Tuesday, May 26, 2015

"2 rupees 20 paise for 100 grams" - Maths class or Ethics class?

Hello friends,

I did not know that I will be back with the new post so soon... But then, this summer has given me a wonderful opportunity to work with the children Daily. And hence, I am so lucky to be a part of (learn from) such stories daily. 

If some of you have been unable to read the earlier post, where Poonam is intentionally allowed to make a spate of mistakes in the multiplication and division algorithms, how she arrives at a (erroneous) conjecture by observing / analyzing some patterns in these mistakes, and finally how she spots her mistake to counter/ discard her own conjecture. A beautiful cycle of discovery that probably mathematicians and scientists would go through. 

This is the link to this story: 


It all started with just a casual inquiry to one of my students - "what do you feel how much does my bag weigh?"

From which the discussion gradually navigated to the fact that how some shopkeepers cheat the consumers by fixing the std. weights. Sachin claimed that he has seen the 'hole' on the other side of the standard 1kg weight so that no one can spot it. To which Sushma responded that in such cases, the vendor would earn more money.  This as seem did not at first augur well with Sachin because his opinion was stationed on the fact that consumer would get any quantity lesser than the weight on the other side of the balance.

It was interesting for me to learn that what is sometimes so obvious for one student (& the teacher) may not be so obvious for the other student. I allowed Sushma to explain her view and this quickly brought a smile on Sachin's face.

Sushma had already brought into this discussion her experience of purchasing 1-kg rice from the vendor. So I thought to just built upon it. I did not know that my next question would help me learn something so interesting from my students.

"If we assume that the vendor has removed the piece of weight worth 50 gms from the std. weight of 1 kg, then how much will he earn from the transaction of 1 kg of rice, sold at Rs.24 per kg?"

Of course, both the above values -- 50 gms and Rs.24 per kg were arrived at with the help of "students", they were not my (the teacher's) enforcement!  It was equally interesting to study their estimation sense and even help that develop using this real-life example) But I am not going deeper into those conversations this time. Why?  Well, Because I hardly get any acknowledgement from the readers for this effort :-)

Yes, coming back to the problem and how my students saw this and solved this.... Again, here too I am going very quick this time i.e I am not mentioning all the (beautiful) conversations that Really happened. 

Sachin finally could settle down with this argument that if 1 kg costs Rs.24, then half kg would cost Rs.12. So 50 grams would be worth Rs.2.20

It was interesting for me to see him arrive at the cost of 50 grams directly from half kg.  I would suggest you to pause for a while and answer this question. (of course, I will be much happier if you even reply to me with your answer) - 'What according to you must be the way that Sachin would have devised to arrive at Rs.2.20?'    I hope you will honestly pause and think before reading further :)

Thursday, May 14, 2015

22 - 9 is 11 or 13 ?

Hello friends,

Hope you must have got and read my previous email about the starting of Maths Teachers Study Group.  If not, then plz read it and also let me know if you are coming. I will send you the exact address, etc. I am so happy that 9 Teachers have expressed their interest! It is on Monday 18th May at Airoli, Navi-Mumbai. For more details, plz check that email. 

I remember I had mentioned in that email, about sharing one of the fantastic experiences I had while working with students on fractions that day, but then I thought of first sharing with you what happened Today!   :-)

Meanwhile, the word fractions remind me of one more interesting thing. A group of students were asked what is the half of 2/8 (two upon eight)  And it was interesting to listen to the response of few students. They said it is 1/4 (one upon four)  :-)

If possible, plz share your views on reading the conversation below. Will be happy to read.


We were solving a problem which encouraged her to make a list of all the possible numbers that would leave a reminder of 1 when divided by 3. And then, even hunt for any possible pattern in this list. So she wrote: 1, 4, 7, 10, 13, 16.....

After few seconds, I ask her,” Could you figure out anything?”

“Yes Sir. There is a common difference of 3 between any two adjacent numbers in the list. But I am wondering, why we got this difference of 3, because these numbers are not the multiples of 3.”

And I was like, Waaaaowww! What an interesting query! I paused for a while, to think as to how I should respond to this.

“So do you mean, they should not have the common difference of 3?”

“Yes. I have added one to every multiple of 3 to get these numbers.”

“Hmmm... Can you write down all the numbers from 0?”

Once she is done, I ask her to highlight the movement of multiples of 3 from the beginning. She draws the path. Now I further ask her to repeat the process for ‘her’ list i.e. for 1, 4, 7, 10....  She does that too. But after this, I choose to stay mum for a while. I wanted the bulb to glow, but what’s fun in it if the student gets it so easily, isn't it? J

So she asks me,” Sir, now what?”

“Means? Now it’s your job dear! I have guided you enough.”

She smiles at me and turns at the board. After few seconds, she again looks at me with a smile, but also with wrinkle on her forehead. “Sir, I am not getting.”

I realized that it’s the time to roll up my sleeves now.

‘Let’s say, you (Poonam) and Yogita are standing two meters apart. How will this distance change if both of you move ahead by the same amount?”

{While narrating, I also represent this situation pictorially on the board. But now I realize that ‘she’ could have been encouraged to draw the diagram}

She responded correctly that the distance between them would still remain the same; and she could also reason for this. I further probed her for the other case viz. she travelling more than Yogita. And she again responded correctly, along with the justification. So Now, I drew her attention to our original problem.

And she was like – “Yes Sir, I got it now.” with a wide smile J

“Please explain it to me then.”

Wednesday, May 6, 2015

Starting the "Maths Teachers' Study Group" - at Airoli, Navi-Mumbai from 18th May

Hello friends,

It’s that time of the year again -- end of April and most of the teachers must be on the verge of finishing their academic responsibilities. Some of you might have already planned your holiday-trips, isn’t it? Hmmmm...  J

You know what? Today morning, I had a fantastic experience with my students, while working on fractions. And that’s when I decided, that I will share this story with you in the evening. So I sit down, write few lines, and all of a sudden, some other thing comes to my mind. I pause. I thought that the latter one is more important and even interesting. So, what next? I press the Ctrl+A, Ctrl+X, Ctrl+N, Ctrl+V. Yes, you guessed it right. The fraction story will come to you ‘after’ this broadcast in the next email J

A strange yet interesting thing happened last week (And I am so-so-so-happy that Finally, it did happen!) I got an email from couple of maths teachers. They wrote to me that this time, they want to make a better use of their month-long vacation - for their own professional growth.  (Waaaaaaaaow!) They wish to dive deeper into this mighty and beautiful ocean of mathematics.

Isn’t this really exciting? I really appreciate their decision – because they are embarking upon this learning journey, completely on their own, without any support (or push? :) from their respective schools. Excellent!! My dream to start a Maths Teachers’ Study Group has come to a reality, finally!!

So - to be very honest, I am personally much more excited than these couple of teachers now. To start working with them, to listen to them – about their classroom stories, their challenges, discussing about the most common maths mistakes that students make, analyze and learn from these mistakes, mathematics content and pedagogy related matters, investigation and inquiry-oriented mechanisms of teaching and learning mathematics, and of course, share with them my book-readings, experiences and even insights of senior global mathematics educationists -- their articles and host of educational videos, and ,.....and........and........ – there will be loads of FUN – like Playing mathematical games, solving ancient mathematics puzzles, and trying to unlock and appreciate the value embedded in these (often ignored) mathematically rich entities.... Oooooffff :-)  :-)

All this might remind some of you about my initiative of starting the maths-learners google group, and then even the compilation and circulation of "Math Energizer", isn't it? For the new folks in this group, this is the link that will navigate you to all the documents and maths stories that have been shared in this group till now: (you may esp. like to check out the oldest posts):  https://groups.google.com/forum/?nomobile=true#!forum/maths-learners-group/join

But then, I am sad that I am unavailable till 16th May, because of some other prior-commitments. Hence, despite these teachers being ready to start immediately, we will be able to start only from 18th May.

So friends, here’s an Invitation to All of you.....

If you or any of your colleagues would be interested to embark upon this thrilling-learning journey of mathematics, you are Most Welcome!! Write an email to me about your interest and participation in this "Maths Teachers’ Study Group" and you are IN! So simple, isn’t it? J

But what about the Fees, Time/ Duration, Frequency of sessions/meetings, Number of hours? 
Well, nothing is decided on these 'trivial' matters - as of now. We will work out all these details later, as the group evolves (when I say evolve, I do not mean by quantity - but by wisdom :-). We, the interested teachers and me, believe that all these details are important, but still are secondary and hence, can be easily worked out later, esp. by a person or group who is really hungry to learn!

I can personally relate to this fact because some time back, I used to travel for around 6 hours by ST buses, on the first Sunday of every month, to be a part of similar Teachers’ Study Group based at Wada Taluka of Thane district. To reach there, I had to first travel by a train, then change two buses and then again an auto. J Yes, the journey drained me out completely, but the peer-teachers and the discussions in the Study Group recharged and refreshed me, much more!

The only thing we are sure about now is that We Are Beginning – without worrying too much about the nitty-grittes. We are also not much concerned now about the destination and the challenges that we may face in this journey.

We are meeting on 18th of May at Airoli, Navi-Mumbai at sharp 10 am – to Begin! 

I am eagerly waiting to hear those precious three words from you --  "I am IN"  :)   I will then share with you the necessary guidelines and documents. 

Imp: I am not taking any space on rent and all... So the group size will (unfortunately) be limited by the size of the room.
I never use this phrase - First come First Serve -- but sadly, it will be applied this time :-)

PS: I am also happy to share with you all an article that was recently published on Divya Bhaskar, a marathi newspaper. Though some statements and figures do need some correction, however I am thankful to the reporter for sparing few minutes to listen to me and even the editor for to share my story, work and vision with people around. People often wonder about my switch from engineering to teaching school maths. And it has been Real challenge for me to answer this question to anyone (esp. strangers) in even half an hour... So, I guess, this 2-minute quarter-page article will turn out be a good handy beginner to quench their curiosity :)