## SET Theory Game

A set is a collection of objects or groups of objects. These objects are often called elements or members of a set. For example, a set of all squares.

A set can be understood playfully using a set game that constitutes 3 components. The three components are

• Colour
• Shape
• Size

It comprises:

Colour: Blue, yellow and green

Shape: Square, triangle, and circle

Size: small, medium, and large.

In total, there are 27 pieces which include

9 triangles (x3 colours, x3 shapes):

The three blue triangles are small, medium, and large.

The three yellow triangles are small, medium, and large.

The three green triangles are small, medium, and large.

9 squares (x3 colours, x3 shapes):

The three small blue squares, medium, and large.

The three small yellow squares, medium, and large.

The three small green squares, medium, and large.

9 circles (x3 colours, x3 shapes):

The three blue circles are small, medium, and large.

The three yellow circles are small, medium, and large.

The three green circles are small, medium, and large.

This set game can be used by children for a better understanding of set theory concepts.

Set Operations:

The four important set operations that can be performed using this set game are:

• Union of sets
• Intersection of sets
• Complement of sets
• Difference of sets

Union of sets:

The union of two sets is a set containing all elements that are in A or B (possibly both). The union of sets can be denoted using the symbol ‘U’. Symbolically, we can represent the union of A and B as A U B.

For example, A = Set of blue colour triangles and B = a Set of Green colour triangles.

Then the union will be all the triangles which are in blue and green.

The intersection of sets:

The intersection of two sets A and B is the set of all those elements which are common to both A and B. The intersection of sets can be denoted using the symbol ‘∩’. Symbolically, we can represent the intersection of A and B as A ∩ B.

For example, A = Set of blue colour objects and B = a Set of all triangles.

Then the intersection will be the triangles which are in blue.

Compliment of sets:

The complement of set A is defined as a set that contains the elements present in the universal set but not in set A. The complement of set A can be denoted using the symbol A’.

For example, A = Set of blue colour circles and U = Set of all circles

Then the complement of A, A’ will be circles which are in yellow and green.

Difference of sets:

The difference between sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B and read as “ A minus B”.

For example, A = Set of all green colour objects and B = Set of all squares.

Then the difference between A and B, A-B will be set of all green colour objects except squares.

Fundamental Properties of Set operations that can be observed:

The operations such as union and intersection in set theory obey the properties of associativity and commutativity. Also, the intersection of sets distributes over the union of sets.

Similarly, the set theory game can be used for understanding three sets and their operations.

## LAST SCHOOL STUDENTS VISIT STEMLAND

On the 14th of July students from the Last school, Auroville visited STEMLAND. The forty students accompanied by the teachers enjoyed their afternoon session by exploring STEMLAND.

The arrangements were done by the STEMLAND team. There were 8 stalls which include

1. Mindstorms
2. Games and puzzles
3. Science projects
4. Makey-Makey
5. Arduino
6. Electronics
7. Scratch programming
8. 3-D printing.

Mindstorms:

Mindstorms is a hardware and software structure that develops programmable robots based on Lego building blocks. Each version includes computer Lego bricks, a set of modular sensors and motors, and Lego parts from the Technic line to create the mechanical systems. The system is controlled by the Lego bricks.

Games and puzzles:

Logic and strategy games were present. They include Abalone, Gobblet, Quads magnetic, Aadu Puli (Puli Meka), Linja, Quarto, Quoridor, Othello and Eternals were put on view to play. Puzzles like Rubik’s cube, Cast puzzles, and holograms were displayed to solve and play with.

Science Projects:

Science projects based on concepts were exhibited. The exhibits include

• Magnetic levitation
• Electromagnetism
• Acid-base indicator
• Dc electric motor model
• Crank’s model
• Lungs- diaphragm model
• Magnetism- properties.
• DIY microscope
• Series and parallel connection
• Lights color – arithmetic model.

These models were made using the Arvind Gupta toys which are made of scrap materials.

Makey – Makey:

Makey Makey is an invention kit by the MIT media lab. With Makey Makey, everyday objects are transformed into touchpads empowering students to interact with computers as creative tools. The computer becomes an extension of their creativity, fostering imaginative play and discovery.

“Makey Makey” is a play on words – students having the ability to Make their Keyboards (“Ma-Key”). The mundane and boring keyboard is replaced by any object that conducts electricity – pie pans, Play-Doh, bananas, and even potted plants – the list goes on.

The projects can be coded by scratch and use the Makey Makey kit as a joystick controller.

Arduino:

Arduino is an open-source hardware and software that can be used for designs. It is a microcontroller and microcontroller kit for building digital devices. It can be programmed and built using the Arduino software. Exhibits include a Distance measurement kit, Automated street light was displayed.

Electronics:

The field of electronics is a branch of physics and electrical engineering that deals with the emission, behavior, and effects of electrons using electronic devices. Projects like Automatic street light controller and automated sound sensor control model, Automatic dustbin were displayed.

Scratch programming:

Scratch is a visual programming language that allows students to create their own interactive stories, games, and animations. As students design Scratch projects, they learn to think creatively, reason systematically, and work collaboratively.

3-D printing:

A machine allows the creation of a physical object from a three-dimensional digital model, typically by laying down many thin layers of a material in succession. The models are designed using software called Tinkercad and converted to the printing g code to feed to the machine using Ultimaker CURA software. This paves for creative models.

The visit session was facilitated by Dr.Sanjeev Ranganathan and the team of STEMLAND. The session started with a few minutes of concentration meditation and a few words about what we stand for, a casual talk on the similarities and differences between the last school and STEMLAND. Students had to choose any two stalls they can spend time on. Some of them wanted to explore all the activities.

Students and facilitators had a great time exploring. Few of them made hands-on projects using the kits provided. They played strategic games and got fascinated by them. It was a pleasure to have them in STEMLAND. The team had wonderful learning, growth, and fun having them.

## BHARATHA TIRTHA II- International conference on Indian knowledge systems by IIT Kharagpur.

BHARATHA TIRTHA II- International conference on Indian knowledge systems was organized by IIT Kharagpur. Dr. Sanjeev Ranganathan, founder of STEMLAND was invited to present and he presented on the topic of Rajju ganit (string geometry, cord geometry).

He demonstrated briefly the concept of squaring the circle can be done using the Rajju ganit method. Using the rope, a circle, and a square of the same area can be constructed and observed.

There are two main new features:

(1) The cord replaces the entire compass box.

(2) Empirical methods are admitted in geometry contrary to the philosophy of formal math and using instead the philosophy of approximation.

Some other interesting topics that were presented at the conference were trigonometry in Ancient India and how that led to many discoveries and applications.

Jyotpatti: Trignometry in India

Trigonometry in India is called Jyotpatti.” Ja” means chord in a circle and “Jia” means string in a bow. Mathematicians used this to find the relation between the arc of a circle and the chord of a circle. The sine function is ubiquitous in all disciplines. It is very important to study the application part of sine and cosine functions.

Bhaskara’s metaphor for sine and cosine:

Bhaskar Acharya is a 12th-century astronomer and mathematician. He brought in the importance of science in astronomy, and the application of it is beautifully brought out with a nice simile.

He says that,

Just as fabric(pata)is made up of crisscrossed threads Likewise the spherics or science of astronomy is crisscrossed with sine and cosine functions.

Sines and cosines are everywhere in astronomy:

Interestingly, sines and cosines from the earliest times were formally a part of astronomy rather than a separate discipline of mathematics, it is because applications in astronomy fall all over the place.

The main phenomenal applications such as

1. Ascensional differences between planets. (Spherical trigonometry)
2. Epicyclic orbital corrections to planetary longitudes.
3. Zenith distances and the length of the shadows.

Arcs and chords: The origins of trigonometry in India:

In the 17th century, a famous mathematician named Nityananda Sarvasisiddhantaraja explicitly links the advantage of looking at half chords.

Mathematicians paid more attention to what a chord concerning a given arc is, What is half of the chord of double the arc, and the right-angled triangle which is used for mathematics and computes various line segments concerning half of the chord made computations much easier for astronomers.

Technical terminology introduced bow and bow string:

The evolution of trigonometry in India:

Practitioners needed to compute:

1. Half chords and other line segments in right triangles using the geometry of polygons inscribed in a circle.
2. Tables of Rsines are computed for various values of R.
3. Linear(or occasionally second-order) interpolation is used to determine non-tabulated values.

Addressing these led to brilliant discoveries and the results from the middle.

Mathematicians like Brahmagupta, Aryabhatta, and Varahamihra have given the tables of sine and their geometric dimensions of it.

## The Possible Missing Ingredients in Engineering Higher Education

The Possible Missing Ingredients in Engineering Higher Education – Mastering Self, Agency to Shift Disempowering Norms and Socialization, and Mastering Technical Skills

Context and Autoethnography

• We are youth who completed our engineering bachelors from rural colleges.At the end of our bachelor’s, we found that we lacked skills and any specific guidance on meaningful employment or life.
•  This research paper represents our experience in Becoming and Being a Shifu (Master) program (BnB Shifu) is a 1-year residential program where we experienced being our full potential and developing the five minds of the future not addressed in college.
• Autoethnography offers a way of giving strength and voice to personal
experience to extend social understanding of being.
• We feel that the autoethnography methodology based on our reflections is appropriate for this paper as we are addressing the lack of reflection in youth and our education system. We hope the multiple (five) reflections reduce the weakness of autoethnography of not being general enough.

## Vaughn cube

Vaughn cube is for children who find visualization easier rather than memorizing the multiplication tables.

Elements of Vaughn cube:

• Numbers.
• Pictures.
• Colours.

Construction of Vaughn cube:

• 4 sides = 4 walls.

Each wall has a specific color.

• Numbers are arranged as follows:

Odd numbers- Diagonal.

Even numbers- In the middle.

• Pictures-Specific arrangement based on the sound they make.

For eg: Tuna- T, and n.

Nose -N and s.

Working with Vaughn cube:

• Create a room as shown in the image with the numbers marked.
• Ask children to practice the objects along with their position on which number the object comes.
• Make it clear for children to see that it is the same object between 3 to 4 and 4 to 3.
• Let children study the base picture and introduce the different words.
• It’s important for the children to know the orientation of the room as they will remember objects based on their location rather than the numbers they are in between. This is how the mind castle works.
• There are different charts for tables 3,4 5, etc.

• Introduce all the images in the Vaughn cube and ask children what they are along with the sounds.
• Make children practice the names of the objects and see if they can identify the sounds while saying the names of the objects.

Eg: Tuna-t,n

Deciphering the sounds and numbers:

Map the numbers from 0-9 with the sounds.

• 1 looks like t.
• N written sideways as z looks like 2.
• M written sideways looks like 3 especially small m.
• Cursive r has a hidden 4 in it.
• L is logged the bar on top of 5.
• Ch written with c inside h looks like a 6.
• Cursive k has a 7 inside it.
• Cursive f looks like an 8.
• P reversed looks like a 9.
• Practice making children map the numbers with the sounds for all the objects.
• See if children can say the numbers instead of the object name between the two numbers/on top of the number in the room.

Vaughn cube can help children learn multiplication as well as division effectively by visualizing.