Learning is rapid. Some children, by age 11, beat their elders at chess, play music that adults pay to hear, publish poems, or solve complex math problems. Others survive on the streets or fight in civil wars. Children can learn almost anything. Adults must decide how and what to teach.

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Piaget called cognition during these years concrete operational thought, characterized by new concepts that enable children to be logical. Operational comes from the Latin word operare, meaning “to work; to produce.” By calling this period operational, Piaget emphasized productive thinking.

The school-age child, no longer limited by egocentrism, performs logical operations on concrete experiences and problems, those that are grounded in actual experience, like the concrete of a cement sidewalk. Concrete thinking arises from what is visible, tangible, and real, not abstract and theoretical (as at the next stage, formal operational thought). Children become more systematic, objective, scientific—-and educable.

ADVANCES IN LOGIC One logical operation is classification, organizing things into groups (or categories or classes) according to some characteristic. For example, family includes parents, siblings, and cousins. Other common classes are animals, toys, and food. Each class includes some elements and excludes others; each is part of a hierarchy.

Food, for instance, is an overarching category, with the next-lower level of the hierarchy being meat, grains, fruits, and so on. Most subclasses can be further divided: Meat includes poultry, beef, and pork, each of which can be divided again. The mental operation of moving up and down the hierarchy (understanding that bacon is always pork, meat, and food, but most food, meat, and pork are not bacon) is beyond preoperational children.

Piaget devised many classification experiments. For example, a child is shown a bunch of nine flowers—seven yellow daisies and two white roses. Then the child is asked, “Are there more daisies or more flowers?”

Until about age 7, most children answer, “More daisies.” The youngest children offer no justification, but some 6-year-olds explain that “there are more yellow ones than white ones” or “because daisies are daisies, they aren’t flowers” (Piaget et al., 2001). By age 8, most children can classify: “More flowers than daisies,” they say.

In addition to classification, two other logical concepts (i.e., conservation and reversibility) were mentioned in Chapter 5. Piaget described a fourth concept, seriation, the realization that things can be arranged in a logical series. Seriation is crucial for using (not merely memorizing) the alphabet or the number sequence.

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By age 5, most children can count up to 100. However, because they do not yet grasp seriation, they may be unable to estimate where any particular two-digit number would be placed on a line that starts at 0 and ends at 100. In many other ways, the advancing logic of the concrete operational child helps with arithmetic—that 12 + 3 = 3 + 12 and that 15 is always 15 (conservation), that all the numbers from 20 to 29 are in the 20s (classification), that 134 is less than 143 (seriation), and that if 5 × 3 = 15, then 15 ÷ 5 is 3 (reversibility).

BRAIN CONNECTIONS Brain scans were not available to Piaget, but it is easy to see that his understanding of logic was prescient, reflecting what we now know as brain maturation. As children grow older, connections form between the various lobes and regions of the brain. Such connections are crucial for the complex tasks that children must master, which require “smooth coordination of large numbers of neurons” (P. Stern, 2013, p. 577).

Certain areas of the brain, called hubs, are locations where massive numbers of axons meet. Hubs tend to be near the corpus callosum, and damage to them correlates with brain dysfunction, as in dementia (now called neurocognitive disorders) and schizophrenia (Crossley et al., 2014).

Particularly important are links between the hypothalamus and the amygdala, because emotions need to be regulated so that learning can occur. Stress impairs these connections: Slow academic mastery is one more consequence of early maltreatment (Hanson et al., 2015).

On the other hand, the development of many logical concepts, including classification as Piaget described it, depends on neurological pathways from the general (food) to the particular (bacon) and back again. Those paths are not forged until brain maturation allows connective links in the hubs.

One example of the need for brain connections is learning to read, perhaps the most important intellectual accomplishment of middle childhood. Reading is not instinctual: Our ancestors never did it, and until recent centuries, only a few scribes and scholars could make sense of marks on paper. Consequently, the brain has no areas dedicated to reading, the way it does for talking or gesturing (Sousa, 2014).

Instead, reading uses many parts of the brain—one for sounds, another for recognizing letters, another for sequencing, another for comprehension and more. By working together, these parts foster listening, talking, and thinking, and then put it all together (Lewandowski & Lovett, 2014).

Indeed, every skill, every logical idea, every thought suddenly applied from one circumstance to another requires connections between many neurons. As Piaget recognized, a cascade of new intellectual concepts results when connections allow a logical idea to be applied to many specifics.

Like Piaget, Vygotsky felt that educators should consider children’s thought processes, not just the outcomes. He appreciated children as curious, creative learners. He wrote that rote memorization rendered the child “helpless in the face of any sensible attempt to apply any of this acquired knowledge” (Vygotsky, 1994a, pp. 356–357).

THE ROLE OF INSTRUCTION Unlike Piaget, Vygotsky stressed teaching. He thought that learners need a bridge between developmental potential and necessary skills via guided participation and scaffolding, within the zone of proximal development (all concepts already explained).

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Confirmation of the role of instruction comes from a U.S. study of children who, because of their school’s entry-date cutoff, are either relatively old kindergartners or quite young first-graders. At the end of the school year, achievement scores of the 6-year-old first-graders far exceeded those of kindergarten 6-year-olds who were only one month younger (Lincove & Painter, 2006).

Internationally as well, children who begin school earlier tend to be ahead in academic achievement compared to those who enter later, an effect still evident when the children were in high school. But we shouldn’t be too quick to decide that early schooling is necessary. As the author of this study noted, there are many possible explanations, and early schooling did not advance later learning in every nation (Sprietsma, 2010).

Remember that Vygotsky believed that education occurs everywhere, not just at school. He would not be surprised that fifth-grade children from ten U.S. cities who scored high on tests of math and reading had had extensive cognitive stimulation long before fifth grade from three crucial sources:

In this study, most children from families of low SES did not experience all three sources of stimulation, but those who did showed more cognitive advances by fifth grade than the average high-SES child (Crosnoe et al., 2010).

Perhaps the most important role of teachers is to help children focus. Selective attention, the ability to concentrate on some stimuli while ignoring others, improves markedly at about age 7. For example, many new readers confuse the letters b, d, and p—which are actually all the same, a small circle connected to a line. An astute mentor is needed to call the child’s attention to the placement of that line.

Similar crucial distinctions are present in every script, not just Roman ones—and are confusing to young children and to everyone not guided in that script. (That is why Web sites require decoding of wavy letters and numbers in order to prove that a human, not a robot, wants to access certain information: Humans have learned what to attend to and what to ignore, and it is difficult to program a machine to do so.)

School-age children not only notice various stimuli (one form of attention) but also select appropriate responses when several possibilities conflict (Wendelken et al., 2011). Selective attention improves with guidance and neurological maturation (Stevens & Bavelier, 2012).

For example, children in school listen, take notes, and ignore distractions (all difficult at age 6, easier by age 10). Ignoring the din of the cafeteria, children react quickly to gestures and facial expressions. On the baseball diamond, mentors (coaches and teammates) teach batters to ignore attempts to distract them and teach fielders to move into position as soon as the bat hits the ball. That’s selective attention, guided by culture and the brain, as the prefrontal cortex continues to mature.

INTERNATIONAL CONTEXTS Vygotsky’s emphasis on sociocultural contexts contrasts with Piaget’s maturational, self-discovery approach. Vygotsky believed that cultures educate via customs, structures, objects, and mentors. For example, if a child is surrounded by full bookcases, daily newspapers, street signs, and reading adults, that child will read better than a child who has had little exposure to print, even if both are equally bright and in the same class.

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Context affects more than academic learning. A stunning example of knowledge acquired from the social context comes from Varanasi, a city in northeast India. Many Varanasi children have an extraordinary sense of spatial orientation. In one experiment, children were blindfolded, spun around, and led to a second room, yet many still knew which direction was north (Mishra et al., 2009). How did they know? Consider social context.

In Varanasi, everyone refers to direction to locate objects. The English equivalent might be that the dog is sleeping not by the door but southeast. From their early days, children learn north/south/east/west. By middle childhood, they have internalized a sense of direction.

Many studies in the United States validate that the social context shapes what and how children learn. The process is reciprocal: Children are eager to learn, and that drives them to learn in whichever manner their culture presents.

For example, children who are used to learning by observation (as in some American Indian cultures) are better at remembering overheard folktales than children who expect direct instruction (Tsethlikai & Rogoff, 2013). Again, Vygotsky would not be surprised.

Educators and psychologists regard both Piaget and Vygotsky as insightful. International research confirms the merits of their theories.

A third approach to understanding cognition adds crucial insight. The information-processing perspective benefits from technology that allows much more detailed data and analysis than was possible for Piaget or Vygotsky.

Thousands of researchers who study cognition benefit from the information-processing approach, although “information processing is not a single theory but, rather, a framework characterizing a large number of research programs” (Miller, 2011, p. 266). The basic assumption of this framework is that, like computers, people can access large amounts of information. They then:

(1) Select relevant units of information (as a search engine does),

(2) Analyze and connect (as software programs do), and

(3) Express their conclusions so that another person can understand (as a networked computer or a printout might do).

By tracing the paths and links of these neurological functions, scientists track learning. The brain’s gradual growth, increasingly seen in detailed scans, confirms the usefulness of the information-processing perspective. So do data on children’s school achievement: Absences, vacations, new schools, and even new teachers may set back a child’s learning because repeated experiences are needed to solidify brain connections.

LEARNING MATH One of the leaders of the information-processing perspective is Robert Siegler, who has studied the details of children’s cognition in math (Siegler & Chen, 2008; Siegler & Lortie-Forgues, 2014). Apparently, children do not suddenly grasp the logic of the number system, as Piaget seemed to expect.

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Instead, math knowledge accrues gradually. New and better strategies for calculation are tried, ignored, half-used, abandoned, and finally adopted. Siegler compared the acquisition of knowledge to waves on an ocean beach when the tide is rising. There is substantial ebb and flow, although eventually a new level is reached.

One example is the ability to estimate where a number might fall on a line, such as where the number 53 would be placed on a line from 0 to 100. This skill gradually builds from the first grade on, predicting later math skills (Feigenson et al., 2013). Understanding the size of fractions (e.g., that is smaller than ¼) may also be crucial, as this predicts later math achievement in many nations (Torbeyns et al., 2015). Some other early math achievements (such as counting to 100) do not correlate with math achievement, an interesting finding from information-processing research.

MEMORY Many scientists who study memory take an information-processing approach. Each of the three major steps in the memory process—sensory memory, working memory, and long-term memory—is affected by both maturation and experience.

Sensory memory (also called the sensory register) is the first component of the human information-processing system. It stores incoming stimuli for a split second, with sounds retained slightly longer than sights. To use terms explained in Chapter 3, sensations are retained for a moment, and then some become perceptions.

Once some sensations become perceptions, the brain selects the meaningful ones and transfers them to working memory for further analysis. It is in working memory (formerly called short-term memory) that current, conscious mental activity occurs.

Processing, not mere exposure, gets information into working memory. As Siegler’s waves metaphor suggests, strategies for processing information do not appear suddenly. Children gradually develop ways to increase working memory (Camos & Barrouillet, 2011). For this reason, working memory improves markedly in middle childhood (Cowan & Alloway, 2009) (see Table 7.1).

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Cultural differences are evident. For example, many Muslim children are taught to memorize all 80,000 words of the Quran, so they learn strategies unknown to non-Muslim children to remember long passages (Hein et al., 2014).

Finally, information from working memory may be transferred to long-term memory, to be stored for minutes, hours, days, months, or years. The capacity of long-term memory—how much can be crammed into one brain—is huge by the end of middle childhood. Together with sensory memory and working memory, long-term memory organizes ideas and reactions, fostering more effective learning (Wendelken et al., 2011).

Crucial to long-term memory is not merely storage (depositing material into the brain) but also retrieval (bringing past learning into working memory). Retrieval is easier for some memories (especially vivid, emotional ones) than for others, but for everyone, long-term memory is imperfect. We all forget and distort memories.

Memory depends on review and repetition, with the learner engaged in practice that involves thought (not mindless review) (Brown et al., 2014). Memories fade unless the information is processed. Children might memorize 3 × 9 = 27, but without processing, they might not know how many Valentine’s Day candies to buy to give three to each of their nine friends.

THE MORE YOU KNOW . . . Research on information processing finds that the more people know, the more they can learn. Having an extensive knowledge base, or a broad body of knowledge, makes it easier to remember and understand related new information.

Three factors affect the knowledge base: past experience, current opportunity, and personal motivation. The last item in this list explains why children’s knowledge base is not what their parents or teachers would choose. Some schoolchildren memorize words and rhythms of hit songs, know plots and characters of television programs, or recite the names and histories of basketball players. Yet they do not know whether World War I was in the nineteenth or twentieth century or whether Pakistan is in Asia or Africa.

CONTROL PROCESSES Memory, processing speed, and the knowledge base come together via control processes, which regulate analysis and flow of information. Control processes are related to metacognition, which is an understanding of one’s own learning. The better a person is at metacognition, the more efficient their control processes become.

According to scholars of cognition, “Middle childhood may be crucial for the development of metacognitive monitoring and study control processes” (Metcalfe & Finn, 2013, p. 19). Metacognition can be considered the ultimate control process because a person can evaluate a learning goal, decide how to accomplish it, monitor performance, and finally adjust effort to make sure it is accomplished.

Control processes require the brain to organize, prioritize, and direct mental operations, much as the CEO (chief executive officer) of a business organizes, prioritizes, and directs business operations. For that reason, control processes are also called executive processes, and the ability to use them is called executive function (already mentioned in Chapter 5).

Executive function improves each year of middle childhood (Masten, 2014; Bjorklund et al., 2009). For example, unlike first-graders, fourth-grade students can listen to the teacher talk about the river Nile, ignoring classmates who are chewing gum or passing notes.

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Older children can decide to do their homework before watching television or to review their spelling words before breakfast, creating mnemonics to remember the tricky parts. They can anticipate what teachers will ask. All these signify executive function.

Recall that emotional regulation, theory of mind, and left–right coordination emerge in early childhood, the outcome of brain maturation. The developing corpus callosum connects the hemispheres, enabling balance and two-handed coordination, while myelination adds speed.

Maturation of the prefrontal cortex—the executive part of the brain—-allows better control processes, evident in all three theories—Piaget, Vygotsky, and information-processing. We now describe two additional advances.

THINK QUICK; TOO SLOW Advance planning and impulse control are aided by faster reaction time, which is how long it takes to respond to a stimulus. Increasing myelination reduces reaction time every year from birth until about age 16. Skill at games is an obvious example, from scoring on a video game, to swinging at a pitch, to kicking a speeding soccer ball toward a teammate.

Many more complex examples involve social and academic skills. For instance, being able to calculate when to utter a witty remark and when to stay quiet is something few 6-year-olds can do. By age 10, some children have quick reactions, allowing them to (1) realize that a comment could be made and (2) decide what it could be, (3) imagine someone else’s response, and in the same split second (4) know when something should not be said.

Both quick responses and quick inhibition develop. Children become less likely to blurt out wrong answers but more likely to enjoy games that require speed. Interestingly, children with reading problems are slower as well as more variable in reaction time, and that itself slows down every aspect of reading (Tamm et al., 2014).

AUTOMATIC PROCESSING One final advance in brain function in middle childhood is automatization, when a sequence of thoughts and actions is repeated so often that it seems to be automatic. Firing one neuron sets off a chain reaction, just as saying a few words brings to mind an entire phrase.

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Consider again learning to read. At first, eyes (sometimes aided by a guiding finger) focus intensely, painstakingly making out letters and sounding out each one. This slowly leads to the perception of syllables and then words. Eventually, the process becomes so routine that people driving along a highway read billboards that they have no interest in reading. Children do the same, gradually learning to read without conscious control.

Automatic reading aids other academic skills. One longitudinal study of second-graders—from the beginning to the end of the school year—found a reciprocal interaction from one type of academic proficiency to another, with automatic processing advancing as learning continued (Lai et al., 2014). Learning to speak a second language, to recite the multiplication tables, and even to write one’s name gradually becomes automatic.