A rolling stone gathers no moss. Mick Jagger has moss? Don't cry over spilt milk. It's only milk, why cry? Too many cooks spoil the soup. I hate soup. Water under the bridge. Of course there is water under a bridge! A tiger's stripes do not change. Of course they don't! Birds of a feather flock together. Yeah, those Grackles downtown are so annoying. There must be millions of them.
A college-ready student can think figuratively, or in other words associate abstract ideas with concrete examples. One of the best ways to help students think abstractly is to engage them in the ancient wisdom of metaphors and sayings. Initially, their reactions will be like the ones above, but with a little practice, students will be able to arrive at the real meaning of the sayings.
Thinking abstractly is useful in understanding the richness of literature, both classical and modern. Carol's Alice in Wonderland, Dr. Suess' Horton the Elephant, Milton's Paradise Lost would all be incomprehensible without the ability to think abstractly.
The reason that algebra, geometry, and general mathematics challenge students is that they require students to think abstractly. The bane of most students -- the word problems -- are all about taking something concrete and transforming the situation into abstract symbols and numbers. Most problem-solving techniques require students to step back (figuratively) from the problem at hand (it could be at foot) and state the problem in abstract terms.
In order to help my students thinking and using the Spanish language, I printed a dicho (saying) such as, "En boca cerrada no entra mosca!" (in a closed mouth, flies don't enter -- my favorite) on the board and asked them to decipher the Spanish and then the true meaning. Once we got passed the literal interpretations, then students were usually able to arrive at approximate meanings. Some dichos just stumped them: "Al hambriento, no hay pan duro." (to the hungry, there is no hard bread), or "En casa del herrero, cuchillo de palo" (in the house of the blacksmith, a wooden knife). I found that the key was not to give the students the answers. I simply put on my Socrates robe and asked questions. These were very hard for my students, at first, but with practice, I had to ask fewer and fewer questions. The students began to see the deeper messages in the dichos and were able to transfer that skill to see deeper messages in Spanish humor and literature.
It was always illuminating and inspiring to watch as students caught the joke, or the meaning of a passage of literature. Students are often smarter than we give them credit for: El leon no es como lo pintan (the lion is not how it is painted).
How do you get your students to think abstractly?