sourabh Garg
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