Second STEM Land at Isai Ambalam

We started a second center of STEM Land at Isai Ambalam School on 1st March. The children at the school had been learning the games and puzzles and had set up stalls to engage those who had come. Some had created small projects like a name board with a welcome sign to a few 5 graders explaining a small LED circuit with a switch and a resistor, to games that the children had put up.
The 9th graders from Udavi had come for the inauguration and also brought their own games, rubiks cubes, etc to show the younger ones at Isai Ambalam the spirit of STEM land.

The opening is well documented in the following posts. 
http://www.auraauro.com/stem-land/stem-land-inauguration-at-isaiambalam/
http://www.auraauro.com/school/inauguration-stem-land-isai-ambalam-overview/

I wanted to talk about one moment of the opening ceremony when the entire Aura Auro team (7 people) were at the entrance. We could see all the people engage with the stalls and no one noticed any of us missing or all of us had gathered together. I just let it soak and we waited for a few minutes before starting the silent clap that slowly gathers steam till everyone was paying attention.

The best moments of a teacher are the moments when you are no longer needed.

Experiences at STEM Land...

A few recent experiences at STEM Land that touched me...


- I have been touched how elder and younger children with similar interest are willing to work together as equals. How open elder children are to learn from younger children who have developed an expertise at something.
- We didn't spend a single rupee on labor to set up STEM Land. A big we (Aura Auro, our friends, volunteers and the children) did it ourselves.


- I had decided that I was going to let STEM Land self organize. One day some younger children came to me and told me that a couple of elder children had taken their laptops. I told them to work it out among themselves. About 10 mins later I had opportunity to work with the elder children and I enquired what happened. The elder children without batting an eyelid said that STEM Land is a place of work and they only took the laptops from two children who were playing computer games and not working seriously.


- We started working with the 9th grade girls only this term and in the beginning they would only stay in the games, materials room and not explore the technology room. This week I had a couple of girls working hard to create a story using programming in a 3-D environment and connect their mathematics to what they wanted to accomplish. Another group has been working on soldering a display for STEM Land with N.


- A few Isai Ambalam (the other school I work with) children come to STEM Land on Sat (their day off). They just felt at home and the Udavi children took care of them as their own when they are here for the whole day. A couple of Auroville children have started coming to STEM Land once a week and were unfamiliar with the programming environment and some Udavi children sat next to them and worked and helped them when they were stuck and I was only called once for help during two sessions of 1-1/2 hrs that they worked here.

- N who has completed his undergrad in EE wanted to volunteer at STEM Land I asked him not to worry about teaching children and just focus on using STEM Land facilities for his own growth. When he started working he realized that children could do many more things than him and learnt from them. 
When we were opening STEM Land we split the opening speech in 2 min sections between four of us at Aura Auro and the children were cheering for each of the youth. When we had completed the children cheered and asked N also to speak. He said, he comes here to learn and have fun.

- A couple of other youth who graduated from Udavi also come in on Sat in the afternoons and engage with children or play abalone among themselves. I get back to Aura Auro at 2:00 so I wasn't quite sure what to do when the Isai Ambalam kids were here the first week and needed to stay later. The youth said don't worry I'll stay here and lock up once they leave. Next week the Isai Ambalam kids were telling me that they will lock up themselves!

On work and play...

At an educational meeting we went about making a distinction between 'work and play'. The closest I could come up with was that work was an activity being done that is useful for others and play was an activity not meant to be useful. Of course, I knew it was flawed, self-work is useful for others intangibly and for professional cricketers play is actually work. Of course this doesn't start to capture where work and play seem all mixed up! I could not define it in terms of enjoyment as there have been many times when I enjoyed myself being at work and at play.

An incident with the children helped me understand this distinction differently.

While creating an animation of the Earth going around the Sun in an ellipse (with the Moon rotating around the Earth) the children had use the computer to create the solution for ellipse equation they got from geogebra. It was all done and they had created the following animation. 
(If you are having trouble viewing animations please update your flash player).

Here is a short clip of the part where children noticed that the earth was rushing past at the top extreme in the program that they had created.




I had felt that being able to solve a complex algebraic equation was enough of a challenge and the children had already spent a week on this project and would want to move on, but the glitch really bothered the children, they were unsatisfied with what they had created. This created an opportunity for conversation about slopes and how things were changing differently when solving in one part of the curve, but faster in the other part of the curve. That we needed to compensate with more points where things were changing faster. It took another three days till the children were happy with their work and it looked like the one below:



On reflecting on the incident I learnt that its play when you do something that you don't have to. Of course this definition seems obvious when you are at 'play'. But, it applies equally to 'work'. The moments where I felt I had done something special were the moments when I did what I had to, but pondered over it and did something more. There were already solutions and I didn't have to do more, but I made work play and kept going. 

It helped me connect to the idea of the next right answer, the pursuit of excellence in getting an answer and continuing to look makes work play.

What a world we would create if all our children could make their work into play.

Copy-Paste (the hard way)...

The children had been thrilled with being able to animate the moon going round the earth and wanted to show the solar system with the earth going round the sun. 

Thanks to Arham I had recently seen a video called Earth's motion around the Sun that indicated some of the complexity from the simplistic info that children had:
https://www.youtube.com/watch?v=82p-DYgGFjI

We looked at it and the children felt that it would be interesting to get an object to move in an elliptical path and replicate the earth going round the sun.



The circle was more or less straight forward with moving and turning in each step, but an ellipse...I talked to them of using Geogebra to draw the curve they wanted e.g. an ellipse and then "copy-pasting" it in scratch. Of course the issue was not drawing a shape, but to get an object to travel along the curve so it needed to be true to the curve.

I started with a simple case if x+3 = 5, we went over the story and I reminded them that the answer was not important, it was a trivial case and we were trying to get a method that would help the computer do a repeated simple task till it reached a condition. Also to have a simple condition we changed this to the expression x+3-5 and substituted values of x from -3 to 3 to find when the value of the expression goes to zero giving us the correct x.

We then attempted to solve 2x+3=6 i.e. 2x+3-6 and check when it becomes 0. But, it did the following:
For x=-3-->-9 ; x=-2-->-7 ; x=-1-->-5 ; x=0-->-3; x=1-->-1;  
      x =2-->1  ; x=3-->3    ; x=4-->5    ;x=5-->7 ; basically missing 0. What would then be the way of capturing where the answer lies. The idea that came to the children was that the result of the expression changes direction. Naturally, the last result will need to be remembered, but how do we check if something has changed direction. 
I asked them what they had learnt from integers that might help them do so crisply.They could not quite figure out how to go about it and when they couldn't quite connect after struggle I guided them into the product of integers and checking if the result it positive or negative. Of course here we get the closest integer number, but if the equation is large even though we don't have the decimal parts the curve looks good enough.

We then moved to a real equation x+y=3 and for each value of y we swept x...Once it worked for a line we just moved to the curve and only needed to handle the boundary conditions. 
    

Where is the moon now?

One interesting conversation I had recently was asking the children where they expect the moon to be. When we talk about how disruptive technology can be an app line startracker that shows the position of the moon 'right now' gets into a lot of how children think.

From the first answer in the sky to where in the sky then conversations on what happens during the day and night. I asked the same question over time to different children and with the changing position of the moon it enlightned different aspects of learning. Here are some of them:

1) In an initial thought most children thought the moon rises and falls consistently at more of less the same time. So it should be the other side of the earth. But on looking for the moon it was noticed in a very unexpected place. 

We then decided to for the moon and record where we see it and the time we saw it. That was a week before the new moon and a lot of children came back with there was no moon this week, but some others noticed that they saw it in the morning. We talked about sometimes seeing moon even after sunrise and sometimes even before sunset. What this all this mean?

2) Drawing the expected position of the moon and trying to represent meaningful information of a 3 Dsetting in 2D that led to frame of reference direction and directions. This led to discussions of which plane we can draw aka where does the moon rise and set. It was interesting that there was a child in each class who through that once the sun sets in the west the moon rises from the west.

3) While most children disagreed to the above they could not give any convincing argument to their peer other than that's the way it is.
There was some discussion of how the moon rises and sets. We have been talking about differentiating science from information i.e. being able to understand a phenomenon so we can use our understanding to explain another phenomenon.
One of them was understanding the revolution of the earth which explained both the sun and the moon rising from the east.

4) The children got some clue of which of their classmates were conveying useful information regarding their sightings and which were just making stuff up :).

5) Discussions on fractions! Based on where the moon we talked about where the moon would have been (w.r.to earth) 12 hrs before 6 hrs before and then the more open ended question of when would the moonrise have been. I say open-ended because it brought up the question of at what degree do we consider it moonrise and what the present angle is...

6) It brought up interest on how to create an animated model of the moon around earth, in fact about the moon and earth around Sun.

7) And then the question, how does the camera see that far in the sky :). 
I moved the discussion to possible ways of doing it including a three axis accelerometer that helps is determine where we are looking + gps + the star map + calculation of the moon and planet movements and how that was a cool way to use math. The children immediately got the wiff that I have switched from anna mode to 'teacher' mode and they started to loose interest. One of them even remarked that then we can't see the man-made satellites. 

I learnt my lesson and decided to keep my agenda of teaching something aside to avoid messing up with their learning. When asked this question the second time by another set of kids  just stuck with, 'no clue, but isn't it cool!'

Hmm...upgrades...

When you get around to doing something the second time...there is always something new that happens to keep things interesting.

Last year I had worked with some 7th graders on integer subtraction by making something move from its current position to a target position. Here is a note on the same

"Children initially tend to understand negative numbers in integers as a loan. However, even a simple situation like 5-(-5)=5+5=10 becomes hard to comprehend. A number line is a better visualization for introducing negative numbers. This happens implicitly when using Scratch as it incorporates the Cartesian coordinate system. A character (sprite) when placed at (0,0) is at the center of the display. Changing x with a positive number takes it to the right correspondingly changing x with a negative number takes it to the left.

As children use a change x function they get a handle of the integers. In time they get curious and check what happens with change y with integers to get a sense of the Cartesian system.

As the children felt more confident they created a simple game with integers: the user needs to give the number to add to take a character from a start location to a target location. Though initially the children put numbers and situations they already knew e.g. two positive numbers start:5, target:10, to add:(10-5)=5. The program would then move from the start to start+to add and check that the result is the target. Once the children are comfortable enough to randomize one and then both the starting point and destination, all possibilities of subtraction scenarios arise e.g. start:10, target:5, to add:(5-10)=-5. They also clearly see the need to move left to get to the target. Similarly, start:-5 target:5 to add:5-(-5)=10 also makes sense as the target is to the right of the object."

The emphasis last time was a bit on programming and getting the strings and numbers to match up well. 

But this time the children were implicitly unconvinced about the motivation of the character (in one case) the crab to move. The crab must have had a reason to have a target, right. So they came up with their reasons. The crab was tired and wanted to sit on a rock!

There were other stories of a diver catching a fish, of a cat catching a mouse, someone looking for a key, etc). The character was at the current location and there was a visible target that the children could see is behind or ahead of the character. This helped them re-look at the result they got to see if it made sense i.e. positive number means the rock should be in ahead and a negative result is a rock behind me.

It takes you 40 yrs to get...

well, of course to 40 yrs of age!

It has also taken me time to figure out that I want to create a learning space of constant growth that makes Science, Math and Engineering natural and fun.

I have already been working on the basis of such a space for the last couple of yrs and now with the team at Aura Auro am ready to create STEM Land.

STEM (Science Technology Engineering and Mathematics)  Land will
- Work with over 100 children from multiple schools for 4-5 days a week on Math and Science using hands on work.
- Work to transform the culture of right answer and 'sums' to discussions on approaches and patient problem solving
- Remap curriculum starting from 6-9 grades to activities and projects using technology, puzzles, games, etc
- Serve as a teachers resource center for Math and Science teaching aids and activities

In short provide an alternative model to the current education system.

I need your help in raising funds for STEM Land. My present target is 23 lakhs over the coming year. Here is a detailed concept note on what STEM Land is about and here is the budget for the same.

Please send me an email if you can support the initiative. Donations in India are 100% tax deductible.

Truth and love,
Sanjeev
---

What was accomplished this schooling year

Primary work has focused on classroom interventions in mathematics and problem solving in middle school 5^th-8^th grade. Many abstract concepts are grounded in middle school and if these are missed they leave gaps unfilled resulting in children having an aversion of mathematics and weak problem solving ability.

One of the aspects of work has been in making learning math fun and accessible for children while changing the perception of what mathematics is both for children and teachers. I had used puzzles, games, educational material, construction of models, electronics to make abstract learning tangible and provide application for children. This is documented in detail in the CriticalThinking_Report.pdf.

This academic year I focused on extensive use of technology starting with programming with Scratch with 6^th-8^th graders and mapping aspects of Math curricula through projects and challenges in programming. Three broad approaches were adopted for Math curricula through programming:

1. A set challenges for children that involved demonstrating their understanding of abstract concepts visually through programming including fractions, long division, pie charts e.g. demonstrating what it means to add numerator and numerator and denominator with denominator in a fraction and what is a meaningful way to add it.
2. A set of challenges were based using programming to understand mathematical ideas visually including linear expressions, percentages, simple and compound interest. As an example 5x+10 was graphed as rectangles of varying heights. Then shapes observed by varying the slopes or varying the added constants were observed and interpretations and explanations explored (stair cases of different kinds including making either the slope or constant a random variable, etc). This was then modified to investigate solutions to equations e.g. 5x+10=75 that used the expression and the pictures and paused when the result was reached.
3. Children created games that helped them understand a concept and then work on rigor to master an aspect including positive and negative integers, cube roots that resulted in two digit numbers. Once children get into the mode of creating their own programs often when the computer is available they do not drift and get carried away and play games, they tend to create them. If this is done step by step with values that they put in place first that they knew the answer of and then randomizing it they still want to be able to better their own programs.

Programming was also used in English to give life into the stories that the children had created by animating them in scratch. We worked on this project with two grades 7^th and 8^th. The 7^th graders had also used programming for math and their results in terms of how elaborate and complex they could make their stories even though they were younger and were attempting the stories the first time as well was interesting.

Beyond Mathematics and English, programming was taken further into sensing the real world using Makey, Makey. This helped children respond to a real life event like touching a plant, water or items with some moisture content (not complete insulators). Using this the children made their own version of a water tank filling alarm and a non-touch (pressure based) burglar alarm. These exercises helped children connect the programming to sensing the real world and think of applications where they can make use of these aspects in real life.

To complete the loop of controlling in the real world we also worked with the Finch robot and controlling the actions of the robot to go around obstacle courses and deliver small paper balls into goal buckets. The most popular game we created was the parking game with a random set of commands that made the robot move around and having to predict where the robot needs to be placed to reach a certain goal. We used this version at a school fair with success.

It should be mentioned that this approach is significantly different from ready-made material available for children like online lectures (those available in local language), or animation videos that are more or less passive. The so-called educational games that attempt to 'replicate' rigor use the same methodology of trying to get a high score used in the traditional system with the same pitfalls e.g. if given a choice children play games that they are already good at to get a higher score rather than stretch themselves with new games.

However, a paradigm shift is made when instead of trying to program the child through the computer, we let the children be in control and program the machine. In the first paradigm the computer is always right, the child is always a user and playing catch-up. In the second the children realize that the computer actually needs to be given step-by-step and can't make the simplest connections on its own.

It changes the dynamics of children using machines and their thought process in how they think of an action and break them down. It also helps children truly appreciate the amount of work that goes into making a computer look smart!

More interestingly the children learn a lot of implicit knowledge and conventions by using them e.g. the Cartesian system when trying to move their objects in the directions needed. Children who feel like failures with test scores in time bound examinations, persevere and feel proud when they are able to demonstrate their learning.

We also used physical technology primarily the DIY bigshot cameras that can be assembled by students and over 60 children from various grades assembled the cameras, took pictures and put them on the computer and then used instructions backwards to disassemble them for the next group to use them. The exercise of group work, reading and comprehending instructions and analyzing the pictures was interesting. The hand crank also gave a context to look into gears, ratios. A lot more could be done in optics, imaging. But, the children were very curious about the 3-D images taken by the camera and experimented quite a bit with depth.

The computer lab at Udavi, Makey, Makey, Bigshot cameras and the finch robot were donated by friends and visitors who saw the impact of technology on children and the interesting mathematics that the children were able to do. Further class notes and work of children is available at (www.smallisbeautiful.blogspot.com).

Just as the response of children to technology is obvious so is the lack of teachers who can play with this interesting resource and engage with children. This was especially true for teachers engaged with village children. As part of filling this gap I founded Aura Auro Design (www.auraauro.com) in collaboration with Aura Semiconductor Pvt. Ltd. this year. Aura Auro Design works with 3 electronics graduates and trains them in state of the art analog design (5 hrs a day) while engaging them for (3 hrs a day) to work with schools with a focus on learning through technology.

This has created a small team of local skilled and technically savvy youth who are learning and teaching at the same time. Aura Auro makes explicit that every teacher needs to be a learner.

It has also created a team that is working on STEM research in rural India to deliver results beyond what one person is capable of.

Finch flops @ fair

As I was recovering from Dengue I was still weak and could not travel to Udavi. I had however received the Finch robot as a gift from Gaurav. It had been a lot of fun to use it and program it for a task (drop a paper ball into a basket) at the Isai Ambalam school. When Poorna school children visited Isai Ambalam they also had a lot of fun programming the Finch to do such a task.

Udavi school organizes a school fair a day before Christmas and some of the children from Isai Ambalam had gone for it the previous year. This year they were asked to put up a stall and the children decided that they would do a stall with Finch. Given that it was the coolest gadget, we already had it made and just needed to show up. Of course in the dry run of designing a challenge and making it happen with teams in the class it took us half an hour...I took the precaution of going to Udavi a couple of days and introducing working with the Finch. My class at Udavi was even upset that I was letting the Isai Ambalam children set up a stall with Finch, instead of them.

D-day the children put up a stall with the game of asking people to program the Finch to start in one location and park in another while avoiding hitting obstacles. People were happy watching the Finch demo, but not many were biting. Only the children from Udavi who had worked with me gave it a try. Some were curious and watched, but very few were in the frame of mind to give it a shot. Soon the obstacles were removed, the problem made simpler, yet the crowd stayed thin watched a demo and walked away. 


Arham had also come to the fair and I was walking around with him trying out various games - dropping a coin in water to a target, tossing a ball to pass through a hoop, kicking a football through a tire, tumbling a tower with balls, rolling a table tennis ball on two ropes and dropping it into the bucket, hitting a ball coming out of a pipe. I walked back to my team after an hour to realize that they looked exhausted and it was because of lack of interest and the effort it took to write in the program.


I realized that most of the games that didn't involve luck involved prediction...watching something happen and trying to correct to make something else happen. It reminded Daniel Wolpert's very interesting TED talk about how our brains evolved primarily to help us move dexterously through prediction (its a fun talk, well worth the 20 minutes). The ease of prediction and correction was missing in our game and hence not in sync with the rest of the fair. What was fun and exciting in a "serious" classroom setting had fallen flat in the light of "real fun". 

An hour and quarter had almost passed (in a two hour fair) we needed to change the game drastically. The new game was this, a random program was written to make the Finch move around a bit. As a user you needed to predict where to place the Finch in order for two wheels of the finch to come on the parking pad. You had two attempts. Once someone solved the problem the program was changed. 
Having to choose location and orientation alone seemed doable and a fair crowd built up at the stall. You could wait and watch someone did to have a better shot at solving the puzzle, but you took the risk of someone solving it before you.

While most games were running out of steam since children and people had already tried them the Finch stall was heating up. The stall running about 15 mins after the fair stipulated time and children played even though the center where tokens (we gave out on completing the challenge) were exchanged for gifts, had closed.

The fact that the game was salvaged in the end seemed to have stayed with the children as they seemed pretty happy with their stall and wrote about how successful it was once we changed the game. A few Udavi children who had stayed till the end asked me to book the game for them for the next years fair.

The finch robot : Programming (1)

Programming with Scratch has been getting more interesting with interacting with the real world with the makey-makey that was able to let the computer receive signals from bananas and vegetables. Gaurav's gift of a Finch robot gave a way for children to control something that happens in the real world.

The setup on Ubuntu 14.04/Scratch 2.0 worked with the given guide. 

I explained and demonstrated the sensors, played with its nose light and then we got down to making the finch move. In the initial exercise I was trying to get the children to move the finch around in a certain order, but what made it interesting was to try to move a crumbled paper ball around and put it in a basket without the Finch falling off.

The finch has two wheels that are controlled independently with (two) motors. The only input possible is a speed from -100 (backward) to +100 (forward). In order to rotate an object, for example, you need to move one wheel faster than the other. Also, since we had not figured a direct relation between the speed and a specific distance there was some guess work involved in the time that it needs to be done for.

The phases involved in solving the problem involved in drawing out what they wanted and what speeds in which wheels for how long will be involved in doing so. The wheels were a little wobbly and even when the two speeds were exactly the same the finch had a bit of a drift to one side. But, that just added to the challenge :).

I split the students in groups of 3 or 4 to allow for discussion and team work. The game was to be able to do it in the least number of attempts. I noticed that groups were not that keen on observing what another group was doing as they wanted to only follow their own program to avoid confusion. But, since my purpose was for them to start predicting the outcome I provided an incentive of an extra attempt if a group predicted the outcome accurately. This got the groups interested in examining each others work as well.

After a couple of attempts the children started to really get into the idea of predicting what a set of instructions is going to do and how to go about solving the puzzle. The reality of a paper crushed into a ball is that it didn't always move with the finch and kept things interesting. Its interesting that while children keep track of the number of tries, etc none of this really matters and the first time a ball falls into a box the children want to do the next puzzle.

The ideas of rotation, positive negative numbers, speed, timing were reiterated. In addition problem solving by prediction, verification and correcting what they were doing and the idea of learning from what happens rather than it just being right/wrong was an aspect looked into.

Makey, Makey...(1)

At Isai Ambalam school we had set up the computer center and this year I was looking at how to best utilize this for the older children (6th and 8th graders) at the school. We have been working with Scratch programming for math concepts and more recently for creating games with English.

Regine is volunteering with us at the school and observed some of the classes got a very interesting gadget called the makey, makey from her friends to see what we could do with it in the school.

The idea of makey, makey is so simple that it adds to elegance of thought to come up with it. It notices if a circuit is complete and sends a signal to the computer that it knows well - the space bar, left, right, up, down arrow keys and a mouse click. Not very interesting in itself, but the subtle part is that it can detect even a large resistance closing the circuit. This makes it possible for it to detect a human body, a banana, a leaf, etc to close the circuit and lets it interact with objects from the outside world not associated with the computer.

The picture above is me playing a drum and a guitar string with each banana using Scratch.

Technically you need to hold one wire in your hand and play with the other hand. 
But, in our class the grounding of the computer room was quite good and since we leave our footwear out we were completing the circuit by simply letting our feet touch the ground. this meant that anyone could just touch the banana and get a space registered which meant in scratch could make a drum beat.

Of course the children were not convinced that it was the ground completing the loop and they pulled up their feet sitting on the plastic chairs and checked. Luckly the internet had been shut down due to heavy rains and we have to open scratch and create our own programs, choice of music and notes.
Once the kids were comfortable with what they were doing they asked the other teachers to come and try out the musical instruments.

Now, we will build on it and see what else is possible. One child has promised to work on a burglary alarm, another is making a full piano, lets see.

Seeds...

With the 6th grade at Isai Ambalam we have did some experiments with measuring the pendulum as an application of decimal numbers (and division by 10). I use my watch as a stop watch for the measurements and kids were having a little bit of fun trying to find out the shortest time they can start and stop a watch. We were talking about time and measurement when Saj asked how often I change the battery in my watch. 
I mentioned that I hadn't changed the battery since I bought the watch so it should easily last a year. Saj immediately got back with the fact that I have been around for 1-1/2 yrs and he has always seen me with this watch. Observation (check).
Then he says, wow, that watch must have "very low Watt". Wait where did this come from?
Vij who is new to the class enquires what is Watt. Saj replies that we did it last year, its the energy that the watch takes. Ani corrects him that its the power. Saj concurs and reminds himself that it is indeed the power. He goes on to tell Vij that the light consumes 40W and the fan 70W of power and its only when it is multiplied by time that it becomes energy, actually Wh. Recall (check), application (check).

Last year I had asked the 5th graders to go around the school and look at the number of lights and fans in each class and estimate the power and look at the time it was on for in a day to estimate the energy (as application of multiplication). 

I said the power is very, very low and you would need to split a Watt many times. Oh said Saj, does this mean it will be a decimal point followed by many zeros? Decimals (check).

I actively look to connect concepts that we have done in the past, but it was interesting to see the seeds that were planted a while back come forward as a regular conversation without any planning.

Government teaching training workshop

Isai Ambalam School has been partnering with the government schools for many years now. Their partnership has been useful for the school in spreading what they learnt and to review any training material that is received by the government schools. They are also informed of any ongoing teacher training. Last month there was a government school teacher training for 6-8th graders math teacher. These are the grades that I have been working with for the last year or so. Subash suggested that I attend the workshop and (if opportunity presented itself) train the teachers. At that time I wasn't very convinced exactly how an opportunity would present itself. I skipped the first day of the three day workshop. But, Kavitha attended it and built a rapport with the coordinating trainers who thought it would be interesting to have me there the next day.

I took along all the TLM that we had used, pizza party, dienes blocks a mini weighing balance and also some of the computer related stuff - geogebra and scratch programs made by children.

The teacher training happening was interesting, on the one hand teachers were told that they need to connect what they teach with everyday life of children most of the time was spent on providing teachers tit-bits of trivia that would help them make the classes interesting e.g. different antiquated units of measurements used in India for land measurement, their conversions (beyond cent, acre and hectare), the number of years it took to build certain temples and some puzzles - two numbers multiply to give a third number and all the digits need to be used only once. Finally, we got to using 10- 5 to get certain numbers and there were many possibilities and I started having fun :).

The teachers were curious as to who this new kid on the block was and I got my turn. I gave then a background of the work with low cost materials as well as the computer based stuff that we had done in the schools and let them choose what they wanted me to talk about. The teachers wanted to see it all. In the first day, for the rest of the morning, I presented the work of the children (on scratch), the tools we used and how we can creatively combine the tools e.g. the denise blocks along with a weighing balance. I also talked about how many of the areas are connected to each other and that they could be linked to each other when they are introduced. They asked for another session the second day to concentrate on areas that they had difficulty with primarily fractions, place values, decimals and algebra.

We talked about fractions can be introduced with pizza party games and addition of at least a set of 10 fractions can be explored with this without formally getting into it. They progressing through equivalent fractions and only then moving to LCM. I also showed some of the work the children had done in explaining how fractions can and cannot be added. The teachers seem to find the approach different and interesting.

The teacher were quite surprised with the work of the children on scratch and while this was appreciated and four teachers even copied the software and the work of the children to view it for themselves at home. They made it amply clear, that they did not consider it possible to take this to their children even though they had a computer lab and an instructor.

The teachers showed most interest with use of materials like the denise blocks, in volume measurements (cc = ml, how much is 1L in number of cubes), algebra and a mini weighing balance. The idea of introducing place value by weighing bunch of blocks on one side and a set of tens and ones on the other to show that the decimal system is more convenient (for humans).

However, when it came to using a program like Geogebra some of the teachers were up in arms. Why would we teach four digit multiplication if it can be done easily with a computer? Good question, why do we teach children four-digit number multiplications? These discussions helped me get deeper into the purpose of math as interpreted from the NCF 2005 document. If 4 digit multiplication is taught it is to help the child's procedural mind. We also talked about the idea of an approximate solution and a feel for the numbers that children do lack which would certainly be worth working on.
Of course, its also a tool that can help in developing an intuition into something that would take them much longer to do e.g. discovering the relationship between the radius and the area of a circle, or a series of lines like x+y=constant.

Given the apparent confusion of children between fractions and percentages/decimal I walked them through the method of looking at the denominator to estimate 50% (1/2 of the denominator), 10% (.1 of denominator) and 1% (.01 of denominator) to compare and build up the numerator. But, by an large the teachers had difficulty in grasping it and told me that even though they had difficulty and children are unable to get a handle on the sense of a fraction it was out of syllabus :). Ah well...

It was nice to see that the teachers were able to notice what the children had difficulty with and when they felt that someone could help them help their children they were quite involved. Teacher training is a mandatory program and teachers get back by taking 1 hr tea breaks, but the same teachers moved their lunch by almost 45 mins to accommodate my session which I much appreciated.

Guided learning: Using computers

One of the fun aspects of learning while having access to a computer center is the exploration style of learning that is possible accurately with Geogebra on the computer. To learn about shapes like triangles, angles, circles, etc through measurements. Looking or patterns and making observations and deriving some sort of a generalization made for an excellent exercise.

Here are some of the things that worked well us:
1) Using geogebra as a drawing tool in practical geometry to draw various equilateral triangles. A line segment is drawn with A as center passing through B. Then a circle is drawn with center of A passing through B and then a circle with center at B drawn through A. The meeting point of the two circles is equidistant from both A and B for the same lenght thus giving the equilateral triangle. The children can then measure the angles and distances. As they create and measure many more triangles using different lengths for a side they realized that all equilateral triangles have the same internal angle of 60 degrees.

2) A triangle with three sides can be drawn with a line of one of the lengths and then circles with radius of the other two sides. The point of intersection of the circles gives the third point of the triangle.
Picking up three random sides of a triangle in a class brings up the triangle inequality, when children are unable to find a point of intersection and naturally moves one to the realization that two sides have to be greater than a third to make a triangle. I encourage the children to try using the first side as any of the other sides and see what happens e.g. 1 cm, 2 cm, 4 cm has the following three ways of looking at it. Interestingly, I only thought of the inequality as the third figure, but some of the children seemed to find one of the other two more sensible.

3) Some other observations about triangles  also came about by this process

- Isosceles triangle has two angles the same

- Sum of the angles was always 180' no matter what the triangle

- The largest side is opposite the largest angle.

Then we did some games using a combination of these e.g.  would the central angle of a triangle 4, 5, 5 be less or more than 60'.

The children were starting to get a feel that sides and angles are not independent quantities.

4) Circles - circumference in relation to circle diameter, area relation to the area of a square with one side as radius. These were fun exercises that I had attempted by getting the kids to do physical measurements last year. It took quite some time and due to measurement inaccuracies (especially when measuring small objects like ear rings) could throw the kids off. The ratio of pi (that they presently know as 3.14) came out like magic as geogebra could be used to measure these quantities of interest no matter how small or how large the circle was. I skipped the calculations at this point and stuck to creating a spreadsheet of the circles that children drew.

The children were each able to document 10 circles or more that we were unable to last year. The number has really stuck with them as an assessment recently (with circumference given and radius/diameter to be calculated) showed with over 75% of the class guessing these right.

5) Algebra

The notion of what lines like x+y=10, x+y=20 look like coupled with stories like you and I share 10 chocolates, if I get one more you should get one less (negative slope) had done. Again an assessment later indicated that most children were able to get this.

On confusions and clarity...

Its interesting how small things can confuse or clarify things for children. At times the children dwell in their confusion and come out with clarity and growth. At other times they reach the end of their patience and look for adult intervention. I often relying on giving time, peer learning, but sometimes peers are unable to fix the problems because they don't have the same problem and can't find the patience to understand the problem. Here something that happened this week at Udavi (6th Grade) and Isai Ambalam (5th Grade)...

We had been working with the weighing balance to apply addition, subtraction, multiplication and division with using things that could be put into pencil boxes. As I was weighing some working with different blocks I noticed that the hand made blocks were not all the same and for a change we went into a puzzle to identify a heavy block among three blocks. In time, I talked about the use of math to document what we learn and create processes. We numbered the blocks so we could distinguish between them and know what you did with them. When the children were comfortable having observed the process with real blocks we thought of ways of writing it out and came up with the following flowchart.

This chart confused quite a few kids. I asked what they had not understood and if they would like me to repeat with the blocks. The children said that they understood the physical measurements. I spent some time revisiting >, < signs and a couple of children did have difficulty with that, but for most that was not the problem. They just felt they didn't understand and something was off. I stared at the picture myself and then some clarity dawned and I drew this one...

Logically it was the same flowchart. Only it had when one is used on the left and when 2 was used on the right with the corresponding >, < signs reversed. This clarified the issue for almost all children instantly. A couple of children go it once they were able to discuss it with their classmates who had now understood.

It was interesting that when the children were working on finding the lighter block they actually switched the signs again to get 1 continuing on the left and 2 on the right. 

Its also interesting that as they started dwelling into more complicated problems of not knowing if the ball was lighter or heavier and with 4 balls they got quite good at the symbols and were able to play around with any order.

I took the same problem with the 5th graders in Isai Amlalam. Having learnt from my experience I did not want them to fall into the same trap and once they were comfortable with what physically happens with 3 balls I went to the pic that I found was flowing in class. 

Apparently the pic didn't make sense to some kids. I went over the signs >, < but still there were 4-5 kids who looked puzzled and few others who seemed to have got it were also a little uncomfortable applying it to another puzzle. Finally, one child articulated that he didn't understand how 2 could be greater than 1. I told him that its only a name to keep track of the balls, but then I took the names of three of the kids in the first row and used these for the name of the balls. I wrote their initials V, D, A and this put the children at ease to work on these puzzles.

Weighing in...math in a pencil box

A fair number of children who have difficulty with algebra have difficulty much earlier with understanding subtraction and division, two areas that we had covered through stories in class. The children felt that they had practiced and were confident that they can create stories, interpret my stories into numbers. I decided to use an assessment that would require application of these concepts in real life using a weighing balance.

I started with one of their pencil boxes, passed it around and asked them to guess its mass. Once they had all recorded their guesses in their notebook we measured it (52 g). I then took 10 pens and put in inside the pencil box and repeated the process. I asked them to guess the mass of one pen. Then scale it with 10 pens. They came up with 90g-100g as their guesses. We then made the measurement (102 g) and I asked for the weight of one pen. As with the previous process the children started guessing. I told them they had already guessed and this time I would like a correct answer. The children could not walk back the path they had come and correct for the measurement they came up with interesting answers including some that were over 10 g. I tried to help them by walking through how I would do it with what the mass of 10 pens would be. I was intrigued that some children were confused by this process and some even managed to add the two measurements (152g). On digging deeper I realized that these children could only think of subtraction when a clear word 'remove' was part of the construction.
I had to move from 
Pencil box mass is 52g. Pencil box with 10 pens mass is 102g. What is the mass of 10 pens 
TO
Pencil box with 10 pens mass is 102g. To find 10 pens mass I need to 'remove' the mass of the  pencil box, which is 52g. 

To open up the puzzle  (well it had become one) for children's participation, I asked the children to each list 10 kinds of items that they could put in the pencil box. With time I added clarifications that the items needed to be something they could find copies of and for a couple of children needed to reiterate that 'kinds' was different kinds of items and 10 pens didn't work. We then measured one of the item they had in mind and the children made their own stories with pencil-box+some number of objects * mass of one object that they had measured. This process involving addition and multiplication that all children find comforting. As they exchanged their stories and solved them they did get practice in handling what they had initially felt a very different problem.


Its actually interesting that I tried these out in different grades and how the numbers change appropriately. For children in 5th grade the number came out as a round number, for the children in 6th grade the objects we picked up had a touch of a fraction and when we did the same exercise in the 7th grades the weights gave some neat decimal numbers. 

Some activities

Here are some activities I have used in class either for refreshing the class, introducing some fun or doing a centering or calming activity.

Big fish, small fish

Just a quick activity to freshen the minds is to hold hands close and call it big fish, and far apart and call it small fish. Using this small twist you go fast and slow emphasize big and small at different times and keep going till the kids can keep up or realize that they made a few mistakes and stop.

1 to 20
Generally acts as a centering activity to let the group count from 1 to 20. The catch, if two people call out at the same time you start from the beginning. There can be no pre-decided format or calling order. You can lift your hand or give indicating that you are going to speak. If the kids start using a pattern you can just call out the number along with the kids and you begin again as a group.

Weighing balance

You can have unlimited fun with weighing balances. Starting with estimation and guesses, you can move to addition, subtraction, multiplication, division and then to algebra. You can also throw in puzzles of trying to find which ball is heavier/lighter in a given set.

Stetescope speaker

Measuing heartbeat can be a fun activity especially when coupled with some exercise like running. In addition getting a child (or adult) to hear heartbeat and act as a human loudspeaker calling out the lub-dubs quietens the entire class trying to count heartbeats.

Place value kits and tables

A neat activity we got going with place value kits (ones, tens and 100s) was to use a few of the blocks - 3x10 and 8 ones or so to come up with as many multiplication possibilities as possible (without repeats and without all in one row) with few or all of the blocks.

The activity really helped getting the idea of the area of a rectangle represents multiplication home for the children.

Taming Frankenstein

As I progressed towards getting children proficient with both positive and negative numbers the 'target' game got tuned further. I allowed students to put the starting number and guessing the number needed to get to target and as part of meta-cognition test I asked how many children felt they were proficient with integer arithmetic 6 children stood up immediately. Most others were able to do 'sums' on integers, but the idea of subtracting the starting point from a target worked ok in their head with questions like 5 going to 10, -11 going to 7, -17 going to -35 got messy.

With a few commands we transformed getting a user number (which some children were sticking to 'simple' numbers) to a random one and putting in a count for correct numbers. The twist was that the count was zeroed out if you got one wrong. I asked children to show their proficiency by getting to 10. Time not being an issue. Every 5 minutes or so the room will have an aaagghh, oh no as children made progress just to be shot down before they could get to 10. I decided not to tell the children about Frankenstein, but they felt that they had created the game and should be able to beat it. Arc was able to beat her game and was quite pleased with herself. Lets see if the other kids get the same high tomorrow.

Teacher Note:

I've made it a little simpler with +1 for a correct answer and -1 for an incorrect one. A list tracks all the problems where the child was confused so you can look at it in detail once they are done.

Phone number of a computer

The children have learnt to program with scratch at different speeds and as part of different groups. Some learnt it over the summer. Some children were in a different grade before being part of the multi-grade classroom (15 kids from 6th to 8th grade) and they have all used different machines. One of the issues that cropped up was that a child wanted to use only one machine since the child would have its work on that machine. I had used sftp and other such protocols, but was not sure how to set it up. Also my time beyond the classroom is limited and I am unable to be a sysad. I checked the minumum needed for a file transfer was to start listening to port 22 and this I did.

I thought the children would find it fun to think of communication across machines. I started with a analogy using cellphones. What if you called someone from another person's cellphone and then wanted to save it on ones own phone. The first solution was that one person can read out and the other can punch it in (I wonder if that is indeed the fastest!), within a second another kid suggested that you can SMS the number. Well, the village kids growing up in this connected world age find the cellphone quite intuitive (memo to andriod - you should not need to install an app to SMS phone numbers!)

We then started talking about what is needed to make this happen. We should know the phone number to SMS to, there should be a network and even one that suggested that there should be a battery in the phone. Since the kids brought up batteries we started talking about the SIM card and what functionality it could have. e.g. What happens if the SIM card from a phone is removed? What happens if the SIM card placed in another phone? Again, its amazing how much kids know about cellphones.

We then talked about how cellphones communicate to each other. The kids immediately brought up 'tower' and then how it goes to a satellite and comes back! Ok. Well what if two phones were close by, would they need to go out of their way? We then talked about networks that are connected to each other and at times when no physical network is available signals needing to take off.

I mentioned that the internet is one more network and pointed out that much more can be done other than going receiving data from the internet. We could also send information, including transferring files between machines. I proposed that it was like making a phone call. You needed to know the number of the person who you were calling, they would need to pick up, but then since these were machines talking not people there would be additional checks and balances.

I had installed Filezilla on one of the machines and tried to transfer to the pseudo server. This had worked the day before. I had, however, not had the time to install this on the other machines. The first step then get the children to go through the process of installing filezilla (minus root password). 

The next step was to figure out how to give filezilla the phone number of the computer. We did this and then entered additional data like the login and password (the information they need to log into machines).

The first try did not work and said that there was no response. I realized that having turned on the ports once the previous day was not enough and I turned it on again. 

Then was the issue of getting the passwd exactly right. This proved a little tough as it needed to be verbatim and the approximations children make to instructions of the teachers simply did not work and voila they were in.

The children seemed quite excited that they could transfer files between machines and one of them even looked up at the big monitor (connected to the pseudo server) expecting a visible reaction from the machine having transferred his file.

For closure of this experiment I went ahead and let each group of children who transferred files to present some of their work on the big screen to reward their work and prove to them that the files actually did get transferred.


Of course, we will move to a more permanent solution of mounting a drive on all the machines, but it was fun to enjoy the journey and not only the destination.