I asked my 7-year-old daughter if she knows the times table of half. She immediately responded that she does and here’s what followed.
We were chatting about multiplication tables of some numbers, and I gave her a googly by asking if she knows the times table of half. She said, “Yes, I do”. When I asked her to say it aloud, she said:
Half ones are half
Half twos are one
Half threes are one and a half
Half fours are two
Half fives are two thirty
She bit her tongue immediately realizing that she made a slip of tongue. Can you guess how she calculated the times table of half? Pause and think!
Yes, she was using time (30 minutes = half an hour) to do the calculations. You can see that this was very simple and a no-brainer where one need not remember any rules for operations using fractions that we typically learn in school (rules with numerators and denominators). She was no longer imagining fractions in a numerical form. Rather she was using time to deal with the fraction ‘half’. That is why when she reached ‘half fives…she said two (hours and) thirty (minutes) realizing her mistake immediately.
I was very happy by this good mistake because had it not happened, it would not have given me the idea of a possibility to teach some bit of fractions using the concept of time.
I am reminded of Feynman who says in this talk that we cannot know how the other person thinks even though we both might be thinking about the same thing https://youtu.be/Si6NbKqYEd8?si=CamdG1ub4WSLas__ And how true! Only if we listen to young minds and try to figure out how they think, we may be able to realize how wrong we are when we assume that we know ‘the way’ to teach something to them. We don’t…and we may never know for sure!
Author:
Vinay Nair is a co-founder of Raising A Mathematician Foundation and Vichar Vatika – two organizations that aim towards making math more meaningful. He mentors students who are passionate about mathematics and also focuses on building mathematical and computational thinking skills in students through creative problem solving. He can be reached at vinay@vicharvatika.org
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