So I tell them a story about Sir W. Arthur Lewis. When I was a master's student myself at Princeton, I once attended a lecture that he gave on real wages, the commodity terms of trade, and North-South income differentials. The talk had no math in it. One of the younger faculty members of the economics department was sitting in the front row, and I could see him scratching his head in confusion throughout the talk. A few minutes after Sir Arthur was done, this young professor jumped up in excitement and went up to the board. "Now I get it!" he exclaimed and began to scribble some equations on the board. "This is the equation which relates to what you said in the first part of your talk, and this one expresses the other, and here is a third... and now finally we have three independent equations that determines your three endogenous variables..." Sir Arthur kept on his bemused smile as his lecture was explained to him in mathematical terms.
The moral of the story is that if you are smart enough to be a Nobel-prize winning economist maybe you can do without the math, but the rest of us mere mortals cannot. We need the math to make sure that we think straight--to ensure that our conclusions follow from our premises and that we haven't left loose ends hanging in our argument.
In other words, we use math not because we are smart, but because we are not smart enough.
We are just smart enough to recognize that we are not smart enough. And this recognition, I tell our students, will set them apart from a lot of people out there with very strong opinions about what to do about poverty and underdevelopment.