College Readiness: How to Help Students Think Abstractly

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?

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Understanding metaphors

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Ben, Your skillful questioning unlocks the deeper meaning below the literal level. Do you find students are able to maintain their ability to understand metaphors when they don't have the benefit of your questions to guide their thinking when they are reading independently?

Elementary Teacher and Academic Dean summers

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Half the fun of learning and teaching is to crisscross bridges from the concrete to the abstract and back. We do it all the time. For example, in my latest post I share the way I physically float papers to students as a way to get them to consider the abstract concept of, "Think before you speak." Students delight in figuring out and learning metaphors such as, "The rub is...." Puns, too, help students think. (Of course, all my students know that the arguable reason cows have bells around their necks is because their horns don't work.) Also, morphing common sayings such as, "Speak now, or forever hold you nose," and at the end of the day announcing to the class, "Chair up! Be happy!" are ways to play with images through words. Metaphors, puns, and saying surprising, catchy statements keep students on their mental toes and engaged with the notion of, " What will happen next?"

Metaphors and Visualization

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During my teaching career, I found it useful to help students visualize concepts by using metaphors or similes. It was less important to me that they had it "exactly right" at certain points, but more important that they were getting the picture. For example, parametric equations can be modeled by having students orient rubber bands in three-space. The orientation represents the vector, and the "stretch" represents the scalar quantity.

In chemistry, conservation of matter & energy in reactions became a house which is secure if we can equalize the amount of water coming in with the amount of water going out, and being able to keep track of a known quantity that is currently "in use" within the house. When we can't keep track of everything, there is likely to be a problem caused by the imbalance.

The list is extensive, but these intermediate visualization steps helped me, as well as my students, to have sense-making dialogue that moved us all along.

Change agent and school improvement expert

Relevance

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Sharon:
Application of theory is the pinnacle of learning. After all, what good is knowledge or skills if nothing is done with them? How do you think we can get what you experience in higher ed to happen earlier in k-12?

Good thoughts!

Ben Johnson
San Antonio, Texas