From '15 does not have a square root' to 'what is the square root of 0.05'

After such a long break I though I will start with something simple. A couple of questions from children. A couple of weeks back one child said 15 does not have a square root (only 16 does and that is 4). I wondered what kind of creatures children thought surds are. I had done some square root work with 10 graders using graphs and it seemed to give them some idea that these are also numbers of some sort a month back, but it was a passing comment and I let it go.

Recently, a volunteer started coming into STEM Land and I asked him as I ask all adults to work on some projects to inspire children. I suggested creating some sort of graph in scratch for children to see the squares of non-whole numbers. He started it and got as far as creating squares for whole numbers (similar to what the 7th graders with Sundar did last year) and then gave up, preferring to use his time more productively by finding children who wanted to be taught.

Anyway, another week went by and I decided to take up this project and made a rudimentary squaring version with visual boxes (my hope is always to make something functional, but so terrible that anyone who sees it will want to modify it :-)). I went in yesterday and showed it to the volunteer. One child came by and asked what we were up to (never underestimate the curiosity of a child), I showed him, then another, then another kid. They played with it for some time. Then I modified the program to calculate a square root. This seemed to garner a little more interest. They started playing with the program and one of the 10th graders had an activity class and connected it to the graphs he had drawn and started explaining it to the younger kids. My work was done and I walked off leaving the computer to them.

Towards the later half of the session one girl came to me and asked me what the square root of 60 was. I walked her through my guess and she concurred, but murmered something about off screen. A little later she came back and asked me what the square root of 0.05 was. Hey where did that come from? She explained that she was tying to figure out how small a figure she can get and saw the really small square of just 4 of 1/100 and she triggered the software by asking it to calculate the closest square to 0.05. 

I went back and put 60 into the program and realized she was testing where the program ran out of space to fill the boxes. Boundary conditions, interesting...

[Thanks Swathi for suggesting graph notebooks and that areas up to 2 decimal places can naturally be represented in a graph notebook.]

Boring digression from the story:

If we look at a regular graph sheet it is divided into large 1 cm squares. Within these the squares are split vertically 1 mm lines and horizontally in 1 mm thin lines. There are also helpful guide lines at 5 mm that are a little thicker than the 1 mm lines. These lines divide a single square into 10 vertical pieces (0.1) and 10 horizontal pieces (0.1) and together into 100 smaller 1mm^2 squares. The big square is whole and a smaller square is 0.01.

Here is a picture:

Children are comfortable with decimal numbers on the scale. They can easily mark out 5.4 cm on the graph paper and soon realize that its 5 dark lines and 4 light lines. 

If we marked 5 cm in both x and y axis and completed the square we will get 25 full squares. No surprise, area is multiplication.

The same happens if we mark 5.4 cm in both x and y axis. What is the area of this? The following image may be a helpful... 25 big squares (=25), 4 rods x 5 (4x0.1x5 = 2) vertical and same horizontal (=2) and 4x4 (1/100) (=0.16). 

Now playing with modified program of a square root.

Here are the programs to play, break and make something better!

Squaring program     : https://scratch.mit.edu/projects/115474246/

Square root program: https://scratch.mit.edu/projects/115470991/

A year of Aura Auro Design

Aura Auro Design is now a year old! We put together a small reflection of the year gone by! Here is the pdf.

Aura Auro Design – First year reflection

learn, grow, work, teach

Sanjeev Ranganathan, Bala Anand, Sundranandhan Kothandaraman, Vaidegi Gunasekar

Jan 2016

About this note

Aura Auro Design, a project of SAIIER, is a team of engineers Sanjeev (AV), Sundar (AV), Bala (AV) and Vaidegi (Bio-region) who teach in the schools (Udavi and Isai Ambalam) 3 hrs a day and learn, grow and work in electronics 5 hrs a day. The project explores innovative ways of STEM education primarily through their STEM Land initiative. The team also finacially supports Udavi and Isai Ambalam schools, Reach for the starts program and AV maintenance.

At the end of the first year of Aura Auro Design we report briefly our activities in the first year, reflect if we are aligned with our original goals and what direction or goals we set going forward.

Brief summary of goals of Aura Auro Design

- Exploring if an alternative business model where the primary goal is personal development and growth of its staff and contribution to community can be effective in the real world.

- To create an enviroment where skilled youth can engage with children in schools to learn beyond simple procedural learning from 5^th to 8^th grades and move into application and problem solving.

- To create an alternative to examinations as a way for children to demonstrate their learning.

Some activities of the first year

- Engagement with Isai Ambalam school and Udavi school 3 hrs a day

- Participation in the Stewardship for New Emergence workshop and working with Dr.Monica Sharma to look at system parameters to include in our work to be effective in the long term

- Learning about learning – reading and presenting chapters of – what did you ask at school today by Kamala Mukunda

- Taking up two courses of Interactive Python through Coursera and make variety of python games

- Conducting an electonics class open to anyone in and around AV that used simulations and building circuits as a way to practical learn electronics

- Noticing breakdown of replicating and propogating the same patterns of education we wanted to address and the breakthrough of creation of STEM Land

- Creating a space for youth to come in and interact (and learn) with children and build things with them

- Slowly seeing engagement from children from various schools of Auroville in STEM Land (Isai Ambalam, TLC, Last School) in the hope of enabling learning engagement between children of various schools, backgrounds and nationalities

- Making progress on 3 software projects (80% completion) and 1 hardware project (90%) that was proposed by Aura Semiconductor Pvt. Ltd.

- Putting aside time (three hrs a week) during work time to read

- Tracking our growth and documenting the work of children through the blog www.auraauro.com

- Presenting a paper at epiSTEM6 at HBCSE (Homi Baba Center of Science Education)

www.auraauro.com/showcase/

- Learning to work together and collaborate, moving towards a Likert-Emberling Stage 4 organization

Papers and Articles in 2015

- Ranganathan, S., Anand, B., Kothandaraman, S. & Gunasekar, V. (Dec 2015) Using programming with rural children for learning to think mathematically, epiSTEM6, HSCSE (Homi Baba Center of Science Education)

- AV Times (Dec 2015), ALICE in STEM Land

- The Hindu (Oct 2015), Making, tinkering and engineering their way to knowledge

Beief conclusions

- We needed to keep the priority of learning and growth over work often in mind to avoid getting carried away with deadlines, products and short term efficiency. Though it requires a partner company that is understanding of our work holistically, it has been possible to make some progress on projects with Aura Semiconductor Pvt. Ltd and they are continuing to support Aura Auro this year.

- It is possible to create a space where children can learn through inspiration rather than through compliance. It is significantly more effort for teachers vs 'efficient' classroom teaching and requires us to be true to AV goals of constant progress and unending education.

We have been inspired with the work done by children to demonstrate what they are capable of when given a chance. http://www.auraauro.com/category/showcase/

Going forward:

- The work at STEM Land is meaningful not only for the children we are working with, but also for children throughout the country. But, we need a lot more rigor and research to make this happen.

- We need to find mechanisms of accelerated growth as electrical engineers and work on time management and presence to be effective at work in the time we have allocated to it.

- We need additional people to support our work at STEM Land and will be supporting another youth Naveen (AV) to help us organize the space and keep it open from 9:00 a.m. - 2:00 p.m. Mon-Sat.

- We hope for a richer interactive experience with Aura Semi this year and also grow the number of youth supported in the project to 5 over the course of six months (June).

Reflections from the team

1) Bala Anand

I started the year as a novice knowing very little about work and life. Aura Auro has brought a big change to me. I have learnt a lot during this one year.

As Aura Auro is an electronics centre, it is essential that I am good at it. I knew very little at the beginning. Aura Aura has given me an oppurtunity to learn and grow as an Engineer. I have learnt to anaylse circuits, run simulations, build PCB boards, windows and linux administration, programming in python, etc... I am learning to design circuits, working efficiently by managing time and being organized and learning to work being part of a team.

Teaching was completely new to me. Over the year I have come to terms in managing a class. It gives me happiness to guide the children and share some of the knowledge I have.

Setting up STEM land in Udavi was a big learning curve. I was put in situations where I felt I was responsible. Though I did fail at times it was a learning experience.

We presented a paper in Mumabi, episteme 6 – international conference on Stem education. It gave us an oppurtunity to talk about the different things we do at school. The paper was accepted well and felt that we are going in the right direction.

Making contributions to schools and to Auroville makes me feel that I am doing something to the society around me.

Attending Steward for New Emergence (by Monica Sharma) workshop early in the year was a big positive for me. I learnt lots of tools and that helped me at work, school and personally.

Overall Aura Auro has been a place where I am growing daily, learning and experimenting new things.

2) Sundranandhan Kothandaraman

Time Lapse

The year 2014-2015 was diverse and had a lot of beautiful experiences to offer me. Being part of Aura Auro Design team the learning as an engineer was extensive. I can tell this journey is offering me a lot not only as an engineer, but also a teacher. The Whole oneness of learn, grow, work, teach has made me realize something special, that I am exploring on how to offer at various instances of being myself...

Working with children is a sense of blossomness, I see myself grow along with the children. Wanting to learn something comes form a inner space of the freedom to learn it, that is the experience I share along with the children towards their growth at STEM Land. The work shop Stewardship for new emergence has given me a whole new perspective approach to accomplishment of specific goals and evaluation measures on them.

3) Vaidegi Gunasekar

My stands are Perseverance and Agency (capacity to act in any given situation). AuraAuro laid a clear path for my career as well as social activities (teaching). In this duration of one year I learnt many things in Electronics (which I never even thought of in my under graduation) and Teaching (how to teach and classroom management). This gives me satisfaction on what I did in the entire course of learning.

As an Engineer

I can see myself that I'm growing as Engineer. I'm not doing the same work repeatedly. Everyday I'm doing something new or in different way. This makes me think, engage and apply thoughts based on my previous mistakes. AuraAuro also created space to collaborate and discuss when I face an issue or when I build something.

As a Teacher

As per my perspective, a teacher was one who give all the instructions (what to do and don't). But Aura Auro broke that idea. It created a environment where I observe and guide the students instead of giving them each and every instruction to do something. In the middle I learnt being 'effective' is more important than being 'nice' to all the children.

I also learnt that “ If you want to understand something, change it. But, if you want to change something, understand it.”

4) Sanjeev Ranganathan

Aura Auro has been an amazing growth experience and helped me undestand the gaps in my engagement with children. I find I am finally beginning to understand Sri Aurobindo's first principle of true teaching that nothing can be taught and starting to take my first steps towards being an integral teacher.

STEM Land offers a possibility of putting free progress in action with children or attempting to teach not by compliance, but by inspiration...but much work is needed, both on us and by us in the future.

References

Mukunda, K.V. (2009) What Did You Ask at School Today, Harper Collins.

A Big Thank you to

- To Saracon and Chandresh for providing us the workspace to initiate this effort.

- To Aura Semiconductor Pvt. Ltd. for supporting this initiative financially and providing challenges for us technically

- To the stewardship for the new emergence program for leadership development and helping us work as a team from possibility rather than fear

- To the many people who helped us set up STEM Land including (but not exclusively) - SAIIER for their support on purchase of materials, equipment, books, etc. For letting us revamp and use two cupboards that were up for disposal, Freecharge.com for second hand laptops, friends for purchasing robots and puzzles. Sree Nair for donating bigshot cameras he designed. Aura Semi for inverters. PCG for the second mindstorm and some new games and puzzles, children for organizing STEM Land themselves.

About our partner Aura Semiconductor Pvt. Ltd.

Aura Semiconductor is a fabless semiconductor company providing high performance RF & analog solutions. Aura Semiconductor was founded in 2010 with focus on developing technology leadership in the areas of RF, clocking, audio and power management.