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October 27, 2014

Makey, Makey – How it works...(3)

The day after the heavy rains we had an almost full strength in the 6th grade at Udavi. The previous day only seven children had worked with the MM and it felt like a good exercise in observation and expression to see how these children described what they had seen. Based on their descriptions I asked children to write or draw what they felt had happened.

All the pics from the ones who had not come had a computer (or laptop) connected to a leaf/plant and apparently running Scratch and making a sound. The children in their excitement to describe the plants, sticks, communicating with the computer had not been able to describe the MM. However, in their own drawings the MM was present as a black box.

We had a discussion of what we see and observe and what we understand and interpret. Once I pulled out the MM the children were able to recall most of what they had seen, but they could not talk about what they interpreted as to what happened initially. As I gave them time, one aspect of the MM sending signals to the computer was brought forward as something they had not seen, but interpreted based on the reaction of the computer and the lighting up of the board when we touched something. The other aspect of understanding how the board was able to detect that it had been touched was ambiguous.

We went to the computer lab and I gave a 'magic show' with making the MM board respond or not respond to my touching by saying it before hand. The children were very focused on what my hands were doing and whether I was touching the banana gently or not as gently, etc and did not notice that in the times I wanted the MM to respond I was touching my legs to the floor. Once I explained the trick I was able to lift my foot off the floor and use the wire provided to connect to the board with the same effect. Then I made it further simpler by bypassing everything and directly connecting the ground to one of the trigger points and then talking about how the circuit is being closed even by me.

We then discussed why we don't see the same in real life of connecting a battery with a LED and holding the two ends to light it. This brought forward the sensitivity of the MM to detect even not so good conductors. Then we moved to what we saw the previous day with respect to plastic and wood and that even their resistance can drop when things are wet.

We concluded with what precautions a lineman should take when working on main lines. The kid of clothes that he should wear especially when it rains.

I then did the same session with the 7th graders and was a little surprised that they were able to give all the signals given by the MM (space, click and four arrow keys). All their pictures highlighted MM and had it in this kind of detail. Thought when describing it in words they also cound not convey the MM. I then realized that since we have been working with scratch were able to understand not only that the MM sent some signals, but had perhaps read the code and noticed the signals.

I could, however, not pull the 'magic trick' on them. Almost immediately one hand went up and then within 10-15 sec three more went up on what I was doing with my foot. The loop closing made sense to the children and they went overboard asking me to use various chains of objects that would close the loop, e.g. touch this banana to the next, then to your keychain and then touch it.

We talked about possible uses of what we could do with a MM. The most common idea is a burglary alarm, but I'm hoping more ideas will come.

October 22, 2014

Makey all wet (2)

Monday morning, the rain had been very strong and I bicycled to Udavi and found many students were unable to make it. The new building had 6-7 kids in grades 4th, 5th and 6th. There were too few kids to take classes and I thought it would be a good opportunity to introduce the Makey, Makey (MM) board.

The MM board is able to integrate with real life objects (leaves, fruits, vegetables, plants) because of its ability to (measure very large resistances) be very sensitive to any resistive path. But, the sensitivity makes it misbehaves in the rain. It took me many attempts to figure out a mechanism to avoid a 'false' trigger. The wooden table that I wanted to use as base had imbibed some moisture and was itself triggering. We finally needed to hold the leaves and other material under test in the air.

When anyone touched the plant or leaf it would trigger scratch in producing a sound. As there were younger children I changed the sounds often. I also choose the sounds of animals (cats, dogs, etc) so the dog would bark when you touched the leaf, etc. The children were quite excited and I tried to tap into it to further inquiry.

What is happening? What do you see? What do you understand? What kind of objects will trigger the sound? We went from leaves, flowers, metal, to a stick of 'dry' wood, wooden blocks, and finally plastic! Everything triggered in the wet and moist conditions.

The plastic cap triggering was really a surprise, both for the children and for me and it was time to find a drier place. The rain then stopped and I took the 6th grade to the computer lab and was happy to find that the polished tables were able to present a dry environment where false triggers didn't happen.

The MM is able to close the circuit with a person without having to hold the earth wire (as indicated in the instructions) by using the floor and this makes thing appear more magical.

The class then continued with the 7th grade and we made a piano with bananas. The 7th graders have been working with Scratch and understood what was happening at a certain level of abstraction that they called the 'MM keyboard' vs the electronics keyboard that their program responded to.

October 19, 2014

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.

October 18, 2014


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.

October 08, 2014

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.

October 03, 2014

Probability for 6th graders?

As an introduction to fractions the children were playing the pizza party game. They read the rules and the first game they played helps them get accustomed to the pieces (1/2, 1/3, 1/4, 1/6, 1/8). There are fraction sheets corresponding to each of the fractions as shown below.
The children throw a dice with these fractions on it, they pick up the fraction sheet that faces up. They then try to fill the sheet by waiting for their fraction to come up in their turn.

The game is of course terribly unfair for the children who get smaller fractions (and yet children do enjoy playing it), but I wondered if we could use this as an opportunity to see probability in action. I asked each child to write down the fraction (not person) who won the game in their group. Once the game was played a few times I made a tally of how frequently a fraction won.

As each student read our her/his findings it soon became clear that most of the time 1/2 was winning, once in a while 1/3 won and very infrequently 1/4 won. With these rules 1/6 and 1/8 did not win any games played. 

We had a conversation of whether the rules were fair to each fraction. Then we moved to the question of why it is not fair. It was nice that some of the children were able to think this through. The first child who got it said that its because 1/8 fraction needs 8 pieces and you need to get 1/8 8 times, vs 1/2 where you only need to get 1/2 2 times. Getting something two times is 'easier' than getting something 8 times. In a few minutes most children were also giving their explanations along the same lines.

I proposed a different set of rules for the next game to try to help the 1/6 and 1/8 (and get them comfortable with equivalent fractions). If you get any piece that lines up with the lines on your sheet you can take that many pieces i.e. on a 1/8 fraction sheet, if you roll 1/2 you can take 4 pieces, if you roll 1/4 you can take 2 pieces and if you roll 1/8 you can take one piece. But, if you roll 1/3 or 1/6 you need to pass. I asked if this set of rules would even the odds...the children were unsure so we went for a few rounds of the game with the new rules.

We had just enough time to come together and tally the results. 1/8 followed by 1/6 were the most common winners, 1/4 was next followed by 1/2. 1/3 was the least common fraction to finish first.

I asked them to think up game rules that would both be interesting and fair to the fractions. A couple of days later, they came up with some games. Some of the games  proposed were repeats (apparently arrived at independently). I asked the children to rate the games in two parameters, their interest in playing the game and if they thought the game was fair. 

Game 1: Like the first game, but you can take a piece of your fraction even if you get a nearby fraction e.g. 1/6 for 1/8. 
Q & A: What about 1/3 & 1/2? Yes you can take these pieces as well.
Interesting - 13, Fair - 1

Game 2: Have all pizza common, you place the fraction you get. The person who finishes a pizza first wins.
Interesting - 11, Fair - 8

Game 3: Like first game, but if you get a fraction you can't use, you give it to another person who has that card.
Interesting - 11, Fair - 11

Game 4: You just need to make a full pizza based on whatever your dice gives.
Interesting - 14, Fair - 10

Game 5: You can give and take pieces from others. 
Q & A: On what basis? Not clear, it needs to be figured out. (Calvin Ball!)
Interesting - 16, Fair - 6

5 children were not participating in the fair/not fair question as they were in doubt, but a large number of the remaining were able to guess that 1 was unfair; 2 was fair (to people); got tricked in 3 because it seemed that you were being nice (so it must be fair!); that 4 is fair. I am unclear about the rules of 5, clearly the children found the lack of clarity appealing :), but were less sure of its fairness!

Need to update this blog when we play the games again.

October 01, 2014

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.