Learning occurs when learners assimilate information through existing structures and then modify these structures in reaction to the new information. These processes occur within the brain of the learner: teachers cannot assimilate or accommodate for their students. What teachers can (and must) do is (1) become aware of the conceptions that learners initially possess about a given concept and help the students activate these structures, (2) expose students to tasks that contain information which is optimally different from the existing structures and that the students can assimilate through these structures, (3) supply some guidance regarding what accommodations would be appropriate, and (4) give feedback to help the learners determine the degree to which they are satisfied with their new structures. Since learning consists of changing conceptions, then good teaching consists of discovering students' conceptions and helping them to change these conceptions in productive ways (Ramsden, 1988). According to constructivist theory, probably the single most common mistake that teachers make is to fail to understand the conceptions that students bring to learning situations.
The constructivist insight has tremendously important implications for teaching. For example, it is more important to know why a student gave a correct or incorrect answer to a problem than to know how many answers the student got right; and yet this information is almost never available from standardized tests and is rarely obtained by classroom teachers. To get this kind of information, teachers need to take a diagnostic stance, focusing on the student's process of learning. If teachers do not take this stance, then there are only two possible outcomes: (1) the students themselves must realize and correct their own process errors, or (2) the students are likely to build future learning upon the weak foundation of misconceptions and faulty processes. From an instructional perspective, therefore, it is often more useful for a teacher to understand the inappropriate model that a student has employed to make mistakes than it is to be aware of the errors the student makes (Pines & West, 1986).
The importance of developmental principles can perhaps most easily be seen when we examine instances in which educators ignore these principles. Here are some examples:
Mathematics: Children in very early grades are often taught that subtraction is simply the opposite of addition. "Eight minus five equals three" is simply the reversal of "three plus five equals eight." This concept makes perfect sense to early concrete operational children, but it may make no sense whatsoever to later preoperational children. Thus, these two problems may represent identical operations to concrete operational children:
8 - 5 = __
8 + __ = 5
A child who can perform mental operations (reversals) would benefit from examining the second equation and relating it to the first. However, children who cannot perform mental operations would be confused by the second equation. Requiring them to relate it to the first would be an unnecessary burden. Preoperational children faced with the second equation typically do not do the reversal at all. They instead follow a rote algorithm of converting the second equation to the first and then giving the memorized answer. In fact, they are performing an additional task that does not even focus on the task at hand. It would be better to let them learn addition and subtraction as distinct activities, and let them examine the reversal at an age when they can easily understand the relationship. In addition, it can be argued that almost all of the "bugs" that tend to appear in children's computational procedures (VanLehn, 1990) arise because children simply memorize and misapply algorithms instead of understanding the processes. A more appropriate understanding would occur if children studied these processes in a more appropriate Piagetian manner (Kamii, 1985).
Science: My son's fourth grade science textbook told children that we get energy from the sun. That's already a pretty tough concept for concrete operational learners to grasp. The book then went on to tell children even more about sunlight. It clearly stated that sunlight behaves sometimes like a particle and sometimes like a ray. Albert Einstein may have been able to picture that statement, but not when he was concrete operational! My other son's tenth grade chemistry book includes a careful discussion of oxidation numbers. The presentation is comprehensible to fully formal operational students, but how many tenth graders fit that description? (See Table 4.6 for an answer to that question.) The irony is that although most science textbooks abound with concepts that are too abstract for their intended audiences, absolutely all major science organizations and nearly all science educators vehemently preach against such nonsense. They adopt a largely Piagetian stance: give concrete operational children a sound basis in concrete experience, so that they can later integrate these experiences into more abstract understandings and applications. Research even indicates that if we delay the initial discussion of certain abstract concepts (like oxidation numbers and their derivation) until learners are formal operational, they eventually learn these concepts as thoroughly as other learners who study them once when they are concrete operational and a second time when they become formal operational (citation, 19xx).
Discipline: Teachers and parents sometimes develop effective discipline strategies that lead to appropriate behavior among young children. These techniques work so well, however, that the teachers or parents continue to use these techniques long past the time when the children have developed the appropriate cognitive structures to deal with their behavior problems in a more mature way. With self-discipline, as with any other type of learning, it is important to take into consideration the existing structures and the level of thinking of which the child is capable.
Behavior Modification: As cognitive structures and levels of thinking change, learners will revise what they consider to be pleasant or unpleasant situations. Many educators make the mistake of over-generalizing what they think they know about consequences that will reinforce or punish the learners they deal with.
Motivation: An important aspect of modern motivation theory is that learners devise attributions for pleasant and unpleasant consequences that follow their behavior. (See the discussion of attribution theory in Chapter 5.) What learners assimilate and accommodate from their environment influences their attributions, and hence their motivation. For example, a child who possesses a cognitive structure of himself as "bad at arithmetic" may assimilate a simple high grade on a paper as an indication of luck. On the other hand, if the grade were accompanied by feedback specifically tailored to that child, this may lead to an accommodation that may revise this negative cognitive structure and lead to higher levels of motivation.
Early education: Writers like David Elkind (1981) have suggested that many parents and educators are mistakenly taking childhood away from children. They are removing play from preschool and early education experiences and emphasizing academic topics instead. While this pressure toward academic achievement may initially sound beneficial, it could actually backfire - not only by causing emotional stress (as many people suspect) but also by making it less likely that young children will lay the proper foundation of cognitive structures for subsequent academic growth. In other words, the active involvement inherent in play enables children to assimilate numerous objects, ideas, and activities into their existing structures and to make appropriate accommodations to form new schemata. Reducing opportunities for play may result in either very few cognitive structures available for future use or very superficial structures that have been applied to very few concrete examples.
While Piaget's impact cannot be denied, it is also true that reputable scholars disagree with aspects of his theory. In his own later writings, Piaget himself modified and expanded on his theories. In the restricted space of the present book, it is impossible to deal with all these refinements. The aspects of Piaget's theory presented in this chapter should provide a solid base for understanding Piaget's theories and other constructivist theories of human learning and development.
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