solution

All new learning requires a foundation of prior knowledge. You need to know how to land a twin engine plane on two you can learn to land it on one. To learn trigo- engines before nometry, you need to remember your algebra and geometry. To learn cabinetmaking, you need to have mastered the proper- ties of wood and composite materials, how to join boards, cut rabbets, rout edges, and miter corners. In a cartoon by the Far Side cartoonist Gary Larson, a bug- eyed school kid asks his teacher , “Mr. Osborne, can I be ex- cused? My brain is full!” If you’re just engaging in mechanical repetition, it’s true, you quickly hit the limit of what you can keep in mind. However, if you practice elaboration, there’s no known limit to how much you can learn. Elaboration is the process of giving new material meaning by expressing it in your own words and connecting it with what you already know. The more you can explain about the way your new learning relates to your prior knowledge, the stronger your grasp of the new learning will be, and the more connections you create that will help you remember it later. Warm air can hold more moisture than cold air; to know that this is true in your own experience, you can think of the drip of water from the back of an air conditioner or the way a stifling summer day turns cooler out the back side of a sudden thunderstorm. Evaporation has a cooling effect: you know this because a humid day at your uncle’s in Atlanta feels hotter than a dry one at your cousin’s in Phoenix, where your sweat disap- pears even before your skin feels damp. When you study the principles of heat transfer, you understand conduction from warming your hands around a hot cup of cocoa; radiation from the way the sun pools in the den on a wintry day.com vection from the life-saving blast of A/C as your uncle squires you slowly through his favorite back alley haunts of Atlanta, Putting new knowledge into a larger context helps learn you know, the more of it you can learn. And the more ways ing. For example, the more of the unfolding story of history you give that story meaning, say by connecting it to your un- derstanding of human ambition and the untidiness of fate, the better the story stays with you. Likewise, if you’re trying to learn an abstraction, like the principle of angular momentum, it’s easier when you ground it in something concrete that you already know, like the way a figure skater’s rotation speeds up as she draws her arms to her chest. People who learn to extract the key ideas from new mate- rial and organize them into a mental model and connect that model to prior knowledge show an advantage in learning com- plex mastery. A mental model is a mental representation of some external reality. Think of a baseball batter waiting for a pitch. He has less than an instant to decipher whether it’s a curveball, a changeup, or something else. How does he do it? There are a few subtle signals that help: the way the pitcher winds up, , he throws, the spin of the ball’s seams. A great batter winnows out all the extraneous perceptual dis- tractions, seeing only these variations in pitches, and through practice he forms distinct mental models based on a different set of cues for each kind of pitch. He connects these models to what he knows about batting stance, strike zone, and swing- ing so as to stay on top of the ball. These he connects to men- tal models of player positions: if he’s got guys on first and the way second, maybe he’ll sacrifice to move the runners ahead. If he’s got men on first and third and there is one out, he’s got to keep from hitting into a double play while still hitting to score the runner. His mental models of player positions connect to his models of the opposition (are they playing deep or shal- low?) and to the signals flying around from the dugout to the base coaches to him. In a great at-bat, all these pieces come together seamlessly: the batter connects with the ball and drives it through a hole in the outfield, buying the time to get on first and advance his men. Because he has culled out all but the most important elements for identifying and responding to each kind of pitch, constructed mental models out of that learning, and connected those models to his mastery of the other essential elements of this complex game, an expert player has a better chance of scoring runs than a less experienced one who cannot make sense of the vast and changeable infor- mation he faces every time he steps up to the plate. Many people believe that their intellectual ability is hard- wired from birth, and that failure to meet a learning challenge is an indictment of their native ability. But every time you learn something new, you change the brain-the residue of your experiences is stored. It’s true that we start life with the gift of our genes, but it’s also true that we become capable through the learning and development of mental models that enable us to reason, solve, and create. In other words, the elements that shape your intellectual abilities lie to a surprising extent within your own control. Understanding that this is so en- ables you to see failure as a badge of effort and a source of useful information-the need to dig deeper or to try a differ- ent strategy. The need to understand that when learning is hard, you’re doing important work. To understand that striv- ing and setbacks, as in any action video game or new BMX bike stunt, are essential if you are to surpass your current level of performance toward true expertise. Making mistakes and correcting them builds the bridges to advanced learning.