How I learned 2+2 can equal 3
A few months ago I was substituting for our Hindi tutor and was giving an assessment to a group of elementary age students (they were in the 1st or 2nd grade) .
Given how my Hindi is a bit rusty I wanted to give them an assessment that would challenge them but also be within the realm of the Hindi that I understood.
For some background: this was a conversational Hindi class that our company teaches at a local private school, and many of the students learned English as their first language, so they were learning Hindi from English, using words transliterated into the English Script.
This was a class designed for American students, and 2 of our students were not of South Asian origin so learning Hindi was completely new to them.
They were also in 1st and 2nd grade, so doing math was also relatively new to them as well, but by that grade they knew how to count and do 2 operations (addition and subtraction).
So I decided to quiz the students by asking them a math problem in English, and had them answer it in Hindi.
But This ended up being a much more difficult exercise than expected…
The first question I started simple- What is 0+1 equal to, in Hindi?
The students broke out their fingers and started counting, and said out loud “Shunya, Ek, EK!” (Zero, One!).
Then I gave them a harder one- What is 10 + 6 in Hindi?
This time the students thought for a second, and then once again broke out their finger counters, counted for a few minutes, and then she was ready. But her answer was the first surprise of the afternoon.
Out loud, the little girl exclaimed “Shunya(0), Ek(1), Do(2), Theen(3), Char(4), Panch(5),Cheh (6) Saat(7), Aath (8), Nao (9), Das (10), Gyaarah (11)…Baarah (12)…Tehrah (13)…Chaudah(14)...Pandrah(15)…SAULAH (16!!)
I noticed that unlike when doing math in English, the students did not have reference points to go off of when counting, since they remembered the numbers in order, regardless of the answer they started from the beginning and counted up.
Even using the finger calculator method, although it may be easier to count from 10 so that you have fresh hands, and then go up to 16, because they remembered the numbers in order, the girls were starting from the beginning, even though that wasn’t the most optimal way to count.
I asked the girls why they were counting that way because it was taking longer than if they counted by 10s, and their answer was
Math is hard, and Hindi is hard, so this is DOUBLE HARD! We just learned how to do this in English!
I had promised them that we would have a dance party if they did a good job, so after this question I didn’t want to wait for them to count so I thought I would give them a much easier one.
Or so I thought. ..
The final question was… What is 2 + 2, in Hindi
The girl broke out her finger counters and then this was where they either blew my mind or were just tired.
“Shunya(0), Ek (1), Do (2), Theen (3)- THEEN!” She had four fingers on her hand, but had answered 3.
“Are you sure about that?” I asked her…
“YEAH!” Then she started counting again on her finger counters- “See? Shunya, Ek Do, Theen! Yeah Theen!” She was certain that the answer was Theen (3) because it matched her finger counter math.
She was getting confused because in order, Theen (3) was the Fourth Number in the set of numbers she had learned, even though the assigned meaning was different.
This was where it hit me that learning math, and learning a language are two separate but related concept- and math was almost like it’s own language.
Since the students were new at both, they had to manually connect the two concepts.
I corrected her- “So 2+2=3? Is that what you’re telling me?”
“NOO, it’s 4!!” — She corrected herself.
“So why did you tell me Theen, which is three?”- I was genuinely curious.
“Because that’s what it said on my fingers! But I KNOW that it’s 4”
Going by the method we were using, she was computing the answer in English, and then to get the number in Hindi was then counting through the array of Hindi numbers that she knew.
It was almost like the students were doing a For Loop from computer science but doing a very simple counting program.
Or in other words- Give me a problem, find an answer, use this answer to lookup some other value from a list, using the answer or the answer+1 as the index to stop counting.
This opened my eyes and from there I tried to use a different approach to make sure they understood what I was talking about.
So no, they didn’t prove to me scientifically that 2+2=3, but they did show me that the way we learn how to do math is more complicated than it seems.