Chapter 3. Dimension 2: Acquiring and Integra...

Chapter 3. Dimension 2: Acquiring and Integrating Knowledge
Copyright © 1992 by the Association for Supervision and Curriculum Development. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission from ASCD.
A fundamental goal of schooling is for students to learn whatever is deemed important in a given subject—in other words, to acquire and integrate knowledge. There is a strong movement afoot to suggest, wrongly I believe, that many educational innovations either ignore the importance of content knowledge or actually work against it. Popular books such as E. D. Hirsch‘s Cultural Literacy: What Every American Needs to Know (1987), Alan Bloom‘s The Closing of the American Mind (1987) and Diane Ravitch and Chester Finn‘s What Do Our 17-Year-Olds Know? (1987) have directly or indirectly blamed the current emphasis on teaching and reinforcing thinking processes (among other things) for the perceived decline in test scores across the nation. Many reviewers of these works, however, say that these are straw-man arguments. For example, Farrell (1991) notes that the critical flaw in all three works is that they generate a false dichotomy between teaching thinking processes and teaching content- or domain-specific knowledge. They also tend to equate an emphasis on domain-specific knowledge with an emphasis on factual knowledge. Farrell, commenting on the works of Hirsch (1987) and Ravitch and Finn (1987), notes that the heavy emphasis on factual recall found in both books would seem to lead inexorably to increased teacher domination and prescriptiveness, thus perpetuating a tradition that many people assert is crippling American education (Goodlad 1984; Powell, Farrar, and Cohen 1985).
The belief underlying the Dimensions of Learning model is that both content knowledge and thinking and reasoning processes need to be taught if we want students to become proficient learners. As Glaser (1984, 1985) and Resnick (1987) point out, reasoning processes are an integral part of content knowledge. Moreover, an emphasis on content knowledge does not translate into an emphasis on factual knowledge. Although facts are important, they are often rather meaningless in isolation. As both Project 2061 (AAAS 1989) and the "standards project" of the National Council of Teachers of Mathematics (NCTM 1989) affirm, facts are most relevant when they illustrate, reinforce, or make concrete some larger concept or principle.
There is no debate, then, about the importance of content knowledge nor is there an attempt to undermine it. There is, however, a growing body of research and theory identifying the most useful content knowledge and how to learn it.
How can educators best help students acquire and integrate knowledge? Before answering this question, recall the story of Miguel (in Chapter 1), who learned to perform the back kick in Mr. Tully‘s phys ed class. Learning the kick initially involved linking new information with old information. Miguel compared the back kick with the side kick that he already knew how to perform. Next, he had to work out some of the kinks and organize the information into simple steps. Finally, he had to internalize the information so that he could easily use it again. Miguel‘s story illustrates some of the basic dynamics of acquiring and integrating new knowledge, but to fully understand how we acquire knowledge, we need to consider the nature of knowledge itself.
The Nature of Knowledge
Noneducators tend to think all knowledge is pretty much the same. But many theorists believe there are different types of knowledge, each involving somewhat different learning processes. At the most basic and general level are the two categories of knowledge shown in columns A and B below.
Column A contains examples of knowledge that involve processes. These processes may or may not be performed in a linear fashion. For example, performing long division is a process: You perform one step, then another, and so on. Reading a map also involves certain steps, but these steps, unlike those in long division, do not have to be performed in any set order. You might read the name of the map first, then look at the legend, or you might just as effectively perform these steps in reverse order. Knowledge of this sort is usually called procedural knowledge. You might think of it as the skills and processes important to a given content area.
The examples in column B do not involve a process or a set of steps. Acquiring this type of knowledge involves understanding the component parts and being able to recall them. For example, knowledge of the concept of "democracy" includes understanding that decisions are made by the people, each person has a single vote, votes are weighted equally, and so on. It also includes the ability to remember this information or at least recognize it at some later date. This type of knowledge is commonly called declarative knowledge.
What is important about these two types of knowledge is that they involve somewhat different learning processes (though both require the three general phases exemplified in Miguel‘s story). The distinction between the two types of knowledge is reflected in current efforts to define standards for what students should know and be able to do. Let‘s compare the examples below. Ms. Baker‘s class illustrates how procedural knowledge is learned, and Mr. DiStefano‘s class illustrates how declarative knowledge is learned.
Ms. Baker‘s Class
Ms. Baker is introducing her students to the process of three-column addition. She begins by telling them not to worry—what they are about to do is just like what they did with two-column addition. To calm her students‘ fears, she takes some time to review the steps of two-column addition. As she does so, she writes the steps on the board. Then she works on the board the problem 374 + 251, thinking aloud as she does so: "Let‘s see, I add the 1 and the 4 in the first column. That doesn‘t go over 10 so I don‘t have to carry anything over to the second column. Now I just add the numbers in the second column because I didn‘t have to carry anything. OK, the 7 and 5 add up to 12. If this were two-column addition, I‘d just write the 12 down, but it‘s three-column addition so I have to consider the next column. Well, it‘s just like what I have to do with the first column of two-column addition. I have to carry over the 1 from the 12. Let‘s see, I bring the 1 over to the column that has the 3 and the 2; they add up to 5 plus the 1 that I carried from the second column. That‘s it, 625. That wasn‘t so hard. It‘s the same as two-column addition, only you have to think of carrying twice, not just once."
When Ms. Baker completes the problem, she adds the steps for three-column addition to those already on the board for two-column addition. She then reviews the steps for three-column addition by performing one more example, pointing out each step as she goes through the problem. Students then pair up and work on two practice problems she has given them. She tells them to take their time and think through every step. When pairs are done, Ms. Baker works the problems on the board with the entire class, pointing out each step.
The next day, she works another problem on the board. With this one, however, she asks the class questions as she goes along: "What would happen if this were a 7 instead of a 4? Would I have to carry or not? How small a number would have to be here for me not to have to carry? What happens if I don‘t have to carry in the second column but I do in the first and the third? Show me an example. What happens if I‘ve had to carry in the second and third columns but not the first? Show me."
It seems as though Ms. Baker is trying to cover every possible situation that might occur with three-column addition and, in fact, she is. She is trying to expose students to as many variations as possible. She is also trying to point out common kinds of mistakes. It takes her more than fifteen minutes to go through a single problem and all its variations. She then gives the class more problems to solve. Again, students do them in pairs. The students very quickly discover that these problems involve all the "tricky parts" and variations Ms. Baker just covered. Even though the problems are tough, the students do well. As they work on the problems, Ms. Baker walks around the room, helping them with the difficult parts and making sure both students in each pair understand the many variations she has reviewed.
Over the next few days, Ms. Baker gives more problems on three-column addition. She gradually begins to emphasize speed, but she never stops emphasizing the understanding of each step. Within a week, students in her class have become proficient solvers of three-column addition problems.
Mr. DiStefano‘s Class
Mr. DiStefano is introducing a new chapter on alcohol in health class. He begins by asking students what they already know about the topic. Being a typical group of 11th graders, they begin with statements like "It‘s OK for adults but they won‘t let us have any" and "It‘s fun." Mr. DiStefano records their remarks on the board as students call them out. After a few minutes, the class starts providing more "academic" responses: "It‘s addictive." "It ruins your life."
After students have generated about ten ideas, Mr. DiStefano gives each student a piece of paper divided into two columns. In the left column is the phrase "Effects of Alcohol on the Body" and in the right column is the phrase "Effects of Alcohol on Behavior." Mr. DiStefano asks his students to read the chapter and add items to each column as they do so. He says, "By the time you are done reading the chapter you should have at least five things listed under each heading."
The students begin reading. It‘s a short chapter, so in about fifteen minutes everyone is finished. Mr. DiStefano then says, "Let‘s see what you‘ve come up with." As a class, they go over the information in their outlines, and Mr. DiStefano makes a large graphic representation of the information. At the top of the graph, he writes, "Alcohol is a very powerful drug." Under that he writes the two areas he asked students to attend to, "Effects of Alcohol on the Body" and "Effects of Alcohol on Behavior." As students call out what they have identified, Mr. DiStefano lists the information under the appropriate heading.
When they finish the list, Mr. DiStefano says that he would like everyone to remember a few of the items they‘ve listed. He then puts a check mark next to the pieces of information he considers particularly important. To help students remember the marked information, he tells a story about someone he once knew who drank too much alcohol. The students love the story because Mr. DiStefano makes it realistic. He describes sounds, smells, tastes, and emotions. It‘s almost like watching a movie. By the time he‘s finished, he‘s covered all the pieces of information he checked off on the board.
 
In her class, Ms. Baker was helping students learn a new skill, three-column addition. Because it involves steps or rules to follow—in this case, rules that must be applied in a relatively strict order—this is a type of procedural knowledge. Learning procedural knowledge involves three phases that researchers usually call the cognitive, associative, and autonomous phases (Anderson 1982, 1983; Fitts and Posner 1967). In the Dimensions of Learning framework they have somewhat different names that highlight specific aspects of each phase.
The first thing Ms. Baker did was to help students identify what they already knew about three-column addition by likening it to two-column addition. She did this because the first step in learning any new skill or process is to establish a rough model of it—to get an idea of what the skill or process involves. Consequently, we call the first phase of learning procedural knowledge model construction. At this stage the learner cannot actually perform the skill; he simply has an idea of the steps involved. For example, when I first learned how to drive I took time to memorize the position of the gears, and I created a model of the process of shifting into the various gears that I would frequently rehearse in my mind—even though I had never actually tried it.
After students had a rough model of the process, Ms. Baker engaged them in an in-depth analysis of it. Using a single example, she showed several variations of the process and pointed out some common pitfalls. This is called the shaping phase of learning procedural knowledge. It is probably the most crucial part of learning a new skill or process because without it errors can easily creep into the new procedure. As we shall see, many of these errors can go unnoticed by even the most discerning teacher.
Finally, Ms. Baker set up a practice schedule for students. The intent here was for students to focus on speed and accuracy and develop their skill at three-column addition to a point where they could solve problems without thinking about each step involved. This is called the internalizing phase to emphasize that skills and processes are most useful when they are learned to such an extent that they can be done with little conscious effort.
Whereas Ms. Baker was helping students acquire and integrate procedural knowledge, Mr. DiStefano was helping students acquire and integrate declarative knowledge: specific facts and pieces of information about alcohol. Here, too, there were three phases of learning. At first, Mr. DiStefano asked students what they already knew about alcohol. The purpose of this activity was to help students construct meaning: to associate what they already knew about alcohol with the new information they were reading about alcohol. The first step in learning declarative knowledge is to link new knowledge with old knowledge. It‘s a rather curious paradox in learning theory that we have to know something about what we are learning to learn it well. But if you stop to think about it, we are constantly using what we know to help us figure out what we don‘t know.
The second phase of learning declarative knowledge is an organizational phase. Here the learner arranges the new information to create some meaningful pattern. In this case, Mr. DiStefano helped his students by giving them a graphic organizer. This phase is similar to the shaping phase of learning procedural knowledge. It involves honing information down to the necessary ingredients and identifying important relationships among pieces of information.
Finally, Mr. DiStefano helped students store the information in their long-term memory. This is the final phase of learning declarative knowledge: overtly representing information in long-term memory in a way that makes it easy to remember later. Mr. DiStefano helped students create mental pictures of the information by telling them a story about a friend.
Helping students acquire and integrate basic declarative and procedural knowledge requires attention to the three aspects of learning specific to each type of knowledge. Because much of the content students encounter in schools is declarative in nature, we will consider declarative knowledge first.
Helping Students Learn Declarative Knowledge
Learning declarative knowledge involves three phases: constructing meaning, organizing, and storing. We will explore each of these phases and discuss a few strategies for helping students move through the three phases.
Constructing Meaning for Declarative Knowledge
The driving force behind constructing meaning is using what we already know about a topic to interpret what we are learning. Without prior knowledge with which to interpret new declarative knowledge, nothing makes much sense. From a learning perspective, it is impossible to overestimate the importance of using prior knowledge to interpret new information. Bartlett (1932) illustrated this when he asked British readers to discuss a story from the oral tradition of a tribe of Indians on the west coast of Canada. The story fit well with the Indians‘ view of the world or their "schema" for how the world works. It made sense to them. It did not, however, make much sense to the British readers, whose view of the world was quite different from the Indians‘. The British readers saw the story quite differently. The story Bartlett used is printed on the next page. Read it and see if it makes any sense to you.
The War of the Ghosts
One night two young men from Egulac went down to the river to hunt seals, and while they were there it became foggy and calm. Then they heard war-cries, and they thought: "Maybe this is a war-party." They escaped to the shore, and hid behind a log. Now canoes came up, and they heard the noise of paddles, and saw one canoe coming up to them. There were five men in the canoe, and they said:
"What do you think? We wish to take you along. We are going up the river to make war on the people."
One of the young men said, "I have no arrows."
"Arrows are in the canoe," they said.
"I will not go along. I might be killed. My relatives do not know where I have gone. But you," he said, turning to the other, "may go with them."
So one of the young men went, but the other returned home.
And the warriors went on up the river to a town on the other side of Kalama. The people came down to the water, and they began to fight, and many were killed. But presently the young man heard one of the warriors say: "Quick, let us go home: that Indian has been hit." Now he thought: "Oh, they are ghosts." He did not feel sick, but they said he had been shot.
So the canoes went back to Egulac, and the young man went ashore to his house, and made a fire. And he told everybody and said: "Behold I accompanied the ghosts, and we went to fight. Many of our fellows were killed, and many of those who attacked us were killed. They said I was hit, and I did not feel sick."
He told it all, and then he became quiet. When the sun rose he fell down. Something black came out of his mouth. His face became contorted. The people jumped up and cried.
He was dead (Anderson 1990, p. 196).
 
The story probably seems bizarre to you. It certainly did to Bartlett‘s readers, who were products of upper-class Edwardian England. In fact, Bartlett found that his readers actually had to change what they read to understand it. As Anderson (1990, p. 197) notes, they distorted the story to fit their own cultural stereotypes. For instance, "something black came from his mouth" in the original story translated to "he frothed at the mouth" or "he vomited."
The power of our background knowledge to influence what we perceive was also demonstrated in a study by Brewer and Treyens (1981). They brought thirty subjects, individually, into a room and told them that it was the office of the experimenter and that they were to wait there for a short time. After thirty-five seconds, the subjects were taken to another room and asked to write down everything they could recall about the office. Brewer and Treyens‘ hypothesis was that the subjects would recall items that were part of the standard schema for a psychologist‘s office, but not recall very many items that did not fit their schema for a psychologist‘s office. And this was, in fact, what they found. Specifically, twenty-nine of thirty subjects remembered that the office had a desk and a chair, but only eight recalled that it had a bulletin board or a skull. And nine subjects recalled that the office had books, which it did not.
Constructing meaning using prior knowledge, then, is a vital component of learning declarative knowledge. A number of strategies can facilitate this process. Such strategies basically help learners access what they already know about information, use it to make predictions about what they are learning, and then confirm or disconfirm their initial guesses. One of the most popular strategies is the K-W-L strategy developed by Donna Ogle (1986). During the first phase of the strategy, students identify what they think they Know about the topic. For example, before reading a chapter describing how lakes die, students would list the facts they already know about this phenomenon. Next, they would list what they Want to know about the topic: interesting questions that have come to mind as a result of identifying what they think they know. For the topic of dying lakes, students might ask these questions: How long does it take for a lake to die? What exactly is the process? Can dead lakes be revived?
Students then read the chapter with an eye toward answering the questions they have posed. The last step in the K-W-L process is for students to identify what they have Learned. Here students record the answers to their questions as well as other information they have learned. In many cases, they also find out that what they thought they knew was inaccurate.
Another powerful strategy for the constructing meaning phase of learning declarative knowledge is the concept formation strategy described by Joyce and Weil (1986) and based on the research of Bruner, Goodnow, and Austin (1956). In the process described by Joyce and Weil (and adaptations of it), students are initially presented with examples and nonexamples of a new concept. To illustrate, if a teacher wanted to help students acquire the concept of "an adjective," she might first present students with the following examples and nonexamples:
Example: Our triumphant team came home after the game.
Nonexample: We were happy about our triumph.
Example: He fixed the broken chair.
Nonexample: He sank into the chair.
Example: The bright light hurt my eyes.
Nonexample: He listened attentively.
 
As the teacher presents these examples and nonexamples, students try to determine the critical attributes of the concept being formed. In situations like this, learners commonly devise a model containing hypothetical characteristics and then use each new example and nonexample to test the validity of that model. After one round of examples and nonexamples is presented, students are given time to reflect on the model they have generated. Another set of examples and nonexamples is provided to allow students to further test their models. At the end of this round, students share their model with the rest of the class so that a composite model can be built. More examples and nonexamples are provided to test this composite model. Students are then asked to find or create their own examples and nonexamples for a final round of testing. The concept is then named and a definition constructed by the group. The last activity in the process is for students to describe the reasoning they used during the concept formation process.
Strategies for helping students construct meaning for declarative knowledge are many and varied. Brainstorming, analogizing, semantic webbing, and reciprocal teaching are a few that teachers might use. The important point of any of these strategies is that before exposing students to new content, teachers overtly help each learner tap into his or her prior knowledge and use that knowledge to guide understanding and comprehension.
Organizing Declarative Knowledge
You might think that constructing meaning is all there is to acquiring and integrating declarative knowledge. But another process is necessary for learners to truly make the information their own. In the Dimensions of Learning model, this process is called "organizing." At a very basic level, organizing involves representing information in a subjective way. It includes identifying what is important and not important and then generating a semantic or symbolic representation of that information.
Walter Kintsch and Teun van Dijk have been particularly influential in helping us understand this process. In a series of studies (Kintsch 1974, 1979; Kintsch and van Dijk 1978; van Dijk 1977, 1980; van Dijk and Kintsch 1983), they have shown that we create our own internal representation (a macrostructure) of the information we comprehend (a microstructure). We do this by replacing specific pieces of information with more general ones. For example, if we read that "the dog named Spot picked up the tennis ball," we might construct our macrostructure using the phrase "the dog picked up a ball."
We often unconsciously summarize large sets of specific information and thus tend to remember the gist of information rather than specifics. To confirm this for yourself, try writing down the details of a movie you saw a week ago. Then take your written account and watch the movie again. You‘ll find that you probably remembered the general theme of the movie but forgot many details. This is because you created a macrostructure of the movie; you organized the information in the movie in a subjective, concise way.
Perhaps the most obvious strategy for helping learners organize information is to use advance organizers, as described by Ausubel (1968). These usually take the form of questions provided to students before they read a section in a textbook, watch a film, or complete some other activity. The questions guide students in organizing the information they will encounter. Some other ways of helping students organize information include using physical and symbolic representations, using organizational patterns, and using graphic organizers.
Using Physical and Symbolic Representations
The most basic type of organizational representation is physical or symbolic. As the name implies, a physical representation is a physical model of the information. For example, in a science class students might create a physical model of the solar system using materials like plastic balls and wire. They would also be creating a physical model if they "acted out" the parts of the solar system (as in the class described in Chapter 1). Physical models include any three-dimensional representation of information. The emphasis is on a realistic image of the component parts.
Symbolic representations are not intended to be as realistic as physical representations. Let‘s use the following equation as an example: F = [(M1,M2 )G]/r2
The equation states that force (F) is equal to the product of the masses of two objects (M1 and M2) times a constant G divided by the square of the distance between them (r). With this explanation, you might understand the equation at the level of constructed meaning, but to truly understand it you would have to create a symbolic representation that allows you to internalize the relationships among the various quantities. Hayes (1981) suggests an image of two large globes in space with the learner in the middle trying to hold them apart:
If either of the globes were very heavy, we would expect that it would be harder to hold them apart, than if both were light. Since force increases as either of the masses (M‘s) increases, the masses must be in the numerator. As we push the globes further apart, the force of attraction between them will decrease as the force of attraction between two magnets decreases as we pull them apart. Since force decreases as distance increases, r must be in the denominator (p. 126).
 
Physical and symbolic representations, then, force the learner to recast information to make salient important information and relationships.
Using Organizational Patterns
Over the last twenty years, researchers in the field of discourse analysis have demonstrated that a great deal of declarative knowledge can be organized in various types of semantic patterns. Combining the work of Cooper (1983), Frederiksen (1977), and Meyer (1975) yields at least six general organizational patterns:
Descriptive patterns organize facts or characteristics about specific persons, places, things, and events. The facts or characteristics need be in no particular order. For example, information in a film about the Empire State building—its height, when it was built, how many rooms it has, and so on—might be organized as a simple descriptive pattern.
Sequence patterns organize events in a specific chronological order. For example, a chapter in a book relating the events that occurred between John F. Kennedy‘s assassination on November 22, 1963, and his burial on November 25, 1963, might be organized as a sequence pattern.
Process/Cause patterns organize information into a causal network leading to a specific outcome or into a sequence of steps leading to a specific product. For example, information about the events leading to the Civil War might be organized as a process/cause pattern.
Problem/Solution patterns organize information into an identified problem and its possible solutions. For example, information about the various types of diction errors that might occur in an essay and the ways of correcting those errors might be organized as a problem/solution pattern.
Generalization patterns organize information into a generalization with supporting examples. For example, a chapter in a textbook about U.S. presidents might be organized using this generalization: "U.S. presidents frequently come from influential families." It would be followed by examples of specific presidents.
Concept patterns organize general categories or classes of persons, places, things, or events. Concept patterns usually include the defining characteristics and specific examples of the concept. For example, a film on the concept of "U.S. presidents" might contain defining characteristics of this concept, such as "they are elected by the citizens," and specific examples of presidents.
 
Students can use any one of these six patterns to organize information when they listen to a lecture, read a book, watch a film, and so on. Figure 3.1, for example, shows information adapted from a social studies textbook. Students might organize this information as a description of specific events that occurred in Italy and Germany before World War II. Or they might organize the information as defining characteristics about the general concept of "dictators," along with the specific examples of Mussolini and Hitler. Finally, they might organize the information as examples of the generalization "Dictators can easily rise to power in countries that are experiencing severe economic depression." With the aid of a few basic organizational structures, this one piece of expository information can be organized in several ways.
Figure 3.1. Information from a Social Studies Text
The United States was not the only nation to suffer from the Great Depression. The nations of Europe also were hard hit. Moreover, many Europeans had been trying to repair the damage to their countries caused during World War I.
Because of the hardships under which they were forced to live, some Europeans were willing to listen to leaders who promised to make their nations rich and powerful again. Some of these leaders brought about total changes in their countries. Their actions also caused another world war.
Dictators rise to power. In the 1920‘s and 1930‘s new leaders formed governments in Italy, Germany, and Japan. The governments formed in these countries were dictatorships. In a dictatorship, the leader or leaders hold complete authority over the people they rule. The people living in a dictatorship have only those rights that their leader, the dictator, chooses to give them. Dictators alone make all the important decisions in their nations. The decisions made by the dictators of Italy, Germany, and Japan led to World War II.
Mussolini takes over in Italy. After World War I, many Italians wanted to feel pride in the strength of their country once again. Benito Mussolini, the founder and organizer of the Fascist Party, convinced the Italians that he and his party could strengthen the nation. To succeed, the Fascists had to take control of the economy, the government, and many other parts of Italian life.
In 1922, the Fascists took control of the Italian government, creating a dictatorship with Mussolini as leader. Italians who were against Mussolini or his government were either thrown into prison or were forced to leave the country.
Mussolini planned to increase Italy‘s power and wealth by taking over weaker nations. He turned to Africa and, in 1935, attacked Ethiopia. Within a few weeks the Italian army overran this East African country and added it to the Italian empire.
Hitler becomes dictator in Germany.. After losing World War I, Germany continued to struggle with severe economic problems throughout the 1920‘s. These difficulties and the memory of their defeat in World War I brought many Germans to the Nazi Party. Its leader, Adolf Hitler, promised to make Germany the most powerful country in the world. In 1933 the Nazis won control of the German government. Hitler became Germany‘s dictator and silenced anyone who opposed him.
The people against whom Hitler directed his greatest hatred were the Jewish citizens of Germany. He unfairly blamed them for all of Germany‘s problems. By constantly repeating these false accusations, Hitler aroused public opinion in Germany against its Jewish citizens. Then he took away all civil rights and property of the Jews. Next, the police rounded up Jewish men, women, and children and sent them into concentration camps, or prison camps.
Hitler promised the Germans that he would add to the territory of their nation. He immediately put the country to work making weapons and other war materials. The first nation he moved into was Austria, in 1938. Hitler annexed Austria, he explained, because most of its people were Germans.
Source: Marzano 1991. Copyright © 1991 by National Council of Teachers of English. Reprinted by permission.
Using Graphic Organizers
Using graphic organizers to outline information is very popular in the classroom. Examples of how graphic organizers can be used across different content areas have been offered by Jones, Palincsar, Ogle, and Carr (1987), Heimlich and Pittelman (1988), McTighe and Lyman (1988), and Clarke (1991). Using different types of graphic representations to organize information is tantamount to using different organizational patterns. Figure 3.2 shows a graphic representation for each of the six types of organizational patterns described earlier.
 
If students wanted to organize the information in Figure 3.1 as a generalization about dictators, they might use a graphic representation like that in Figure 3.3 (on page 46).
 
If students wanted to organize that same information around the concept of dictators, they might use the graphic representation shown in Figure 3.4.
 
Again, the same information can be organized in a variety of ways using a variety of formats. Remember that organizing information is a somewhat subjective process in which the learner structures information in ways unique to her perspective. She highlights some ideas, makes others subordinate, and even disregards a few.
Storing Declarative Knowledge
Storage strategies would be unnecessary if learners didn‘t have to remember information over an extended period of time. Being able to recall some information, however, is vital for success in all content areas; imagine, for example, how difficult much of mathematics would be if you couldn‘t remember the times tables. There is growing national pressure for students to recall more and more factual information. Witness Ravitch and Finn‘s (1987) review of 141 specific pieces of information in assessing how much American 17-year-olds know about literature and history. Indeed, Doyle (1983) asserts that recall of information is still the primary task required of students.
Cognitive psychologists have taught us a lot about storing information in long-term memory. In fact, we know more about how information can be stored for easy retrieval than we do about almost any other aspect of learning. Unfortunately, what we know is usually not taught in the classroom. Most students use only verbal rehearsal, perhaps the weakest of all the strategies available, to help them remember what they have learned. Verbal rehearsal involves saying, reading, or writing information several times. Although verbal rehearsal works, its effectiveness is surpassed by other strategies, all of which fall under the general category of elaboration.
Elaboration involves making many and varied linkages between new information and old. An experiment by Owens, Bower, and Black (1979) illustrates the working principles underlying elaboration. Subjects studied a story that followed the principal character, a college student, through a day in her life: making a cup of coffee in the morning, visiting a doctor, attending a lecture, shopping for groceries, and attending a cocktail party. The following is a passage from the story:
Nancy went to see the doctor. She arrived at the office and checked in with the receptionist. She went to see the nurse who went through the usual procedures. Then Nancy stepped on the scale and the nurse recorded her weight. The doctor entered the room and examined the results. He smiled at Nancy and said, "Well, it seems my expectations have been confirmed." When the examination was finished, Nancy left the office.
 
Two groups of subjects studied the story. The only difference between the groups was that the "theme group" had been told that Nancy had been feeling nauseated when she woke up in the morning and was wondering if she was pregnant.
The researchers hypothesized that the subjects who had the extra information would develop a theme about Nancy that would automatically stimulate elaboration. When subjects in both groups were asked to recall the information twenty-four hours later, those in the theme group recalled it in significantly more detail. Those in the "neutral group" recalled very little. Elaborating on the information they had been given helped the subjects in the theme group store the information in an easily retrievable manner.
Virtually all memorization techniques use some form of elaboration. One of the most powerful ways to elaborate on information is to imagine mental pictures, physical sensations, and emotions associated with the information. Mr. DiStefano was helping students elaborate on the information about alcohol when he told the story of the person he knew who drank too much. As he described sounds, smells, tastes, and so on, he was helping students create images that were elaborations on the basic information about alcohol.
Many formal memory systems use imagery as an elaboration tool. Two of these are the rhyming pegword system (Miller, Galanter, and Pribram 1960) and the method of "places" or loci (Ross and Lawrence 1968), both of which are described in detail by Hayes (1981) and Lindsay and Norman (1977). One of the most commonly used imagery strategies is the "link technique." Here, the learner creates a mental image for each piece of information he wants to recall, making sure to create vivid patterns by imagining sounds, tastes, smells, and so on. He then links the separate images in story fashion.
For example, if a student used the link technique to store the information about dictators, he would first form an image of a dictator, perhaps using Saddam Hussein as that image. As he formed the image, he would try to incorporate touch, feel, smell, sound, and emotion. To remember that dictators rise to power when countries are weakened by promising them strength, the student might imagine Saddam in a city that is in grave disrepair, where buildings are falling down and people are starving. The dictator would be making a speech promising that he will make the city strong again. As the dictator makes the speech, he might become larger and larger until he towers above the skyline. To link the information about Hitler, the student might then imagine Adolf Hitler walking into the scene and shaking hands with Saddam Hussein, and so on. In short, the student creates elaborated images and then "chains" them together in story fashion.
Planning for the Acquisition and Integration of Declarative Knowledge
Planning instruction that will help students learn declarative knowledge is one of the most difficult tasks a teacher faces, because most of what students read, hear, and experience in any unit of instruction is declarative in nature. Consequently, the teacher must sift through the information students will be exposed to and make important decisions about how students will construct meaning and then organize and store that information. Let‘s look at how Ms. Conklin approaches this task.
Ms. Conklin‘s Planning for Dimension 2: Declarative Knowledge
Ms. Conklin is planning a unit on weather. Although she has a general sense of what she wants students to know at the end of four weeks, she hasn‘t really thought through the specifics. She starts by identifying some general topics. She knows that she‘d like students to understand something about tornadoes and weather forecasting because tornadoes occur frequently in the region. She also wants students to have a general idea of how weather affects our lives. She records these general topics in a unit planning guide (see column 1 of Figure 3.5 on page 51).
If Ms. Conklin knew all about weather forecasting, tornadoes, and the effects of weather, she could identify the specific pieces of information included in each of these general topics. But when she asks herself, "What exactly should students know?" she realizes that she doesn‘t really know, so she decides to investigate the topics further. She starts by looking through the textbook and finds information about all three topics. She also reads a few articles in the encyclopedia, looks through some filmstrips at the library, talks to the weather forecaster from Channel 9, talks to a meteorologist at the university, and even visits the forecasting center at the university. She‘s amazed at how much information she has to collect just to answer this one question.
For the topic of forecasting weather, Ms. Conklin decides that students should know about barometers and thermometers and the rise and drop in air pressure. For the topic of tornadoes, she concludes that students should know the sequence of events that leads to the formation of a tornado. Finally, for the topic of how weather affects our life, she thinks students should realize that weather influences us in many ways every day. She records these specifics in the planning guide (see column 2 of Figure 3.5).
Now that she has identified the specific information she wants students to learn, she concentrates on deciding what learning experiences she will use in the classroom. She begins with the information about weather forecasting. She decides that students will read pages 15–18 in the textbook to initially learn about barometers and thermometers. They will also watch a filmstrip. And she has invited the weather forecaster from Channel 9 to talk about air pressure. She records all these decisions in the planning guide (see column 3 of Figure 3.5).
Ms. Conklin also plans how students will be aided in constructing meaning for each of the three learning experiences she has identified. She decides to use brainstorming for the pages in the textbook, the K-W-L strategy for the filmstrip, and an analogy for the lecture. These decisions are also recorded in the planning guide (see column 4 of Figure 3.5).
For each of the learning experiences, Ms. Conklin also thinks about activities that will help students organize information. For the textbook and film, she decides that she will provide advance organizer questions, and with the guest lecture, she will provide students with a graphic organizer (see column 5 of Figure 3.5).
Ms. Conklin‘s final decision is about storing information. As she thinks about strategies, she concludes that she is not so concerned that students remember the information about barometers and thermometers, but she does want them to remember the information about air pressure. To help students store the information in a way that will help them recall it easily, she will guide them through the creation of mental pictures, physical sensations, and emotions about that information (see column 6 of Figure 3.5).
The set of decisions made, Ms. Conklin goes through the same process for the specific information about tornadoes and the effects of weather. The whole planning process has taken Ms. Conklin a lot longer than she anticipated, but she feels very good about what she has done. She has established a strong direction for her unit on weather.
 
Figure 3.5. Unit Planning Guide for Dimension 2: Acquiring and Integrating Declarative Knowledge
Topics
What are the specifics?
How will information be experienced—directly or indirectly?
How will students be aided in constructing meaning?
How will students be aided in organizing information?
How will students be aided in storing information?
Forecasting weather
Barometer
Thermometer
 
Textbook pp. 15–18
Filmstrip
 
Students will brainstorm before reading
K-W-L
 
I will provide set of questions to be used for both activities
cause/effect of rise/drop in air pressure
Guest lecturer from Channel 9
Guest will use analogy
I will provide graphic organizer
I will guide students thru mental pictures, sensations, etc.
Tornadoes
Sequence of events from formation to disappearance
Textbook pp. 21–25
Field trip to university forecasting center
 
Students will develop set of questions to use for both
Students will create graphic organizers from responses to questions
Students will create their own mental pictures, sensations, etc.
Weather affects us
Weather affects us daily, directly and indirectly
economy
history
recreation
moods
 
Read article "Weather and War"
Film—"Partly Cloudy, Cold, and Humid"
 
Before, During, After Strategy
Brainstorm effects of weather
 
Students will build a class collage graphically organized around generalization
As this example illustrates, a teacher must consider several fundamental questions when planning instruction for Dimension 2, acquiring and integrating declarative knowledge:
1. What are the general topics? Identifying general topics makes good curricular sense because, as noted earlier, most of the major curriculum efforts in the content areas are focusing on themes that embrace "big ideas." For example, the California K-12 science framework identifies broad themes such as energy, evolution, and patterns of change (California State Board of Education 1990). The Bradley Commission‘s report on history in the schools (Gagnon and the Bradley Commission 1988) and Project 2061: Science for All Americans (AAAS 1989) place similar emphases on broad topics.
Teachers should not select topics arbitrarily. They should think carefully about the possible reasons for selecting topics:
The topics are important to the general culture.
They are important to the community.
They are of interest to students.
They are of interest to the teacher.
They will be useful at a later date.
They are specified by the district or state.
They are topics for which resources are readily available.
 
2. What are the specifics? Within any general topic are numerous specific areas that can be focused on. Students should have some freedom and flexibility to focus on the information they consider important, but educators have a responsibility to provide guidance about the important information within a general topic. This guidance is the heart of the "heritage model" of schooling, which says that it is the duty of the education community to help society maintain a common culture by passing on specific information to students (Farrell 1991). Although there are some efforts at the national level to identify these specifics (e.g., Ravitch and Finn 1987), making such decisions at the local level seems to be a more valid practice. It makes far more sense for individual teachers like Ms. Conklin to decide which specifics to emphasize so that adjustments can be made to account for individual student needs and interests and the culture of the local community.
Regardless of who makes the decision, at this level of planning it is important not to equate identifying specifics with identifying facts. Klausmeier and his colleagues (Klausmeier 1985, Klausmeier and Sipple 1980, Katz 1976) have illustrated that large cognitive structures are more robust learning constructs than facts. Focusing on concepts and generalization naturally organizes the facts that support them, making the information easier to understand and recall.
3. How will students experience the information? One of the most important decisions a teacher can make about declarative information is how students will experience it. In a very general sense, there are two ways that students can experience declarative information, directly or indirectly, as depicted in Figure 3.6.
 
A direct experience, as the name implies, involves physical activity by students. This physical involvement can be real or simulated. For example, a real, direct experience for students studying the topic of democracy would be one that involved students in a democratic activity. The teacher might have students use the democratic process to make all classroom decisions during a two-week period. Unfortunately, not all classroom content can be experienced directly in a real way. For instance, students cannot learn about hibernation by experiencing it directly because hibernation is physically impossible for human beings. They can simulate the experience, though, by lying very still for ten minutes and consciously trying to slow their heartbeat and their breathing.
Indirect experiences are those in which students are not physically involved. Demonstrations, films, readings, and lectures are all indirect experiences. Some indirect ways of learning about hibernation would be observing a classroom pet that goes into hibernation for the winter, watching a film on hibernation, reading about hibernation, or listening to an oral presentation about hibernation.
I often use Figure 3.6 when I ask teachers to rate their use of various types of direct and indirect experiences. Lecture and reading are the most common experiences used, primarily because they require the least amount of time and preparation. If at all possible, though, teachers should attempt to vary the ways students experience content. For example, in Ms. Conklin‘s unit on weather, students will have the indirect experiences of reading, watching films and filmstrips, and listening to lectures. They will also have the direct experience of visiting the weather forecasting center at the university and getting some hands-on use of the equipment. Over the course of the school year, every teacher should be able to use at least some direct experiences and to frequently use indirect experiences other than lecture and reading.
4. How will students be aided in constructing meaning? Given the importance of constructing meaning, teachers should use overt activities with every learning experience to aid students in this process. As Figure 3.5 on page 51 shows, Ms. Conklin has decided to use a variety of techniques, including brainstorming, questioning, and the K-W-L strategy.
5. How will students be aided in organizing the information? A key aspect of this decision is how much guidance the teacher will provide. Given the constructive nature of learning, it‘s important that students create their own organizational schemes. But if certain ways of organizing information are important, then students need guidance. Consequently, a balance of organizing activities, some directed by the teacher and some by students, is usually appropriate. Note that in some situations Ms. Conklin has decided to provide students with an organizational schema; in others, she has decided to have students direct the organizing process (see Column 5 of Figure 3.5).
6. How will students be aided in storing the information? Every unit of instruction contains an immense amount of declarative information, and teachers cannot expect students to remember all of it. Some information, though, might be considered important enough for the use of overt storage activities. As Figure 3.5 indicates, Ms. Conklin has decided that she will guide students through storage activities for the information about air pressure and the formation of a tornado. In one case, she will provide the mental pictures, physical sensations, and so on, to elaborate on the information. In the other, she will ask students to create their own elaborations.
Helping Students Learn Procedural Knowledge
Learning procedural knowledge involves three phases: constructing models, shaping, and internalizing. As with declarative knowledge, we will explore each of these phases and outline some ways you can help students move through the three phases.
Constructing Models for Procedural Knowledge
To understand the role of model building in procedural learning, it is important to understand the three basic types of procedures that might be taught in a content area class: algorithms, tactics, and strategies. Algorithms are sets of steps that guarantee a certain result (Anderson 1990, p. 226). For example, the procedure for multiplication is commonly thought of as an algorithm because it involves a series of steps that, when followed, will always result in a correct answer. Tactics are somewhat different. According to Showman and McCown (1984), tactics aid in the accomplishment of a goal but do not necessarily ensure its accomplishment. They involve general rules rather than a series of steps. For example, the general rules for reading a bar graph are more tactical than algorithmic in nature. They don‘t ensure success in reading a bar graph, but they increase the probability of success. Strategies, unlike algorithms and tactics, are not specific to any one task. You would have a tactic for accomplishing the specific task of reading a bar graph, whereas you would have a general strategy for approaching problems of any type. Larkin (1981) found that experts in any field are far more strategic in their thinking than nonexperts in that field.
The initial models a learner builds, then, are somewhat different for each of the three types of procedures. The model for an algorithm would be a series of steps to be performed in a specific order: first you do this, then you do this, and so on. The model for a tactic would be a set of general rules (sometimes referred to as heuristics) that have a general rather than rigid order of application. The model for a strategy would be an even more general set of rules or heuristics that are not specific to one task. Although the initial models for algorithms, tactics, and strategies are somewhat different, the instructional techniques for helping students construct models for the procedures are the same. Among the most powerful techniques are analogizing, think-aloud modeling, and flow charting.
Analogizing is the process of providing students with an analogy that will help them construct an initial model of an algorithm, tactic, or strategy. The power of using analogy to help students understand a procedure was demonstrated in an experiment by Gick and Holyoak (1980). They presented their subjects with the following problem (which was adapted from Duncker 1945).
Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient, but unless the tumor is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumor. If the rays reach the tumor all at once at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity, the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor either. What type of procedure might be used to destroy the tumor with the rays, and at the same time avoid destroying the healthy tissue? (Gick and Holyoak 1980, pp. 307–308).
 
Few subjects were able to solve this problem when it was first presented because they had no process (tactic) to follow. Gick and Holyoak then presented their subjects with an analogy for the solution:
A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a full-scale direct attack. However, the general then learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator needed to move his troops and workers to and from the fortress. However, any large force would detonate the mines. Not only would this blow up the road, but it would also destroy many neighboring villages. It therefore seemed impossible to capture the fortress. However, the general devised a simple plan. He divided his army into small groups and dispatched each group to the head of a different road. When all was ready he gave the signal and each group marched down a different road. Each group continued down its road to the fortress so that the entire army arrived together at the fortress at the same time. In this way, the general captured the fortress and overthrew the dictator (p. 351).
With this story as a hint, nearly all of the subjects were able to construct a tactic that allowed them to solve the problem.
 
Perhaps the most frequently used technique for helping students construct initial models for procedural knowledge is think-aloud modeling. Although think-aloud modeling has been used for years to teach behavior modification strategies, Madeline Hunter (1976) has brought this technique to the attention of American educators (see Meichenbaum 1977 for a review of the use of think-aloud modeling). Think-aloud modeling involves the teacher expressing her thoughts and, thus, presenting a model for the procedure as she works through a skill or process. For example, if a teacher were to use think-aloud modeling to help students construct a model for the process of reading a bar graph, she might use an overhead of the graph and say to the class, "Let‘s see, what‘s the first thing I should do here? I‘ll read the title to get a sense of what this graph is all about. Then, I‘ll look at the horizontal axis—that‘s the line on the bottom." As the teacher thinks through the algorithm, tactic, or strategy, students get a glimpse of the steps or heuristics that are involved and the pattern of decisions that are made within the skill or process.
A flow chart is another, slightly more structured, method of model construction. Lewis and Green (1982) note that flow charts provide students with visual representations of algorithms, tactics, or strategies and greatly improve their ability to construct a model. Figure 3.7 shows a flow chart that might be presented to or constructed by students to help them build a model to develop a tactic for reading a bar graph.
 
Flow charts like the one in Figure 3.7 are meant to be nonrigorous and informal. Flow charting for the purpose of model building does not have to follow the strict conventions used in computer programming, where specific symbols (e.g., circles, triangles) have specific meanings. In fact, following these strict conventions would probably inhibit students‘ model building because they would have to try to remember all the rules and symbols every time they drew a flow chart.
Shaping Procedural Knowledge
The shaping process is probably the most important part of developing procedural expertise. In this phase, learners alter the initial model of the skill or process (which was either provided by the teacher or constructed by them). Researchers have found that during this stage systematic errors are commonly introduced into a skill or process. For instance, Brown and Burton (1978) observed a middle school student produce the following two errors: According to Anderson (1990), the response of most people (including some teachers) to such errors is to conclude that the student is extremely careless, is guessing randomly, or knows nothing. But this student was actually following faithfully a rule that he had constructed: 0−N=N; that is, "if a digit is subtracted from 0, the result is the digit." The infusion of systematic errors like this into an algorithm, a tactic, or a strategy is referred to as a "bug." Brown and Burton found 110 such bugs that young students may introduce into the subtraction process during the shaping phase of learning.
It is during the shaping phase, too, that learners attend to their conceptual understanding of a skill or process. When students lack conceptual understanding of skills and processes, they are liable to use procedures in shallow and ineffective ways. The Mathematical Science Education Board (1990) warns that procedural learning in itself does not ensure conceptual understanding. And Clement, Lockhead, and Mink (1979) have shown that even a solid knowledge of the steps involved in algebraic procedures does not in most cases (over 80 percent) imply an ability to correctly interpret the concepts underlying the procedures. Additionally, several studies have shown that mathematical procedures are best used when learned at a conceptual level (Davis 1984, Romberg and Carpenter 1986).
Guided practice is a powerful instructional technique for helping students understand procedural knowledge at a conceptual level. Although the term is most commonly associated with the work of Madeline Hunter, it has a rich tradition and theory base stemming from Vygotsky‘s work on the zone of proximal development and the more recent work on scaffolding. Vygotsky (1978) hypothesized that a learner needs the most guidance when working in the zone of development in which she has not yet acquired a skill but has some initial idea of it—in effect, when the learner is shaping a procedure she has been introduced to. What is now called scaffolded instruction is, at its core, guiding a learner through the shaping of a skill or process.
In guided practice, a teacher (or anyone else familiar with the procedure being learned) supervises the learner as she slowly moves through the process. The job of the expert guide is to help the learner experience possible pitfalls when performing the procedure. Recall Mrs. Baker‘s actions. She took great pains to illustrate a variety of errors that learners can make while performing three-column addition.
During the shaping process, it is also important to illustrate the different situations in which the skill or process can be used. To do this, Ms. Baker would have provided students with a variety of types of problems that require three-column addition. This is described as "developing the contextual knowledge important to a skill or procedure" (Paris and Lindauer 1982; Paris, Lipson, and Wixson 1983).
It‘s important to deal with only a few examples during the shaping phase of learning a new skill or process. The shaping phase is not the time to press students to perform a skill with any speed. Unfortunately, Healy (1990) reports that American educators tend to prematurely engage students in a heavy practice schedule and rush them through multiple examples. In contrast, Japanese educators attend to the needs of the shaping process by slowly walking through only a few examples:
Whereas American second graders may spend thirty minutes on two or three pages of addition and subtraction equations, the Japanese are reported to be more likely at this level to use the same amount of time in examining two or three problems in depth, focusing on the reasoning process necessary to solve them (Healy 1990, p. 281).
In short, shaping through guided practice requires a knowledgeable teacher who slowly works with students at a conceptual level.
 
Internalizing Procedural Knowledge
The final stage of learning a skill or a process is to internalize the knowledge: to practice it to the point where you can perform it with relative ease. Actually, it is most accurate to think of skills and processes as being located on a continuum of skill levels ranging from controlled processing to automaticity (LaBerge and Samuels 1974, Shiffrin and Schneider 1977). Algorithms are commonly learned to the point of automaticity. For example, many algorithmic aspects of driving a car or comprehending language are learned at the automatic level. Controlled processes, on the other hand, require conscious thought even when perfected. For example, many of the strategies used in chess require conscious thought, even when used by experts. Internalizing, then, involves learning a procedure to the point at which it can be used with ease, whether it is performed automatically or with conscious control.
Regardless of whether a process is learned to the level of automaticity or the level of expert control, it is extended practice that gets the learner there. This was dramatically illustrated by Kollers (1976, 1979), who taught subjects to read passages that were inverted and backwards. After reading 200 pages, Kollers‘ subjects were able to read the inverted passages almost as quickly as they could read regular passages. As Anderson (1990) notes, such studies demonstrate that with enough practice, we can internalize skills and processes regardless of their nature. When skills are internalized, we don‘t have to pay attention to them and, thus, we can devote more attention to processing new information.
There does not seem to be any limit to the effects of practice, though after a certain amount of time the returns certainly diminish. Describing a study done on a woman who made her living rolling cigars in a cigar factory, Anderson notes:
There do not appear to be any cognitive limits on the speed with which a skill can be performed. Her speed of cigar making. . . [improved] . . . over a period of ten years. When she finally stopped improving, it was discovered that she had reached the physical limit of the machinery with which she was working! (Anderson 1990, p. 261).
In short, it is practice—a lot of it—that enables the learner to internalize a skill or process.
 
Probably the most detailed work on practice as an instructional device has been done in the field of precision teaching, an instructional method developed by Ogden Lindsley (1972). The techniques of this method have been used in virtually every academic discipline, and a powerful organization headed by Carl Binder has sprung up to support it. Highly behavioristic in nature, precision teaching involves periodically measuring students‘ speed and accuracy in performing a skill and then marking each measurement on a "Standard Behavior Chart." Using the chart, students and teachers can observe progress until a specific goal is met.
Precision teaching is a time-consuming and rigorous way of internalizing a skill. Although very powerful, this method is probably far too labor-intensive for most teachers. Some aspects of precision teaching, however, can be readily adapted to classroom instruction—namely, practicing with specific goals of speed and accuracy in mind. For example, a teacher in San Diego who uses an adaptation of precision teaching explained to me how she emphasizes speed and accuracy when her students practice a new skill, such as dividing by fractions. To enhance accuracy, she periodically provides students with sample problems, which they perform independently in a set period of time. They then chart their accuracy. Over two weeks, students might do this four to seven times. Their chart provides a visual record of their progress. The same technique is used to enhance their speed.
Planning for the Acquisition and Integration of Procedural Knowledge
Instruction that will help students acquire and integrate procedural knowledge is usually the result of a teacher‘s careful planning. To illustrate, let‘s consider Ms. Conklin‘s planning for the weather unit.
Ms. Conklin‘s Planning for Dimension 2: Procedural Knowledge
As Ms. Conklin plans how she will help students acquire and integrate declarative knowledge, she also considers procedural knowledge. She starts by asking herself a basic question: "What skills and processes will students encounter in the unit?" She comes up with three ideas:
Predict weather
Read a barometer
Operate the computer simulator at the university forecasting center
 
The more she thinks about it, though, the more she realizes that students don‘t need to know how to perform some of these processes; they simply need to be aware of them. For example, Ms. Conklin doesn‘t really expect students to be able to use the computer simulator with any level of expertise. She only wants students to have the experience of using a simulator. With this realization, she changes her question: "What skills and processes do students really need to master?" She decides there is only one: the process of reading a barometer, which students will be expected to be able to do later in science class.
Next, Ms. Conklin thinks about how she can help students develop a model for the process of reading a barometer. She decides that she will think aloud as she performs the process and write the steps on the blackboard as she does so. She will also ask students to create a flow chart of the process. She records her decisions in the planning guide (see column 2 of Figure 3.8 on page 64). To help students in the shaping process, she decides that she will ask a few students to read the barometer in front of the whole class. As they do so, she will ask "what if" questions that will make students aware of the errors they might easily make when reading a barometer. She realizes that she will have to practice reading a barometer herself to be able to identify and point out the pitfalls in the process. Finally, to help students develop their ability to a level of automaticity, she will establish a practice schedule for them and ask them to keep track of their accuracy. Again, she records her decisions in the planning guide.
 
Figure 3.8. Unit Planning Guide for Dimension 2: Acquiring and Integrating Procedural Knowledge
Skills/processes to be taught
How will students be aided in constructing models?
How will students be aided in shaping skills/processes?
How will students be aided in internalizing skills/processes?
Reading a barometer
Think-aloud demonstration; write steps on the board.
Students will develop flow charts in cooperative groups.
 
Demonstrate variations and errors
Have students work problems; ask "what if" questions
 
Time will be provided for students to practice in pairs-goal is 5 consecutive correct readings
Practice schedule will include spaced 1/2-hour sessions
 
Ms. Conklin‘s example illustrates four questions important to planning for procedural knowledge:
1. Which skills and processes do students really need to master? Many teachers fall into the trap of trying to help students master all the skills and processes presented in a unit. Students don‘t need to master everything. To decide which skills and processes to teach in the manner described in this chapter, the general rule of thumb is to select that those are necessary for students‘ present or future success. For example, the process of using a telescope might be covered in an introductory course on astronomy, even though it is not considered essential to successfully acquiring and integrating the important knowledge of the course. In this case, the teacher would probably simply demonstrate the process, so that students are aware of it, and ask them to try it a few times.
Some skills and processes, though important to present or future success in a content area, are familiar enough to students that extensive instruction isn‘t necessary. For example, if students are already quite proficient at reading a bar graph, they might easily internalize the process of reading another type of graph without going through the model building, shaping, and internalizing phases described here. Selecting the skills and processes that actually require attention to the three phases of learning procedural knowledge is a key curricular decision.
2. How will students be aided in constructing models? Given the importance of model building to procedural learning, teachers should be sure to attach some type of model-building instruction to important skills or processes in a unit. Ms. Conklin used think-aloud modeling, writing out the steps of the procedure, and flow charting. Such techniques help students establish the initial model. Without that model, procedural learning is reduced to trial and error.
3. How will students be aided in shaping the skill or process? Shaping is the most often overlooked part of learning procedural knowledge. Besides requiring an in-depth knowledge of the skill or process being taught, shaping demands time and energy, commodities that the typical school atmosphere works against. Successful shaping requires teachers to think about the various kinds of errors that can be made within the skill or process and the various contexts in which the skill or process might be used. In short, if teachers plan to help students shape a skill or process, they themselves need to have a high level of expertise in it. Recall that Ms. Conklin found that she had to practice reading a barometer herself before she could guide students through the shaping process.
4. How will students be aided in internalizing the skill or process? Key considerations here are how much and what kind of practice will be considered. Following the axiom of combined, massed, and distributed practice, a teacher might set up several practice sessions spaced fairly close together in the early stages of internalizing a skill or process. Over time, the practice sessions would be spaced further and further apart. The teacher must also decide what emphasis she will place on speed and accuracy during practice. In general, the more accuracy and speed with which a skill or procedure can be performed, the freer learners are to devote the limited capacity of short-term memory to dealing with other issues, thus increasing the flexibility of their performance.
In summary, the acquisition and integration of declarative and procedural knowledge is basic to the learning process. Although somewhat similar, the two types of knowledge require different emphases. When acquiring and integrating declarative knowledge, the learner must initially construct meaning by associating new knowledge with prior knowledge. Then she must organize the information so as to emphasize important ideas and relationships. Finally, if she wants to retain the information in long-term memory, she must do something to help her store the information. When acquiring and integrating procedural knowledge, the learner must initially build a detailed model of the process involved. Then he must shape the process by eliminating errors and identifying the most efficient techniques for completing the process. Finally, he must practice the process until he can perform it with relative ease.
To help students acquire and integrate declarative and procedural knowledge, a teacher must have a keen understanding of both types of knowledge and be able to plan instruction that is sensitive to their differences.