“Assume that Gurgaon is 20 kms from Delhi and Manesar, 40 kms. Midway between Gurgaon and Manesar is a small village called Keshunagar. How far is it from Delhi?”
Simple question eh? It took me over an hour to get one of my students to understand this problem on his own and then work it out. I made three additional examples changing names and distances, and each time he had a tough time of it. I guess it could be like showing me how to solve a quantum mechanics problem – but probably a bit harder… I’ve got year’s of training behind me. This kid has about 3 years of schooling – and he’s about 18 years old.
Working at Tara Homes, I’ve been trying to help a few of the adolescents with their Math skills. And in this time I’ve found that often even a simple idea can be extremely difficult to transmit. I’ve been meaning to write about this subject for a while now, but I’ve never found the inclination to write it up. Now that I have, I’m at a loss to figure out what I can learn from my experience – except that it’s only through practice that one learns.
Working with calendar dates posed a similar trial. First my ward had a tough time recalling how many days a month had, and then he had an issue computing the number of days between Jan 15 and Feb 15, or something similar. Again, I had to work through a few examples and let him examine his own way through it. However, one curious thing I found with my ward’s computations was that while he was ready to follow the pattern – and it was a matter of following the pattern – he had a tough time really understanding the operations involved. For example, when I asked him how much coke would he dole out of a 2 liter bottle of coke when sharing it between 10 guests – he fumbled with various numbers before he realized that division was the way to proceed. I’m hoping that laboring through the process, he’s understood when and how to apply division.
What I think I’m discovering is that the world is not as clearly seen by all of us. It applies to math and as easily, to politics. And with the varying amounts of knowledge and experience out there, I wonder how we can make things stick together.