CHC Theory

Fluid and Crystallized Intelligence in the Classroom and on the Job

Fluid intelligence is the ability to solve unfamiliar problems using logical reasoning. It requires the effortful control of attention to understand what the problem is and to work toward a logically sound answer. People with high fluid intelligence are able to figure out solutions to problems with very little instruction. Once they have found a good solution to a problem, they are able to see how it might apply to other similar problems. People with low fluid intelligence typically need hands-on, structured instruction to solve unfamiliar problems. Once they have mastered a certain skill or solution to a problem, they may have trouble seeing how it might apply in other situations. That is, their newfound knowledge does not generalize easily to other situations.

— Schneider & McGrew (2013, p. 772)

Gf in the Classroom and on the Job

Crystallized intelligence is acquired knowledge. When people solve important problems for the first time, they typically remember how they did it. The second time the problem is encountered, the solution is retrieved from memory rather than recreated anew using fluid intelligence. However, much of what constitutes crystallized intelligence is not the memory of solutions we personally have generated but the acquisition of the cumulative wisdom of those who have gone before us. That is, we are the intellectual heirs of all of the savants and geniuses throughout history. What they achieved with fluid intelligence adds to our crystallized intelligence. This is why even an average engineer can design machines that would have astounded Galileo, or even Newton. It is why ordinary high school students can use algebra to solve problems that baffled the great Greek mathematicians (who, for lack of a place-holding zero, could multiply large numbers only very clumsily).

Crystallized intelligence, broadly speaking, consists of one’s understanding of the richness and complexity of one’s native language and the general knowledge that members of one’s culture consider important. Of all the broad abilities, crystallized intelligence is by far the best single predictor of academic and occupational success. A person with a rich vocabulary can communicate more clearly and precisely than a person with an impoverished vocabulary. A person with a nuanced understanding of language can understand and communicate complex and subtle ideas better than a person with only a rudimentary grasp of language. Each bit of knowledge can be considered a tool for solving new problems. Each fact learned enriches the interconnected network of associations in a person’s memory. Even seemingly useless knowledge often has hidden virtues. For example, few adults know who Gaius and Tiberius Gracchus were (Don’t feel bad if you do not!). However, people who know the story of how they tried and failed to reform the Roman Republic are probably able to understand local and national politics far better than equally bright people who do not. It is not the case that ignorance of the Gracchi brothers dooms anyone to folly. It is the case that a well-articulated story from history can serve as a template for understanding similar events in the present.

— Schneider & McGrew (2013, pp. 772–773)

Gc in the Classroom and on the Job
Gf Gc Typology

The pictures are previously unpublished (and not to be taken too seriously).

Definitions from:

Schneider, W. J. & McGrew, K. S. (2013). Cognitive performance models: Individual differences in the ability to process information. In S. Ortiz & D. Flanagan (Sec. Eds.), Section 9: Assessment Theory, in B. Irby, G. Brown, & R. Laro-Alecio & S. Jackson (Vol Eds.), Handbook of educational theories (pp. 767–782). Charlotte, NC: Information Age Publishing.

CHC Theory, Cognitive Assessment, Principles of assessment of aptitude and achievement

IQ Tests: Is Knowledge of Useless Knowledge Useless?

Now I wish I could write you a melody so plain

That could hold you dear lady from going insane

That could ease you and cool you and cease the pain

Of your useless and pointless knowledge

– Bob Dylan “Tombstone Blues”

There is much pleasure to be gained from useless knowledge.

– Bertrand Russell

When critics look though the items in a general verbal information test, they, with some justification, sometimes sneer at the usefulness of the content. Is there any money in being able to list off the names of the planets? Can I oppose injustice, armed with my knowledge of state capitals? Will any babies be saved because I know who Julian the Apostate was? Probably not.

Many (most?) facts I have learned are unlikely to ever be of practical use. If I knew which ones they were, I might happily surrender them to forgetfulness. However, because it is impossible to know what might be useful in the future, I will hang onto my useless and pointless knowledge for a little while longer, thank you very much.

When Francis Bacon wrote parenthetically that “knowledge itself is a power…” in the context of an argument attempting to discredit the theological beliefs of certain religious sects, he probably did not mean the phrase in the sense that it is invoked today (i.e., that knowledge confers power). However, the phrase “knowledge is power” has survived because it resonates with our experience and pithily expresses something that is increasingly true in an age that gives increasing returns to those who can profit from information.

Good items in a test of General Information should not be about random facts. Easy items should not be merely easy (e.g., “What is the color of the sky?”). Rather, they should test for knowledge of information considered essential for living independently in our culture. A person who does not understand why dishes should be washed is not ready to live unsupervised. More difficult items should not be merely difficult (e.g., “What is the largest city in Svalbard? How many teeth does an orca whale have?”). Rather, they should measure knowledge that is relevant to what is considered core aspects of our culture (e.g., “Why do banks loan people money? Why do people still learn Latin and ancient Greek? Who was Isaac Newton? What is the purpose of the United Nations?”).

Just as language development consists of many narrow abilities, there are many sub-categories in General Information. Typically these sub-categories consist of academic domains such as knowledge of the humanities and knowledge of the sciences. These categories have further subdivisions (e.g., physics, chemistry, biology, and so forth – and each of these, in turn have further subdivisions).

General Information consists of knowledge that each person in a culture is expected to be familiar with (or would be admired if he or she knew). However, much (if not most) of a person’s knowledge is not of this sort. For example, although it is expected that everyone in this culture should know what airplanes are, only pilots are expected to know how to fly them. In CHC Theory, knowledge that is expected to be known only to members of a particular profession or enthusiasts of a particular hobby, sport, or other activity is classified as Domain-Specific Knowledge (Gkn). Most subject-specific academic achievement tests (e.g., European History, Geology, Contemporary American Literature) would be considered measures of Gkn, not Gc. That is, typically (but not always) achievement measures are the relevant outcomes we wish to explain, not explanatory aptitudes. In contrast, measures of General Information (e.g., WISC-IV Information) are intended to be estimates of the body of knowledge from which a person can draw to solve a wide range of problems.

Like Lexical Knowledge, General Information has a bi-directional relationship with reading comprehension. Very little of what is written is fully self-contained; authors presume that readers have considerable background knowledge and often do not bother to explain themselves. Drout (2006) describes how difficult and amusing it is to explain to non-native speakers of English what newspaper headlines such as “Under Fire from G.O.P., White House Hunkers Down” mean.[1] Children who know more understand more of what they read. Understanding more makes reading more enjoyable. Reading more exposes children to more knowledge, much of which is inaccessible via oral culture.

[1]Why would anyone be under a fire?

It means being shot at.

People are shooting at the White House?

No, it is just a vivid way of saying that the G.O.P. is criticizing the administration, which is symbolized by the White House, where the president lives.

Who is the G.O.P.?

It stands for the Grand Old Party.

If they are old, why haven’t I heard of them?

They are the Republicans.

Oh! Is the Democratic Party the new party?

No, they have been around longer than the Republicans. The nickname GOP was first used when the party was only a few decades old.

I don’t understand.

I don’t either, really. I just know that “old” is an affectionate way of describing something you have liked for a long time.

Could I say that I enjoy old ice cream?

No, that doesn’t sound right. You should probably just avoid using “old” that way.

What does “hunker”mean?

I really have no idea. I just know that when you are under fire, you should hunker down.

If you don’t know what it means, how do you know what to do?

True! I just looked it up. It means “to squat, to sit on your haunches.” I guess it all makes sense now.

So, when the Republicans criticize the president, he sits on his haunches?

That is an amusing image, but no. It means that you stick to your guns…er…I mean…

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford.



CHC Theory, Cognitive Assessment

Crystallized Intelligence, Visualized