I wonder...(and 6th graders pics and survey)

The surveys including and the one I did with the 6th graders (below) made me wonder about various aspects of my work with children. The survey for 6th grade is embedded below for those interested.

Pree said that the one thing she learnt well this year was listening. Listening to each other (and peer learning) was an important aspect of our classroom environment, but for Pree to notice this as her best learning for the year felt special. I wonder if I would have emphasized listening as something I work on, if she had not reminded me.

My best classes have been when I have been happy and calm. When some children say - a teacher should teach well and offer no explanation, I wonder if they are trying to refer to what they want us to be, rather than what they want us to do.

A very large number of children seem to care about how the teacher feels about them (and not what their own classmates think of them). I wonder if I utilize this to always help them grow.

Almost all the children I work with enjoy math, I wonder if they always enjoyed Math or our definition of what constitutes Math makes them feel this way.

I saw the grit in children I worked intensively with grow significantly over the year. I wonder if I can figure out what I did right to achieve this.

I went to the furthest village where the children come from to IA school and met their guardians. I wonder, if I should step in for the 6th grader whose grand-mom is going to send her to the local government school because the she feels she will no longer be able to afford the child's bus fare.

Background of work with 6th graders @ Udavi:

@Udavi my work with the 10th graders in the first term enabled me to see that gaps in learning of abstract concepts in 6th and 7th grade fail to get filled. I then focused on these two grades in the other two terms. 
The 6th graders had a lot more freedom and flexibility in the classroom and I tapped this to work with games - short mental board games, pizza games, (dis-)entanglement puzzles. Moving towards stories of multiplication and its equivalent two division stories, integers, fractions, decimals, areas with geoboard, cartesian divers, introduction to algebra and many puzzles. 
I worked closely with the class teacher Sudhir and we worked a fair bit on classroom environment where children could listen to each other e.g. multiplication stories and convert it to division stories. We were also able to wait out conversations to subside on their own when the children realized that the class was waiting for them.

Album of the 6th graders
:

Survey:

Survey of children in 7th Grade @ Udavi

At Udavi in the first term I had worked with a few kids from 7th grade in sort of remedial classes using teaching aids. In the second and third term I took the entire class (with the teacher observing). I had two classes (1-1/2 hrs each) a week in the second term and three a week in the third. This was that I initially relied on class room delivery - use of teaching aids - densiel blocks, geo-boards, pizza party. Slowly as I got more comfortable not sticking to script, we worked on basics stories to understand multiplication and division and extended it to fractions, puzzles, algebra, practical geometry, geogebra (connecting algebra and geometry). We were able to do one project on common mistakes children make in fractions, algebra, decimals using the computer and incorporate some electronics classes for interested students on LEDs, measurements and building lemon batteries.

At the end of the year, I wanted to do a survey with children on aspects that would help me understand how children view themselves and their learning and also take inputs to improve the classes for next year students. I took some inputs from a survey conducted by sri.com to review usage of Khan academy resources in Math and made it much crisper.

I took the surveys through one-on-one conversations to translate the questions into Tamil, if required, and get individual inputs. I zeroed in on the exam time being the best time to get time to talk to children without them being biased by other children's inputs. One issue was that some of the children were tense or  worried about the exam, however, they had made their own examination and I expected this to be lower. 

Here is an album of the children taking the examination:

Udavi School 7th Grade Math Final Examination

The first question, 'how do you feel?', also gave the children an outlet for their emotions. A child who had lost her grandparent a couple of days back was sad and expressing her sadness helped her notice it and feel listened to, after a couple of minutes she felt ready to participate in the survey.

I asked for a couple of things they had learnt well this year and areas like making an abstract equation real with a story, algebra and its link to geometry, fractions and puzzles figured often in the list.  Of the 17 children, 12 said that their goal in the next grade was understanding and learning new things, 5 felt that their priority was getting good marks.

During my very first interview I added a question about what a child expected from his/her teacher because this is how the first child interpreted the next question. It seemed something she wanted to talk about, I thought it would be interesting to see what children had in mind. A teacher who is friendly, understanding, provides clarity and introduces something new constructed this image.One reply was, they should be like me. This kid likes to have a good laugh and I looked up from my laptop to see if he was kidding, but his eyes had no humor just earnestness. Ok, sweet.


9 children felt it mattered to them what the teacher thought of them and primarily some of those said they cared about what other students thought of them.

12 kids said they liked math, 4 others said they like it at times. One child felt that he doesn't enjoy math because he only seems to enjoy it when its extremely easy. Another child felt that he needs to feel challenged to enjoy math.

I'm not sure how children interpreted - do you learn easily? The children who struggle in class can see it and the ones who are doing well know it too, but for the rest I am unable to process any trends.

The replies on grit - can you continue to work when things get tough or boring suggested that most of the children who struggle in the class in Math said it was difficult for them to keep going when it got tough or boring. This is in line with my current understanding of one of the skills that we need to develop in children.

Suggestions on what could be added or changed in class included field trips, more projects and puzzles, more science, games (I primarily did this with 6th graders), more electronics classes. A few children wanted to go beyond peer learning and teach the 6th/5th graders what they learnt. 
When some of the children realized that I was not planning to continue teaching them in 8th grade they went into denial. One suggested that the 6th grade teacher should graduate to 7th grade and I can continue with them. Another used logic saying that the survey of how to do things better constituted a contract to continue and implement it next year. One of them resigned and just wanted me to be around in the breaks so he could ask me something he didn't understand in class.

Three children brought up the need for daily/more classes. Having seen the improvement at Isai Ambalm with daily classes I plan to increase it to 4/5 classes a week.

The survey (minus children names) is embedded below and available here.

Conversations for completion of the schooling year at Isai Ambalam school

From June last year I have been working with five 7th graders (and one 6th grader). It was a small classroom and I tried to merge math and science in the first term, created a multi-grade classroom by adding 5 fifth graders in the second term and encouraged the 7th graders to get into self learning in the third term (I felt their basics were sound) and also made the newton's cradle, wind chimes and actively worked with geogebra with them. 

The school only goes up to 7th grade and its quite likely that I may not see the graduating kids .

I extended the idea of self prepared papers from Udavi to Isai Ambalam school.  The 7th grades each prepared impressive question papers with over 60% of the questions being word problems for fractions, interpretation of word problems as algebraic expressions, writing stories for algebraic expressions, graphs representing algebraic expressions, puzzles, pie charts. What really brought a smile to my face was that they could handle the beast they created. Their meta cognition has been improving over the year, but for it to actually culminate with all six of them being able to do it to such a high degree (all over 96) was a nice farewell gift. 

The examination seems the great time to talk to children one-on-one and get feedback from them as it avoid biasing their replies based on what other kids told them. The one drawback of anxiety of an examination was generally lower as the kids made their own examinations.

I let them get their emotions out by asking how they felt and after the reply the kids seem to ease out to talk about what they learnt well, what their aim when they enter their next year math class, what they expect from a teacher, whether it is important what their teacher or friends feel about them, whether they enjoy math, if they learn easily, if they are able to be persistent and their inputs on what we could do new and different for the next class.

In the 7th grade, 5/6 children felt they learnt algebra well. For the 5th graders a big thing was fraction addition. 9/11 talked about their aim in the next grade being learning new things. One child in 5th grade talked about how she wanted not only to learn what was there in 6th, but also things from 7th like she did this year. 9/11 felt what the teacher thought of them was important but on 3/11 felt what their fellow students think about them is important. Only 1/11 children put riders on enjoying math :). 

Then it got interesting, we talked about whether they learn easily, many children interpreted it a little broader and talked about how they learn. Most were consistent with my observations in the classroom. Next came persistence and grit as it is claimed that it is directly related to how a child does in math. But, we talked about it in terms of a project. It doesn't appear that younger children have a clear handle on that.

The incoming 5th graders is a huge class (19 children) and the challenge next year is going to be very different...but for now I enjoy the small pleasures of life :). I'm embedding the detailed feedback below. Its also available at this link. I have removed the names of the children, but left in how they did (for anyone who wants to co-relate what they said with what they did).

Children building a Speedometer/odometer

For Monday morning every week I have been working with few four kids from Deepanam on electronics and Arduino based projects. These kids were up for bicycling to the electronics lab in Udavi.

After tinkering around a few things we finally decided to build a speedometer for the cycles. One and a half hours a week was not getting us there and I let them access the lab for 1-1/2 hrs more as I merged the class with 6th grade electronics-mathematics classes in the lab.

For the speedometer the first work was on the LCD display. We first got a 16x2 that got burnt because the kids wired it one pin off and switched supply and ground. We then used a 16x1 which actually needs to be accessed as a 8x2 and eventually the next order of 16x2 came in. The lesson of the switched supply as well learnt as the displays have been hooked on and off tens of times without loosing another display.

We planned to measure the rotations of the cycle using a reed switch. (A reed switch has two metal wires placed in such a way that if a magnet gets close it would close the connections).
Unfortunately the experience with the reed switch was comic almost approaching tragic proportions. We only had a couple of appropriate reed switches. I had a couple from Bangalore, but once we got the first working (perhaps) it looked good enough to be stolen off the bike. The second was burned out when both ends of the reed switches were connected between power and ground. We soldered a couple of really delicate reed switches and put them in ball pen refill for protection. Two of those broke off because the magnet was too strong and the reed switch wire just kicked off its glass body to join the magnet. We finally seem to have one that has lasted a couple of weeks, but its still the weak link.

We calibrated the rotations by printing the frequency measured based off the switch with a multimeter measuring Hz. We also realized that using pin13 for reading was convenient as it showed when the switch got close to the magnet with the built in LED on the board.

 

For the software, a basic polling routine worked fine for reading the reed switch and we didn't encounter a limit of the speed of the routing even when we were spinning really fast (or tricking it with a jitter around where the magnet activates the reed switch). Using the radius of the cycle both the speed and the distance are reported. We made some optimizations to avoid rewriting the fixed letters.

Math does not understand life...

Some of the stories children made for two unknowns (linear algebra) were not making sense to them. I decided help them by making things worse and pointing out:
1) Solutions of the two variable was not just the points corresponding to integers on the line, but all points of the line i.e not just of whole mangoes/chocolates, but a continuous line of ml of a liquid e.g. for

x+y=10

then you could talk about 10 ml of oil being divided between two test tubes with 5.2 ml and 4.8 ml. Then of course, someone brought up that even a mango can be cut. 
The discussion led to whether counting mangoes in numbers was even a good story as it assumes that all mangoes are exactly the same and perhaps we should be referring to mangoes in a more measurable way like weight.

2) In the story where Var and her sister share 10 chocolates we were only thinking about both numbers being positive, but the straight line extends to solutions in which one number is actually negative. We talked about how we could possibly extend the story for this to make sense - It was Sha's b'day and he gave 10 sweets to everyone in the class. Var being a considerate sister gave all her 10 sweets to her sister (who is in the other class) and even went out of her way and borrowed 2 sweets from Ezu. Now her sister had 12 sweets and Ezu would come tomorrow and ask Var for sweets.

We talked about Math being abstract and not understanding life and that we needs to understand the context of real life to meaningfully interpret results obtained by using Math.

I came across this interesting quote from Einstein after the class: 

"As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality."

Make your own examination

I had met a teacher who corrected 10th grade board papers and said that he would fill out answers if a child was failing in the examination as failure unnecessarily ruins the child's life. He had suggested that children should just be asked to write whatever they know. I had started preparing graded papers for different children in the final examination...but I wondered if I holding back from experimenting the whole way.

For the term examinations there was scope of formative assessment being useful for areas that I could work with the kids on, but this is not the case with the year end examinations. Perhaps, like a Dojo it was time for the kids to show what they could do.

I gave the areas we had covered over the year and a score for the questions in that area. For the Udavi 7th graders this was:
A=(addition), S=(subtraction), M=(multiplication) and D(division)
Integers  -  ASMD- 10 marks

Fractions - MD - 20 marks

Fractions - AS (including using %) - 10 marks
Decimals - ASMD - 10 marks
Algebra - Curves, Puzzles, equations, story for equation - 10 marks
Geometry - rotation, angles of a triangle, relational (complementary, etc) angles - 10 marks
Practical Geometry - 10 marks
Ratio/Proportion - 10 marks

Area - 10 marks
Puzzles - 10 marks

Anything else they could think of could be for another 10 marks.

The guideline for making a question in any area was that 
a 'sum' is for 2 marks, 
a word problem is for 4/5 marks, 
a picture question is for 2 marks, 
a picture question that involves algebra is for 4/5 marks and
the puzzle can be just one and is 10 marks.

To cover 10 marks in an area you could use 2 (5 mark) word problems or 5 (2 mark) sums.

I wanted to see if children given a chance would just do sums and check meta-cognition - can the kids really do the questions they come up with.

One of the first questions the children asked is if they can make the questions really simple. I let them know that this demonstrates what they can do, so if simple questions is what they can do, so be it. The idea of demonstrating how much you can do appealed to them though I was not sure to what extent it would be implemented.

I mentioned that I expected them to understand what they were doing and not just copy a question from an example and repeat it by rote. I mentioned that I would change the numbers in the question paper if I felt they were too tailored.

Though I did not allow the cheat sheet that I usually do, stating that its their own examinations and they know the questions I did allow it to be open book on the examination day.

The children were very excited with the prospect and worked seriously in class, through only a few students worked at home to complete it and and we made most of the question papers over two classes. The classes also served as an opportunity to review some of the topics that the children wanted. 

Come exam day, Fif (clinical clown) had made a bunch of clown noses with plastic bottle caps, so it was quite a sight with the kids writing their examinations with clown noses. One kid in her feedback even remarked that this doesn't feel like an exam, it feels like a party.

I used this time for retrospection and did a one on one interview with each child. The inputs were interesting and something I need to ponder over.

I have put together a chart of how each of the 17 children organized their paper in Level 1: sums (blue), Level 2: advanced sums with multiple operations (brown), Level 3: Word problems and those involving abstraction in algebra (green). These fill up the score of the bottom 100. It was interesting that almost all children tried at least 10% of word problems. The graph also shows how they did in their examination from 100-200, 7 children were able to do more than 90% of what they felt they could and 6 of them were confident enough to use more then 40% of Level 2/3 questions in their paper.

Science exhibition: Did anyone ask questions?

The science exhibition came and went more or less as it usually does. I briefly went to the exhibition and it seemed the wave of - "experiment description, demonstration and explanation" had pretty much wiped clean any possibility of getting people to think and getting them to figure things out on their own. Our detailed analysis of how we could present the Cartesian divers was also unused.

At the next class I asked if anyone with exhibits asked any questions at the exhibition. Five hands went up, the questions were: 
1) Which of the vessels sounds louder? 
2) Why does the vial go down when you press the bottle?
3) Will this float of sink?
4) Why can't you see the coin when we point water into the glass?
5) I asked them to hold the corn seed between the finger and thumb.
I'll let you figure out what the experiments the first four corresponded to. The fifth was intriguing because it was not a question, so I inquired further.

5) I asked people - "Can you hold the corn seed between your index finger and thumb?"
Pree  happily added, it only popped out for one person, but most others could do it. 

I'm still lost, so Pree gives context:
I had made this chart for solid, liquid and gas and put up a table with these in containers. My chart said that solids have definite shape and liquids and gases take the shape of the container. In the last class you said that salt also seemed to take the shape of the container I had put it in, this confused me. I could not change my demonstration chart or my collection of boxes, so I asked people to hold the corn seed between their fingers and they could do it. You see, you can't hold a liquid between your fingers.

Ah! Inquiry lives :).

I decided to drop being subtle and brought up a discussion of what the kids feel a science exhibition should be. I asked them to answer the question they could use what they enjoy most at an exhibition:
1) The presenter should be able to tell in both Tamil and English
2) There should be games that you can take part in
3) There should be something you can turn on and it does something
4) It should be unexpected
Interesting...

Generating intuition in algebra(3): story of ax+by=10

The kids had gotten comfortable with a story of 
x+y=constant
and what it looks like.

It was time to move to the story for:

 x+2y=10
Once we cleared the confusion with 
x+2 = 10 and remembered that 2y = 2*y=y+y
The story that Sub came up with was
I have some oranges, my mother gave me some oranges and my father gave me the same number of oranges as my mother. Now I have 10 oranges.

How would this extend to
x+5y=10
Now the extended family was joining in and the kids felt that the stories were making less and less sense and I should now start contributing to the discussion. 

I reminded them of a simple multiplication story which Arc used to come up with the following
I don't know the price of a liter of milk or the price of 1 liter of oil, but the cost of one liter of milk and 5 liter of oil is 10. 
Though we all agreed that given the price of milk and oil the story was difficult to believe it made sense in principle. As in case of addition of variables if one went up the other went down, we talked about the relative steepness of the curves without entirely venturing into slope and that we should try different curves in geogebra to get a handle of what happens if these numbers change.

Using geogebra we concluded that what mattered is the relative index of x vs y. The larger the index of x vs y the flatter the curve.

We then used the method of putting x zero to get y (y intercept) and putting y zero to get x (x intercept) to draw a few lines. Once we drew a line we used the intuition from the stories to check if the line made sense. This helped catch some mistakes when trying to find x and y intercepts.

We then pushed into freeing up the limits of what indices and constants were including 
3x-5y=-10
that involves division of two negative numbers and if something went wrong with the intercepts looked at the final direction of the line constructed.

Apprentices of electronics class

 I kept some time aside to prepare (on Tue) for Xth grade electronics classes at Udavi (on Thu). One of my colleagues asked if I could use an apprentice for that slot. I took up the offer and soon realized that I had picked up one more opportunity to stretch myself - prepare for the Xth class and and find a way to engage Ab. I merged the two for some time working on the demos for the Xth graders e.g. on how AC becomes DC through rectification (half-wave and full wave), then filtering, then the load creating ripples connecting it to regulators. I also was able to use help for checking the connections of counters with seven segment displays. 

When En joined I felt that I needed to create a small independent project that they owned and delivered on. I had received a request for a buzzer circuit that could be used in the school fair that when two wires touched will get triggered and stay on. I thought it would be a good (and challenging) design exercise for them.

 

They attempted to build it on bread board, but had limitations with the relay integrating well into the bread board. They tried to solder a wire on the relay, but got cold solders and the wire would fall off. I let them work through their struggles and once I realized they had understood the components and an intermediate solution even asked them to present it to the 6th graders I work with. In that class, they really seem to notice that they were 'getting it' themselves.

As we were getting towards the end of the year I asked them to direct me step-by-step and offered to do the soldering for them. Once we were done with a basic design of a relay and a switch in series it only buzzed when the wires were touched. I tried to let them explore the puzzle of making it work with a single wire. They couldn't get it and I showed them the positive feedback. As we talked about how it worked Ab came back with, 'oh, that's clever'.

Of course, as all real things in design the circuit did not immediately work and we got down to debugging it by measuring voltages at different parts of the circuit before finally realizing that one of the traces connecting two nodes had got burnt out due to soldering and de-soldering.

It was even more interesting that the circuit worked the first time, but the second time as soon as the switch was turned on, even before wire W1 and W2 were touched to each other the buzzer went off. Can you figure out why? 

We found a work around by connecting the W2 to ground before starting and I realized that I could have asked them to add a diode, but the complexity seemed just right for them and I left it with their understanding of the issue and the work around.

We had a conversation for completion:

How do you feel?
Ab: Happy
En: Like I learnt a lot of things
Me: Complete

What is the first thing that comes to mind about what you learnt in this class?
Ab: Seven segment displays
En: Relay

The second?

Ab: Multi-digit seven segment displays!
En: Piezo buzzer

What would you was missing in the classes?
Sometimes the classes were hard. Would have liked to do a remote controlled car as well. 

Here is them giving a demo of the circuit without realizing that I had turned on the video well in advance ;) - 

Music (and girl power)

The work on oscillations led up to the work on Music. I felt a real introduction to musical instruments would be appropriate and it was wonderful to have Magesh from Svaram who works on musicological research come and talk about wind chimes. He demonstrated how different lengths produced different notes and gave (and quizzed) the children on the different aspects (beater, wind catcher). We then moved on to some math on how they calculate the lengths of each of the seven rods. Magesh simplified this to an arithmetic progression (3cm for each pipe) for the width of pipes he brought and described how each rod was hung at 22% of its length. We had a good exercise calculating 22% of each pipe and I have to admit I was impressed how they went about it (and so was Magesh).
For a pipe of length 19 cm
10% -> is 1/10 -> 1.9 cm (move one decimal point)
20% -> 2x10%-> 3.8 cm
2% -> 1/10 of 20% -> 0.38 cm (move one decimal point)
22%-> 4.18 cm
I had shown them this sort of method to convert a fraction into a percentage, but it was exciting to see them apply it to take a % and progressively tend to a more accurate answer from an approximate one.

What was more interesting was the possibility of making a wind chime. In time Magesh was able to provide one set of chimes and three of the girls in the class really wanted to make a chime. The chime requires fairly hard work sawing the metal pipes to the right lengths, polishing with sandpaper to make the finish smooth, drilling holes, logically wiring the setup with a single thread. 

Educationally I found that a lesson on rounding off and approximation came for free when they calculated the numbers and didn't see the point of getting it accurate beyond 1 mm!

The girls spent a class sawing the metal pipes and polishing the end and now the project got socially exciting as I knew that the drilling hole required a power drill (thanks Susan). I took my drill to the class and more or less did what they had expected me to do, set it up and drill the first hole. Magesh has also given a couple of pipes that already had holes (meant for a different instrument). At this point, I talked about safety precautions and handed the drill over to them.

After they realized that their pleads of only 4 more holes left me unmoved their efforts so far forced them to complete the holes for remaining pipes. Pri was the first to step up for the role, then Arc did one only Sub stayed somewhat hesitant.

 

 


I had asked Kavitha to ask the girls how they felt the conversation went something like this:
Kavitha: How do you feel?
Pri: When Anna first put the drill in my hand I was shivering.
Kavitha: How do you feel now?
Pri: Its jolly.

From the leftover pieces of the metal pipes they decided to make another mini chime and got down to drilling holes in all of them. Even their teacher got involved and worked with them on the mini chime.