When things don't work...

There are days when classes just flow both you and the kids have fun, they learn and and with some formative assessment you even know that they have learnt. There are other days that build on what was done though seem uninspired. There are very rarely some classes that leave you drained out.

I have tried to relate this to preparing for the classes. I find that this is not the case. While some of my best classes were with preparation there were some lovely ones that were impromptu.

I then tried to relate it to the amount of freedom children had in the classes. As an experiment I had two sessions of no holds bar take anything you like apart in the electronics lab. A monitor a few adapters and other pieces of equipment were rendered unrecognizable. The children especially the girls got some confidence dealing with equipment, when I honestly sat down and analyzed the class with the kids they agreed that they did not learn much. Much freedom, but no progress.

I then turned my attention to the classes that left me drain me out. Generally these were classes when I was already tired/unwell or that went out of hand - be it behavior of kids in terms of being completely distracted or when I pitched things too high and missed something that the kids were unable to grasp. The children do carry a lot of their home or at school to the classroom, but a lot of boils down to how I handle it and handle myself. A lot had to do with how centered and calm I was in handling the classes.

One day a kid walked in and asked me if she could drink water, better at the beginning than in the middle so I asked her to go ahead, she went up till the door and came back and asked the same question and did the same loop 6 times. I can imagine that something like this would have thrown me off and I would have probably given a lecture on how valuable time is as a rookie even four months back. But, I was able to stay quiet and let it play out, by the 6th time the kids had lost their patience with her and she sat down. The class went well though I had not figured out what was going on with her.

A few days later I remembered that in one of the classes I had repeated an explanation of an algebraic solution to a problem every time I was interrupted and perhaps she was replicating something like that :). We live in interesting times...

More recently I have been able to have good and reasonable classes and avoid crash and burn classes mainly by working on myself. Hope I can sustain the self work.

Simulator

We have been trying to change how 'theory' is presented by the faculty and I had attempted to make some demos using the equipment they had. However, they felt that experiments were taking time and were unable to fit it in the schedule. They had a few doubts about the theory themselves and we were looking for solutions. One such solution was the introduction of a simulator both to them and the students.

This experiment made some simple gains:
- The questions they asked were related to design which they had not done and with a simulator we could design and iterate in a short time.
- Demos to students could be done in a shorter time by doing some amount of prep and making the schematics and testing without needing lab equipment.

Though we have had to pause all this due to the approaching examinations it may be something that can give a new twist to what we do in future.

Ah Oscilloscope...

I was able to borrow a single probe oscilloscope from the Auroville ITI for a few weeks. There is nothing like an oscilloscope to understand transient signals. I was able to use it with the 10th graders at Udavi who had been working on time changing circuits and with the 5-7th graders in Isai Ambalam (IA) who had been working on understanding Energy and had visited a solar energy company in Auroville and encountered AC/DC, but didn't know what this really meant.

The primary demonstration I gave was of a voltage regulator (AC mains to 12V 'DC' output) - transformer with center tap, half-wave, full wave rectification and what happens when we add a capacitor followed by what happens when you put a load across the capacitor.
Having only a single probe I could not show them that a center tapped transformer has in and out of phase components at its output. This had to be inferred by the full wave rectification.

I was able to couple it with a cute experiment I discovered of taking capacitors of varying values, charging it by touching them to a 9 V battery and connecting it across and LED to see that the time for which the LED is on increases as the value of the capacitance increases.

The 10th graders made a couple of astute observations at the end of their class:
1) Sun - Yes, Sanjeev this makes sense. I always wondered why on turning off the power in some devices the LED of its charger is still on for some time. I think this must be because the LED works off the output of the charger which has a capacitor. Is that right?
2) Des - If the output with a load always has dips then we can't use this directly as a good DC. Should we create a higher supply and feed it to a chip like 7805 (voltage regulator IC we had used in class) and then use its output? This way as long as we maintain the ripple to be beyond 5V it will give a 5V output.

Multi grade classroom (IA school)

I have been working with the seventh grade kids at Isai Ambalam (IA)since Jun 2013. Its a small class of 6 kids (actually, one kid is in 6th grade). Though IA is presently bottom heavy it is steadily changing with the strength of the kids in fourth grade onward jumping to 16. I had started working with the oldest kids in the school. This gave me a chance to work with kids as they were getting into abstract concepts in Math and Science. It also give me a chance to identify potential areas that teachers can provide support with in earlier grades.

I worked with these kids for a good part of the first term and we built a good learning environment even with the large variation in the skill levels in Math and language within the class. The Vth grade teacher was also supposed to join my class, but she was unable to find something for the kids to do and do so. Given the small strength of my class and the rapport I had built with them I merged the class with he Vth graders for this term. I had handled larger classes in Udavi and the ITI and so a multi grade classroom with 11 kids seemed possible.

Eevery activity we did together now needed to be graded so the fifth grade was able to follow and seventh could build on it. When this was not possible we split the classes through projects or separate activities. But, I'll focus on the journeys we were able to take together as a class and what I found.

Word problems:
The fifth graders had been doing multiplication and division 'sums', but 4/5 had difficulty in putting it in a story or understanding if a story was for multiplication or division. There was also a general discomfort to English which is an escalating problem as the grades progress. The first thing we did was work on a vocal discipline.

We told stories of multiplication and division. I quickly noticed that kids stick to the script of Rs.5 for one pen and cost of many pens. Money stories were quickly abolished. Its amazing how kids can't think of multiplication without money! 
It took some time, examples and prodding for the 2 pens in one box, how many pens in 5 boxes or the stuff they made up about 5 stones in one round how many in 10 rounds. We had already gone through this exercise with 7th grades and they started to get a little smug till I upped their level and asked them to tell such stories using speed, distance and time.

We didn't put pen to paper for these classes and this save enormous time. We just told stories based on who I pointed to and what I asked for division/multiplication. The mental stamina of the children who are not doing well in school is quite low and kids generally zone out in classes so the idea of picking up kids at random (not really  :)) kept them guessing who was going to be next and got them into the groove and pay attention to what was being said.

Within 3 days the 5th graders had moved to speed. distance and time and the 7th graders had graduated to stories of  mass, density and volume; power, time and energy and then to stories involving fractions. 
The 5th graders seem, to look forward to what was going to come next. The kids who were struggling in 7th grade got a chance to revisit the ideas and everyone started getting comfortable  with speaking English and the structure of word problems. 
The kids no longer blink an eyelid when a story is told and I have only one 5th grader who still is confused between multiplication and division stories.
In two weeks the English teacher informed me that the sentence construction of 7th graders had suddenly become much better in general.
They also got good at units. They heard and made so many stories that the speed was now automatically km/hr. They also finally started to get dimensional analysis using the units.

Of course, we kept making the games more complex, one person told a story and another inverted it (changing a multiplication story to a division one) by using the result. Then we started to record the stories with just numbers which essentially is the process of abstracting a story into math. The inversion was understanding the basic dual nature of multiplication and division (apparently, not so obvious to kids).

Fractions
Another set of classes that worked very nicely were fractions. I had already done fractions for the 7th graders in the first term and this was a refresher though we focussed on decimals and conversion of fractions to percentages (using 50% and 10% of the denominator) and creation of pie charts to understand the proportion of various objects. This helps kids who struggle with the whole LCM and other process of adding fractions.

I was able to let the 5th graders explore fractions with games and San and Ani really wanted to know how to add fractions. I asked them explore it with the games themselves and find every fraction they could add using the game. They found 10 things they could add already, they wanted more and I led them to equivalent fractions. They did that for some time and then said that they wanted to do it faster like the 7th graders and that led them to using LCM. Seeing them the other kids got into it and even Var our 6th grader 'one who shall not learn how to add fractions' decided that she would do it. It was interesting that adding fractions with LCM figured as the first thing for all the 5th graders in what they learnt well (even though it wasn't the last thing they did).

Algebra
Before everyone jumps on me for initiating Vth graders to algebra. I should clarify that I realized that at least a few puzzles that are solved using algebra can be solved without it as well algebra. Its just that you need to think of a new logic/methodology for each new kind of puzzle and it would have been easier to have just learnt algebra.
I also taught kids how to make their own puzzles and the fifth graders could make some to give to seventh graders.

Energy

We have been doing a project on Energy at Isai Ambalam. As with anything worthwhile it has been something we have been slowly working on, with discussions, experimentation, calculations and more recently a visit to Sunlit futures (a solar energy based company).

The most interesting discussion we had was regarding the law of conservation of energy. In 5th and 6th grade the children learnt that energy is the ability to do work. Work was implicitly understood through everyday activity and the idea that energy is used up in doing work. In 7th grade, however, the law of conservation of energy is introduced. 'Energy is neither created, not destroyed. It only converts from one form to the other (I added under normal conditions, without adding in E=mc^2).' The children seemed happy to have one more piece of info to rattle out, at which point I posed the following question.

Since energy is neither created nor destroyed how does any work, that apparently uses energy, get done? If they were getting out of confusion I gave sufficient examples of areas they thought energy is used up. Hmm...small pleasures of being a science teacher, let children mull over a gotcha and get them to a point they really want to know something :).

When energy is converted from one form to another, we call it work. Clear? Great when you clap kinetic energy gets converted to heat and sound energy. What happens to the sound energy that does not reach the ears of people when you clap...

We also did a bunch of Arvind Gupta's experiments that were quite informative and fun!

p^2 -1 = (p+1)x(p-1)

During preparation for my class with the idea that a p^2-1 (where p is prime > 3) is divisible by 24 I was trying to find a way to explain p^2-1 = (p+1)x(p-1).

I found the following way with the place value kit. Say you have 13^2. You have 13 rows of 13 each. When you remove one. You get 13 rows of 12 and one additional column of 12. Moving the column to a row you get 14 rows of 12. i.e. 13^-1 = 12x14. It can be seen from the picture that this would always hold.

In fact this is a nice way to see that any a^2-b^2 (where b
I didn't get a chance to use it in class, but i thought it was cute anyway.

The how of the two digit squaring method (2)

With the distributive property 'demonstrated' I continued splitting areas to get comfortable with the idea.

If we look at the square of a two digit number say 13. As shown below its 13x13. The 13 at the top and the left side are meant to act as rulers and are not to be added to the count.

The distributive property can be seen as a vertical split in this area

This can be written as
13x13 = 13x(10+3)
          = 13x10 + 13x3

We can now split the figure horizontally as well by splitting 13 as 10+3 again.

This is equivalent to 

13x10 + 13x3 = (10+3)x10 + (10+3)x3

                    = 10x10 + 3x10 + 10x3 + 3x3

All that remained is connecting the method to the madness :).

The how of the two digit squaring method (1)

The sixth graders I work with are (have become) a curious lot.

Following the exercise of p^2-1 (prime number square is divisible by 24) there were many questions of how things worked. My goal had been for them to look at the beauty of numbers and I had asked them which their burning question was why p^2-1 is divisible by 24 or how the technique of squaring works.

I had found the property of primes more interesting and as if to remind me that I am an adult the children overwhelmingly selected the squaring method deserved their attention.

There were three aspects that puzzled the kids about the method:
1) Why write the square of the units place is written as a two digit number even if the result is a single digit i.e. 1^2=01, 2^2=04 and 3^2=09.
2) Why the square of the tens place didn't need the same.
3) Why after multiplying the two numbers we needed to double it.
Of course, there was the addition of all these numbers, but apparently that was no puzzle :).

Distributive property of multiplication over addition
I needed to explain the distributive property of multiplication over addition to proceed. I realized that

the algebraic proof that came naturally to me was irrelevant as they had not encountered algebra meaningfully. I used that place value to show the same graphically.

A place value kit has blocks of ones, tens, hundreds (and thousands that I have now shown).

I had used the blocks to explain multiplication as the area of a rectangle i.e. 6x13 is the same as calculating the area of a shape having 6 rows and 13 columns (or 6 columns and 13 rows depending on how you look at it):

In that case, 6x(10+3) implies a split in the figure above of 13 into 10 + 3 i.e.

Which is the same as: 6x10 + 6x3

As a note, many aspects of algebra can be beautifully shown with the place value kit. I have been able to touch upon the following multiplication, squaring, decimals, fractions, area, volume with the same.