These children, who are doing the math required in order to run successful businesses, cannot do the same math when the problems are presented in an abstract, paper- and- pencil
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format. Sternberg argues that this result makes sense when viewed from the standpoint of developing expertise: the children live in an environment that emphasizes practical skills, not academic, and it’s the practical exigencies that determine the substance and form of the learning.10
The other story is about seasoned, expert handicappers at horse tracks who devise highly complex mental models for betting on horses but who mea sure only average on standard IQ tests. Their handicapping models were tested against those devised by less expert handicappers with equivalent IQs.
Handicapping requires comparing horses against a long list of variables for each horse, such as its lifetime earnings, its lifetime speed, the races where it came in the money, the ability of its jockey in the current race, and a dozen characteristics of each of its prior races. Just to predict the speed with which a horse would run the fi nal quarter mile, the experts relied on a complex mental model involving as many as seven variables. The study found that IQ is unrelated to handicapping ability, and “what ever it is that an IQ test mea sures, it is not the ability to engage in cognitively complex forms of multi-variate reasoning.”11
Into this void Robert Sternberg has introduced his three-part theory of successful intelligence. Analytical intelligence is our ability to complete problem- solving tasks such as those typically contained in tests; creative intelligence is our ability to synthesize and apply existing knowledge and skills to deal with new and unusual situations; practical intelligence is our ability to adapt to everyday life— to understand what needs to be done in a specifi c setting and then do it; what we call street smarts.
Different cultures and learning situations draw on these intelligences differently, and much of what’s required to succeed in a par tic u lar situation is not mea sured by standard IQ or aptitude tests, which can miss critical competencies.
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Dynamic Testing
Robert Sternberg and Elena Grigorenko have proposed the idea of using testing to assess ability in a dynamic manner.
Sternberg’s concept of developing expertise holds that with continued experience in a fi eld we are always moving from a lower state of competence to a higher one. His concept also holds that standardized tests can’t accurately rate our potential because what they reveal is limited to a static report of where we are on the learning continuum at the time the test is given. In tandem with Sternberg’s three- part model of intelligence, he and Grigorenko have proposed a shift away from static tests and replacing them with what they call dynamic testing: determining the state of one’s expertise; refocusing learning on areas of low per for mance; follow- up testing to mea sure the improvement and to refocus learning so as to keep raising expertise. Thus, a test may assess a weakness, but rather than assuming that the weakness indicates a fi xed inability, you interpret it as a lack of skill or knowledge that can be remedied. Dynamic testing has two advantages over standard testing. It focuses the learner and teacher on areas that need to be brought up rather than on areas of accomplish-ment, and the ability to mea sure a learner’s progress from one test to the next provides a truer gauge of his or her learning potential.
Dynamic testing does not assume one must adapt to some kind of fi xed learning limitation but offers an assessment of where one’s knowledge or per for mance stands on some dimension and how one needs to move forward to succeed: what do I need to learn in order to improve? That is, where aptitude tests and much of learning styles theory tend to emphasize our strengths and encourage us to focus on them, dynamic testing helps us to discover our weaknesses and correct them.
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In the school of life experience, setbacks show us where we need to do better. We can steer clear of similar challenges in the future, or we can redouble our efforts to master them, broadening our capacities and expertise. Bruce Hendry’s experiences investing in rental property and in the stock market dealt him setbacks, and the lessons he took away were essential elements of his education: to be skeptical when somebody’s trying to sell him something, to fi gure out the right questions, and to learn how to go dig out the answers. That’s developing expertise.
Dynamic testing has three steps.
Step 1: a test of some kind— perhaps an experience or a paper exam— shows me where I come up short in knowledge or a skill.
Step 2: I dedicate myself to becoming more competent, using refl ection, practice, spacing, and the other techniques of effective learning.
Step 3: I test myself again, paying attention to what works better now but also, and especially, to where I still need more work.
When we take our fi rst steps as toddlers, we are engaging in dynamic testing. When you write your fi rst short story, put it in front of your writers’ group for feedback, and then revise and bring it back, you’re engaging in dynamic testing, learning the writer’s craft and getting a sense of your potential. The upper limits of your per for mance in any cognitive or manual skill may be set by factors beyond your control, such as your intelligence and the natural limits of your ability, but most of us can learn to perform nearer to our full potential in most areas by discovering our weaknesses and working to bring them up.12
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Structure Building
There do appear to be cognitive differences in how we learn, though not the ones recommended by advocates of learning styles. One of these differences is the idea mentioned earlier that psychologists call structure building: the act, as we encounter new material, of extracting the salient ideas and constructing a coherent mental framework out of them. These frameworks are sometimes called mental models or mental maps. High structure- builders learn new material better than low structure- builders. The latter have diffi culty setting aside irrelevant or competing information, and as a result they tend to hang on to too many concepts to be condensed into a workable model (or overall structure) that can serve as a foundation for further learning.
The theory of structure building bears some resemblance to a village built of Lego blocks. Suppose you’re taking a survey course in a new subject. You start with a textbook full of ideas, and you set out to build a coherent mental model of the knowledge they contain. In our Lego analogy, you start with a box full of Lego pieces, and you set out to build the town that’s pictured on the box cover. You dump out the pieces and sort them into a handful of piles. First you lay out the streets and sidewalks that defi ne the perimeter of the city and the distinct places within it. Then you sort the remaining pieces according to the elements they compose: apartment complex, school, hospital, stadium, mall, fi re station. Each of these elements is like a central idea in the textbook, and each takes more shape and nuance as added pieces snap into place. Together, these central ideas form the larger structure of the village.
Now suppose that your brother has used this Lego set before and dumped some pieces into the box from another set.
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As you fi nd pieces, some might not fi t with your building blocks, and you can put them aside as extraneous. Or you may discover that some of the new pieces can be used to form a substructure of an existing building block, giving it more depth and defi nition (porches, patios, and back decks as substructures of apartments; streetlights, hydrants, and boule-vard trees as substructures of streets). You happily add these pieces to your village, even though the original designers of the set had not planned on this sort of thing. High structure-builders develop the skill to identify foundational concepts and their key building blocks and to sort new information based on whether it adds to the larger structure and one’s knowledge or is extraneous and can be put aside. By contrast, low structure- builders struggle in fi guring out and sticking with an overarching structure and knowing what information needs to fi t into it and what ought to be discarded. Structure building is a form of conscious and subconscious discipline: stuff fi ts or it doesn’t; it adds nuance, capacity and meaning, or it obscures and overfreights.
A simpler analogy might be a friend who wants to tell you a rare story about this four- year- old boy she knows: she men-tions who the mother is, how they became friends in their book club, fi nally mentioning that the mother, by coincidence, had a large load of manure delivered for her garden on the morning of the boy’s birthday— the mother’s an incredible gardener, her eggplants took a ribbon at the county fair and got her an interview on morning radio, and she gets her manure from that widowed guy in your church who raises the Clydesdale horses and whose son is married to— and so on and so on. Your friend cannot winnow the main ideas from the blizzard of irrelevant associations, and the story is lost on the listener. Story, too, is structure.
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Our understanding of structure building as a cognitive difference in learning is still in the early stages: is low structure-building the result of a faulty cognitive mechanism, or is structure- building a skill that some pick up naturally and others must be taught? We know that when questions are embedded in texts to help focus readers on the main ideas, the learning per for mance of low structure- builders improves to a level commensurate with high structure- builders. The embedded questions promote a more coherent repre sen ta tion of the text than low- structure readers can build on their own, thus bringing them up toward the level achieved by the high structure- builders.
What’s happening in this situation remains an open question for now, but the implication for learners seems to reinforce a notion offered earlier by the neurosurgeon Mike Ebersold and the pediatric neurologist Doug Larsen: that cultivating the habit of refl ecting on one’s experiences, of making them into a story, strengthens learning. The theory of structure building may provide a clue as to why: that refl ecting on what went right, what went wrong, and how might I do it differently next time helps me isolate key ideas, or ga nize them into mental models, and apply them again in the future with an eye to improving and building on what I’ve learned.13
Rule versus Example Learning
Another cognitive difference that appears to matter is whether you are a “rule learner” or “example learner,” and the distinction is somewhat akin to the one we just discussed. When studying different kinds of problems in a chemistry class, or specimens in a course on birds and how to identify them, rule learners tend to abstract the underlying principles or “rules”
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that differentiate the examples being studied. Later, when they encounter a new chemistry problem or bird specimen, they apply the rules as a means to classify it and select the appropriate solution or specimen box. Example learners tend to memorize the examples rather than the underlying principles.
When they encounter an unfamiliar case, they lack a grasp of the rules needed to classify or solve it, so they generalize from the nearest example they can remember, even if it is not particularly relevant to the new case. However, example learners may improve at extracting underlying rules when they are asked to compare two different examples rather than focus on studying one example at a time. Likewise, they are more likely to discover the common solution to disparate problems if they fi rst have to compare the problems and try to fi gure out the underlying similarities.
By way of an illustration, consider two different hypothetical problems faced by a learner. These are taken from research into rule learning. In one problem, a general’s forces are set to attack a castle that is protected by a moat. Spies have learned that the bridges over the moat have been mined by the castle’s commander. The mines are set to allow small groups to cross the bridges, so that the occupants of the castle can retrieve food and fuel. How can the general get a large force over the bridges to attack the castle without tripping the mines?
The other problem involves an inoperable tumor, which can be destroyed by focused radiation. However, the radiation must also pass through healthy tissue. A beam of suffi cient intensity to destroy the tumor will damage the healthy tissue through which it passes. How can the tumor be destroyed without damaging healthy tissue?
In the studies, students have diffi culty fi nding the solution to either of these problems unless they are instructed to look
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for similarities between them. When seeking similarities, many students notice that (1) both problems require a large force to be directed at a target, (2) the full force cannot be massed and delivered through a single route without an adverse outcome, and (3) smaller forces can be delivered to the target, but a small force is insuffi cient to solve the problem. By identifying these similarities, students often arrive at a strategy of divid-ing the larger force into smaller forces and sending these in through different routes to converge on the target and destroy it without setting off mines or damaging healthy tissue. Here’s the payoff: after fi guring out this common, underlying solution, students are then able to go on to solve a variety of different convergence problems.14
As with high and low structure-builders, our understanding of rule versus example learners is very preliminary. However, we know that high structure-builders and rule learners are more successful in transferring their learning to unfamiliar situations than are low structure-builders and example learners. You might wonder if the tendency to be a high structure-builder is correlated with the tendency to be a rule learner.
Unfortunately, research is not yet available to answer this question.
You can see the development of structure- building and rule- learning skills in a child’s ability to tell a joke. A three-year- old probably cannot deliver a knock- knock joke, because he lacks an understanding of structure. You reply “Who’s there?” and he jumps to the punch line: “Door is locked, I can’t get in!” He doesn’t understand the importance, after “Who’s there?”, of replying “Doris” to set up the joke. But by the time he’s fi ve, he has become a knock- knock virtuoso: he has memorized the structure. Nonetheless, at fi ve he’s not yet adept at other kinds of jokes because he hasn’t yet learned the essential element that makes jokes work, which, of course,
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is the “rule” that a punch line of any kind needs a setup, explicit or implied.15
If you consider Bruce Hendry’s early lesson in the high value of a suitcase full of scarce fi reworks, you can see how, when he looks at boxcars many years later, he’s working with the same supply- and- demand building block, but within a much more complex model that employs other blocks of knowledge that he has constructed over the years to address concepts of credit risk, business cycles, and the pro cesses of bankruptcy.
Why are boxcars in surplus? Because tax incentives to investors had encouraged too much money to fl ow into their production. What’s a boxcar worth? They cost $42,000 each to build and were in like- new condition, as they had been some of the last ones built. He researched the lifespan of a boxcar and its scrap value and looked at the lease contracts. Even if all his cars stood idle, the lease payments would pay a pretty yield on his investment while the glut worked through the system and the market turned around.
Had we been there, we would have bought boxcars, too.
Or so we’d like to think. But it’s not like fi lling a satchel with fi reworks, even if the underlying principle of supply and demand is the same. You had to buy the boxcars right, and understand the way to go about it. What in lay terms we call knowhow. Knowledge is not knowhow until you understand the underlying principles at work and can fi t them together into a structure larger than the sum of its parts. Knowhow is learning that enables you to go do.
The Takeaway
