Angle of 5:45 on an analog clock

In the geometry class the children were calculating all kinds of angles so I thought I will give a thought break and look at a place where we can estimate angles in everyday life.

I asked for the angle of 4:00 on an analog clock. I need to draw it for the kids to understand what I am talking about. Once I do I immediately got an answer obtuse angle. I realize that the only thing the children have every been asked to guess when an angle is whether it is acute, right, obtuse, straight (180'), reflex, complete (360'). I say great, now tell me what the angle is. I need to repeat myself 3 times before it sinks in that this dude wants us to tell the actual angle.

They ask for hints and I ask them what 3:00 would have been and they say 90'. I let them know that that is the hint.

It takes a few minutes to settle in, one kid gets it. He is all excited and gives the answer. I ask him to explain and he does and most of the kids don't get it. A couple of others do and they explain it quite nicely dividing the 90' as 3 sets of 30' one for each hour and adding an additional hour to 120'. Now, everyone joins in we do 5:00, 6:00, 7:00. Ok, everyone is getting it and its getting boring now. We pull it up one notch and I ask for 4:30. Immediately the smart cookie thinks he has got it, I let him know he needs to think more. He is flabbergasted, he tells me I don't even know the answer, I let him know I know how he thinks and he got 60' and he needs to think more.

I need to walk them through why its not 60' and mention that the hour clock needs to move some...now he figures it out. Again explanation only gets across to a couple and again the couple explain it in a way that 90% of the class gets it. We try a few 5:30, 6:30, ok everyone is getting it by now.

Right then 5:45 it is! Three of them actually get it and we run out of time... 

On being vegan...

I found an incomplete blog from 2009 that I wrote after concluding a vegan experiment...
One of our friends had mentioned that he ran his fastest marathon when he was vegan and was more careful about what he ate. I decided to give it an honest shot six months back as a ramp up to the Auroville half-marathon. It has been an interesting experience especially with a trip to France almost a few weeks after the decision and the Learning network conference which was in WB in the Sandesh season.

I run my fastest half marathon 2 hrs 15 mins (with possibly having got lost and missed a mile somewhere, but the official record stands :)).

I gave up being vegan when I started getting sores in my mouth and was worried that I needed to take vitamin supplements. I also felt that the sores went away if I had buttermilk and that was that.

Fast forward 2013, Ani and I have been off dairy for over a year. I'm not sure if I meant to write more in 2009, but there isn't much more to share, other than that we have been enjoying our food and now have a larger content of fruits and veggies than we did before.

This round of  veganism, primarily non-dairy diet, was prompted by an Ayurvedic doctor who advised me to get off milk to help with my frequent and lengthy bouts colds and nasal allergies.

We had also spent some time at a farm. It was not a profit making venture where animals were beaten or abused or overused and run by nice caring people. They had a cow (Lakshmi) and a calf (Kari). This made local, organic milk available to them and they took care of the cow. Kari was a good friend of Ani, he would lie down and put his massive head on Ani's lap (no serious horns yet) and let her pet him. He associated me with Shifu and unfortunately they didn't get along.

Kari needed to be tied during the day and when Kari was not tied well, he would run around and find his mother and drink the milk, and there would not be much left for the people on the farm. The calf would get to be with the mother for some time once she had been milked. Many times he was tied around where we lived and when he was tied well, he would bawl with something that sounded like 'Amma' and the cow would reply with something that sounded like 'Engay'. It would go on for sometime and it was a little surreal.

I knew that for me to get milk the calf would get less. But, I never connected it with the calf needing to be away from his mother most of the day. I also never gave thought that the calf may actually need the milk and not eat grass as soon as he/she was born. Kari would chew on a single blade of grass for an hour even when he was a couple of months old. I was even more surprised when Lakshmi stopped giving milk after 3 months. This period can vary among cows, the nati varieties can extend to 6 months and the Jersey cows 10 months. Nonetheless, I realized that for me to have milk, cows need to be repeatedly impregnated.

Some of these realizations had made me wonder if I needed milk so badly that such a complicated arrangement needs to be maintained...the possible need of supplements had made me give up being a vegan earlier. I felt that perhaps, if such a diet it lacking, its not for me.

Ani went for a workshop by Nandita Shah who explained that only vitamin B-12 is missing from the diet of vegans. Vitamin B-12 is made only by bacteria and is available in naturally occurring grass, veggies, etc. Of course we wash most of the veggies and so they do not get any vitamin B-12 from veggies. Cows and other animals consume the bacteria as part of their food and so its available in dairy, meat, etc.

We did a test to get our baseline B-12 levels and realized that we had low B-12 levels even without a vegan diet and needed to take the supplements. Given our experience and our need to take supplements irrespective of our diet, I turned vegan.

Diet is a personal choice, no statistics change because of my choice. I find this liberating. I do not need to make choices because it makes sense for the world, the world will take care of itself (or not!), I just need to make choices that take care of myself and makes sense based on what I know about the food I eat.

What I find is that generally I lack knowledge about where my food comes from, how it is made, the invisible costs, how it is processed, etc. It takes an effort to find this out, but to make an informed choice I need to take this effort.

What does this do?

I felt it was time to take the Electronics class up a notch. I do an assessment. Well, an assessment is not a test, of course you try telling that to children who have heard all the keywords in the world :).

We have been using a two pole two throw switch as a one pole two throw switch (actually as just an on off switch). I thought it was time to introduce the kids to the true power of the switch, series, parallel circuits and also throw in some real life circuit that most people have seen, but don't know how it works.

Thanks to having installed xfig, I get good looking pictures and I can crunch up three in one sheet and the entire assessment can take just three sheets. I split the 16 kids in pairs of two which allows them someone to discuss and debate with, but does not turn into a brawl. The rules of the game are - you can talk to your partner all you want, you collaborate, but you do not cheat i.e. you can get ideas from each other, but you can't just copy what your partner does.

After giving the assessment due respect with a few groans, we get cooking. In a couple of minutes some have oversimplified the problems, but most are in serious discussion. A few o the kids are a little faster and write reasonably long stories to explain what the circuit does. I ask them to keep it brief, but accurate. We come up with conventions LEDs get labels L1, L2 to differentiate them. The switch positions get labels A, B. The answers now look as simple as

SW in A: L1, L2 glows.

SW in B: L1 glows

Nice, we are actually mathematizing the problem.

In time the kids finish 2-3 problems, now, they want to know if their answers are right. I must admit I gave into the temptation and asked some of them to think some more (which of course meant it was incorrect), then I got smart. I told them they could build it and find out. Great, mad rush to get their breadboards (which is nice for an Electronics teacher), except, new rule, you can use the breadboard once you have solved all the questions to check your answer. I am quite impressed that the kids did not take a short cut and continue to work seriously.

It helps me figure out what each child is missing, I fill in some gaps by questioning some of their assumptions. The kids push to figure out if they are doing right I push back with poker face (memo to me: poker face needs more work).

Four groups finish and put the circuits together. The two throw switch gives them some trouble, but they put some of the circuits together and confirm their answer. But, doubt still creeps up and they need an affirmation from me to see if its 'right'. At this point my friend and fellow teacher Ramjee walks in (he is setting up a general workshop for kids to take things apart and put something else together :)). Ah, new meat. The kid tries his hand with Ramjee, 'is what I did right?'. Ramjee asks him to explain how he arrived at the answer and put the circuit together. The shocked kid mumbles something to the effect of not knowing which one of us is worse and decides to take his chances with me.

From having only drawn one circuit before and being all confused about nodes (where you measure independent voltages) before the class to having drawn 6 figures (or more), figured out how to label nodes and name components, to making sense of how the circuit would work...my work was done.

Assessment

In the act of auditing classes I see a clear need to improve where things stand. I am also applying for a small SAIIER grant for the various interventions and the electronics classes. All these aspects got me thinking regarding assessments.

ASSET tests
I had heard of the ASSET tests being aimed at focussing on children's understanding of concepts and I thought that this would be as good a place to get ideas. I enrolled myself on their website and took the examinations from 3rd to 9th grade. I went down to 3rd grade as I was not sure if the level of papers would be something that the children of the villages can handle and wanted to know which of the papers we could give them.

There are a few good ideas (reminders of things that already exist) with problems that require some abstraction of a real life problem (Mathematization).

Its a little annoying that these people allow you to cut and paste the model paper, but do not 'allow' you to cut and paste the actual examination (yeah, that will stop me). I mean the emphasis is in the evaluation, so why the cheapness in the exam when I have paid for it.

The teachers at Isai Ambalam school took the 4 grade test (best way to go through a paper). As they went through the paper they also marked questions they liked/could use in their class and which they thought assessed the understanding of the children.

The first response I got from the teachers to describe the paper was twisted :). The teacher further clarified that they tend to over simplify things and the exercise gave them some idea of what else could be done.

A volunteer in the US who works with poor neighborhood schools talked about her experience with standardized tests and how they are extensively used in the US. She also mentioned how it is possible to significantly improve the scores by simply training the children how to take these examinations. Techniques like elimination instead of solving problem, looking at the answers and finding out the short cuts needed, etc.

This exercise made me realize that my purpose is not to assess how children take standardized tests, but their understanding of concepts. For a large scale operation like a standardized test where you lack manpower to go through how children are thinking of a problem, the multiple choice and how quickly children eliminate possibilities may be important, but in a school setting where the student to teacher ratio is under 20, this is unnecessary.

I decided not to use the assessments as such and simply use it as one more source of ideas from which the teachers can frame an examination that can test the understanding of the children.

PISA tests
Programme for International Student Assessment (PISA) is a worldwide study by the Organisation for Economic Co-operation and Development (OECD) in member and non-member nations of 15-year-old school pupils' scholastic performance on mathematics, science, and reading.

The problems clearly display more thought has gone into the organization of the examination. It requires data analysis, modeling and interpretation of real life problems. It also requires that children show how they went about doing something. The problems are also sometimes not oversimplified so they can have many different answers and each child is assessed based on what she or he did.

Of course the limit is the lack of graded examinations if the need is to assess the children at different stages. However, the teachers can use this as a starting point.

Limitation of standardized tests
This is an addendum. As I have started working with children on 'math' I realize that the biggest limitation of standardized tests is that its about quick solutions. If what we want children to actually learn patient problem solving, of making complex simple, something they can internalize and take with them through their life, these tests don't touch this space.

Electronics with Xth grade

I have been taking a session (1-1/2 hrs) of electronics for the Xth grade kids. This is their only non-academic class in the week. We have so far been working on the basics without looking into any 'theory'.

First Class
We got familiar with the multi-meter as a continuity meter and went around school looking for things that will 'beep'. It was a chaotic class, the best kind to begin with and some of the girls even removed their gold ornaments to measure them.

We found that most things that we consider metallic are actually coated and need to be scraped to get to the metal and rust is not conductive.

The children also tried out measuring plants, hands, metal, wood, etc.

We put the fear of getting a shock by getting a mild shock from a 9 V battery. True, there were only two volunteers who were willing to put the leads in our mouth. It was agreed that we would not eat the circuits that we build and only work with 9 V circuits for now.

We then switched over to measuring resistance of various objects that have a high resistance, but not insulators like wood. We used water, moist skin, etc.

We also took some 1/4 W resistors and measured them as groups and got a handle of a range of resistors from a few ohms, to k ohms to M ohms. We did a few conversions between kilo and Mega and the children looked through their measurements and found that water had the highest resistance that was still measurable.
We understood how to do the above with a multimeter that required the range to be fixed manually.

Second Class
By now I had got a little more organized and bought a few prototyping boards (bread boards) and we used the knowledge of using the meter as a continuity meter and finding out how the board was hooked up. This took a little longer than expected, but it was perhaps better than explaining it each class. They also built their first circuit of LEDs in series with a resistor and the battery.

I also got notebooks for all students so I can track what they understood (no, they couldn't copy from the board yet as I didn't have a board).

They learnt that putting an LED across a battery causes it to burn out and it does look different once it has burnt out.

I didn't have enough batteries and had to dig out my stock from a long time back and got all kids of different voltages with the 9V battery. One child tried to put a switch in series with his circuit, but was unable to figure out how a two throw two pole switch works.

Third Class
By now I'm a pro and start things exactly where one of the kids gave up and gave them the nasty two pole two throw switch to put in series with two LEDs and a 1k ohm resistor.

We spend 15-20 mins figuring out how the switch works and then the groups put it together. It takes time one group manages to hook up a circuit where both LEDs light up with the switch is off and one lights up when the switch is on (they put the switch across one LED). Fantastic, now they have a circuit to debug and once they do I let everyone know what the group was able to do. What they got one LED to glow in one position and two in the other, everyone is trying to figure out how to do that now. The wheels are turning and some people come up with an alternative way of doing the same, cool.

I ask everyone to draw one of the circuits. I get feedback that they are not artists, but the LEDs looking like light bulbs starts to light up the notebooks. Some draw the exact dimensions of the bread board. I break their art class and introduce symbols for various components. There is still confusion as to how to represent the bread board, I decide to deal with this later.

Some of the folks are finished. I ask them to use the switch to light up one light at a time. They are catching on and starting to use both the poles of the switch though this is confusing their sense of direction of the LEDs. Great.

Lets work on abstractions and circuit diagrams next. Perhaps, its time to bring ohms law to the party...lets see.

Auditing Math...

I audited the Math classes in both Udavi and Isai Ambalam for the week of 24-29 Jun 2013. One obvious thing in almost all classes is the spread between the children following the class and those struggling to keep up. The teachers don't feel equipped to keep the 'smart' ones engaged while giving the time the 'slow' learners require. This disparity keeps the class in a bit of flux with the ones that finish not knowing what to do. There is also a strong drive to 'finish' a problem and in doing so have nothing to do with it anymore. There is no dwelling over the problem and once it is finished boredom begins.

The teachers at Udavi were kind enough to give me some 10 mins towards the end of the class. I was showing ways for the children to cross check their answers, areas that the children had difficulty with, puzzles based on what they were working on or just put it in context. A few children seem to see something that can be done with a problem once they are finished it.

At Isai Ambalam three sets of grades were doing work on shapes 3, 4 and 5th grade. The same four shapes triangle, circle, rectangle and square (differentiated from a rectangle) were covered. In the higher standards we gave names to the vertices, but the rules supplied to the children to identify a rectangle were quite limited in all the grades - 4 corners, 4 sides and opposite sides are the same. The rules are not sufficient to differentiate a rectangle from a parallelogram.
Surprisingly it was the younger children were able to come up with a rule that a general parallelogram was not 'L' shaped and they are yet to encounter our definition of an angle.
What was surprising was that most of the time a triangle was represented as a delta (Δ) and most children find it difficult to identify a right angled triangle as a triangle. This time of course I applied their rules and it fit :).
I gave a puzzle of a rectangle with diagonals and asked them to identify all triangles beyond the obvious 4. It took half the class time to identify them. I turned the rectangle around and the children again set off to identify it for the new shape...perhaps, a little more work is required in pattern recognition. We also did the same for a running star (5-line star that you make without lifting your pencil).
In higher grades was that they were also labeling the corners of the triangle and other shapes. I wonder if we are asking enough of children...

Fractions are a heavy source of confusion in both schools. These problems start at and early age and keep getting bigger and bigger as more and more things that can be done with fractions (dividing negative fractions! comes along).

Another common problem are negative numbers and operations based off these. Even if you can get children to associate negative numbers with having money vs having a loan they are soon tied up in knots.
I give stories of many operations, but the multiplication of two negative numbers was tough. I put in a sense of direction with the number line and my frog that jumped two negative steps at a time, where would it land if it started at origin and jumped three time in the opposite direction...I know, the children didn't get it either. Please feel free to post a story for the product of two negative numbers.

I found it very difficult to work with the reallly young kids. I wanted to hit my head against a wall with a kid who would not remember what she said 2 seconds ago and had no association with what she wrote and what she did. It seems she was just pulling out numbers at random. Finally with teaching aids I settled down and asked her to count and realized that she doesn't know what comes after 39 and fills this in with anything she wants 60, 70, 44 (nope no 42). Even though the teacher was there she still doesn't believe that the child doesn't know...

I also notice a lot of what 'us teachers' do when the children are unable to get to the 'right' answer. The children are just fabulous at reading our facial expressions and body language.

Its amazing that even at the Xth class level most of the examples and exercises in the textbook have whole number answers. Apparently, its these questions that will come in verbatim in the examination!

I also had a few funny experiences where I wanted children to use what they knew from other compartmentalized sections of mathematics in their geometry and some of the kids just found the answer by drawing it out. Serves me right for being a smart Alec.

I also kicked off my puzzles sessions - Tue and Thu every week at Udavi. I received a few solutions for them, but by and large the Xth grade seems to have picked it up and at least discuss it. This is thanks to Ramji who was their class teacher in VIII grade and gave them much practice. They keep me on my toes and I need to come up with something they have not encountered. I am yet to get the younger children interested in the same.
I did have my fun by asking them to draw what they did in class, a triangle with zero area called a 'co-linear' triangle. Apparently, they don't look too deep in the names co-linear points. It was like a huge ah, ha moment in class that all points on a line are co-linear!

There are alternative teaching techniques (beyond the text book) in both schools for lower grades. But, these aids completely dry up as the children get to 7th grade as it is assumed that they can now magically abstract all that they see and do.