Newton's Law of Cooling Verification

Studying and solving ordinary differential equations of first order is a part of the CBSE curriculum for grade XII. Students are aware of how to form a differential equations and find their general and particular solutions with given initial conditions.
But most of the time students do not get the opportunity to observe differential equations in action or do some real computation.

The model in the video can provide an opportunity for students to validate and verify if the Newton’s Law of Cooling holds true  for different liquids and it also can be used to study Newton’s Law of Cooling for different liquids at different ambient temperatures.

This model is made under the Semester long project of Differential Equations and Mathematical Modelling by the students (Jahangir, Robin Sharma and Sourabh Garg) of M.Sc. Mathematics Education, Meta University, A joint degree concept by Jamia Millia Islamia and Delhi University.

"The Magical Adventures" - Module for Learning after School

Learning after school is as much as important as learning within school. It should happen as unconsciously as possible because of the developed hatred for homework among students. In current education scenario much emphasis is given upon the homework. But the traditional way of homework is not very much appreciated by the learners. The learning module is designed for homework purpose in which NCERT questions are portrayed with some modifications and inculcating them in the story of the module. This module is for revision, recapitulation, concepts clarity, strengthen learning and visualizing math in real world.

The module contains Chapter 1 ‘Integers’ & Chapter 2 ‘Fractions and Decimals’ (exercises 1.4 & 2.1 in particular), NCERT Mathematics book grade 7th. Theme line of the story is about a Magician and his disciples looking for his magical tools. They come across various obstacles in the journey, and each obstacle is based on the NCERT book problems. Students have to help magician by solving the problems for them. Some of the features of the module are creativity, curiosity to learn, imagination, and problem solving attitude.

This module is the intervention tool for the research dissertation "Tranforming students' engagement in Learning after School" by Sourabh Garg student of M.Sc. Mathematics Education, Meta University, A joint degree concept by Jamia Millia Islamia and Delhi University.

"Tarsia Puzzles" and "Jigsaw Puzzles"

Few shots of the games "Tarsia Puzzles" and "Jigsaw Puzzles" from the event Matrix 1.1 conducted by the mathematics education society of Cluster Innovation Centre

Games designed by: Robin Sharma and Sourabh Garg

"Hope to 100" and "Rejuvenated Ludo"

Few shots of the floor games "Rejuvenated Ludo" and "Hope to 100" from the event Matrix 1.1 conducted by the mathematics education society of Cluster Innovation Centre

Hope to 100: This floor game has 100(10X10) blocks marked from 1 to 100 and a dice. Each block is coloured randomly and 10 different colours are used. Each colour corresponds to 10 cards each have a different Math question. So in this way, the game has 100 cards and 100 questions.

Rules:

1. The first player has to roll the dice

2. He/She has to move the number of steps equal to the number on dice

3. Then he/she has to withdraw card from the same colour he is standing on

4. Then he/she has to complete the task given on the card (if he/she answered correct, if not then not to be moved) 

5. Next player will do the same from rule 1

6. First player to reach 100 will be the winner

Tasks/Question examples:

*Move ahead steps equal to the number of faces in a Tetrahedron.

*Swap your position with anyone else in the game

*Move back steps equal to the largest even prime number's cube

Rejuvenated Ludo: All the rules in this game are same as Ludo. The modifications made are:

1. Each colour team can have upto 2 players.

2. There are 3 dice instead of 1, 2 dice are marked with numbers from 1 to 6 and the third dice has operations marked on it such as +, -, X, /. 

3. Players have to roll all three dice and then they can use the 2 numbers and 1 operation in any manner. (for example 2,3,- can be used as 3-2 to move 1 step ahead or 2-3 to move 1 step back)

4. First team to reach to home will win

*in case of decimal number, Greatest integer function is to be used

Games designed by: Robin Sharma and Sourabh Garg

"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.