Multiple Representations

Dan Meyer’s recent post got me thinking. I commented there, but for my own recording purposes, I’ll expand here.

1933

1944

When I first went to Europe, I had never been on a subway. Well, actually that’s a lie. As a junior in college I interviewed on Wall St. for a programming job. It was my first time in NYC and I had no clue how the subways worked. I walked two miles to Times Square before realizing if I was going to catch my taxi back to the airport on time I would not be able to just walk. So, I jumped on the subway having very little idea of how it worked other than the fact that I was following the stops in the reverse order that I walked them towards Times Square. I never understood the map.

In Europe, I became an expert at subway maps because I had to. However, at the time, and even now, I think I would have preferred the first representation of the map over the second.

  • When deciding between walking and riding the train, the first map gives you a better idea.
  • There’s no easy way to understand the layout of the city from the second map.

I remember in Paris we had no idea how far north our hostel was because all we knew was it was right next to a Metro station. When, on the last day, we decided to go to the Sacre-Coeur, we were surprised it was such a short ride – less than 5 minutes. The representation of the subway map hid from us our location in the city!!! It was one of those strange experiences and looking back on it, it’s pretty awesome to see all these connections to how we teach abstraction.

I’m pretty sure my students would agree with me that the first representation is better. The question I would then pose to them is, if the first representation is better, why does every subway system in the world now use the second representation?

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