Dividing With a Difference
by P R Guruprasad
1980. It is dawn in a remote village in eastern Bhutan. The aromatic cup of Assamese tea and the spectacular Himalayan splendour make me ecstatic! But inside me, there is something in contrast: Worry. Yes, I am greatly worried about my previous day's mathematics class in Std II [In Bhutan 'Grade' is called 'Standard']. I was trying to teach single digit division to my children but with no success despite meticulous lesson planning and 'proven' teaching methods. I have failed in my self administered litmus test.
1995. One morning in a village in Orissa. It is a primary school catering to children of tribal folk. After several years of handling crests and troughs of classroom interaction, here I am, undertaking classroom observation of a young teacher. She is teaching exactly the same lesson that I had taken in Bhutan 15 years back. The difficulty that this teacher faces is strikingly similar to the one that I had encountered. Children cannot understand the concept.
The teacher is teaching the problem: 122 ÷ 3 = ? I am glad that I am there to witness the difficult circumstance so that I can help the teacher as an outsider. As the academic watchdog I also feel responsible for the issue. That evening I get back to my hotel room with a slightly heavy heart and ponder over the problem. 11.30 PM. Eureka! I get up to scribble down the solution stemming from somewhere in my inner mind. The solution that flashed through my mind is documented below:
122÷3 = 122÷3 = (90+30+2)÷3 = (90÷3) + (30÷3) + (2÷3) = 30 +10 + (2/3) = 40 + (2/3) = 40 2/3
Next day the teacher tries my strategy in her class and thanks me that her children understand the concept well this time.
Though this process is longer than the commonly used methods, it has the following advantages:
- The algorithm offers 'transparency' as children progress through the problem.
- Children apply their knowledge of 'factors' to split the dividend.
- It presents a logic behind fractions [for instance as to how we get the fraction '2/3' in the above illustration]; children not only learn 'what' but also 'how'.
- It serves as an effective springboard to teach LCM.
- It displays the flexibility [within a framework] that numbers offer.
- Panamalai R Guruprasad
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