"Creative Exploration in Math Classroom" - Research Paper

ABSTRACT:

Mathematics expresses itself everywhere around us, in all phases of life. Sometimes presence and application of mathematics seems separated from the natural world but in reality, small reflections and thinking can help us to see math all around us. ‘Everyday Mathematics’ is a set of expressions on the role of mathematics in everyday life, through science, technology, tradition, culture etc. The presence of ‘Math in Nature’ is a tremendous resource for the classroom but too often mathematical concepts are forced on students with no relevance in real/natural world. This insufficient conveying of concepts lead to faulty development of various concepts which further results in developing aversion towards mathematics among students. Shortfall of examples, discussions and reflections on Math around us can lead to contribution in the abstractness of it which further advances the barricades in achieving one of the aims of Mathematics Education given in National Curriculum Framework 2005, i.e. students should be able to handle abstractness.

Mathematics’ teaching shall empower students to feel the presence of math around them and to use math in sharing/expressing their observations and experiences. Students should be able to visualize mathematical aspects around them and they should be able to explain the same creatively. Visualizing mathematics helps students to handle real life problems and embraces the problem solving approach of mathematics.

This paper presents an empirical study done on 40 students of IX grade about how students see their surroundings and nature through mathematical lens. This paper helps to understand mathematical thinking of students that they use to visualize the nature and surroundings.  It also suggests the scope to enhance creativity in mathematics classroom and highlights the domains where students are lagging behind to relate mathematical knowledge in their surroundings.

Creative representations and explanations given by students through sketches in math classroom during the study provide some exceptional insights which expose how uniquely students can interpret the same topic.

*the paper was presented in NCERT's National Conference on Mathematics Teaching – Approaches and Challenges in RIE Bubhneshwar 2016 by the authors Jahangir and Sourabh Garg

Trigonometry Phobia - Docudrama

https://youtu.be/8wgwIcF_bvA

This video was made under the semester long project by the students of M.Sc. Mathematics Education, a joint degree programme under Meta university(Jamia Millia Islamia & Delhi University)

Trip to bhangarh- LCM story

This storyboard is for L.C.M. of grade 6th. This story is about the spooky journey of Jak and his friends for the horrific quest of a ghost named Soru. Jak and his friends came across various adventures and along with all the fun they had in the trip, they also learned about Multiples, Common Multiples and Least Common Multiple.

This storyboard and video was made by Jahangir and Sourabh under the project of M.Sc. Mathematics Education, Meta University, A joint degree programme concept by Delhi University and Jamia Millia Islamia.

"Geometrical Representation of Irrational Numbers" - Research paper

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

Salute!!

Video made by: Jahangir, Sourabh Garg

Demonstration of Circle theorems

Video made by: Sourabh Garg

When children study about Circle, they unknowingly develop some misconceptions, for example when they study tangents they think such tangent can possible that do not make a 90 degree angle with the circle. This video demonstrate some Circle theorems geometrically through which their misconceptions can be clarified.

Top 10 Universities of India...........

Top 10 Universities in the country
1. Indian Institute of Science, Bangalore
2. Institute of Chemical Technology, Mumbai
3. Jawaharlal Nehru University, New Delhi
4. University of Hyderabad, Hyderabad
5. Tezpur University, Tezpur, Assam
6. University of Delhi, Delhi
7. Banaras Hindu University, Varanasi
8. Indian Institute of Space Science and Technology, Thiruvanathapuram
9. Birla Institute of Technology and Science –Pilani
10. Aligarh Muslim University, Aligarh