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An Information Processing View of Learning and Cognition
How does the human mind work? What happens when someone learns or when someone solves a problem? According to the information processing view, the human mind works by forming mental representations and applying cognitive processes to them. This definition has two elements: (a) The content of cognition is mental representations, and (b) the activity of cognition involves cognitive processes. In learning, the learner takes incoming information received through the eyes or ears and applies a series of cognitive processes to the incoming information, resulting in the construction of a series of mental representations. For example, as you read the words in this paragraph you form a series of mental representations by applying appropriate cognitive processes such as mentally selecting important ideas, mentally organizing them into a coherent cognitive structure, and mentally relating them with prior knowledge. In this research paper I provide a brief historical overview of the precursors to the information processing view of learning and cognition, describe two versions of the information processing view, examine three major contributions of the information processing view, and then exemplify how it contributes to theories of learning and cognition.
For more than 100 years psychologists have conducted research aimed at understanding how knowledge is represented and processed in human minds. Such issues fell under the domain of science as psychology entered the twentieth century, heralded by the publication of Ebbinghaus’s pioneering memory studies in 1885 (Ebbinghaus, 1964) and Thorndike’s pioneering learning studies in 1898 (Thorndike, 1965). During the first half of the twentieth century two competing views of learning emerged—the associationist view of learning as strengthening of associations and the Gestalt view of learning as building cognitive structures.
According to the associationist view, the content of cognition consists of nodes and associations between them and the process of cognition consists of the strengthening and weakening of associations. For example, in Thorndike’s (1965) classic study of animal learning, a hungry cat was placed in a wooden box. The cat could escape by pulling a hanging loop of string that opened a door allowing the cat to get out and eat some nearby food. Thorndike noted that on the first day, the cat engaged in many extraneous behaviors before accidentally pulling the string, but on successive days the number of extraneous behaviors decreased. After many days, the cat pulled the loop of string shortly after being placed in the box. According to Thorndike, the cat began with a habit family hierarchy—an ordered set of responses associated with being placed in an enclosed box.The cat would try the most strongly associated response first (e.g., thrusting its paw through the slats of the box), and when it failed, the strength of the association to that response would be weakened. Eventually, the cat would pull the loop of string and get out, thus increasing the association to that response. Over many days, the extraneous responses became very weakly associated with being in the box, and pulling the string became very strongly associated with being in the box. Thus, Thorndike offered a clear vision of learning as the strengthening and weakening of stimulusresponse (S-R) associations and memory as the processing of linked nodes in a network—a vision that dominated psychology through the 1950s and still flourishes today in revised form.
According to the Gestalt view, the content of cognition consists of coherent structures, and the process of cognition consists of building them. For example, Kohler (1925) placed an ape in a pen with crates on the ground and a bunch of bananas hanging overhead out of reach. Kohler observed that the ape looked around and then suddenly placed the crates on top of one another to form a ladder leading to the bananas, allowing the ape to climb the stairs and grasp the bananas. According to Kohler, the ape learned by insight—mentally reorganizing the objects in the situation so they fit together in a way that accomplished the goal. Thus, insight is a process of structure building (Mayer, 1995). The Gestalt approach rose to prominence in the 1930s and 1940s but is rarely mentioned today.Nonetheless,theGestaltthemeofcognitionasstructure building underlies core topics in cognitive science including the idea of schemas, analogical reasoning, and meaningful learning.
By the 1950s and 1960s, the associationist and Gestalt views were reshaped into a new view of cognition, called information processing (Lachman, Lachman, & Butterfield, 1979). The information processing view eventually became the centerpiece of cognitive science—the interdisciplinary study of cognition. A core premise in cognitive science is that cognition involves computation; that is, cognition occurs when you begin with a representation as input, apply a process, and create a representation as output. For example, in a review of the field of cognitive science, Johnson-Laird (1988, p. 9) noted, “Cognitive science, sometime explicitly and sometimes implicitly, tries to elucidate the workings of the mind by treating them as computations.” Human cognition on any task can be described as a series of cognitive processes (i.e., a description of the computations that were carried out) or as a series of transformations of mental representations (i.e., a description of the inputs and outputs for each computation).
Two Views of Information Processing Theory
A central problem of the information processing approach is to clarify the nature of mental representations and the nature of cognitive processes. This task is made more difficult by the fact that researchers cannot directly observe the mental representations and cognitive processes of other people. Rather, researchers must devise methods that allow them to infer the mental representations and cognitive processes of others based on their behavior (including physiological responses). In the evolution of the information processing approach to learning and memory, there have been two contrasting versions: the classical and constructivist view (Mayer, 1992a, 1996a).
Leary (1990) showed how progress in psychological theories can be described as a progression of metaphors, and Mayer (1992a, 2001) described several major metaphors of learning and memory that have emerged during the last century, including viewing knowledge as information versus viewing knowledge as cognitive structure. A major challenge of the information processing view—and the field of cognitive science that it serves—is to clarify the status of the knowledge as information metaphor (which is part of the classical view) and the knowledge as cognitive structure metaphor (which is part of the constructivist view).
The classic view is based on a human-machine metaphor in which the human mind is like a computer; knowledge is represented as data that can be processed by a computer, and cognition is represented as a program that specifies how data are processed. According to the classical view, humans are processors of information. Information is a commodity that can be transferred from one mind to another as a series of symbols. Processing involves applying an algorithm to information such that a series of symbols is manipulated according to a step-by-step procedure. For example, when given a problem such as “x + 2 = 4, solve for x,” a learner forms a mental representation of the problem such as “x + 2 = 4” and applies operators such as mentally subtracting 2 to both sides in order to generate a new mental representation, namely “x = 2.”
The classical information processing approach developed in the 1950s, 1960s, and 1970s, although its roots predate psychology (Lachman et al., 1979). For example, more than 250 years ago De La Mettrie (1748/1912) explored the idea that the human mind works like a complex machine, and the classical information processing view can be seen inAtkinson and Shiffrin’s (1968) theory of the human memory system and Newell and Simon’s (1972) theory of human problem solving.
For example, Newell and Simon (1972) developed a computer simulation designed to solve a variety of problems ranging from chess to logic to cryptarithmetic. In the problem-solving program, information consists of “symbol structures” (p. 23) such as a list, tree, or network, and processing consists of “executing sequences of elementary information process” (p. 30) on symbol structures. A problem is represented as a problem space consisting of the initial state, the goal state, and all possible intervening states with links among them. The process of searching the space is accomplished by a problem-solving strategy called means-ends analysis, in which the problem solver sets a goal and carries it out if possible or determines an obstacle that must be overcome if it is not (see Mayer, 1992b). Thus, problem solving involves applying processes to a symbolic representation of a problem: If the application is successful, the representation is changed; if it is not successful, a new process is selected based on a means-ends analysis strategy. In a complex problem, a long series of information processes may be applied, and many successive representations of the problem state may be created.
Two limitations of the classical view—humans as information processors—concern the characterization of information as an objective commodity and the characterization of processing as the application of algorithms. Although such characterizations may mesh well with highly contrived laboratory tasks, they appear too limited to account for the full range of human learning in complex real-world situations. For example, Metcalfe (1986a, 1986b; Metcalfe & Wiebe, 1987) showed that people use different cognitive processing for insight problems (requiring a major reorganization of the problem) and noninsight problems (requiring the step-by-step application of a series of cognitive processes). For insight problems people are not able to predict how close they are to solving the problem (inconsistent with the step-by-step thinking posited by the classical view), but for noninsight problems they are able to gage how close they are to solution (consistent with the step-by-step thinking posited by the classical view). Apparently, the classical view may offer a reasonable account of how people think about noninsight problems but not how they think about insight problems.
The constructivist view is based on the knowledge construction metaphor, in which the human mind is a sort of construction zone in which learners actively create their own knowledge based on integrating what is presented and what they already know. According to the constructivist view, learners are sense makers who construct knowledge. Knowledge is a mental representation that exists in a human mind. Unlike information, which is an objective entity that can be moved from one mind to another, knowledge is a personal construction that cannot be moved directly from one mind to another. Construction involves cognitive processing aimed at sense making, including attending to relevant portions of the presented material, mentally organizing the material into a coherent structure, and mentally integrating the material with relevant existing knowledge. Unlike the view of cognitive processing as applying algorithms, cognitive processing involves orchestrating cognitive strategies aimed at sense making. For example, as you read this section, you may mentally select relevant ideas such as the classical view of information and processing and the constructivist view of knowledge and construction; you may organize them into a matrix with classical and constructivist as rows and nature of information and nature of processing as columns; and you may integrate this material with your previous knowledge about these topics.
The constructivist approach developed in the 1980s and 1990s, although its earlier proponents include Bartlett’s (1932) theory of how people remember stories and Piaget’s (1971) theory of how children learn. For example, Bartlett argued that when learners are presented with a folk story, they assimilate story elements to their existing schemas and mentally reorganize the story in a way that makes sense to them. Similarly, Piaget showed how children assimilate their experiences with their existing schemas in an attempt to make sense of their environment. More recently, the constructivist view can be seen in Ausubel’s (1968) theory of assimilative learning and Wittrock’s (1990) theory of generative learning. In both theories, learning involves connecting what is presented with what the learner already knows, so the outcome of learning depends both on the material presented by the instructor and the schemas used by the learner.
Although the constructivist view addresses some of the limitations of the classical view, major limitations of the constructivist view include the need to account for the social and cultural context of cognition and the need to account for the biological and affective bases of cognition. In particular, the constructivist view focuses on cognitive changes within individual learners, but this view can be expanded by considering how the learner’s cognitive processing is mediated by the learner’s surrounding social and cultural environment. The constructivist view focuses on what can be called cold cognition (i.e., cognitive processing in isolation), but this view can be expanded by also considering the role of the learner’s emotional and motivational state.
Major Contributions of Information Processing Theory
Three important contributions of the information processing approach are techniques for analyzing cognitive processing (e.g., “What are the cognitive processes involved in carryingoutacognitivetask?”),techniquesforanalyzingmental representations (e.g., “How is knowledge represented in memory?”), and a general description of the architecture of the human cognitive system (e.g., “How does information flow through the human memory system?”).
Cognitive Processes: Cognitive Task Analysis
Afundamental contribution of information processing theory is cognitive task analysis—techniques for describing the cognitive processes that a person must carry out to accomplish a cognitive task. For example, consider the analogy problem dog : bark :: cat : ____, which can be read as “dog is to bark as cat is to what?” and in which the a-term is “dog,” the b-term is “bark,” the c-term is “cat,” and the d-term is unknown. What are the cognitive processes that a problem solver must go through to solve this problem? Based on a cognitive task analysis, solving an analogy problem can be broken down into five basic steps (Mayer, 1987; Sternberg, 1977):
- Encoding—that is, reading and forming a mental representation of the words and accompanying punctuation,
- Inferring—that is, determining the relation between the a-term and the b-term (e.g., the b-term is the sound that the a-term makes),
- Mapping—this is, determining what the c-term is and how it corresponds to the a-term (e.g., the a-term is a kind of animal that makes sounds, and the c-term is another kind of animal that makes sounds),
- Applying—that is, generating a d-term based on applying the relational rule to the c-term (e.g., the sound that the c-term makes is _____), and
- Responding—that is, physically making the response such as writing “meow” or circling the correct answer (“meow”) on a list.
Cognitive task analysis has useful educational applications because it suggests specific cognitive processes that students need to learn. For example, the cognitive task analysis of analogy problems suggests that students would benefit from instruction in how to infer the relation between the a-term and the b-term (Sternberg, 1977).
To test this idea, Sternberg and Ketron (1982) taught collegestudentshowtosolveanalogyproblemsbyshowingthem how to infer the change from the a-term to the b-term and how toapplythatchangetothec-term.Onasubsequenttestofanalogical reasoning involving new problems, trained students solved the problems twice as fast and committed half as many errors as did students who had not received training.
Cognitive task analysis also offers advantages in evaluating student learning outcomes. For example, instead of measuring the percentage correct on a test, it is possible to specify more precisely the knowledge that a student possesses— including incomplete or incorrect components. For example, suppose a student gives the following answers on an arithmetic test:
A traditional evaluation would reveal that the student correctly solved 25% of the problems. However, a cognitive task analysis reveals that the student seems to be consistently applying a subtraction procedure that has one incorrect step, or bug—namely, subtracting the smaller number from the larger number in each column (Brown & Burton, 1978). In specifying the procedure that the student is using, it becomes clear that instruction is needed to help the student replace this smaller-from-larger bug.
Mental Representations: Types of Knowledge
According to the information processing approach, knowledge is at the center of cognition: Learning is the construction of knowledge; memory is the storage of knowledge; and thinking is the logical manipulation of knowledge. Therefore, information processing theorists have analyzed the types of knowledge (or mental representations): factual, conceptual, procedural, and metacognitive (Anderson et al., 2001). Factual knowledge consists of facts—that is, simple descriptions of an object or element (e.g., “apples are red”). Conceptual knowledge involves relations among elements within a coherent structure that enables them to function together, and includes classification hierarchies, cause-and-effect models, explanatory principles, and organizing generalizations (e.g., the model presented in Figure 3.1). Procedural knowledge involves a procedure, method, or algorithm—that is, a step-bystep specification of how to do something (e.g., the procedure for how to carry out long division). Metacognitive knowledge involves strategies for how to coordinate one’s cognitive processing (e.g., knowing how to monitor the quality of one’s essay-writing activity). As you can see, factual and conceptual knowledge are knowledge of “what” (i.e., data structures), whereas procedural and metacognitive knowledge are knowledge of “how to” (i.e., processes for manipulating data structures).
Knowledge is a mental representation: It is mental because it exists only in human minds; it is a representation because it is intended to denote or signify something. Representations can be classified based on the coding system used to represent them in the cognitive system such as motoric (e.g., bodily movement images), pictorial (e.g., mental images), verbal (e.g., words), or symbolic (e.g., some higher level coding system). Representations can be classified based on the input modality including haptic/kinesthetic/vestibular (e.g., bodily sensations), visual (e.g., imagery sensations), or auditory (e.g., acoustic sensations).
Cognitive System: Architecture of the Cognitive System
An Information Processing Model
Figure 3.1 presents a model of the human information processing system, consisting of three memory stores (represented as labeled boxes), five basic cognitive processes (represented as labeled arrows), and two channels of knowledge representation (represented as the top and bottom rows). The three memory stores are sensory memory, where sensory input is stored briefly in its original form; working memory, where a limited number of elements of the presented material are stored and manipulated within one’s conscious awareness; and long-term memory, where large amounts of knowledge are stored for long periods of time. The five cognitive processes presented in Figure 3.1 are selecting images, selecting words, organizing images, organizing words, and integrating. The two channels are the auditory-verbal channel (in the top row of Figure 3.1), in which material enters the cognitive system through the ears and eventually is represented in verbal code, and the visual/pictorial channel (in the bottom row of Figure 3.1), in which material enters the cognitive system through the eyes and eventually is represented in pictorial code.
On the left side of the top row, spoken words enter the cognitive system through the ears, resulting in a short-lasting acoustic sensation in auditory sensory memory. If the learner pays attention, parts of the sensation are transferred to verbal working memory for further processing. The arrow from acoustic sensation in auditory sensory memory to sound base in verbal working memory represents the cognitive process of selecting sounds, and the resulting representation in verbal working memory is a collection of sounds that can be called a sound base. If the learner generates visual representations based on the sounds (e.g., imagining a dog when the word “dog” is spoken), this process is represented by the arrow from sound base to image base. The arrow from sound base to verbal model in verbal working memory represents the cognitive process of organizing sounds, and the resulting representation in verbal working memory is a coherent structure that can be called a verbal model.
On the left side of the bottom row, printed words and pictures enter the cognitive system through the eyes, resulting in a short-lasting visual sensation in visual sensory memory. If the learner pays attention, parts of the sensation are transferred to visual working memory for further processing. The arrow from visual sensation in visual sensory memory to image base in visual working memory represents the cognitive process of selecting images, and the resulting representation in visual working memory is a collection of images that can be called an image base. If the learner generates verbal representations based on the images (e.g., mentally saying “dog” when a picture of a dog is processed or the printed letters for “dog” are read silently), this process is represented by the arrow from image base to sound base. The arrow from image base to pictorial model in visual working memory represents the cognitive process of organizing images, and the resulting representation in visual working memory is a coherent structure that can be called a pictorial model.
The final cognitive process—integrating—is represented by arrows connecting pictorial model from visual working memory, verbal model from verbal working memory, and prior knowledge from long-term memory. The result is an integrated representation based on visual and verbal representations of the presented material as well as relevant prior knowledge. Overall, the construction of knowledge requires that the learner select relevant images and sounds from the presented material, organize them into coherent pictorial and verbal representations, and integrate the pictorial and verbal representations with each other and with prior knowledge.
Three Assumptions Underlying the Model
The information processing model presented in Figure 3.1 is based on three assumptions from the cognitive science of learning: the dual channel assumption, the limited capacity assumption, and the active learning assumption (Mayer, 2001). The dual channel assumption is that humans possess separate information processing channels for visual-pictorial material and auditory-verbal material (Baddeley, 1998; Paivio, 1986). For example, printed words and pictorial material (e.g., illustrations, graphics, animation, and video) are processed as visual images (at least initially) in the visualpictorial channel whereas spoken words are processed as sounds (at least initially) in the auditory-verbal channel. Eventually, printed words and pictures may be represented in the verbal channel even if they were presented visually, and spoken words may be represented in the visual channel if they elicit images in the learner. However, the way that verbal and pictorial material is represented in working memory is different, so there is a verbal code and a pictorial code. An important aspect of controlling the flow of visual and verbal information is for learners to build connections between corresponding visual and verbal representations of the same material—an accomplishment that Paivio (1986) calls building referential connections.
For example, Mayer (2001) reported research in which students learned about how a scientific system works (e.g., a bicycle tire pump, a car’s braking system, or the process of lightning formation) and then took a transfer test that measured their depth of understanding. Students performed better on the transfer test when they listened to an explanation and viewed a corresponding animation than when they only listened to the explanation. This multimedia effect is consistent with the idea that people process visual and verbal material in separate channels.
The limited capacity assumption concerns constraints on the amount of material that can be processed at one time in workingmemory(Baddeley,1998;Sweller,1999).Thus,only a few images can be held and organized into a coherent visual model at one time, and only a few words can be held and organized into a coherent verbal model at one time. An important aspect of the limited capacity assumption is that the learner’s cognitive system easily can become overloaded, such as by presenting a great amount of information simultaneously.
For example, Mayer (2001) reported research in which students learned about how lightning storms develop by receiving a narrated animation and then took transfer tests. When the presentation contained extraneous words (e.g., interesting facts about people being struck by lightning), pictures (e.g., interesting video clips of lightning storms), and sounds (e.g., background music), students performed more poorly on subsequent transfer tests than when extraneous material was excluded. This coherence effect is consistent with the idea that the extra material overloaded the learners’ working memories, thus making it more difficult to construct a mental representation of the cause-and-effect system.
The active learning assumption is that meaningful learning (or understanding) occurs when learners engage in appropriate cognitive processing during learning—including selecting relevant information, organizing the material into a coherent representation, and integrating incoming visual and verbal material with each other and with prior knowledge (Mayer, 1996b, 1999). The balanced and coordinated activation of these kinds of processes leads to the construction of a meaningful learning outcome that can be stored in long-term memory for future use. In short, meaningful learning is a generative process in which the learner must actively engage in cognitive processing rather than passively receive information for storage (Wittrock, 1990).
For example, signaling (Loman & Mayer, 1983; Lorch, 1989; Meyer, 1975) is a technique intended to improve students’ understanding of prose in which the key material is highlighted (thus fostering the process of selecting) and the organizational structure is highlighted (thus fostering the process of organizing). For example, Mautone and Mayer (2001) presented a narrated animation on how airplanes achieve lift and then asked students to solve some transfer problems that required applying what they had learned. Some students received a signaled version that included a short outline stating the main three steps, headings keyed to the three steps, and connecting words such as “because of this” or “first . . . second . . . third.” The signals were part of the narration and added no new content information. Other students received a nonsignaled version. On the transfer test, there was a signaling effect in which the students in the signaled group performed better than students in the nonsignaled group. Thus, techniques intended to prime active cognitive processing (e.g., selecting and organizing relevant material) resulted in better understanding.
Information Processing and Instruction
In this section I examine three examples of how the information processing approach can be applied to instructional issues in three subject matter domains: reading, writing, and mathematics. In each domain the driving question concerns the cognitive processes or knowledge that a student needs to perform competently as an authentic academic task such as comprehending a passage, creating an essay, or solving an arithmetic word problem. I focus on these three domains because they represent exemplary educational tasks that have been studied extensively in research.
Information Processing in Reading a Passage
What are the cognitive processes involved in comprehending a passage? Mayer (1996b, 1999) analyzed the readingcomprehension task into four component processes: selecting, organizing, integrating, and monitoring.
Selecting involves paying attention to the most relevant portions of the passage. This involves being able to tell what is important and what is not (Brown & Smiley, 1977). For example, Brown and Smiley (1977) broke stories into idea units (e.g., single events or simple facts) and asked children to sort them into four categories ranging from most to least important. Third-graders seemed to sort randomly, such that an important idea unit was no more likely than an unimportant idea unit to be sorted into the important category. However, college students were extremely accurate, such that important idea units were usually classified as important and unimportant idea units were usually classified as unimportant. Apparently, as students acquire more experience in reading for comprehension, they develop skill in selecting important information.
Organizing involves taking the relevant pieces of information and mentally connecting them into a coherent structure. For example, some possible structures are to organize the material as cause-and-effect sequence, classification hierarchy, compare-and-contrast matrix, description network, or simple list (Chambliss & Calfee, 1998; Cook & Mayer, 1988; Meyer & Poon, 2001). In an exemplary study, Taylor (1980) asked fourth- and sixth-grade students to read and recall a short passage. The sixth-graders recalled much more superordinate material than subordinate material, indicating that they used the higher level structure to help them organize and remember the lower level material. In contrast, fourth-grade readers recalled more subordinate material than superordinate material, indicating that they did not make much use of the higher level structure to help them mentally organize the passage. Apparently, as students acquire more experience in reading for comprehension, they develop skill in organizing the material into a high-level structure.
Integrating involves connecting the incoming knowledge with existing knowledge from one’s long-term memory. This involves activating relevant prior knowledge and assimilating the incoming information to it (Ausubel, 1968). For example, Bransford and Johnson (1972) asked college students to read an abstract passage about a procedure. If students were told beforehand that the passage was about washing clothes, they remembered twice as much as when they were told the topic afterward. Apparently, priming appropriate prior knowledge before reading a new passage is a powerful aid to comprehension.
Monitoring involves a metacognitive process of judging whether the newly constructed knowledge makes sense. For example, in comprehension monitoring readers continually ask themselves whether the passage makes, whether parts contradict one another, and whether parts contradict their past experiences (Markman, 1979). In an exemplary study, Vosniadou, Pearson, and Rogers (1988) asked third and fifth graders to read stories that had inconsistent statements. When prompted to point out anything wrong with the passage, the fifth graders recognized more than twice as many of the inconsistencies as did third graders. Apparently, students develop skill in comprehension monitoring as they gain more experience in reading.
There is overwhelming evidence that the cognitive processes underlying reading comprehension can be taught (Pressley & Woloshyn, 1995). For example, Cook and Mayer (1988) taught students how to outline paragraphs from their chemistry textbooks based on some of the structures just listed. Thus, the training focused on the organizing process.
Initially, most students organized passages as lists of facts, but with training they were able to distinguish between passages that best fit within the structure of a cause-and-effect sequence, a classification hierarchy, and so forth. When students were tested on their comprehension of passages from a biology textbook, the structure-trained students performed much better than did students who had not received training. Research on teaching of organizing strategies offers one useful demonstration of the positive consequences of teaching specific ways to process information.
Information Processing in Writing an Essay
What are the cognitive processes involved in writing an essay, such as “how I spent my summer vacation”? Hayes and Flower (1980; Hayes, 1996) analyzed the essay-writing task in three component processes: planning, translating, and reviewing.
Planning involves mentally creating ideas for the essay (i.e., generating), developing an outline structure for the essay (i.e., organizing), and considering how best to communicate with the intended audience (i.e., evaluating). For example, the learner may remember specific events from his or her summer vacation, may decide to present them in chronological order under the theme “too much of a good thing,” and may decide that the best way to communicate is through humor.
In a study of the role of planning, Gould (1980) asked people to write (or dictate) a routine business letter for a specific purpose. People spent about one third of their time writing (or speaking) and two thirds of their time in silence—presumably as they planned what to write (or say) next. It is interesting to note that people began writing (or speaking) immediately, indicating that they engaged in no global planning. These results suggest that writers spend most of their time in local planning and therefore point to the need for training in global planning.
Translating involves actually putting words on paper, such as through writing, typing, or dictating. For example, the learner may sit at a word processor and begin to type. In a study of the role of translating, Glynn, Britton, Muth, and Dogan (1982) asked students to write a first draft and then a final draft of a persuasive letter. Some students were told to write a polished first draft paying attention to grammar and spelling, whereas other students were told to write an unpolished first draft minimizing attention to grammar and spelling. Students wrote a higher quality final draft when they were told to write an unpolished rather than a polished first draft. Apparently, the process of translating places a heavy cognitive load on the writers’ working memories, so if they have to pay attention to low-level aspects of writing (e.g., spelling and grammar), they are less able to pay attention to high-level aspects of writing (e.g., writing a persuasive argument). These findings suggest the need to minimize cognitive load when students are translating.
Reviewing involves detecting and correcting errors in what has been written. For example, the learner may read over a sentence and decide it needs to be made more specific. In a study of the role of reviewing, Bartlett (1982) found that middle-school students performed poorly on detecting errors in their own essays but well on detecting errors in their peers’ essays. Less than half of the detected errors were corrected properly. These results point to the need for training in how to detect and correct errors.
Research on writing shows that learners often have difficulty in the planning and reviewing phases of writing, but these cognitive processes can be taught with success (Kellogg, 1994; Levy & Ransdell, 1996; Mayer, 1999). For example, Kellogg (1994) asked college students to write an essay on the pros and cons of pledging to give all of one’s income over a certain level to poor families in the community. One group of students was not asked to engage in any prewriting activity (no-prewriting group), whereas another group was asked to begin by producing an outline containing the relevant ideas (outlining group). The outlining group, therefore, was encouraged to engage in planning processes such as generating ideas, organizing ideas, and evaluating whether the message is appropriate for the audience. When judges were asked to rate the quality of the essays on a 10-point scale, the essays written by the outlining group received much higher quality ratings than did those written by the no-prewriting group. Apparently, students often ignore the cognitive processes in planning, but when they are encouraged to engage in planning processes, their writing is much improved.
Information Processing in Solving a Mathematics Problem
What are the cognitive processes involved in solving an arithmetic word problem, such as, “At ARCO gas sells for $1.13 per gallon. This is 5 cents less per gallon than gas at Chevron. How much do 5 gallons of gas cost at Chevron?” (Lewis & Mayer, 1987). Mayer (1992b) analyzed the task in four component processes: translating, integrating, planning, and executing.
Translating involves building a mental representation for each sentence in the problem. For example, for the first sentence the learner may build a mental representation such as “ARCO = 1.13”; and for the second sentence the learner may build a mental representation such as “ARCO = CHEVRON ‒ .05.” In an exemplary study, Soloway, Lochhead, and Clement (1982) asked college students to write equations for statements suchas,“There are six times as many students as professors at this university.” Approximately one third of the students translated the statement incorrectly, yielding answers such as “6S = P.” Students need training in how to represent some of the sentences in word problems.
Integrating involves building a mental representation of the entire situation presented in the problem. For example, the learner may visualize a number line with ARCO at the 1.13 point on the line and Chevron .05 spaces to the right. In an exemplary study, Paige and Simon (1966) gave students a problem with an internal inconsistency, such as: “The number of quarters a man has is seven times the number of dimes he has. The value of the dimes exceeds the value of the quarters by $2.50. How many of each coin does he have?” Most students failed to recognize the inconsistency; some constructed equations such as Q = 7D and D (.10)= 2.50 + Q(.25), and solved for Q. Students need training in how to integrate the information into a meaningful representation that can be called a situation model (Kintsch & Greeno, 1985; Mayer & Hegarty, 1996).
Planning involves creating a strategy for solving the problem, such as breaking a problem into parts. For example, the learner may develop the plan: Add .05 to 1.13, then multiply the result by 5. Reed (1987) has shown that giving students worked examples with commentary can help them apply appropriate strategies when they receive new problems. Chi, Bassok, Lewis, Reimann, and Glaser (1989) found that students who spontaneously produced self-explanations as they read worked examples in textbooks tended to excel on subsequent problem-solving tests. Students need practice in understanding the strategies used to solve example problems.
Executing involves carrying out a plan, resulting in the production of an answer. For example, the learner may compute .05 + 1.13 1.18, 1.18 х 5 = 5.90. An accompanying process is monitoring, in which the learner evaluates whether the plan is being successfully applied. Fuson (1992) has identified four stages in the development of simple addition for problems (such as 3 + 5 = ___): counting all, in which the student counts 1-2-3, and then 4-5-6-7-8; counting on, in which the student starts with 3 and then counts 4-5-6-7-8; derived facts, in which the student changes the problem into 4 + 4 and gives 8 as the answer; and known facts, in which the student simply retrieves 8 as the answer. When the lower-level skill is automatic—requiring minimal attention—the student can devote more cognitive resources to understanding the problem and planning the problem solution.
Together, translating and integrating constitute the phase of problem understanding, whereas planning and executing constitute the phase of problem solution. Research shows that learners have difficulty with problem understanding— translating and integrating—although instruction emphasizes problem solution, particularly executing (Mayer, Sims, & Tajika, 1995).
An important contribution of the information processing approach to mathematical cognition is the design of programs to teach students how to process mathematics problems. For example, Lewis (1989) taught students how to represent arithmetic word problems in pictorial form as variables along a number line. Asentence like “Megan has $420” is represented by placing “Megan” along a number line along with “$420.” Then, the sentence, “She saved one fifth as much as James saved” means that “James” should be placed on the number line to the right of “Megan,” indicating that the amount James saved is greater than the amount Megan saved. By converting the sentences into an integrated number line, students learn how to engage in the cognitive processes of translating and integrating. Students who practiced these processes on a variety of problems for approximately 60 min performed much better on tests of solving new arithmetic word problems than did students who spent the same amount of time working with the problems without explicit training in converting them into number-line representations. These findings encourage the idea that students can learn to improve the way they process mathematics problems.
Future research on the psychology of subject matter (Mayer, 1999) is likely to provide detailed analyses of the cognitive processes needed for success on a variety of academic tasks, to uncover individual differences, and to discover instructional techniques for fostering the development of appropriate learning skills.
The premise underlying information processing theory is that human mental life consists of building and manipulating mental representations. The information processing view has important implications for education, including implications for how to improve instruction in subject matter areas such as reading, writing, and mathematics. Research and theory on human information processing points to the reciprocal relation between psychology and education: Educational practice can be improved when it is informed by an understanding of how the human mind works, and theories of how the human mind works can be improved when they are informed by studies involving how students perform on authentic academic tasks.
Admittedly, the information processing approach is limited. For example, by focusing mainly on cognition in individual learners, it fails to incorporate affective, motivational, emotional, social, and biological aspects of learning and instruction. All of these aspects must eventually be integrated into a far-reaching theory of how the human mind works. One promising approach is to include motivational strategies along with cognitive strategies in teaching students how to learn (Mayer, 2002).
Yet the information processing approach—now a dominant force in psychology for nearly half a century—also leaves a worthwhile legacy. The information processing approach enabled the rebirth of cognitive psychology by providing an alternative to behaviorism, created a unified framework that stimulated useful research and theory, highlighted the role of mental representations and cognitive processes, and fostered the transition toward studying cognition in more authentic contexts. Many of the current advances in educational research—ranging from cognitive strategy instruction to the psychology of subject matter— were enabled by the information processing approach in psychology. Examples were provided in the foregoing sections, but much more work is needed.
Overall, the information processing approach continues to play a constructive role in the development of educationally relevant theories of how the human mind works. In particular, the constructivist view of learners as sense makers and mental model builders offers a potentially powerful conception of human cognition. A particularly useful approach involves the refinement of techniques for analyzing academic tasks into constituent processes that can be evaluated and taught.
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