Analogy word problems offer teaching solutions

Use course vocabulary for analogies practice

Analogy word problems are commonly used on standardized tests to assess students’ higher level thinking abilities.

Many students find such problems bewildering because they lack an adequate understanding of the meanings of the words used in the problems.

You can address this difficulty by creating analogy practice items that use your course vocabulary. That way you can be sure the words used in the analogies are ones students have at least encountered even if they didn’t master them initially.

The analogies practice activity below shows you can use analogy word problems to review content in English language arts. The idea will work equally well for content review and teaching critical thinking in social studies, geometry, art, etc.

Materials you will need

You need a list of word pairs that illustrate common analogy types. For younger students, or those you are just beginning to introduce to word problems, you can stick with simple types:

  • category : example
  • part : whole
  • object : use
  • cause : effect
  • word : synonym
  • word : antonym

With more mature students, you can add some more complex relationships, such as the dozen identified by the University of Hawaii reading lab. [Information no longer available; link removed]

Vocabulary websites and test prep websites may also provide useful lists. The more examples you have, the more useful the results of the analogy practice activity will be.

Create your list from the topics you study in your course. Here are some ELA examples:

fiction : novel
limerick : poem
sentence : paragraph
nonfiction : biography
PowerPoint : speech
reasoning : persuasion
perspective : viewpoint
novel : book-length fiction
introduction : beginning
fiction : nonfiction
oral : written
grammar : punctuation
conclusion : thesis
analogy : metaphor
advertisement : editorial

In addition to a generous sprinkling of word pairs whose relationship is obvious, include word pairs whose relationship is debatable or not easily described in one or two words.

Groups encourage diverse opinions

Have students work in small groups to identify the relationship(s) between the words of each pair.

Word pairs that are open to interpretation encourage discussion about the meanings of each word. Ambiguity leads to higher-level learning as students discuss the definitions of terms and look for the most logical relationships (plural) between vocabulary words. Some relationships may be more obvious than others, but there are no right or wrong answers for the word pairs.

When students don’t agree on a relationship, they should list all the relationships they observe.

If you have some shy students who resist public discussion, give the entire class opportunities to describe in one written sentence the relationships they observe in two or three examples. Often such informal writing is enough to convince the shy student she or he has something to contribute to the group’s discussion.

Essential skills addressed in this activity

This activity gives students practice in several important skills at the same time they review course material. Those skills include:

  • critical thinking
  • discipline-specific vocabulary
  • teamwork
  • oral communication

Just because an activity has one primary objective doesn’t mean it cannot provide practice in multiple skills.

Learning by analogies

I’ve been thinking about analogies. I don’t mean the kind of A : B =  C : ? analogy questions on standardized tests, which, even to folks like myself who enjoy them, don’t do much more than pass the time.

The kind of analogies I’m thinking about are critical thinking strategies that enable fast, efficient learning of processes and procedures in new situations.  They are the kinds of cognitive skills that a new hire needs to get up to speed quickly without company-provided training.

Such cognitive abilities are particularly important in this economy: when big companies retrench, one of the first budgets to be cut is training.  Small busineses—those with 10 or fewer employees who comprise the bulk of American businesses—never had a training budget: they must hire people with good skills because they haven’t time or money for training.

Faced with learning some new process or procedure, a savvy learner approaches the material to be learned as an analogy problem.

Analogies are essentially extended comparisons. Unlike similes and metaphors which compare a single feature of two elements, (“swift as a deer,” “bovine eyes”), analogies compare multiple features of two elements.  They work rather like this:

Feature 1  of item 1 ~ Feature 1 of item 2

Feature 2 of item 1 ~ Feature 2  of item 2

Feature 3 of item 1 ~ Feature 3 of item 2

Anyone who has ever used an analogy to explain a concept or process has probably uttered the cliché “every analogy breaks down at some point.”  An analogy is bound to break down unless the two items being compared are identical. That’s where the value of the analogy as a learning strategy comes into play.

Once learners identify something in their experience that’s analogous to the material to be learned, they can zero in on what’s essential to master immediately, with this kind of analysis:

Feature 1 of the process I must learn ~ Feature  of a process I already know.

Feature 2 of the process I must learn ~ Feature  of a process I already know.

Feature 3 of the process I must learn ~ Feature  of a process I already know.

Feature 4 of the process I must learn  is totally unlike any features of a process I already know.

This type of critical thinking process effectively and efficiently isolates for the learner what new processes must be mastered quickly. It also helps the learner identify how steep the learning curve will be.  Having to master a new process that requires learning to use new tools and a new vocabulary will require concentrated effort. On the other hand, for example,  someone who knows  Microsoft® Word® can figure out how to use OpenOffice™ Writer by examining how the features of Word® they are accustomed to are rendered in OpenOffice™ Writer.

It’s worth noting that even though learners see broad similarities between the processes or procedures to be learned and those they already know, they still probably will need to master specific facts. Having an analogous situation to which to compare required new learning does not eliminate the need to do new learning. Rather it changes the kind of learning required from systemic information to more discrete data bits. New hires can jot down terms or job-site specific filing procedures far more easily than they can learn, for example, what an accounting office does.

The critical thinking processes needed for this type of analysis can be taught and learned through classroom activities.  Since the learners who are best equipped to do this kind of cognitive work are those with the broadest range of experiences, schools can support their students by  integrating learning experiences across the curriculum.  That does not mean just that the English teacher allows students to write research papers about preserving the rain forests. It’s equally about the biology teacher pointing out how life science uses language to convey facts and attitudes.

Above all, however, it’s about teaching students that they need to demonstrate the ability to apply and modify their prior learning in each new situation.

Fiction as a perceptional lens

Library seen from outside in the dark
Books are windows, too.

Reading vintage fiction is a hobby and a compulsion for me. I not only enjoy old books, but also find looking at contemporary life through the lens of another era makes patterns easier to spot.

This week I reread A. M. E. Hutchinson’s If Winter Comes. First published in August 1921, it became a bestseller, going through 34 reprints by April 1923. If you aren’t fortunate enough to pick a copy for a quarter at a library book sale, as I did, you can read a digital version from Project Gutenberg.

The story is about Mark Sabre, a young man who was called “Puzzlehead” at school because of his extraordinary habit of being able to see anything from the other guy’s side. Mark has principles that he believes are absolutely true, but he doesn’t always find it easy to know how to apply those principles. Mark’s world is complicated, full of subtleties.

Mark’s ability to see how things might appear to someone else is in singular contrast to folks around him. From his wife to his boss, they are what Marks calls people of Conviction, with a capital C.

People of Conviction have rods and cones, but their brains perceive only black and white.  They absolutely believe that their beliefs are true, and they cannot imagine that any other belief could be held by anyone who isn’t at best a moron, at worst an immoral moron.

People of Conviction are righteous bullies.

Looking at contemporary life with Hutchinson’s novel fresh in my mind, appears that people of Conviction still hold the whip hand.  Puzzleheads are scarce, even in arenas where puzzleheaded people are most needed: politics and education.

Getting rid of the people of Conviction is impossible. Shooting them’s not legal, and, as Mark says, they mean well and they are often right.

Converting them may be impossible, too. They do not listen to anything with which they know they don’t agree.

Perhaps the only solution is to give them novels that let them a look at life through a different lens.

Photo credit: Windows and Books uploaded by sphaera

Essay writing requires thinking

An essay is a statement of reasoned opinion. To write an essay, a person must:

  • Have some information.
  • Reflect on that information.
  • Compare it to other information.
  • Add information from other sources.
  • Reach a conclusion.

When we say writing an essay requires students to employ critical thinking skills, it’s that list we have in mind. That list doesn’t tell how to write an essay; it only relates the thinking that essay writing entails before the author can begin writing.