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!'