Generating intuition in algebra (2): story for x+y=10

I split each class that we use computers into a primer and an execution. In the primer I asked them for a story of x+y=10. I got some interesting replies and I wrote them down and we analyzed them together:
1) I have 2 mangoes. My mother gave me 8 mangoes. How many total mangoes do I have?
2) My sister has 5 sweets, I have 5 sweets. Together we have 10 sweets.
3) I have some mangoes. My mother gave me the same mangoes. Total mangoes are 10. How many mangoes did my mother give me?
4) I have some oranges, my sister has 10 more mangoes than me.
5) Total biscuits are 10. The dog ate 6 biscuits and the cat eats something. How many biscuits does the cat eat.
6) Ramu and Ravi collect some sticks. The total number of sticks is 10. Ravi collected 2 more sticks than Ramu.

There was generally a fixation with having one 'answer' which came from the one variable one equation situation they had encountered thus far...

I started listing the specific examples they had given 1) and 2) 
x + y  = 10   
5 + 5 = 10 (possible, but only one of the possibilities)
2 + 8 = 10 (possible, but only one of the possibilities)
this was enough to get them kick started in getting a load of other possibilities
1 + 9 = 10
3 + 7 = 10
4 + 6 = 10
0 +10= 10
and their flips.
I mentioned that there isn't just one answer like they have always been used to there are simply many possibilities. 
I also pointed out that if one value increases then the other decreases as the total is the same. We took an example, if Var received 10 chocolates on Sha's b'day and she shared it with her sister, if she decided to be a generous elder sister and gave them all to her sister, her sister would have 10 and she none, if she kept one her sister would get only 9 and so on. They seemed to think I went to too much effort to state the obvious. 

We then considered each case of the other stories they had come up with and went through what they mean and if they sufficiently cover x+y=10 or not.
3) Is like having twice the number of the mangoes indicating 5+5=10. Doesn't seem to cover everything.
4) You can't add mangoes to oranges unless you start treating them as fruit and forgetting that they are mangoes and oranges. The source of confusion was that x and y needed to be different as mangoes and oranges are! But, if they needed to add up to 10 they needed to be of the same kind. The child came back with, ok, they just need to be different numbers not different fruit. Another child corrected its possible they are different and its possible that they are the same!

By now they figured out that 5) was incomplete as I didn't give the number 6. 
This led us to 6) and that the first part made sense, but where did the second part of the story came from? Arc pointed out that that's how some puzzles were and more condition was needed for an answer. Hmm...I asked them to work with what we have right now and that the reason for the other condition was coming soon.

Back to the possibilities, I drew out the x and y axis and started putting in values for x and y as ordered pairs on the axis starting with (10,0) and (0,10). I put a few more points and then jumped the gun and stated that it turns out that all these points actually lie on just one line. Magic! The kids were impressed and pointed out that it seems believable as every time Var gets a chocolate her sister looses one so the line going down makes sense.

We then handled x-y=10. The kids had of course gotten the hang of it and made the stories. We tried to look at how we could make the stories believable! The best we could come up with were - The fruit vendor delivered some bananas and my sister ate some in the morning and left, now I see that there are 10 bananas left.

We then analyzed that how if the sister took more bananas then there should have been more to start with and how this line (they already guessed that this would be a line) would go up.

Computer assignment, plot 
x+y=10
x+y=20
x+y=30
x-y=10
x-y=20
x-y=30

Generating intuition in algebra (1) : Geogebra : introduction

We had worked on one variable algebra with puzzles and looking at abstracting something real and taking an abstract equation and interpreting it in real terms. I introduced geogebra as part of this effort to get an intuitive feel of what two variable algebraic equations look like.
On the resource front computers were available for all the students of 7th grade a couple of days a week which could be used for some unique learning.

To get comfortable with the tool I worked through practical geometry. I had worked with one grade for 2-1/2 weeks to construct 90, 60, 30 degree angles. After a demo (only geometry) in one class their first assignment was to draw an equilateral triangle for a line segment they drew, measure the sides (to see if they are equal), measure the angles (to see if they are equal) and label the vertices.

I noticed how quickly the children become comfortable with a tool that is marginally intuitive and how differences like lines and line-segments become quite clear as they try out different menu options. The references of constructions become obvious e.g. for a circle what was the center and which point was used as reference for radius. 
The measurements add a self-check so the children notice something is incorrect and try to figure out what could have gone wrong.Perhaps, if I had introduced practical geometry this way I would have saved a lot of paper from having holes and trying to make sure everyone had compass, scale, protractor, etc.

Not everyone was interested in trying out geogebra and in the first class I focused on the early adopters and allowed the rest to work on mathlab (computer games that are based on math concepts) . By the second class everyone was in and some of the students who had been able to complete their assignments well were paired to support the ones who were doing it for the first time.

For those who had completed I asked them to make a square with each side 4 cm using arcs and lines. It was a fun challenge and one child claimed that he did it. Most others were able to get squares, but not of the same length as their original line segment. 

Newton's Cradle: momentum

We built a Newton's Cradle at Isai Ambalam. In case, the name doesn't ring a bell you can look at the video below:

We were re-connecting with the pendulum experiments for periodicity and resonance (Barton's pendulum) as a reminder for our work ongoing work on sound. The 7th graders explained the experiments they did before to the 5th graders with videos. Along with showing the videos of the experiments they did they also wanted to show some videos we had seen of stuff they didn't get around doing. One of them that had really caught their attention was the Newton's Cradle.

I have been promoting the kids to be completely comfortable with multiplication and its two associated division stories and told them that a lot of things in science follow this. The cradle served as an introduction to momentum (mass*speed) to continue on our journey (speed, density).

One of the things that limits what you can do with the cradle is that if you try too many tricks the balls no longer stay in the same plane and then the tricks do not work well. We wondered what we could do, possibly use thin enamel wire and solder it to itself to keep the balls in place, etc.

We followed this up with other momentum experiments - heavy ball rolling into light ball and vice versa, what happens to a tennis ball kept on a football when they both land on the floor and wrapped it up with a video on momentum online of stuff we can't actually do in the classroom.

Shifu presses the pause button

Shifu decided that our life was too hectic and even Ani was getting back from her Somatics course she fell quite ill.

The extent of her illness was initially unclear as we called the local vet to come and take a look at her. He felt that there was an infection and gave her an antibiotic shot. She showed no progress, wasn't eating. By the third day she was completely listless and Ani and I went to the vet clinic in Pondy to have her treated. The first day they were closed but made an exception and gave her 100 ml of drip.
The next day they diagnosed her as having a version of tick fever. On the second and third day to the clinic her poop started to show blood. 
Unfortunately, one assumption (hemoglobin low) and one inaccurate lab test (platelets were 1/20 and it showed a normal number) led them to the conclusion that her kidneys were chronically failing and the infection was a secondary issue. It had already been 6 days since she had been sick and I called Shifu's vet in Bangalore. 
Having known Shifu, the doctor felt that she she was young (5 yrs) and generally healthy and a kidney condition is likely to be temporary in response to an illness and she needed continued support.

This started Shifu and my adventure to Bangalore. At least that's what I called it for Arham as I occasionally took pictures of what was going on with us... partly, for him to to have some idea no matter what happened. We reached Bangalore on 21st night.

On 22nd morning was a long drip session and I just sat and pet shifu for 4-1/2 hrs as she lay getting drips. They also took blood for various tests including a new kit that detects if its one of the big four:
Escherichia
Anaplasma
Heart Worm
Borrelia/Lime disease (not sure which of these two)

That evening from the blood tests the doctors felt that the kidneys were under stress primarily due to the illness and should recover in time, but they remained tentative given the discrepancies in the report. They felt that we would be in the clear only when we did a test a couple of days later to see the numbers improving or at least consistent with either report.

They also gave some medicated dog food (k/d diet) that does not require much digestion to see if Shifu can eat on her own. Shifu had not been eating for a while and the drips + visitors + smell of the dog food caught her fancy. She was able to eat what was prescribed (and wanted more)

 

The vets were very happy with her progress with eating and on 23 reduced the drips to a single slow one with her medicines and asked us to slowly increase food intake. They were also feeling a little more confident that the kidneys had not failed and started the antibiotic treatment (imizol).

In the evening Ajay and Neha visited us. Neha overcame her fear of dogs and sat next to Shifu. Shifu dosed off and we also saw her first dream since she had been sick and wondered what  she was chasing in her dream.

Shifu also felt comfortable enough to venture into mom's house (abet briefly) and checked out the bed.

By 24th Shifu was looking better and initially refused to sit down for her single drip but eventually let it go. The doctors also took a blood sample to check the consistency of the reports and to see if there was any improvement in Shifu.

 

Today on 25th the reports confirmed that her hemoglobin in holding and the total cell count has gone up consistent with recovery. The platelets continue to be low that the doctors feel will improve as the month long treatment for tick fever continues.

We still need to go to see the vet for a day or two, but hope its primarily down to medication at home from that point and head back home to Auroville by the weekend.

Thank you all for your emails/messages about Shifu, please consider this post as an update :). Special thanks to Arham, for who, the pics on this blog were taken.

I'm exhausted, but getting better.

Cartesian divers (3): Making it our own

As part of the science exhibition the kids were using Cartesian divers and I felt that we were missing the part of making one ourselves. That morning on my walk with Shifu (I found a straw on the road), a shampoo bottle cap from the trash and borrowed modeling clay from Arham and set out to make some Cartesian divers.

Looking at these divers the kids felt that they could really make it their own and returned my (purchased and self made divers) and committed to make one themselves for their presentation.

In the straw model I put a hole on one of the ends (I remember seeing something like this on instructables). In both cases you add enough clay to just make the object float.

 

 

An interesting conversation started in the class regarding the relative speeds of the different divers.

At my other school the kids made a bunch of divers with pen caps and by the end of the class, there was a litter of caps floating (and sinking) in the bottle we had.

When I got home I thought I would show Arham what Appa made. He found it on his own and set things right, calmly removing the clay that had accidentally made it there and put back in its proper place, his clay box :).

Working towards a science exhibition...

The 6th graders are putting together a science exhibition for the school. A couple of the students had chosen the Cartesian divers as their project and wanted to present it.

Their presentation lasted 20 s. One child pressed a bottle with the vial inserted while the other gave his spheel. "The syringe goes down when you press the bottle, because of the air and water pressure pushes water into the syringe increasing its density and making it sink."

This is quite stark to how we learnt about them and then I realized that this is how children speak at science fairs. 

[In its context, a fair has a large number of exhibits and short attention spans, everyone is looking for something new and cool and hoping to learn a quick keyword to explain it all (osmosis, multiple reflections, citric acid, dynamo, zinc+copper). 

Sixth graders came back from a recent fair knowing keywords and assuming that it meant that they knew concepts e.g. we know density because oil floats on water (which incidentally started the Cartesian divers affair...). 
Tenth graders who have been there and seen that found nothing interesting (new).]

I could only ask - "Was that fun?", to both the kids presenting and those listening.

We started talking about, if it was fun when they were exploring how the diver works. Yes. Ok, what made it fun? We came up with - We had to keep guessing what would happen next and things became clear in time.

We brainstormed on how we can do it differently and include some questions that can be asked of the audience

1) Show the divers

2) Put the bottle in bottoms up and see what happens

3) Ask:  What happened? Why?

4) Press without closing cap

5) Close cap and press and watch it sink.

6) Ask: What happens when you press it on top?

7) Ask: Is it water or air preassure?

8) Fill water fully and repeat experiment

9) Explanation (if required).

There were some questions for clarity

1) Can this happen with any other object?

2) Will it work in any bottle?

3) Will it work with 2 syringes?

4) Will it work if the bottle is only half full?

5) If you cut out the heavy side of the syringe will it work?

6) What is the name of this thing?

There were some additional suggestions:

1) Make model with all three bottle settings open, partially filled, full.

2) Both people should speak

3) Talk about how much pressure is required for half and fully filled bottles. They are not the same.

I asked if anyone else thought that their projects simply does not fit into this sort of example and got a few, this led to some wonderful discussions on not limiting ourselves to one example, but looking at phenomenon as a whole and exploring more possibilities.

I felt there was still something missing in the presentation of the Cartesian divers both for me and the kids. The diver I bought and they used were still not our own i.e. we didn't build from scratch...perhaps, if we had, we would be looking at putting up a different kind of science exhibition - one in which we can talk about ideas and perhaps a space where visitors can build their own contraptions and design their own experiments to observe...and learn by themselves.

Cartesian divers (2): 5th grades present to 3rd and 4th graders

For background please read an older post Cartesian divers.

The Cartesian divers caught the fancy of the 5th graders and they were excited that it was a science experiment that they could explain it (we had briefly gone to a science exhibition a couple of weeks before) and on my suggestion three of them came forward to present it to the 3rd & 4th graders.

My guideline to them was to see if they can get the 3rd & 4th graders to figure it out themselves (by possibly conducting various experiments) rather than tell them the 'answer'.

As they planned the various experiments they were going to show (vial upside down, bottle open, closed and partially full, closed and full, etc) we found gaps in their own understanding and doing the experiments help fill these gaps. Then off we ran to the 3rd & 4th graders.

At a point in the presentation was a good number of the children thought it was the air pressure in the top of the bottle that pushes the vial down. The presenters promptly filled the bottle to the brim (so no air was in the top). Kam, one of the presenters, started a poll, how many thought the diver would go down and how many didn't. Then something I did not expect happened, he started asking why they thought so. This led to a discussion, however, not yielding the 'answer' the presenters had in their mind.

At this point one of the kids was just dying to tell what he knew, remembered the guideline (teacher says guideline, child hears instruction), and started saying - 'look more closely, can't you see'. The other just closed his mouth so he would not speak!

They looked at me for guidance and I gave them closure by telling them that is was ok to say what they knew.

Mass and volume are the same...

A day after I had worked with the sixth grades (Udavi) with Cartesian divers I went over their guesses of what the volume of an object should be based on its mass (in g) and whether it floats or sinks.

Given that they claimed to know density and knew the density of water was 1 g/ml. I wanted to see if the kids  could guess if the number for the volume (in ml) would be greater or less than the mass that we measured in the class (in gm) based on if it floated or rank.

Most sat on the fence and put the same number for mass and volume. At this point a child shared her insight - Anna, mass and volume are the same.

I must mention that this moment showed me how far I had come as a teacher. I did not blow up.
I did have a 2 second shut down and moved on. I inquired if there were others who could help answer her question. 

A few hands went up and the children said mass is measured in kg/g and gave examples of 
potatoes & tomatoes and volume is measured in ml/L water, oil, diesel, petrol. I wondered if the problem was that the unit of volume is always used with liquids. I inquired if they thought solids have volume and liquids have mass...this question made them uncomfortable. Their thinking was liquids were measured in L so if another thing that is not measured is needed, you can take this number, similarly solids have mass ('weight') that is measured in kg/g and since that is all that is measured (reinforced by my 'clever' experiment) the other quantity is what we got from measurement.

There was also a question of why we bothered with the measuring scale. I gave her the battery and eraser that we measured before (one in each hand) and asked her to tell me how many erasers would be needed to weigh the same as the battery. She said 2 to 3. I asked her to look up their weights. The battery was 18g and eraser 3g. She said she understood that we do it to compare accurately.

Another child pointed out that the battery was also much bigger than the eraser and so naturally its weight was more...

We then did an exercise I asked children to close their eyes and placed different objects in their open palms (in two cases I was also supporting some of their weight) and asked them to guess how big the object was based on its weight, we used pencils, magnets and a large cardboard box. I had to pause when one child lifted his desk for the volunteer to weigh. All the estimates were significantly off (and none of the children cheated).

At some point a child came up with the following distinction - 'what I can feel is mass and what I can see is volume'. This seemed an aha moment for everyone and there were smiles all around.

I also clarified that it might be confusing that we seemed to have been comparing two different quantities ml with g. I reminded them that we were doing was finding the density g/ml and then comparing it to 1 g/ml which was the density of water. If the calculated fraction was a proper fraction it would float and if it was an improper fraction it would sink.

I asked if they could think of an object whose volume can increase significantly, but the mass changes only by a bit or even fall. It needed the hint of a 'party' to get to a balloon. We then talked about how to distinguish a balloon that is filled by a helium cylinder and that filled with their mouths.

In the next class, I asked them if they remembered the difference between mass and volume. The children said mass is weight and volume is space. But, what was more interesting is how they said it mass is weight (both hands down palms facing upwards), volume is space (both hands moving away from the body).

I shared the distinction of the child, 'what I feel is mass and what I see is volume'; with the 5th graders who had trouble with the multiplication/division stories for density and they seemed to get it too.

Stewardship for a new emergence : Monica Sharma (Stage 1, Session 1)

From April 2013 (two months before our move to Auroville) I started attending the 'Stewardship for a new emergence' workshop conducted by Monica Sharma.One of the teachers from Isai Ambalam was interested in the workshop, but felt that she needed support at the workshop. This is where I came into picture, I was also moving to a new place a workshop seemed like a good place to explore what all is happening at Auroville.

Monica worked with the UN on large scale sustainable change (and leadership program) in 60 countries. My blog is called small is beautiful...and yet I found myself at the workshop again. I realized that it was because I had imbibed the workshop and used it as a template to organize my own classes and it was a chance to learn more and contribute to the growth of others.

Practically, the workshop is organized as three sets of three days each. They are spaced out a month apart for practice.
I am supporting the workshop this year as a practitioner-coach (PC). The sessions were similar to the ones I attended earlier, but I saw them differently and could see the common threads and the connections between the areas covered in the workshop. My insights were deeper and clearer. Each course was followed by an additional day for Stage 2 where we covered additional areas building on what we had done before.

The workshop offers a set of practical tools, but when I use them I find that I need to be grounded in my wisdom space (or connected to my higher consciousness). The method of the workshop is based of inquiry, sharing insights and planing and looking at work in progress. When others share their insights it often helps to make your own implicit ideas explicit resulting in your own insights.

I'm listing the work in areas/sessions to give a hint of what is to come and possibly encourage people to participate in such workshops at Auroville or elsewhere in the world:

Stage I (7-9 Feb 2014)
1) Self: The first effort is made to understand oneself and look beyond our philosophies and feelings and understand who we are being when we do our best work. It is exploring the qualities we embody when we believe we did our best work or we were at peace with our work. This quality was called stand in the workshop and it was a space of possibility that we could connect with. Harmony, happiness, equality, contentment, self-awareness, self-expression, oneness, integrity, love, unity and self-realizations were all the stands of various people.

One way of identifying the stand was by looking at what we are working towards and what we would be left with when all there is to be done is accomplished. Another approach was to find out the points of most joy and harmony in our life and looking at what we were embodying at that time.

For some it helped to think of a person (they did not know personally) that they looked up to and think of the quality they admired.

My stand in the last workshop was happiness. In this workshop I realized the need to add self-awareness to happiness.

2) Fears
We dealt with our greatest fears some of them were - not being good enough, not being in control, not being recognized, failure, being misunderstood, insecurity, rejection, backstabbing, loosing confidence, discouragement.
Whenever something goes wrong our fight-flight-freeze reptilian brain immediately takes us to this default space as a protection mechanism (Amygdala hijack). In order to transcend the fears we need to be capable of sourcing our inner power (working from our stand).
Courage is not the absence of fear, but the ability to act in spite of fear. The way to deal with a fear is to notice it, name it and let it go and to be in action.
A quote of Chief Seattle of the Suquamish Indians - "When you know who you are, when your mission is clear and you burn with the inner fire of unbreakable will; no cold can touch your heart; no deluge can dampen your spirits" was shared in the session that I found an appropriate way to close this session.

3) 4-profiles
We examined the 4-profiles we possess and use - wisdom (working of inner guidance), social (assumption and conditioning of society), personality (personal style of expression), professional (skills, successes, service, etc). An important insight was that I often think that I am working from my wisdom space, but it is distorted by my other profiles. 

4) Background conversations: This is the most pervasive listening of - I am right and you are wrong. These are judgement we make of something a person is saying while they are saying it e.g. right/wrong, agree/disagree, not responsible, either/or, not enough, us/them. There was an exercise with a partner where we tried one conversation with and without this judgement to see its impact.

An important insight is that response has its place, but only after we are able hear someone with an open heart.

5) We saw a wonderful film on background conversations. I noticed that this time when I watched it I observed a lot of subtle application of the 4-profiles not only verbally, but also in body language.

All through the sessions individuals offer insights of what they have learnt which were extremely useful for my own growth as they make explicit what is sometimes implicit.

6) System Principles
 We saw the movie the story of stuff to look for principles of system shifts. Some principles were making the invisible visible (externalizing costs), looking at the results chains and having strategies that can impact various points on the chain, use of media and advertising, creating matrices to check what is important, mindset changes, need to state explicitly the guiding principles (qualities/values) of the system.

7) Designing my breakthrough initiative for sustainable and equitable change: 
Having reminded the participants of self and system changes we look at the conscious full spectrum response (CFSR) worksheet. CFSR attempts to connect underlying technical solutions with system shifts (workplace, government, society), to our inner capacities and that of the project that would make these actions possible.

In essence, the worksheet helps answer the questions:
a) What are the measurable deliverables: what problem are you solving? (technological solutions)
b) What systems will you need to shift to make the solution sustainable? (systems solutions)
c) What are the core values of your project? (personal/shared stewardship)
d) What inner qualities will be the basis of your actions? (personal stewardship)
at the same time and harmonize these spaces within you.

I found it was much easier to fill out CFSR this time and found that my work with the children and the youth were the same as related to inner capacities and principles of the project - self-awareness, confidence and self-expression.

I also learnt how to support individuals to use CFS by focussing on the questions - what was easy, what was difficult and what can you see or do now that you could not before. It also helped to remind people that it is important to apply the method to day-to-day work rather than for a Sunday morning hobby. The idea is to change/transform yourself in your workspace (hence transforming the workspace itself). Taking a real project makes the exercise real.

This work was the core of the workshop and after people wrote out their ideas they shared it at their tables with a partner and with the PC. It is iterative work and as one fills one section e.g. about embodied qualities with activities themselves could change and vice versa.

8) Complaints as commitment:
Stewardship centres around changing conversations towards progress. The first technique of viewing a complaint as a commitment. We first learnt to classify complaints - recreational complaints - fun (not gossip, not put-downs), expressive complaints - someone just wanting to be listened deeply to, complaints that are commitment for action.
It is important not to take things personally. You need to find your stand and be able to see what the individual is committed to that can benefit the project. There were many examples given and we also enquired in ourselves the complaints we had received and tried to look for the commitment behind those complaints.

9) Inspiring others to commit to action:
For the project one was asked to identify who they would want to talk to in order to move the project (collegue, groups, etc). Methodology connect with your stand, connect with your audience, state your work, make a committed request (specific request, specific group/people, specific time frame). As a PC I organized sessions for people to cover these in about three minutes. This was followed by feedback (10 below) from another individual and a PC.

10) How to give feedback that grows people:
There was a very specific way we gave feedback.
Ask if the person wants your feedback.
Use only use:
a) increase
b) decrease
c) retain
These words have been found to be sufficient to convey what needs to be done without making it personal.

It was interesting that it appeared to be sterile for some people in the beginning, but as they started using it and receiving feedback many found it useful and non-threatening.

11) Conversations for generating action
Promises: for specific actions in specific time frames.
Committed responses: does not always need to be yes even if you can't. Effective responses can include declining, counter-offer or counter-request, promise to respond at a specific later time, accept.
We covered the common breakdowns in applying committed actions - including lack of specificity, asking for behaviour change rather than action, penalizing others for declining requests or revoking promises.

12) Stages of leadership/stewardship
As adapted from Likert-Emberling this conveys the various stages of leadership. Stages are different from levels in that they encompass what is before and build on it. In each stage the individual can be acting as a healthy and unhealthy leader at that stage based on if they are able to generate results or not. These stages are unorganized, autocratic (principle and logic of one individual), manager (based on following rules to the letter), pragmatic (produce results beyond rules, but are not linked by principle and ends justify the means), principled leadership (based on principles, becomes unhealthy if rightiousness becomes self-rightious), perspectivist (able to be principled, able to hold differences as long as principles are not violated)

One of the key areas of how the program works is the splitting up of triads that meet every week to share what each person was able to practice and apply to their projects and daily lives.

One way of looking at stewardship is deep listening, responsible speaking and being capable of shifting conversations to generate action. We learn various aspects of these in the workshop.

Project Based Learning (4): Feedback

Feedback with kids to kids can be a very tricky affair it puts a child in an apparent position of power and not one that most kids can handle. However, since I had made 6 judges it was time to give feedback.

I had done a series of workshops with Monica Sharma (stewardship for a new emergence) and felt that there were many aspects of my teaching and class that originated from it. It was time to put one more to test - giving feedback.

Each feedback needed to start with 
1) I learnt from your presentation
2) What was missing from the presentation
3) Go through the quality criteria list and state
- increase
- decrease
- retain
for each of the 7 items on the list.

The first feedback came from a cocky kid:
"I learnt from your presentation not to make mistakes."
I asked him to explicitly use I for what he should do, it became
"I learn from your presentation that I should not make mistakes", his hesitation was obvious, but one look at me and he knew that both he and I knew his work. The sneer turned to seriousness.
The remainder of the feedback was efficient and to the point. It also made feedback specific and multi-dimensional instead of a +1/-1.

The children were quick to note that 'retain' was 'good'. I reminded them that all mattered is if they knew how to improve their presentations, but I don't think this point landed :).

I added - "May I give you feedback?" as a first step as there can be relationships beyond my knowledge that made it impossible for some kids to take feedback from others (with a limit of 2 no).

Few interesting notes:
1) Judges who had not paid attention to the presentation were less keen on trying to wing it.
2) The judges found what I learnt from your presentation tough and were thrilled when they didn't have to give feedback. Groups enjoyed saying 'yes' to feedback.

3) It made the feedback efficient without having to go into every mistake. One judge had written 2-pages of errors she had found with one group which she didn't get to use.
4) Judges were able to give feedback to their own team which was a very big step for children to be able to do.

Thanks Monica!

Project Based Learning (3): Talk the Walk

It was time for presentations. In each group there was one person who had pulled more than their weight and would have dominated the presentation. It was time to weed them out :).

I asked each group to volunteer one person. Not surprisingly the children who the group expected to present volunteered (and in some cases were volunteered). I made them all judges for the presentation. The reaction of the kids when they found out that the judges were not presenting was amusing. As we walked over to the computer center, one girl even commented that she thought that I had asked a volunteer to make a presentation for the group. Cute.

While many presentations were limited in content, most were original and demonstrated some thought process. Most of the children were engaged when they were going over the presentations and asked a lot of questions (especially when it needed corrections). Interestingly, the kids were able to identify their error (goal of the project) and occasionally think on their feet and even suggest how it could be corrected. 

By and large the discussions were centered around how mistakes creep in, even if they were unintended at times :).

During the creation of the presentation one of the children had been called a daydreamer by her team and I had stepped in and worked with the kid. It was interesting that this child stepped up and made the presentation for her team.

There was one amusing instance in which a child had interpreted an algebraic puzzle of dogs and cats eating 58 biscuits with 5x6+4x7 even though it was unrelated to the question and instead asked, well isn't it 58 to which another child replied well so is 4x10+3x6, why didn't you put that instead. It was interesting that they were talking about two points on the same line without realizing it. But, that's a geogebra story for later.

It took us two half classes and 1 full class to complete all the presentations. I kinda rushed in the end as they were loosing interest.

Projects Based Learning (2): Execution

In the phase of implementation kids really struggled with the idea that a presentation could be about mistakes. They understood making examples of how things are done 'right', but what they were supposed to do with something that was 'wrong'...

Many made presentations that were Q & A or multiple choice questions, some even copied examples from the book (ah, but they finally read the book on their own :), possibly assuming that since I didn't teach from the book I had not looked at it. It was still more amusing when there more conscious partners announced their partners actions. I just pointed out that they would be toast when it came to creativity guideline :).

I also realized that unlike electronics where you need more block time to build something and get it done time allocated for the project, but planning time away from the computer was more useful than a full block of 1-1/2 hrs as children tended to drift off from topic and concentrate on trying templates and beautification.

Consequently, after the second class I started using half the time of the class for other instruction. They worked for 5 classes (2 full, 3 half) on the project when seemed like they were saturating. I asked if they needed more time, but the kids felt that they were done.

There was one group that spent most of their time away from the computer trying to figure out how to solve algebraic puzzles. They were convinced that once they got it they will be able to write it up within a class (they took 2 half classes). 

The longest presentation was on decimals where they covered examples of multiplication, division, addition subtraction and word problems. They did cover an example of when they thought long division goes wrong. For good measure, they even threw in a touching thanks where they thanked Sam/Pai for teaching them decimals and me for inspiring them.

The good part was that most of the kids were engaged in the activity in some capacity. There were a few kids who were not engaged and a couple of instances when I needed to step in. I realized that I had assumed that since the children picked their groups they would be comfortable with each other and decided to focus on ground rules for working with each other (not calling each other names).

Project Based Learning (1): Quality Criteria

Many of the Udavi 7th graders were keen on activity beyond the classroom. I had introduced Electronics as one alternative and they had taken to it with enthusiasm bringing what they had motors/lemons/led display lights.
I was looking for something that would more directly be academic. The computer lab was available for two days in the week and I decided to adopt a project based approach also called education by design (EBD).

The goal was for each student group to make presentations or charts (the discussion started with paper ones, but finally settled to do one with powerpoint).

I was hoping that the children would get a chance to think of their work, quality of work and perhaps even learn to catch their own mistakes.

I gave the class areas fractions, decimals and algebra and asked them to split themselves into groups. There were finally 6 groups with 2-4 children each.

Before the work started we agreed upon a quality guideline on what they like to see in the work. The ones they came up with:
1) Neat, clean, nice
2) Should be free of spelling mistakes
3) Should be free of errors (unless they are used as example)
4) The idea of what is being presented should come across clearly
5) People presenting should be able to explain what they have done
6) Creative
7) Interesting

The topic in each of the areas was the same. To identify what kind of errors can be/are made in each area and to give examples that would help catch these errors. The topic itself was quite difficult and I wanted to see what version of it is adopted by the kids.

Cartesian divers

I had quite some fun with a couple of Cartesian Divers.

Cartesian divers: The couple I got were plastic hollow vials with a weight on the cap of the vial. They are not very well done (tubes that the plastic was not that well stuck on, but they work). The weight is such that they barely float on water (upside down). The air is trapped inside the vial.
If you close the cap of the bottle and press the bottle the divers sink to the bottom and return when you release the pressure.

I got an opening with introducing density (math class) to the 6th graders when they visited a science fair and felt that the kerosene and water layers was something that they understood because they knew density. We did a few measurements but I quickly realized that they didn't feel ready to do multiplication and division with fractional/decimal quantities. A detailed quantitative learning of the subject seemed out of question and I had to switch to will this float or sink exercise.

The children gave 7 objects they had (eraser, stone, pencil sharpener, magnet, etc) and I added three - a (Jodo Gyan) density 1 g/ml ones plastic block, a 10g/10ml tens plastic block and a cartesian diver to take the total to 10 things. I talked about the density and the idea of comparing an object's weight in gm vs the same object's volume in ml is what determines if an object floats or sinks.
Before each guess I weighed the object and talked about what it would mean if it floated or sank.

It seemed that the additional step of weighing was starting to feel a little boring so along with the third measuremnt I casually dropped the cartesian divers into the bottle and started their dives (you develop showmanship). We spent some time playing with them and trying to explain them, luckily we failed and this gave motivation to do the other tests and learn things well.

It was interesting to see their reactions to things they found counter intuitive
- one sharpener (enclosed air gap) floated and another sank (open to allow water to flow in)
- light objects can sink!

Then it got even more interesting when I dropped the density 1 blocks from a height they both sank. The children were apparently pleased as this was what they claimed to have written. A note: 6th graders are young kids and sometimes they quietly 'correct' their guesses while writing the observation alongside (I had asked them to maintain columns for object, mass, guess, actual). My purpose of getting them engaged, having some expectation before a measurement but correctly recording the observation was satisfied, so I am ok with this (my fun starts later).
As they were looking all smug (they had all got all the answers right) I gently inserted the ones block. This time it floated comfortably. This was, of course, an unacceptable development. Next the tens block floated when slowly inserted into water. A student suggested that I only needed to tap it a bit on its head, but this didn't make it sink. I gently tapped it and it recovered.

I asked the children to add the volume of each object given its mass and whether it sinks or floats. This now gave me a chance to see if the kids had been able to connect the relationship between mass, density and volume.

With the 7th graders who had done a bunch of experiments with density before I just showed the cartesian divers and asked them how it worked. We then went over the stories of multiplication and division of the relationships between mass, volume and density and this time around they were able to introduce these stories to the 5th graders as well.

They also tried to explain why the phenomenon works and only when they finally noticed the water raising in the vials due to pressure did they get why it sinks.