Chapter 5. Dimension 4: Using Knowledge Meani...

A Different Kind of Classroom: Teaching with Dimensions of Learning
by Robert J. Marzano
Chapter 5. Dimension 4: Using Knowledge Meaningfully
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.
Generally, we acquire and integrate knowledge because we want or need to use it. For instance, when I was a graduate student with little money to spare, I learned a great deal about automobile engines because I wanted to save money by doing my own tune-ups (since then, I‘ve learned that‘s what grown sons are for). And recently, I learned a lot about stereos because I wanted to make an intelligent decision about buying one. In short, we learn best when we need knowledge to accomplish some goal. It‘s important to note that the extending and refining tasks described in Chapter 4 are not usually the focus of goals. People don‘t often compare just for the purpose of comparing, they don‘t abstract simply for the pleasure of abstracting. Some kinds of tasks, however, do represent common goals—common ways we use knowledge meaningfully. They are decision making, investigation, experimental inquiry, problem solving, and invention.
Decision Making
Decision making is the process of answering such questions as "What is the best way to . . .?" or "Which of these is most suitable . . .?" It is a process that people of all ages use throughout their lives—usually without thinking much about it. Used in the classroom, however, it is an excellent way to improve learning. To find out how decision making can be used in the classroom, let‘s look at Ms. Haas‘ class.
Ms. Haas‘ Class
The students in Ms. Haas‘ class have been studying the 1960s. So far, they have really enjoyed the unit. They especially liked watching film clips from Easy Rider and a documentary about Woodstock. Ms. Haas has enjoyed the unit too because it made her remember her younger days. She even brought in some of her headbands, bell-bottoms, and love beads that were her uniform at Berkeley. She thinks her students know the people of that era well and some of the issues that shaped the times.
One day a student asks who was the most influential person of the 1960s. Ms. Haas thinks for a moment. "Before I give you my answer, give me yours," she says. One student yells out, "Timothy Leary." "Why?" Ms. Haas asks. Before the student can answer, another student says, "No, it had to be JFK." Ms. Haas sees an opportunity. "OK, let‘s not answer it right now," she says, "let‘s take some time." Just then the bell rings, giving her until the next day to plan. She decides to turn her students‘ interest into a project.
When she meets the class the next day she doesn‘t have to remind students of the previous discussion. They ask, "Who was the most influential person?" She doesn‘t answer but instead says, "Let‘s try something. Pretend that you are on a committee for Time magazine, which is publishing an issue commemorating the decade of the 1960s. The cover of this issue will feature the person of that decade. Your job is to decide which person should be selected and justify your decision to the publishers by listing the people that you considered, the criteria you used, and how you rated each person."
 
We make decisions every day. Most are rather trivial and don‘t involve a great deal of thought, like where to go for lunch or what movie to see. Some decisions, however, can greatly affect our lives and others‘. It is when we make these decisions that we involve ourselves deeply in the content surrounding them. For example, John F. Kennedy was engaged in decision making while he was trying to determine what to do about the Soviets‘ shipping nuclear missiles to Cuba. In effect, he was asking himself, "What is the best course of action to take for the American people?" According to some accounts of that decision, Kennedy and his advisory committees studied the situation in depth. Similarly, from August 1990 to January 15, 1991, President Bush was engaged in decision making when he was trying to identify the best course of action for the United States in the conflict between Iraq and Kuwait.
There are several decision-making models, including those by Wales, Nardi, and Stager (1985), Halpern (1984), and Ehrenberg, Ehrenberg, and Durfee (1979). Analyzing these models reveals that decision making typically involves a situation in which you must select among two or more alternatives. At the outset, these two or more alternatives commonly are equally appealing or, at least, it is not immediately apparent which is the most appealing. Consequently, to make your selection you first identify what you want from the situation. In more formal terms, you identify the "criteria" or "outcomes" you wish to incorporate in your final selection. For example, during the Cuban missile crisis, Kennedy might have considered the following criteria or outcomes:
Ensure the long-term safety of the United States.
Exhibit the appearance of power.
Avoid forcing military action between the United States and the Soviet Union.
 
When decision making is done systematically, the next step is to identify the importance of each of the possible outcomes. Kennedy might have concluded that ensuring the long-term safety of the United States and avoiding aggression between the United States and the Soviet Union were high priorities, but appearing powerful was not. Some models of decision making suggest that perceived importance of criteria should be quantified. For example, a weight of 3 could indicate that a criterion is very important; a weight of 2, moderately important; and a weight of 1, not very important. Using this process, Kennedy might have given a weight of 3 to the first and third outcomes and a weight of 1 to the second outcome.
The next step is to identify the alternatives to be considered. Kennedy may have been considering these alternative actions:
Blockade Cuba, but do not announce what actions will be taken if the blockade is broken.
Blockade Cuba and threaten to sink the ships if the blockade is broken.
Allow ships to enter Cuba and threaten to invade the country if the missiles are installed.
Allow ships to enter Cuba and do not announce any kind of retaliation.
 
Once alternative actions have been considered, the outcomes are referenced against the alternative actions. That is, the extent to which each alternative action can bring about each desired outcome is identified. Again, some theorists recommend that this relationship be quantified. A decision matrix like that in Figure 5.1 is a useful tool for such quantification.
 
Figure 5.1 indicates that the first alternative has a moderate probability of affecting outcome A (it has a weight of 2). Alternative 2 has a high probability of affecting outcome A (it has a weight of 3), and so on. As you can see in this figure, if the decision maker multiplies the "alternative weights" by the "outcome weights" and adds up the products for each alternative, he can reach a quantitative decision.
As the example of the Cuban missile crisis illustrates, the decision-making process forces the decision maker to assign priorities to outcomes and analyze the relationships between outcomes and possible alternatives. This is a fairly sophisticated level of analysis.
In the classroom, the decision-making process can be used in a variety of ways in many content areas. Ms. Haas employed the process to help students use the knowledge they had gained about the 1960s in some realistic and intriguing ways. "Who was the most influential person of the 1960s?" is a question that people, especially those who have studied or lived through the 1960s, might realistically ask. The process of answering this question would inevitably make students aware of aspects of the 1960s they would not have understood without tackling such an involved task.
Decision-making tasks can be used in a variety of content areas. Here is an example of a task that might be used in a science class where students are studying nuclear energy and nuclear reactors:
We have learned about three different types of nuclear reactors. We have also studied the resources and environment nuclear reactors require. Assume you are on a panel charged to select the type of nuclear reactor that will be built in the state and where it will be built. Make your selection of both the type of reactor and the site where it should be built. Your report should include the following items:
The criteria you used to determine the type of reactor to build and why you used those criteria.
The extent to which each reactor measured up to each of your criteria.
The alternative sites you considered.
The criteria you used to assess the sites.
The extent to which each site measured up to your criteria.
Your final selection.
 
 
Investigation
There are three basic types of investigation. Definitional investigation involves answering such questions as "What are the defining characteristics of . . .?" or "What are the important features of . . .?" Historical investigation involves answering such questions as "How did this happen?" and "Why did this happen?" And projective investigation involves answering such questions as "What would happen if . . .?" and "What would have happened if . . .?"
All three types of investigation can be used in a variety of classroom situations. To illustrate, let‘s consider the examples of Ms. Whisler, Ms. McCombs, and Mr. Kendall, whose classrooms depict the use of definitional, historical, and projective investigation respectively.
Ms. Whisler‘s Class (Definitional Investigation)
For the past two units, Ms. Whisler and her students have been studying the various ages in history. They have just finished studying the Renaissance. As Ms. Whisler was summarizing what the class has learned so far, one student asked, "Exactly what is an age?" When she tried to respond, Ms. Whisler realized that she really didn‘t have a good answer. She knew historians have identified specific ages—the Renaissance, the Dark Ages, the Age of Discovery—but she wasn‘t really sure how to define an age in general. As a group, Ms. Whisler and her students decided they would like to answer the question "What are the characteristics of an age?" Ms. Whisler explained that in answering this question, they should try to determine the characteristics that define an age in general terms and then look at a few specific ages and see if the characteristics really fit. Ms. Whisler also encouraged students to identify the confusions that exist about the concept of an age: "If we‘re asking what an age is, other people must be too. Let‘s see if we can clear up some of the confusion."
Ms. McCombs‘ Class (Historical Investigation)
Ms. McCombs‘ 4th grade class has been studying dinosaurs. The textbook explains that the dinosaurs died because of severe changes in climate. One student who has been interested in dinosaurs since she was five years old says, "That‘s not why the dinosaurs died. I read that it was because a big comet hit the earth and they all died at once." Ms. McCombs says, "Well, you‘re right. There are a number of explanations for why the dinosaurs died." Rather than describe the various theories, Ms. McCombs decides to turn the question of why the dinosaurs died into a research project. She writes the question on the board: "Why did the dinosaurs die?" She explains to students that they can work in groups or on their own. They have to come up with an answer that satisfies them, but their answer also must take into account other explanations; they must describe why their answer is the best. One of the students asks, "Where do we start?" Ms. McCombs replies, "Anywhere you want. Let‘s go talk to the librarian to see what we have available to help you."
Mr. Kendall‘s Class (Projective Investigation)
One day while studying the concept of the "greenhouse effect," a student in Mr. Kendall‘s science class asks, "What will happen if the greenhouse effect is true? I mean, what will really happen if the temperature of the entire earth goes up?" Mr. Kendall throws the question right back at the students: "What do you think?" To his surprise, they get into a lively and very heated discussion. Some students say they have heard that if the temperature goes up more than 3°F the polar caps will melt and all the coastlines will be flooded; New York and Los Angeles will be under water. Another student says she heard that for the polar ice caps to melt, the temperature would have to go up at least 10°F and that would be impossible even in the worst conditions. The debate lasts until the end of the period.
The next day students want to continue the debate as soon as class starts again. Mr. Kendall responds, "We need more information. Let‘s investigate this issue. What would happen if the greenhouse effect were an undeniable reality?" Mr. Kendall makes the question more specific by identifying some assumptions they will work under, the most important of which is that within ten years the overall temperature of the entire planet will rise by 3°F and then remain stable for a thirty-year period due to the corrective efforts of people around the world. Students have a week to work on the question in small groups. Mr. Kendall tells students that in their reporting they should explain the confusions about this issue and describe the conflicting viewpoints.
 
Definitional Investigation
As Ms. Whisler‘s example illustrates, definitional investigation involves identifying the defining characteristics of a concept for which such characteristics are unknown or, at least, not readily apparent. Although students had been studying various ages, neither they nor Ms. Whisler was sure about the defining characteristics of an age. Additionally, there was no place they could go to easily obtain that information. In most fields, definitional investigation is a continuing process. For example, people are still investigating how to define the concept "legally dead." What is the defining characteristic of that concept? Is it that all vital signs have stopped or is it that the brain‘s higher-order functions have ceased? In fact, many of the current issues facing modern society are issues that can be explored using definitional investigation. Consider the issues of abortion and defamation of the American flag. We can phrase each of these issues in the formal terms of definitional investigation:
Abortion. What are the defining characteristics of a person who has the rights of an individual in our society? Does a fetus have such rights? Are these rights protected from the moment of conception? (And how do we confine conception?) Are they protected from the moment of birth?
Defamation of the American flag. What are the defining characteristics of freedom of speech? Does it extend to the defamation of the American flag?
 
Definitional investigation is basic to an advancing society. It is a powerful tool used to make important distinctions about evolving concepts. In the classroom, it can be used in virtually every content area where understanding concepts is important. Here is an example of a definitional investigation task that might be used in a social studies class:
Identify a past or present amendment to the U.S. Constitution that has caused controversy or confusion. Tell what is known or agreed upon about this amendment and explain where the confusion or contradiction exists. What do you think is the intent of this amendment and how could this amendment be reworded to reflect your views and clear up the confusion?
 
Historical Investigation
Historical investigation involves identifying why or how some past event occurred. This was the type of investigation used in Ms. McCombs‘ class. Much of what is called investigative reporting falls into the category of historical investigation. For example, Bob Woodward and Carl Bernstein were involved in historical investigation when they uncovered and reported the events surrounding the Watergate break-in. Similarly, the researchers and theorists who have been trying to unravel the mystery surrounding the assassination of John F. Kennedy have been involved in historical investigation.
Historical investigation is basic to our attempts to understand the past. Of course, there are many content areas in which such a perspective is a driving force. History, literature, and anthropology are to a great extent driven by such questions as "Why didn‘t Hitler heed the advice of his generals about the inevitability and severity of the Normandy invasion?" "Why did Hemingway commit suicide?" "How did Neanderthal man die out?" There are also many opportunities for historical investigation in fields that, on the surface, do not appear to have an historical bent. For example, here is an historical investigation task that a high school calculus teacher gave to her class:
We now know that Newton discovered calculus years before Leibniz did, but Newton published his work much later than Leibniz. A major row ensued over who had been first. As the row grew, Leibniz made the mistake of appealing to the Royal Society to resolve the dispute. Newton, as president of the society, appointed an "impartial" committee to investigate the issue. The report from the committee officially accused Leibniz of plagiarism. Some people say Newton wrote the report himself. Your task is to find out the truth about this incident. Identify the conflicting theories and defend the one that you think is the most credible.
 
Projective Investigation
Projective investigation involves identifying what will happen if some future event occurs or what would have happened if some past event had occurred. Projective investigation deals with the hypothetical. The current debate about what will happen if more of the rain forests in Brazil are cut down and the debate over what will happen if the ozone layer continues to erode are examples of projective investigation. In school, we can readily use projective investigation in content areas that deal with hypothetical past or future situations. For example, here is an investigation that might be done in a high school sociology class:
The notion that some countries are more "developed" than others implies that one country‘s future may be understood as, in part, the reenactment of another country‘s past. Select some aspect of development for which this might hold true (cultural, military, spiritual, etc.). Working within the aspect of development you have selected, describe those changes in a developing country that you believe you can predict with some confidence. Identify those areas that would be least predictable. Finally, describe the ways in which the aspect of development you have selected can be better understood from the perspective of more developed countries, and in what ways that perspective can be misleading.
 
All three types of investigation involve several common elements. For one, they involve identifying what is known or commonly accepted about the concept, past event, or hypothetical event being studied. Students performing Ms. Whisler‘s project on the characteristics of an age would first have to identify what is already known or accepted about the concept of historic ages. Ms. McCombs‘ students would have to identify what is known and accepted about the disappearance of dinosaurs, and Mr. Kendall‘s students, what is known and accepted about the greenhouse effect. At this identifying stage, students should use primary source materials as much as possible so they can get undiluted information. For example, if students were doing an historical investigation about why Hemingway committed suicide, they should be encouraged to read his letters or his relatives‘ accounts of him.
Perhaps the most important part of any type of investigation is identifying contradictions or confusions. Note that Ms. Whisler, Ms. McCombs, and Mr. Kendall all stressed that students should highlight the confusions and contradictions surrounding their topics. It is the desire to resolve confusions and contradictions that usually moves a person to investigate.
The last element all types of investigation have in common is the solutions to the contradictions and confusions previously identified. The importance of identifying confusions and contradictions and then offering and justifying solutions cannot be emphasized enough. These components are the life force of investigation. Without them, the process is simply a matter of collecting information and reporting it. This was dramatically illustrated to me when my daughter Carmen was required to do a "report" on the Exodus. She approached it as a simple matter of collecting information from various encyclopedias, the Bible, and some books from the library. She was not very enthusiastic about the project until she found a contradiction in some of the materials she was using. Specifically, she found that in most accounts of the Exodus, Moses was credited with parting the waters of the Red Sea so that the enslaved Jewish nation could escape the Egyptian army. When the army tried to pass through the parted waters, they were drowned. In one of the books she had checked out of the library, however, the description of the incident stated that Moses led the Hebrew people across the Reed Sea, which was a shallow marshland. When the Egyptian army tried to cross, their heavy chariots and machinery became bogged down in the mire.
When Carmen asked me about the contradiction, I explained that there are various theories about the literal interpretation of biblical stories. Some believe they describe actual history, whereas others believe they are fictional stories intended to teach important truths. Carmen became intensely interested in this issue and we talked at length about the possibilities. Unfortunately, her enthusiasm was not funneled back into her project because the project was not set up in such a way as to focus on the contradictions and confusions surrounding the topic.
In short, the potential power of definitional, historic, and projective investigation is immense if the investigations are structured in a way that forces students to provide and justify solutions for confusions and contradictions.
Experimental Inquiry
Experimental inquiry is the process we engage in when answering such questions as "How can I explain this?" and "Based on my explanation, what can I predict?" To explore how experimental inquiry might be used in the classroom, let‘s look at Ms. Isaac‘s class.
Ms. Isaac‘s Class
To make the classroom environment a little brighter, Ms. Isaac had brought in different types of plants and flowers and let her students choose where to place them in the room. One vine was placed in a small cubbyhole under a shelf where there wasn‘t much light. After two weeks, one student noticed that the plant had grown in an odd fashion. It hadn‘t grown straight up, as the other plants had, but grew out sideways and took two or three turns until its outermost vines reached the window and the sunlight. Then it grew straight up.
When students asked why this had happened, Ms. Isaac seized the opportunity for a science lesson. She first had students generate their own explanations for the phenomena. Some thought it was because plants need light. Others thought it was because they need fresh air. Although Ms. Isaacs was tempted, she didn‘t correct any of their explanations. She simply asked, "Why do you think that might be?" Then she asked students to make a prediction based on their explanations and set up an experiment to test their prediction. She was amazed at what they came up with.
The next few days were spent setting up the experiments. Some students even brought in their parents, who had become interested when their children began asking related questions at the dinner table. It took two weeks to set up and conduct all the experiments. During that time, the children could hardly wait to finish their other lessons so they could check the progress of their studies. When the experiments were over, the children reevaluated their initial explanations. Three students whose original explanations contained the premise that plants will grow toward the light had the most success with their experiments. As a class, they decided that this principle seemed the most accurate. They all wanted to set up another experiment to reaffirm the principle.
 
Of course, the approach described in Ms. Isaac‘s class is the basis of modern science. The process of observing phenomena, generating explanations, making predictions, and then testing those predictions is frequently referred to as the scientific method. This type of thinking has changed the world. Prior to the scientific revolution some four centuries ago, physical and psychological phenomena were explained by deductive reasoning from "revealed truth." Observations were not necessary because the world could be explained by reasoning from what was known. In fact, anyone who challenged known "truth" did so at a great risk. As the renowned physicist Stephen Hawking (1988) explains, Copernicus anonymously circulated his theory that the sun was the center of the universe because he feared being branded a heretic. Nearly a century later, Galileo was placed under house arrest for the last eight years of his life by a clergyman protecting revealed truth, because Galileo publicly supported the Copernican hypothesis (Gilovich 1991).
In its most basic form, experimental inquiry involves observing, analyzing, predicting, testing, and reevaluating. For instance, a student might first observe that water in a shallow pan left overnight evaporates. The student would then analyze the event in an attempt to explain what happened (e.g., the water evaporated because it was exposed to dry air). Based on this analysis, the student would predict what might happen under certain conditions (e.g., the lower the humidity, the quicker water evaporates). The student would then test his prediction by setting up an experiment. Finally, based on the outcome of his experiment, the student would reevaluate his original explanation.
Many people assume that experimental inquiry is the standard operating procedure of science classes in U.S. public schools. Unfortunately, this is not true. In a recent report on common practices in American classrooms, NAEP reported that only 53 percent of the students surveyed said they daily or weekly do science experiments with others and 18 percent said they never do. Only 29 percent said they daily or weekly do experiments by themselves and 46 percent said they never do experiments by themselves (Mullis et al. 1990).
If experimental inquiry is rare in science classrooms, it is virtually nonexistent in other classrooms. This need not be the case; experimental inquiry can and should be used in all content areas. In my teacher workshops, I often say this, and I usually see puzzled looks on teachers‘ faces. Social studies or literature teachers usually react by saying that experimental inquiry is meant to explain physical phenomena. What these educators overlook is that experimental inquiry is also the preferred method of explaining psychological phenomena or human reactions. The realization that experimental inquiry can be used to explain human reactions opens the door for its uses across all disciplines.
For example, in a literature class, a student might become aware that she is easily confused by the writing of Faulkner. This represents the observational phase of experimental inquiry as it applies to psychological phenomena: noting a reaction in yourself or in others. During the analysis phase of the experimental inquiry process, the student would try to determine why she reacts this way to Faulkner. She might conclude that it is Faulkner‘s use of long, syntactically complex sentences that confuses her. During the prediction phase, she might hypothesize that information written in long sentences is more difficult to understand than information written in short sentences. During the testing phase, she would set up an activity to test her hypothesis. She might write two short essays covering exactly the same content, but write one essay using long, syntactically complex sentences and write the other using short, syntactically simple sentences. She could then test classmates on the content, perhaps by using an essay question. The student scientist would then evaluate the essay answers to determine which group best understood the content—the students who read the information presented in short sentences or those who read the information presented in longer sentences. Finally, during the reevaluation phase, the student would reexamine her initial conclusions, either affirming or altering them based on the results of her activity. The results here might indicate that when sentences become too syntactically simple, the information they convey is also difficult to comprehend. Hence, she might conclude that information is more easily understood by the reader when the syntax used to express it is moderately complex.
Experimental inquiry, then, can be applied powerfully to almost any subject. The first example below is an experimental inquiry task that might be used in a physics class. The second is an experimental inquiry task that might be used in a social studies class.
Example 1
You‘ve observed that when you are descending in an elevator, you feel heavier as the elevator comes to a stop. Do you suddenly gain weight, then lose it again? How can you explain this feeling? Based on your understanding of the principles involved, make a prediction about the extent to which a given object will have a different weight in a specific situation. Set up an experiment that will test your prediction, carry out the experiment, and then describe whether your experiment proved or disproved your hypothesis. Discuss the extent to which the principles you‘ve described still hold true.
 
Example 2
The people who entered adulthood in the 1960s are now in their forties. Some would say the 1960s have had no long-term effects on these people. Others would argue that, in subtle ways, the experiences of the 1960s are influencing the way these people are living their lives today. Try to determine what effects the experiences of the 1960s are having on life in the 1990s. Test your hypotheses by applying them to a number of people who were in their early twenties in 1960.
 
Problem Solving
Problem solving involves answering such questions as "How will I overcome this obstacle?" or "How will I reach my goal but still meet these conditions?" At its core, it is the process of achieving a goal that is blocked by some obstacle or limiting condition. But this is a fairly narrow definition of problem solving. In a very broad sense, any attempt to achieve a goal can be characterized as problem solving. In fact, Anderson (1982, 1983) and others have built computer programs that can "learn" using an algorithm that assumes all learning is problem solving. Conceptualizing problem solving in the narrow sense of overcoming overt obstacles to a goal, however, allows teachers to devise tasks that reinforce a specific and highly important type of thinking. Roger von Oech makes this point in his book A Whack on the Side of the Head (1983). Fundamentally, he says that we become truly creative when we are forced to perform routine operations in a new way. To explore how problem solving can be used in the classroom, let‘s look at Mr. Grossman‘s class.
Mr. Grossman‘s Class
Mr. Grossman‘s class has just finished studying the preservative effects of salt on food. In fact, they spent two weeks studying the exact chemical reactions that create the preservative effect. One student asks, "How could people have preserved food without salt?" Another student replies, "They could have used ice." Mr. Grossman points out that in the days when people used salt as a preservative, they had no way of keeping ice from melting. Another student asks, "What if they hadn‘t found out about salt? Was there any alternative?" Mr. Grossman says, "You know, you‘re raising a very interesting question. How could we accomplish the same preservative effects of salt without using salt or refrigeration? Let‘s make it even tougher. How could we achieve the preservative effect of salt without using any of its basic components—sodium or chlorine—and without using refrigeration of any sort?" At first the students think Mr. Grossman is joking, but then they realize he really wants them to answer this question. One student asks, "Can it be done?" Mr. Grossman responds, "I don‘t know, let‘s give it a try."
 
It is the type of thinking that springs from Mr. Grossman‘s challenge that has led to some of our great inventions. The powerful thinking skills program Odyssey of the Mind (Gourley 1981, Gourley and Micklus 1989) poses similar problems that require students to achieve goals under specific conditions or constraints. Here are some examples:
Present the Gettysburg address in a new artificial language. You cannot use any English words or conventions. Be prepared to explain the words and any rules you have created for your language.
Create a freestanding structure that is as tall as possible using only playing cards and masking tape.
Build as complex a structure as possible inside a clear plastic, two-liter container for soft drinks without cutting or altering the container in any way. Entry to the inside of the container should be only through the mouth of the plastic bottle.
 
The process of solving a problem begins with specifying a goal. For example, if you get up one morning and find that your car won‘t start, you have a problem. In this situation, the goal is obvious: getting to work. The next step might be described as identifying the constraint. Here, the constraint is that your usual method of transportation is not available. An important part of problem solving is identifying alternative ways of accomplishing the goal. In this example, that means determining other modes of transportation: taking a bus, finding a ride with a friend, or riding your bicycle. Finally, problem solving involves selecting an alternative and trying it out.
Teachers can use this process in a wide variety of subjects. An English teacher once related to me the results of asking students to devise a method of signaling complete thoughts and questions in oral language without using pitch (conventionally we lower pitch to signal the end of a complete thought and raise pitch to signal a question). The teacher explained that this task led students to explore aspects of language they would otherwise never have considered. For example, one group of students began a study of the nature and function of inflection in various languages. They found that one tribe of people signals complete thoughts by making clicking noises with the tongue, so they adapted a variation of these conventions to solve the problem.
Similarly, an elementary mathematics teacher described to me a problem she gave students that greatly enhanced their understanding of the conventions of long division. She explained that her students were quite good at performing long division using the standard method in which the divisor is placed next to the dividend on a horizontal plane: As a problem-solving task, she asked students to devise a method of performing long division in which the divisor is placed on top of the dividend: The teacher noted that while formulating their solutions to the problem, students carefully considered the importance of keeping track of place values.
We saw earlier that experimental inquiry is not limited to science, and, likewise, problem solving is not limited to mathematics. Problem solving can help students explore issues in virtually any content area. Here is an example of a problem-solving task that might be used in a social studies class:
You are the wagon master of a wagon train of pioneer families on its way from Ohio to California. Unfortunately, none of the wagons can go through water and your bridge- and raft-building capabilities on the trail are extremely limited. It is your job to find a new route for the wagon train or a process that will eliminate taking the wagons through water. Your journey may take as long as you like, but you must consider the effects of the seasons. Trace your route on a map and describe the terrain you cross. How far will you go? How much longer is your route than an actual pioneer trail and how much longer would it take?
 
Invention
Invention is the process of creating something that fills an unmet need or desire. In effect, you are inventing when you attempt to answer such questions as "What would I like to create?" "What is a new way?" "What is a better way?" To explore how invention might be used in the classroom, let‘s look at Mr. Barlow‘s class.
Mr. Barlow‘s Class
Mr. Barlow‘s class has just come back from a trip to a local housing project (where some of the students live) as part of their unit on current issues in the community. They have been studying how city funds are used to meet local needs. In their field trip, students also visited the various city agencies that provide service to the housing project. During the discussion they have back in the classroom, a couple of students say that although tenants have places they can go for health care and for food and clothing, they have nowhere to go for help with their day-to-day lives, no place where they can air their gripes and talk about the difficulties they‘re having. The students who live in the projects agree that domestic violence is high and that much of it is a result of tension within families.
Mr. Barlow paraphrases what they are saying: "What you want to do, then, is create a new service. Is that it?" The students agree. "OK, what would it do? What would be its purpose?" Students begin calling out all the things that the new service would provide and Mr. Barlow writes their suggestions on the board. After a while, it becomes obvious that this project is going to take more than one class period. Mr. Barlow says, "I‘ll give you six days to work together over the next week and a half. Let‘s see if you can really do it—create an agency, that is. You can work individually, in pairs, in small groups, whatever you like, but you have to come up with a detailed plan for your new agency. Specify what it would do, how much it would cost to make it work, how it would work, and how you would know when it‘s successful. When we‘re done, we‘ll take the plans to our city council."
 
Mr. Barlow‘s class was involved in invention, whereas Mr. Grossman‘s class was involved in problem solving. What is the difference? Basically, both involve creating a product or a process. Mr. Grossman‘s class was developing something that would have the preservative properties of salt but not use any of the basic elements. Mr. Barlow‘s class was developing a new service. In problem solving, however, the product or process is created under specific constraints or conditions. Thus, the emphasis is on overcoming a specific obstacle or constraint. You might say that Mr. Grossman‘s class had very few "degrees of freedom."
In invention, there is usually no obstacle (although the inventor might encounter obstacles along the way); rather, the emphasis is on filling some perceived need by improving on something or creating something totally new. Because of this difference in emphasis, the process of invention is qualitatively different from that of problem solving. Rather than initially focusing on obstacles or constraints, the invention process initially focuses on the product. This involves setting specific standards that will be met. Once standards are set, the inventor, like the problem solver, must work within specifications. The inventor, though, is usually free to change the standards, whereas the problem solver is rarely free to change the constraints.
Once standards or criteria are identified, the inventor‘s next step is to create a rough sketch or plan. For example, in Mr. Barlow‘s class students would have to outline how the new service would operate. A sketch or rough description created, the inventor then develops a first draft or working model. If Mr. Barlow‘s students were to complete the invention process, they would eventually create a working model of their new service—a pilot project, so to speak. This draft or working model then goes through successive revisions until the final product meets the criteria for success that were initially established. This is another major difference between problem solving and invention: the result of invention is a product that has been extensively revised and polished, whereas the result of problem solving is simply the satisfaction of overcoming the constraints.
Invention, then, involves the conception, development, and polishing of a product that meets a perceived need and specific standards established by the inventor. There are thousands of examples of invention. The Wright brothers saw a need for manned flight and set out to meet that need. They established certain standards for their new invention, the most important being that it would carry a full-grown adult over a significant distance. Within the invention process, they were free to change their standards—and by some accounts they did so several times. They also spent a long time refining their product.
Invention is one of the most open-ended and creative tasks that students can be involved in. It can be used in virtually every content area. Here is an example of an invention task that might be used in a home economics class:
People in wheelchairs have many problems in houses designed for people who are able to maneuver, reach, and stand. Your task is to design a kitchen that is "wheelchair friendly," using any arrangement and materials you think are appropriate. You might want to think about redesigning the appliances, sinks, lighting, layout, access, and storage areas. Develop a detailed model of your kitchen and invite a person in a wheelchair (preferably an adult who cooks and cleans) to critique it and offer suggestions. Revise your design until it meets the standards of utility and efficiency determined by the wheelchair-bound community.
 
What Makes These Tasks Meaningful?
In this chapter I have asserted that decision making, investigation, experimental inquiry, problem solving, and invention are types of tasks that involve students in the meaningful use of knowledge. But what makes these tasks meaningful? In general, meaningful classroom tasks fall into three categories: application-oriented tasks, long-term tasks, and student-directed tasks.
Application-Oriented Tasks
All the tasks described in this chapter focus on the application of knowledge. Each can be conceptualized as answering specific types of questions. For example, decision making answers the question "What is the best?" Definitional investigation answers questions like "What are the defining characteristics?" These tasks require students to use their knowledge to accomplish specific goals or to apply their knowledge when answering specific questions. Their emphasis is not learning for learning‘s sake, but learning as a by-product of trying to accomplish something, of trying to answer questions that are common human concerns. This is always the most powerful kind of learning.
Long-Term Tasks
The length of the class period and the length of the course determine the lower and upper limits of long-term tasks in the classroom. In the traditional fifty-minute class period, a long-term task should last at least three classes. It could, however, last as long as the course itself: a quarter, a semester, or a year, depending on the classroom setting. In most classrooms, though, the most practical way to use long-term projects is to tie them to units of instruction. Many teachers break instruction into theme units that last from one to six weeks. Within a unit of instruction, then, a task could last up to six weeks.
Unfortunately, the principle that classroom tasks should be long-term flies in the face of current practice. These learning tasks rarely take even one or two periods to finish; besides that, they are usually directed by the teacher and require little higher-order thinking (Doyle 1983, Fisher and Hiebert 1988). The most common task is probably reading a selection from a textbook and then answering questions at the end of the selection or completing a textbook exercise.
Student-Directed Tasks
The characteristic that is most important if a task is to be called meaningful is the extent to which it is student directed. This means two things: (1) students have control over the construction of the tasks, and (2) students have control over the products generated from the task.
At the very least, students should have control over the construction of tasks: they should identify the questions they would like to answer about the topic they are studying. The teacher and students might first discuss issues that have come up in the unit, but students should then be able to identify questions relating to these issues and construct appropriate tasks. Of course, when an issue of particular importance surfaces, the teacher may still devise tasks for students. And when students are first introduced to the five types of tasks described in this chapter, they will no doubt need a great deal of guidance from the teacher. In general, though, students should have the freedom to create their own tasks and be encouraged to do so.
Students should also have some control over the products generated from the tasks. Generally, outcomes and products in school are limited to written and oral reports (Durst and Newell 1989). That is, students are commonly required to write an essay or make an oral report describing what they have learned. As useful as these methods of presentation are, they exclude other methods of presenting information. Video- or audiotaped reports, newscasts, graphic organizers accompanied by explanations, slide shows, dramatic presentations, demonstrations, debates, and panel discussions are all valid ways of reporting the results of the tasks described in this chapter.
For instance, the students in Ms. Haas‘ class might have presented the results of their investigation of the most important person of the 1960s in a video or in a debate. And the students in Mr. Kendall‘s class might have presented the results of their investigation of the greenhouse effect in a newscast or dramatic presentation.
The products of meaningful-use tasks can be expanded even beyond the list presented above if students are allowed and encouraged to develop artifacts along with their tasks. Artifacts are artistic or symbolic representations of affective experiences associated with a task. For example, in a decision-making task about which action would have been best for the United States to take in the conflict between Iraq and Kuwait, a student might develop a sketch to supplement her written report. The written report would be used to communicate the process used in the decision-making task and the conclusions drawn from it, while the artifact (the sketch) would be used to communicate a specific feeling associated with the learner‘s conclusions. In short, the learner would use the sketch to represent the emotion she had experienced while gathering information for the decision-making task.
Introducing Meaningful-Use Tasks
Because of the complexity of the meaningful-use tasks described in this chapter, students generally need to be taught the critical aspects of the processes underlying the tasks. It is in introducing the meaningful-use tasks that Beyer‘s (1988) five-step process for teaching a complex process makes sense:
The teacher introduces the process by describing and demonstrating the steps of the process, explaining when the process should be used, and naming the process.
Students experiment with the strategy using "neutral" content; that is, the teacher provides students with familiar and interesting content, allowing them to focus on the process without the interference of struggling with new or uninteresting content.
Students think about what goes on in their minds as they use the process. This may be done in cooperative groups.
As a result of their reflection or group discussion, students may make changes in the strategy.
Finally, students try out the modified process and again reflect on its use.
 
If the processes underlying the meaningful-use tasks are not taught in this manner, then teachers should be prepared to guide students through the tasks or to provide them with highly structured tasks. Over time, then, tasks can shift to a more student-structured format.
Planning for the Meaningful Use of Knowledge
To explore the decisions a teacher needs to make when planning for the meaningful use of knowledge, let‘s look at Ms. Conklin‘s planning for Dimension 4. We can assume that over the year Ms. Conklin has introduced students to the processes involved in decision making, investigation, experimental inquiry, problem solving, and invention, so she is free to present a variety of options to students.
Ms. Conklin‘s Planning for Dimension 4
Ms. Conklin is confident of her students‘ ability to use knowledge meaningfully through decision making, investigation, experimental inquiry, problem solving, and invention, thus she has a wide range of activities she can use in the classroom. She thinks to herself, "What are some big or unresolved issues relating to weather and the information we‘ll go over in this unit? Are there important decisions to be made? Are there problems that are still unsolved?" She thinks through the questions the meaningful-use tasks address: "Is there an issue about who or what is the best?" "Is there an issue about the defining characteristics of something or why something happened or what would happen if . . .?"
After a while, Ms. Conklin concludes that the issue of weather forecasting can be explored further; specifically, she thinks that forecasters could create a better way of warning people about tornadoes. And this issue naturally lends itself to an invention project. She knows her students could not possibly invent a warning system in a four-week unit, but they would probably enjoy trying.
Ms. Conklin also identifies another issue: how weather affects people‘s moods. She decides that she‘ll present students with an invention task and an experimental inquiry task as possible projects. For the invention task, she‘ll simply provide some general guidance by giving students the following directions:
One of the major needs in weather forecasting is being able to warn people about tornadoes as soon as possible. Study this situation and identify an area that is ready for a new invention. Describe what the invention would do and state the standards it should meet. If you can, create a rough outline or plan for how it would work.
 
For the experimental inquiry project, she sets up a slightly more structured task:
Some people believe that weather and climate affect people‘s personality or moods.
Describe something you have noticed about the relationship between weather or climate and personality or mood. Explain what you think is happening.
Make a prediction based on your explanation.
Gather information to test your prediction.
Describe the extent to which your information agrees with your prediction.
Finally, decide what you learned from your study. What were you right about? What were you wrong about? What interesting insights did you have?
 
 
Ms. Conklin also wants to make sure that she leaves room for students to create their own tasks. She‘ll encourage them to make up their own projects using the ones she presents as models.
While putting the tasks together, Ms. Conklin thinks to herself, "These projects would take any one person a long while to finish." She concludes that these projects should be accomplished in cooperative groups. Although she‘ll allow students to do the projects independently, she‘ll encourage them to work cooperatively. She also thinks about the various ways students can report what they have learned. Again, she wants to leave open many possibilities. She decides that she will tell students they have four basic ways to report on their work:
A written report duplicated and distributed to the rest of the students
An oral report given to the entire class
A videotaped report
A newscast
 
Each of these options will, she knows, require her guidance. For example, she‘ll have to go over the format for a newscast and the components of a good videotaped report. She thinks it will be worth it, though, because her students will have the chance to express themselves in a personal way.
 
Ms. Conklin‘s example illustrates five major decisions involved in planning for Dimension 4, the meaningful use of knowledge:
1. What are the big issues? As in Dimension 3 (extending and refining knowledge), it is important that the content drive the selection of tasks in Dimension 4. A teacher should look for the big issues that naturally stand out in the content. Below are questions a teacher might think about to identify such issues: Decision Making
Is there an unresolved issue about who or what is the best?
Is there an unresolved issue about who or what has the most or least?
Investigation
Is there an unresolved issue about the defining characteristics or defining features of something? (Definitional)
Is there an unresolved issue about how or why something occurred? (Historical)
Is there an unresolved issue about what would happen if . . . or what would have happened if . . .? (Projective)
Experimental Inquiry
Is there an unexplained phenomenon (physical or psychological) for which students could generate explanations that can be tested?
Problem Solving
Is there a situation or process that has some major constraint or limiting condition?
Is there a situation that could be better understood if constraints or limiting conditions were placed on it?
Invention
Is there a situation that can or should be improved on?
Is there something that should be created?
 
2. How many issues will be considered? On the one hand, the more issues considered, the more options students have for choosing projects. On the other hand, the more options presented, the more familiar students have to be with the various types of meaningful-use tasks. The meaningful-use tasks are complex enough that students usually need a teacher‘s guidance as they progress through them. Consequently, teachers often initially present only one type of task per unit until students become familiar with all five types of tasks. Only then do units include multiple types of tasks.
3. Who will structure the tasks? Ultimately, students should identify the issues they want to deal with in their projects and the specifics of those tasks. Again, teachers must usually first provide structured activities to help students become familiar with the five types of tasks. Gradually, the teacher can provide less-structured activities and perhaps simply supply examples for students to model their own tasks on. Eventually, the teacher can encourage students to create their own tasks.
4. What types of products will students create? This is one of the most important decisions relating to Dimension 4. Again, the principle is to encourage a variety of options so that students have many opportunities to use their talents and explore their interests. As mentioned previously, teachers typically offer students few options other than oral or written reports for reporting what they have learned. Teachers should think about what other legitimate ways of communicating information would be useful in the unit (e.g., newscasts, simulations, panel discussions). They should also reflect on the aesthetic experiences that could be associated with the topic (e.g., poems, songs, murals).
5. To what extent will students work in cooperative groups? Although cooperative learning is quite compatible with all the dimensions of learning, it is especially suited to the meaningful-use tasks of Dimension 4 because the tasks are complex and lend themselves to such aspects of cooperative learning as individual accountability, positive group interdependence, and group rewards and task specialization (Slavin 1983). These characteristics are discussed in some depth in Chapter 7.
In summary, it is within Dimension 4 that students are provided with explicit opportunities to apply knowledge in meaningful ways that allow them to explore personal interests and direct their own learning. They do this in complex tasks such as decision making, investigation, experimental inquiry, problem solving, and invention. Dimension 4 is the heart of the Dimensions of Learning model. Its effectiveness depends on the teacher‘s careful planning and orchestration and her willingness to turn over control of learning to students.
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