Read the handout on Theories of Intellectual Development and answer the following question

Read the handout on Theories of Intellectual Development and answer the following question:Give an example of how you can use each of the strategies listed in your own classroom.

THEORIES OF INTELLECTUAL DEVELOPMENT

Piaget’s Theory

We begin with the theory of the famous Swiss psychologist, Jean Piaget (Gruber & Voneche, 1995). Piaget disagreed with the behaviorist notion that children come into this world as “blank slates” who simply receive and store information about the world from other people (Driver, Asoko, Leach, Mortimer & Scott, 1994). Instead, Piaget argued that, at all ages, humans actively interact with their world, and through those interactions try to interpret and understand it in terms of what they already know. He also thought that humans change the ways in which they interact with and interpret the world as they grow older and more experienced. What is important for teachers to understand is (1) how children are likely to interact with and interpret the world at particular ages and (2) what factors lead children to move from less sophisticated to more sophisticated forms of interaction and interpretation.

In describing how children interact with and interpret the world, Piaget proposed four stages of intellectual development. He believed that these stages were universal, that is, that children everywhere, regardless of culture or experience passed through the same stages. He also believed that children progressed through the stages in an invariant order, that is, all children move from simpler, less adequate ways of thinking to increasingly more complex, sophisticated ways of thinking. Piaget did allow that some children might develop faster than others and that some might never achieve the highest stage(s) of thinking.

Piaget’s claims about stages of intellectual development have faced many criticisms, as you have no doubt read in your human development text. For example, it has been suggested that development is much more gradual and piecemeal than implied by the notion of a stage (Santrock, 2008, 2009). Nevertheless, these stages still provide a useful framework for teachers. In particular, Piaget’s stages provide clues about how students will interpret and approach many of the problems that you pose, as well as clues about the types of problems and experiences that are most likely to engage students and be beneficial for them (Elliott, Kratochwill, Littlefield & Travers, 2000; Feinburg & Mindess, 1994; Santrock, 2008).

The four stages that Piaget proposed are described briefly below. Please note that the age ranges listed are only approximations.

Sensorimotor period. This stage characterizes the thinking of children up until the age of 2 years. During this stage, infants and toddlers learn about the world by acting on it directly through motoric and sensory activities, such as sucking, grasping, and looking. In this way, they gradually learn about the physical properties of objects and develop rudimentary understanding of space, time, and causality.

Preoperational period. This stage characterizes the thinking of children between the ages of 2 and 6 years. Preoperational children try to understand the world through symbolic activities, such as pretend play, deferred imitation, drawing, and language. In contrast to the sensorimotor child, who can be characterized as a doer, the preoperational child is a thinker. Preoperational thought is immature, however, in that the child fails to approach problems in a systematic, logical way, and is often fooled by how things look to him or her.

Concrete operational period. This stage covers the period between 7 and 11. The concrete operational child has learned to approach problems in logical ways. This leads to success on such famous Piagetian tasks as conservation and classification. (See your human development text for an explanation of these tasks). The concrete operational child, however, tries to understand the world in strictly realistic, or factual, terms. This means that the world of the possible, or hypothetical, is a puzzle to him or her.

Formal operational period. Piaget believed that this final stage emerges during early adolescence, near 11 or 12. In this stage, the adolescent is not only logical, but applies his or her logic to understand the possible and hypothetical as well as the real and observable. The formal operational adolescent, for example, can generate and systematically test hypotheses about cause and effect. Although this is the final stage in Piaget’s scheme, teachers should not be misled into believing that development has ended by early adolescence. Even Piaget believed that formal thought is refined over several years, and other researchers see cognitive development as continuing even well into adulthood (Dacey & Travers, 2009; Jolley & Mitchell, 1996; Santrock, 2008, 2009).

In describing what leads children to move from one stage to the next, Piaget introduced the notion of functional invariants. By that term, he meant that the same processes operate throughout development to foster learning. He proposed two functional invariants: adaptation and organization.

Adaptation captures the idea that humans are inherently motivated to change their ways of thinking and understanding so that they become increasingly more effective in dealing with the world. Adaptation occurs through assimilation and accommodation. Assimilation is the process of interpreting or understanding a problem in terms of what one already knows or in terms of some preferred way of thinking. An infant, for example, tries to learn about new objects by sucking, grasping, banging, and looking. Those activities are what the infant knows how to do and are its means for learning. Accommodation is the process of changing one’s thought or behavior to match the unique features of a problem. An infant, for example, gradually learns that a square block cannot be sucked in the same way, or with the same effect, as a nipple. If the necessary accommodations are beyond the capabilities of the child so that the problem cannot be assimilated, the child is said to be in a state of disequilibrium, or cognitive conflict. For Piaget, cognitive conflict is what motivates “leaps” in the child’s thinking about the world. This implies that the role of the teacher is to provide experiences that create cognitive conflicts for the students (Brooks & Brooks, 2001; Driver et al., 1994; Feinburg & Mindess, 1994).

Organization, the second functional invariant captures the notion that the mind is not simply a collection of separate bits of knowledge. Instead, Piaget claimed that humans are inherently motivated to connect pieces of knowledge and mental skills to each other, thereby forming a system of thought. Consider, for example, what you know once you have classified an object you see as a “dog.” You know, of course, that it can bark, has fur, and stands on four legs. But you also know that it is an animal, a mammal, and a living thing. You also know that it is not a cat, a zebra, a chair, and so on. In other words, your concept of dog is connected to a variety of other concepts, such as animal, mammal, cat, and chair. Your concepts are organized, or connected. This notion of organization implies that the role of the teacher is to help children make connections between the knowledge and skills to be learned in the curriculum (Brooks & Brooks, 2001; Feinburg & Mindess, 1994).

Although Piaget’s characterization of the stages of cognitive development and his concept of the functional invariants are useful in the classroom, they do not provide a complete model of development or of instruction (Driver et al., 1994). And so, we turn to other models that can be used to supplement Piaget in the classroom.

Vygotsky’s Theory

Like Piaget, Lev Vygotsky (1962, 1978), the famous Russian psychologist, also focused on children’s interactions with the world to explain intellectual development. But Vygotsky disagreed with Piaget’s emphasis on the children’s interactions with the physical world, and his neglect of the role of social interaction in shaping thinking. For Vygotsky, children learn to solve problems by tackling those problems within the context of interactions with an adult, or other, more-highly skilled teacher. At first, the adult assumes primary responsibility for solving the problem, and the child’s role is minimal. During these interactions, the adult encourages, prompts, and demonstrates the behaviors to be used in solving the problem. The child gradually internalizes what he or she has experienced in these interactions. As he or she does, the adult requires the child to assume more and more responsibility, until the child eventually can solve the problem independently.

Parent-child picture book reading provides a glimpse into the instructional process Vygotsky has described (Bruner, 1992; Ninio & Bruner, 1978). At first, the parent or caregiver may do all the work in the interaction. The child’s role may be limited to pointing at particular pictures that capture his or her interest, which elicits responses from the parent like “Yes, that’s a blue bird.” Over time, the adult may expect more from the child when the book is read. Now the adult may point to the picture of the blue bird and await the child’s “bird.” The child has learned this response by internalizing the behavior modeled by the adult. Later still, the adult might wait for the child to say “blue bird” before reading on.

Vygotsky used the term scaffolding to capture the ways in which adults structure the child’s participation in this type of instructional interaction (Rogoff, 1990). The implication of the scaffolding concept for the classroom is that teachers must do more than provide their students with experiences that lead to cognitive conflict. Teachers also must interact with their students in ways that allow them to master the skills needed to resolve those conflicts, and this must involve the process of scaffolding (Collins, Brown & Newman, 1989; Driver et al., 1994; Rogoff, 1990).

In thinking about the role of teachers in promoting learning and development, it is particularly useful to turn to Vygotsky’s concept of the zone of proximal development (Vygotsky, 1962). At the lower end of the zone are the problems the child can solve independently. At the upper end, are the most complex problems that the child can solve with assistance from a teacher, be it an adult or more-highly skilled peer. The zone of proximal development, then, represents a child’s potential to benefit from instruction (Belmont, 1989). The zone has two implications for the classroom: (1) Teachers should not focus solely on what children have achieved, but on their potential for growth (Feinburg & Mindess, 1994); and (2) Teachers should focus on those problems that are in each student’s zone of proximal development, for those are the problems the student is ready to master (Elliot et al., 2000).

A final, but extremely important feature of Vygotsky’s theory is the concept of a mental tool. Vygotsky claimed that cultures create mental tools to solve their important problems. These mental tools include language (in both its spoken and written forms), mathematical systems, and scientific systems of thought (Bruner, 1992; Driver et al., 1994). Children acquire these mental tools through their interactions with adults, and other, more-highly skilled people. The implication for the classroom is that teachers must ensure that their students engage in the use of these mental tools (Collins et al., 1989; Driver et al., 1994; Rogoff, 1990).

Gardner’s Frames of Mind

Although Vygotsky criticized Piaget for neglecting children’s social interactions, others have criticized Piaget for his emphasis on stages, arguing that his stages imply that there is more uniformity in children’s thinking than there is (Berndt, 1996; Dacey & Travers, 2009; Santrock, 2008). It is not unusual, for example, to find a 7-year-old who behaves like a concrete operational child on some problems, but like a preoperational child on others. This has led some theorists to suggest that there is a separation, or independence, between how we think about and solve different types of problems (Brooks & Brooks, 2001).

One such theorist is Howard Gardner, who has proposed a theory of individual differences in intelligence (Gardner, 1993, 1989). The centerpiece of this theory is the idea of independent domains of cognitive ability, or frames of mind. In fact, Gardner proposes that there are at least seven intelligences. These are separate areas of ability in the sense that a person can do well in one area but not in others. The seven include those we typically think of when we think about “intelligence,” such as verbal (or linguistic), spatial, logical-mathematical, and musical ability. Also included, however, are less “traditional” intelligences, such as the interpersonal, intrapersonal, and the bodily-kinesthetic. (For definitions and examples, see Dacey & Travers, 2009; Santrock, 2008, 2009.)

Gardner’s theory leads to a cautionary note for teachers: expect and respect variability! Children who are doing well in one area of the curriculum may not do well in others. Instruction should be sensitive to such variability. At the same time, teachers should look for, and build on, those areas of each student’s strengths, even if those areas fall outside of what we traditionally think of as intellectual or academic (Berndt, 1996).

Sternberg’s Triarchic Theory

Like Gardner, Robert Sternberg (2007) sees intelligence not as a single ability, but as consisting of several, separate abilities. One of the distinctions that Sternberg draws in his triarchic theory is particularly relevant for the classroom; namely, the distinction between componential intelligence and contextual, or practical, intelligence. Componential intelligence includes those cognitive skills that are measured on most standardized tests of intelligence and academic achievement. Practical intelligence refers to the ability to use one’s cognitive skills to succeed at real-life tasks such as finding and keeping a job, managing one’s money, and so on.

Sternberg argues that people who do well in the area of componential intelligence may not do well in the area of practical intelligence, as in the case of someone who has “book smarts” but is not “street wise” or lacks common sense. The reverse situation is possible as well. The implication for the classroom is that instruction should be designed not only to give students the cognitive tools they need, but also to show them how to use those tools to succeed at important academic and nonacademic tasks. So, for example, instruction in writing should do more than teach the mechanics (e.g., good penmanship), it should teach students how to express their ideas through print in a creative way.

STRATEGIES FOR THE CLASSROOM

In this section, we develop further the implications for the classroom of the four theories of intellectual development we have considered. We begin by describing a hypothetical classroom so that you can see these theories in action. We then state in a more formal way the instructional strategies suggested by the theories.

Ms. Washington’s Kindergarten Classroom

Ms. Washington teaches 22 kindergartners in a public school in a rural community in the Midwest.

A glance around the room and one gets the unmistakable impression that Ms. Washington loves mathematics. Numbers are everywhere. Signs display the numbers of various objects in the room. A sign above the windows, for example, says “We have 3 windows” and a sign above the door reads simply “1 door.” On the wall above the blackboard is a banner filled with simple addition and subtraction problems, such as 1 + 1 = 2 and 2 – 1 = 1. And hung on the cage of the class pets is a sign proclaiming “1 mama + 4 babies.” There also is a math center located prominently in the front of the room. It consist of two tables that are always filled with a variety of objects to be used for math activities. This week there are measuring devices like rulers, yardsticks, and even measuring cups. Even the pretend play corner, which is set up this week as a grocery store, provides an opportunity to practice math because there is money to count and scales on which to weigh produce.

It is the start of the day and Ms. Washington begins by taking attendance. She calls each child by name and finds that two are absent. She then embarks on the following dialogue:

Ms. W.: How many kindergartners do we have?

Class: Twenty-two.

Ms. W.: Well, usually we have twenty-two. But Sarah and Isabella are absent today. So now how many do we have?

No response is forthcoming. Ms. Washington waits a few seconds before continuing.

Ms. W.: What should we do when we don’t know the answer to a number problem?

Class: Count!

Ms. Washington touches each child on the head as the class counts up to 20.

Ms. W: Twenty! Very good! Twenty-two children MINUS two who are absent leaves twenty. [The word “minus” is stressed.]

This type of exchange is very common in Ms. Washington’s class. She tries to turn many routine activities into miniature lessons in math, reading, or science. So, for example, the announcement of a student’s birthday is the occasion for polling the students as to the months of their births, and then working with the kindergartners to present the results of the poll in bar graph form on the blackboard. In fact, Ms. Washington has often been heard to remark, “Everything that happens in my class is an opportunity to teach and learn.”

A bit later in the day, Ms. Washington explains that the children are going to play a game called Measure Your Friend. She assigns the children to pairs. She does most of the pairings randomly. In one case, however, the pairing is deliberate. She pairs Rob, who has not yet learned to count beyond ten, with Angel, who is the numerical “whiz” of the class. The point of the game is to stack cubes to the height of your partner and then count the cubes to determine his or her height. Some pairs are using 3″ cubes, others 6″ cubes, and still others 12″ cubes. As the students near completion, Ms. Washington moves from pair to pair, asking questions. Here is an excerpt of the dialogue with Rob and Angel:

Ms. W.: Rob, how tall is Angel?

Rob: This tall. [points to the top of his just completed tower of cubes]

Ms. W.: But how many cubes is that? Can you count them? Start at the bottom.

Rob does fine until he gets to 11, and then things fall apart. His counting jumps to 13 and even includes the number “eleven-teen.”

Ms. W.: Angel, you and Rob count together.

Angel: Rob, you say the number after me.

Angel counts each block, with Rob repeating each number in turn. Ms. Washington then poses a new problem for the pair.

Ms. W.: If you were to measure Angel again next year when he was six, would he be bigger or smaller than he is now?

Rob: He’d be bigger.

Ms. W.: Make the tower to show me how much bigger he will be.

Rob proudly adds two blocks and is congratulated by the teacher.

Ms. W.: Good job. If something gets bigger, that means you have to ADD something. You have to count higher. You have to ADD. Great! [The teacher stresses the word “add.”]

Ms. Washington checks in occasionally on Rob and Angel, and the pairing seems to be working quite well. For example, when Rob does not know the next number in a sequence, Angel supplies it and Rob repeats it a few times as though he is trying to commit it to memory. Ms. Washington makes a mental note to pair Rob and Angel in future mathematics activities. She also decides that it would be a good idea to pair Rob and Ava for creative art projects. Rob is good at art and thus could serve as Ava’s “tutor.” Ms. Washington hopes that by showcasing Rob’s artistic side in this way, she may help him to overcome any negative feelings he has about his progress in mathematics.

After all the children have completed their cube towers in the Measure Your Friend game, Ms. Washington asks for a report on selected children’s height. It happens that Anthony, who is quite tall, was measured in 12″ cubes. The partner reports a height of four cubes. Genji, who is short, was measured in 3″ cubes, and is reported to be 14 cubes tall. Here’s what happens next:

Ms. W.: So, who’s taller?

Class: Genji!

Ms. Washington brings Genji and Anthony to the front of the room.

Ms. W.: But who looks taller?

Maria: Anthony?

Ms. W.: Right, Anthony is taller. But Genji is fourteen cubes and Anthony is only four? How could that be?

The class is obviously puzzled, and no response is forthcoming. Ms. Washington then brings the cubes used to measure the two students to the front of the room.

Ms. W.: Do you see any difference?

Class: The ones used for Anthony are bigger.

Ms. Washington then begins a discussion of how different things can be used for measuring, and that it is important to know what is being used as the measuring device. She incorporates a yardstick and one-foot ruler hanging on the wall into the discussion as well. Later, she gives the children rulers, and asks them again to measure their partner (i.e., “How many rulers tall are they?”).

Later that same day, the students in Ms. Washington’s class participate in one final math activity. Ms. Washington assigns each student a number from 1 to 20. The students rehearse their numbers and when they feel they know them, Ms. Washington yells “Ready, set, get in order.” The students’ task is to form a line from one end of the room to the other so that they are in numerical order. The room is filled with giggles and talking as the children try to scurry into line. Although the order is not perfect, the children manage a reasonable approximation. Ms. Washington congratulates them on being good mathematicians.

In our next hypothetical classroom, we consider the application of the four developmental theories in instructing older elementary school children.

Strategies

The foregoing examples illustrate several strategies for the classroom that are based on the four developmental theories that we considered.

1. Provide students concrete experiences out of which they can construct new knowledge. Recall that, according to Piaget, we construct new knowledge through our independent interactions with the world. In the classroom, this means that teachers should minimize the extent to which they give students new knowledge through, for example, lectures. Instead, teachers should allow students to make new discoveries through their own actions on, and interactions with, the world (Brooks & Brooks, 2001; Elliot et al., 2000; Feinburg & Mindess, 1994).

2. Help students connect what they need to learn to what they already know. For Piaget, each interaction with the world involves assimilation and accommodation. Put somewhat differently, learning requires more than simply taking in new information. Learning requires establishing connections and relationships between what is already known — the student’s current interpretation of the world — and the information to be learned (Brooks & Brooks, 2001). In the classroom, this means that teachers must provide experiences that are appropriate for what students know and how they learn (Brooks & Brooks, 2001; Elliott et al., 2000; Feinburg & Mindess, 1994). Again, we can find examples of this strategy in the hypothetical classroom. In Ms. Washington’s kindergarten class, for instance, math lessons involve materials and activities that the children already understand: simple subtraction problems are embedded in the daily routine of taking attendance, instruction in how to graphically represent quantities is occasioned by a child’s birthday, and the concept of a unit of measurement involves blocks, height, and friends. It is important to note that this strategy means more than letting students do only what interests them, which is a frequent but misguided criticism of Piagetian approaches to education (Feinburg & Mindess, 1994). Instead, the strategy requires providing experiences that capitalize on what students know and find interesting but that move them further along on the road of intellectual development. In other words, teachers should expose students to information and skills that students are developmentally ready to learn (Elliott et al., 2000). So, for example, Ms. Washington capitalized on her kindergartners’ interest and skill in symbolic representation and taught them ways in which numerical quantities can be represented through numbers (as in counting), graphs (as in a bar graph of the birthday poll results), and in units of measurement (as in the use of different sized cubes to represent height). She also made use of role play (i.e., when the students “pretended” to be numbers and lined up consecutively), which is a popular symbolic activity among 5-year-olds

3. Introduce cognitive conflict. Again, teachers need to provide experiences that connect with what children already know but move them along further in their development. Piagetian theory suggests that teachers can do this by creating cognitive conflict, that is, the teacher must show students that their perspective is at odds with, or fails to explain, something important about the world (Brooks & Brooks, 2001; Driver et al., 1994; Feinburg & Mindess, 1994). In Ms. Washington’s classroom, the kindergartners, for the most part, understood counting and one-to-one correspondence. For them, a higher number meant a larger quantity. Ms. Washington challenged this notion in an especially compelling way. She showed her class that a greater height actually can be associated with a smaller number if different units of measurement are applied to the objects in question.

4. Help students organize information into systematic wholes. As mentioned previously, Piaget believed that humans attempt to organize their knowledge into integrated systems rather than simply compile a collection of disconnected facts. Teachers can help their students do this by focusing the various skill domains that they want to teach on the same topic (Brooks & Brooks, 2001; Collins et al., 1989; Feinburg & Mindess, 1994; Katz & Chard, 2000).

5. Provide a scaffold for student learning. In the Vygotskyan approach, it is not enough for teachers to introduce activities and experiences that provide the opportunity for students to construct new knowledge. Teachers must interact with students in ways that help the students acquire and practice the skills needed to succeed independently (Collins et al., 1989; Driver et al., 1994; Newman, Griffin & Cole, 1989; Rogoff, 1990). Our hypothetical classroom provided many examples of this scaffolding on the part of teachers. In our kindergarten classroom, for example, Ms. Washington asked Rob how tall his partner was. The problem posed was beyond Rob’s capabilities, as evidenced by the fact that he responded merely by pointing to the tower of cubes he had constructed. Ms. Washington requested another response and, importantly, structured that request in such a way as to make explicit to Rob how he could solve the problem (i.e., “But how many cubes is that? Can you count them for me? Start at the bottom.”).

6. Ensure that students participate in interactions with a range of highly skilled partners. It is important to recognize that, according to the Vygotskyan perspective, students can benefit from interaction with any highly skilled partner, whether a formally trained teacher, a parent, or more advanced peer. In fact, it is valuable to participate with a range of different partners because each will expose the student to a different perspective on the same problem, scaffold the student’s participation in at least slightly different ways, and provide additional opportunities to practice solving the problem (Feinburg & Mindess, 1994). We saw examples of our hypothetical teachers casting both peers and parents in the role of tutor. Ms. Washington, for example, forged a partnership between Rob, who had difficulty understanding counting and one-to-one correspondence, and Angel, who had mastered the basic numerical tasks expected of kindergartners. Although Ms. Washington did not provide any formal structure or ground rules for the pair, we got the sense from the dialogue presented that Angel recognized the need for him to scaffold his interactions with Rob.

7. Involve students in the use of mental tools. Vygotsky and others (e.g., Bruner, 1992) have stressed that an important function of interaction with adults, and other more skilled members of one’s culture, is to expose the student to the important mental tools of the culture, including mathematical symbol systems, scientific modes of reasoning, and language. Again, we can find numerous examples in our hypothetical examples of teachers trying to indoctrinate their young charges into one or more of the mental tools that are important to our culture. So, for example, Ms. Washington introduced her kindergartners to the concepts of addition and subtraction of numerical quantities and of their measurements. In fact, numbers and mathematical symbols pervaded the physical environment of Ms. Washington’s classroom.

8. Address variability between and within students. There are two forms of variability that are of relevance to teachers. In the first, between-student variability, there is variability between students, such that some students demonstrate a more advanced level of thinking, or a different approach to a problem, than other students. In the classroom, this means that teachers should match the problems and experiences they provide to each student’s current level of knowledge and way of thinking (Brooks & Brooks, 2001; Feinburg & Mindess, 1994). Without such matching, of course, strategies 2, 3, and 5 cannot be implemented. It might be argued that while this strategy sounds good on paper, it is not workable — teachers simply cannot plan a separate curriculum for each and every student. In fact, this strategy does not always require different problems or experiences for different students. Instead, the teacher might consider posing problems that allow for different problem-solving approaches and thus, provide different benefits for students. Teachers also can address variability between students by recruiting peer tutors to help their less advanced classmates, as Ms. Washington did when she paired Rob and Angel in the math activities.

In the second form of variability facing teachers, within-student variability, an individual student’s thinking is uneven, or characterized by areas of strength and weakness. This form of variability is at the heart of theories such as Gardner’s (1993), which argue that thought arises out of several independent faculties, or frames of mind. In the classroom, this means carefully monitoring each student’s performance in all academic areas and being prepared to offer him or her dramatically different experiences to induce cognitive conflict or varying degrees of scaffolding across different academic areas. In fact, we saw this strategy at work in the kindergarten example. Ms. Washington was careful to pair Rob with a more skilled peer who could serve as a tutor on problems related to mathematics. At the same time, however, she paired Bob with Sarah when it came to projects in the creative arts, where Bob excelled and could serve as Sarah’s tutor.

Before ending our discussion of this strategy, it is worth noting that the source of at least some of the variability between and within students is culture. Different cultures provide children with different experiences and send them to school with different types of preparations and sets of expectations (see, e.g., Hale-Benson, 1986; Heath, 1989; Shade, 1987; Shade & New, 1993). Matching experiences and scaffolding to all students requires that teachers are knowledgeable about their students’ backgrounds

9. Show students how to use their new knowledge and skills. This strategy follows from Sternberg’s (2007) distinction between practical intelligence and componential intelligence. In the classroom, this means that the skills to be learned should be taught in meaningful contexts and, moreover, these contexts should be those in which the skills are ultimately to be used. Obvious for their absence from our hypothetical classrooms, are the sorts of drills that provide repetitive practice on various components of a meaningful activity but with that meaning removed. So, for example, our hypothetical teachers did not teach reading by providing students worksheets in which they underlined all the words that began with the letter “c” or that sounded the same. And in Ms. Washington’s classroom, the kindergartners did not simply repeat the numbers for 1 to 20; instead, they counted for a reason, such as measuring their friend’s height. Embedding the skills and knowledge to be learned into meaningful activities demonstrates to students not only how to apply this information, but why applying it is useful.

SUMMARY

In this chapter, we began with the premise that learning involves interaction with the world. In Piaget’s theory, the emphasis is on interaction with the physical world. Piaget believed that the nature of those interactions change with age and experience, with the biggest changes being prompted by conflicts between what is known and problems encountered in the world. In Vygotsky’s theory, the emphasis is on social interaction. According to Vygotsky, skilled adults structure their interactions with young learners so that the latter gradually acquire the skills, symbol systems, and modes of reasoning needed to solve the problems that face their culture. The theories of Gardner and Sternberg added the notions that thinking can be variable across different problems areas, such as art and language, and across different situations, such as doing well on tests of abstract knowledge but doing poorly in real life situations.