Chapter 4. Dimension 3: Extending and Refinin...

A Different Kind of Classroom: Teaching with Dimensions of Learning
by Robert J. Marzano
Chapter 4. Dimension 3: Extending and Refining 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.
If the purpose of learning were simply to acquire and integrate knowledge, little more would have to be done instructionally than has already been described in Dimensions 1 and 2. But learning is not a simple matter of being "filled up" with content and skills that rest neatly in niches in the mind. The most effective learning occurs when we continually cycle through information, challenging it, refining it. The content in any field should be thought of as "a landscape that is explored by criss-crossing it in many directions" (Spiro et al. 1987, p. 178). In more cognitive terms, once information is acquired and stored in long-term memory, it can be changed—and in the most effective learning situations, it is changed.
Many researchers attest to this dynamic aspect of human learning. For example, Piaget (1971) described two basic types of learning: one in which information is integrated into the learner‘s existing knowledge base, called assimilation, and another in which existing knowledge structures are changed, called accommodation. Other researchers and theorists have made similar distinctions. For example, Rumelhart and Norman (1981) described three basic types of learning. The first two, called accretion and tuning, deal with the gradual accumulation or addition of information over time and the expression of that information in more parsimonious ways. The third type of learning, called restructuring, involves reorganizing information so that it produces new insights and can be used in new situations.
It is the type of learning described by Piaget as accommodation and by Rumelhart and Norman as restructuring that interests us here. Dimension 3, extending and refining knowledge, is the aspect of learning that involves examining what is known at a deeper, more analytical level. Unfortunately, it is this aspect of learning that American students seem to neglect. The National Assessment of Educational Progress (NAEP), in a summary report of twenty years of findings from all the major content areas, notes that "on one hand, schools can be congratulated for increasing the percentages of students learning basic facts and procedures. However, while we have raised performance at the lower levels of the distribution, we have lost ground at the higher levels" (Mullis, Owen, and Phillips 1990, p. 36). A strong theme in the NAEP report is the need for American students to engage in more analytic activities that require a depth of reasoning about content—activities that extend and refine knowledge.
The number of activities that help extend and refine knowledge is probably infinite. But there is a finite set of activities that are particularly suited to content area instruction. These activities are comparison, classification, induction, deduction, error analysis, constructing support, abstracting, and analyzing perspective. Each of these is briefly described in Figure 4.1.
Figure 4.1. Activities for Extending and Refining Knowledge
Comparing:
Identifying and articulating similarities and differences between things.
Classifying:
Grouping things into definable categories on the basis of their attributes.
Inducing:
Inferring unknown generalizations or principles from observation or analysis.
Deducing:
Inferring unstated consequences and conditions from given principles and generalizations.
Analyzing Errors:
Identifying and articulating errors in your own or others‘ thinking.
Constructing Support:
Constructing a system of support or proof for an assertion.
Abstracting:
Identifying and articulating the underlying theme or general pattern of information.
Analyzing Perspectives:
Identifying and articulating personal perspectives about issues.
Each of the cognitive operations in Figure 4.1 is particularly suited to engaging learners in a way that allows learners to refashion their knowledge of content. In a social studies class, for example, students might compare democracy and dictatorship to discover new distinctions between them. In a science class, students might make deductions about whales based on known characteristics of mammals to refine and extend their knowledge about mammals and whales.
I should point out that the cognitive operations in Figure 4.1 may also be used when initially acquiring knowledge. For example, when first learning about types of governments, students may compare, induce, deduce, and so on, but they will probably do so automatically, without conscious thought. To extend and refine knowledge, students need to use these operations consciously and rigorously and in more complex ways. For example, when students first learn about democracies and republics, they might think casually about similarities and differences between the two. To extend and refine these concepts, however, they would be asked to list these similarities and differences, perhaps using some type of graphic representation or matrix. The difference is a matter of degree, focus, and conscious use.
The mental operations in Figure 4.1 can be used as activities for extending and refining knowledge in two basic ways, as illustrated by Mr. Walker‘s class and Ms. Hildebrandt‘s class.
Mr. Walker‘s Class
Mr. Walker is about to introduce the concept of individual retirement accounts (IRAs) in his business class. Although students have heard the term before and have some knowledge of IRAs, the section in the text they are about to read provides a detailed description of their characteristics. Mr. Walker starts the class by asking students what they already know about IRAs. He writes the term IRA on the blackboard and puts a circle around it. As students call out what they already know or think they know, Mr. Walker records the comments on the board as spokes emanating from a hub, the term IRA. The activity naturally leads to a discussion of IRAs and the notion of saving for the future. When Mr. Walker feels that students have had adequate time to construct meaning for the new concept, he asks them to read pages 95–97 of the text and answer the following questions:
How is an IRA like a savings account and how is it different?
Based on the information in the text, what generalizations can you make about IRAs?
 
At first students don‘t react strongly to the assignment. They think it‘s fairly simple. As they try to answer the questions, though, they discover they have to go well beyond the information presented in the text. For example, they realize they have to rethink what they know about savings accounts. But no matter where they look in their notes and the book, they cannot find a comparison of IRAs and saving accounts. Coming up with generalizations about IRAs is even more difficult. There is nothing in the text or in their notes that even hints at an answer. What looked like an easy assignment turns out to be challenging and time-consuming.
Ms. Hildebrandt‘s Class
Ms. Hildebrandt is in the middle of a unit on modern American artists. She has presented the works of fifteen different artists in two weeks. Students seem to be doing well. They can describe the characteristic techniques of each artist. They even remember something about the life of each artist. Ms. Hildebrandt decides to challenge students by giving them the following assignment:
Classify the fifteen artists we have studied into at least three groups. When you‘re done, describe the defining characteristics of each group and explain why your categories are useful.
 
At first Ms. Hildebrandt gives her students two class periods to work on the assignment in groups of three. She soon finds that they need more time and more guidance. She has to take an entire class period just to teach students how to classify—how to develop rules to form categories and so on. She takes another full period to help students sort through all the different characteristics that might be used to form categories. What she thought would take two periods ends up taking five.
These classes illustrate two basic ways a teacher can use extending and refining activities in the classroom: (1) as a framework for questioning and (2) as directed activities. Mr. Walker used two of the eight extending and refining operations to construct questions. Although these questions were fairly easy to construct and were quickly presented to students, they still challenged students‘ understanding of the content. In Ms. Hildebrandt‘s class, the extending and refining activity was much more structured and directed; the teacher presented criteria and directed classroom activity. In this chapter, we will consider both these methods of using extending and refining activities.
A Framework for Questioning
Teachers have long known and researchers have validated that questioning is an important way to cue students‘ use of specific thinking processes. As Cazden (1986) explains, the types of questions asked in the classroom develop the academic culture of the classroom. A great deal of evidence shows that open-ended essay questions require more analytic thinking than do closed yes/no questions or multiple-choice questions (Christenbury and Kelly 1983), but there has been considerable debate over what constitutes higher-level questions (Fairbrother 1975, Wood 1977). Whether the questions based on the eight extending and refining operations are on a "higher level" is a matter of academic debate and not of much concern in the Dimensions model. What is important is that the questions cue specific types of analytic thinking that have the power to change students‘ existing knowledge. Below are some sample questions for each of the eight extending and refining areas that teachers might use to elicit analytic thinking.
Comparison
How are these things alike? What particular characteristics are similar?
How are they different? What particular characteristics are different?
 
Classification
Into what groups could you organize these things?
What are the rules for membership in each group?
What are the defining characteristics of each group?
 
Induction
Based on the following facts (or observations), what can you conclude?
How likely is it that __________ will occur?
 
Deduction
Based on the following generalization (or rule or principle) what predictions can you make or what conclusions can you draw that must be true?
If __________, then what can you conclude must happen?
What are the conditions that make this conclusion inevitable?
 
Error Analysis
What are the errors in reasoning in this information?
How is this information misleading?
How could it be corrected or improved?
 
Constructing Support
What is an argument that would support the following claim?
What are some of the limitations of or assumptions underlying this argument?
 
Abstracting
What is the general pattern underlying this information?
To what other situations does the general pattern apply?
 
Analyzing Perspectives
Why would someone consider this to be good (or bad or neutral)?
What is the reasoning behind their perspective?
What is an alternative perspective and what is the reasoning behind it?
 
These questions and adaptations of them might be asked before, during, or after learning experiences. For example, before reading a chapter in a mathematics text, a teacher might ask students, "What statements about trapezoids must be true, based on the rules described in the chapter?" This question would stimulate deductive thinking about trapezoids. While students in a literature class are watching a film about Hemingway, a teacher might cue analysis through comparison by asking, "How does the information in this film about Hemingway‘s life compare with the information in the chapter you read?" After students have gone on a field trip as part of a business class, a teacher might ask, "Into what groups would you classify the seven business people we met? What are the distinguishing characteristics for each of your categories?"
An even more powerful use of extending and refining questions is to ask students to construct and answer their own. The teacher need only introduce students to the various types of questions and then invite them to devise their own questions. When I mention this alternative in workshops, teachers frequently respond that students would structure questions that are too easy. Although I have no research evidence to counter this assertion, I do have anecdotal evidence. A mathematics teacher in Michigan told me of her experience in asking students to create their own extending and refining questions during a unit on fractions. In previous units, she had introduced the eight types of extending and refining operations, and on a wall chart were listed questions like those above that related to each of the extending and refining areas. She made sure that students had adequate preparation for the assignment, which was simply to "write at least two questions about the chapter that cover at least two of the eight areas illustrated on the wall chart. Answer your questions in writing and hand in both your questions and your answers."
To the teacher‘s surprise, the questions students asked of themselves far surpassed the level of difficulty she thought them capable of handling. One student, for example, asked a deductive question that required him to infer characteristics about fractions based on axioms implicit in the chapter. Another student asked a classification question that required her to organize all the sample problems in the chapter into groups and describe the defining characteristics of each group. In short, this mathematics teacher found that the kinds of thinking that extend and refine knowledge can be elicited through questions constructed by students.
Directed Extending and Refining Activities
A teacher can also engage students in more elaborate extending and refining activities. Such activities are more detailed and generally require more time and resources than the activities associated with the types of questions described in the previous section. Directed extending and refining activities might be likened to what Stauffer (1970) calls directed reading/thinking activities: well-structured activities that elicit specific types of analytic thinking from students and guide them through the execution of that thinking. Let‘s look at the directed extending and refining activities that are included in Dimensions of Learning.
Comparison
Comparison is one of the most basic of all the extending and refining operations. In fact, it is so basic that some teachers believe it is not a high enough level of thinking to extend and refine students‘ knowledge. They reason that "all students can compare things without much trouble. How could it push their thinking in any way?" Of course, it is true that we quite naturally compare information, but recall that when we use comparison as an extending and refining activity, we use it consciously and rigorously. Unfortunately, American students, once again, do not perform well on this more rigorous type of comparison task. In a summary report of twenty years of testing, NAEP commented on American students‘ ability to perform analytic comparison tasks:
On an analytic task that asked students to compare food on the frontier (based on information presented) and today‘s food (based on their own knowledge), just 16 percent of the students at grade 8 and 27 percent at grade 12 provided an adequate or better response (Mullis et al. 1990, p. 16).
 
Stahl (1985) and Beyer (1988) have each developed comparison strategies that foster a high degree of analytic thinking. These strategies include the following basic steps:
Specifying the items to be compared.
Specifying the attributes or characteristics on which they are to be compared.
Determining how they are alike and different.
Stating similarities and differences as precisely as possible.
 
Creating directed comparison activities generally involves specifying certain aspects of the comparison process and asking students to generate the rest. For example, in a science class, a teacher might identify the processes of meiosis and mitosis. Students would then be asked to compare them using two or more important characteristics of their choice. It is identifying characteristics that are truly important that seems to be the critical feature of analytic comparison and the most difficult aspect of the task. For example, according to NAEP, when students were asked to provide a written response contrasting the key powers of the president of the United States today with those of George Washington, only 40 percent of the 12th graders could muster at least two important characteristics (Mullis et al. 1990, p. 24).
To be an effective analytic tool, then, comparison should focus students‘ attention on characteristics considered important to the items being compared. Teachers can foster students‘ ability to select important characteristics by initially using teacher-structured comparison tasks: tasks in which the teacher specifies both the elements to be compared and the characteristics on which they will be compared. Here is an example of a teacher-structured task:
How do diamond and zirconium compare in terms of their scarcity? What would happen in the marketplace if one or the other should become more scarce? For the two characteristics identified above (their scarcity and the effects of their scarcity on the marketplace) describe how diamond and zirconium are similar and different.
 
After assigning this task, the teacher and students would discuss why "scarcity" and the "effects of scarcity on the marketplace" are important characteristics in relation to diamond and zirconium. Once students were acquainted with the characteristics considered important to this topic, they would then be asked to engage in student-structured tasks. Here neither the elements to be compared nor the characteristics on which they are to be compared are specified:
Select one naturally occurring and one man-made substance that might be usefully compared. Then select two or more characteristics on which to compare the two substances, such as problems that arise in production, differences in marketing and distribution, causes and effects of scarcity, and so on. Finally, describe how the substances are alike or different in terms of the characteristics you have selected.
 
Comparison, then, can be a powerful analytic tool when used rigorously to extend and refine knowledge.
Classification
Like comparison, classification is a type of thinking we engage in daily without much conscious thought. Mervis (1980) explains that we naturally categorize the world around us so we don‘t have to experience everything as new. Nickerson, Perkins, and Smith (1985) say that the ability to form conceptual categories is so basic to human cognition that it can be considered a necessary condition of thinking.
Although we use the process of classification quite naturally, when we use it to extend and refine our knowledge it can be very challenging. Beyer (1988) and others (Jones, Amiran, and Katims 1985; Taba 1967) have identified specific steps in the process of classification:
Identifying the items to be classified.
Initially sorting information into groups.
Forming rules for categories and then reclassifying items based on these rules.
 
Constructing classification tasks to help students extend and refine their knowledge involves specifying certain aspects of the process and asking students to complete the others. For example, in a literature class a teacher might ask students to classify thirty characters from novels they have read. Students would initially sort the characters into rough groups. After this "first cut," there would invariably be some outliers or characters that do not fit into the initial categories. It is the existence of these outliers that makes the learner become more rigorous in defining categories. To place these outliers, students would have to redefine the categories and the rules for establishing the categories.
Classification as an analytic tool is powerful because it forces the learner to analyze semantic features to identify the salient features that determine membership in a group (Smith and Medin 1981). Making semantic feature analysis explicit in classification tasks is becoming increasingly popular, and a growing body of research indicates that classification emphasizing semantic feature analysis is a powerful tool for learning vocabulary (Pittleman, Heimlich, Berglund, and French 1991). Figure 4.2 shows the results of a semantic feature analysis task involving vocabulary words from a primary classroom.
Figure 4.2. Semantic Feature Analysis Task
Classroom SFA Grid for Vehicles
Features
Vehicles
two wheels
four wheels
more than four wheels
motor
diesel fuel
gasoline
people power
handle bars
passengers
enclosed
used on land
used on water
car
−
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bicycle
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motorcycle
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truck
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train
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skateboard
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rowboat
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sailboat
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motorboat
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Source: Pittelman, Heimlich, Berglund, and French 1991. Copyright © 1991 by the International Reading Association. Reprinted by permission.
Like comparison tasks, classification tasks might initially be structured by the teacher. Below is an example of a teacher-structured classification task that might be used in a geography class.
There are many different regions in our state: neighborhoods, mountains, counties, cities, and so on. These regions can be organized into categories by considering how people use them. For example, people can use an area for dwellings, for recreation, or for natural resources; that is, we could classify the regions into three categories, based on their use: (1) those used for dwellings, (2) those used for recreation, and (3) those used for natural resources. In our state, examples of each of these categories of use exist. Provide at least three examples in our state for each of the three categories. Make sure you describe the defining characteristics of each category; for example, describe the characteristics of regions that are used for dwellings.
After discussing the features important to categories in a given content area, the teacher can assign other classification tasks that require students to create their own categories and identify the elements to be sorted into those categories:
Regional categories can be made up of almost anything, depending on the elements you use to create them—people, land, automotive supply stores. Your task is to create categories by selecting a variety of elements that will allow you to distinguish one category from another. For example, you could decide that the presence of one school, one church, a gas station, and a convenience store signifies "a loose social neighborhood." Likewise, you could decide that an area with a ratio of three gas stations to one school may qualify as a business neighborhood, and a region of inverse ratio (three schools to one gas station) could be described as a "residential neighborhood." Make sure you have enough combinations to form at least five categories. Finally, select an area within the greater metropolitan area and identify at least one example of each category you have established. Also explain why your categories are useful ways of thinking about regions.
 
Induction
Induction is probably the most basic of all higher-order cognitive operations. We make inductions anytime we draw conclusions based on evidence. For example, a student makes an induction when he concludes that the teacher is in a bad mood because she slammed her books down on the desk after she briskly walked into the room. Although induction is not treated overtly in all thinking skills programs, it is implicit in all.
Teachers can easily help students practice induction in the classroom, for the core of induction as an extending and refining activity is generating and verifying hypotheses. One teacher described to me how at the start of the Persian Gulf War, she asked students to generate hypotheses about Saddam Hussein‘s reasons for invading Kuwait. The students listed their hypotheses and the information supporting their hypotheses. As the war progressed, students gathered information that confirmed or disconfirmed their hypotheses. Over time, students changed and adapted their hypotheses. Although the students as a group did not reach a consensus, all the students experienced the inexact cycle of generating hypotheses, gathering data, reformatting hypotheses, and so on.
A powerful tool for fostering induction in the classroom is the "induction matrix" developed by Beau Fly Jones and her colleagues (personal communication 1987). Figure 4.3 shows an example of an induction matrix. Content area concepts (e.g., "democracy") head each row of the matrix, and questions to be answered about each concept (e.g., "Who governs?") head each column. Students first fill in the cells corresponding to each concept and each question, which in Figure 4.3 would be information about "who governs" in democracies, in republics, in monarchies, and so on. After they have filled in each of the basic cells, students make row and column inductions. Row inductions would be about democracies, republics, and so on. Column inductions would be about various types of governance, decision making, and so on. Finally, students make a "grand induction" and record it in the bottom right cell.
Figure 4.3. Induction Matrix
Who Governs
How Decisions Are Made
Earliest Examples
Conclusions
Democracy
Republic
Monarchy
Dictatorship
Conclusions
At a more sophisticated level of analysis, students might be asked to make inductions about the intentions behind materials they are reading. Cooper (1984) has identified four basic categories of intentions behind the use of language in oral or written form:
Constatives: expressions of beliefs along with expressions of an intention that the audience form like beliefs.
Directives: expressions of an attitude toward some prospective action by the audience along with an intention that the attitude be taken as a reason to act.
Commissives: expressions of intentions to act along with expressions of belief that such expressions of intentions obligate one to act.
Acknowledgements: expressions of feelings toward the audience.
 
Each of these categories of intentions has subcategories of intentions. These are listed in Figure 4.4 on page 80.
Figure 4.4. Categories and Subcategories of Intentions
Constatives:
You assert if you express a proposition.
You predict if you express a proposition about the future.
You recount if you express a proposition about the past.
You describe if you express that someone or something consists of certain features.
You ascribe if you express that a feature applies to someone or something.
You inform if you express a proposition that your audience does not yet believe.
You confirm if you express a proposition along with support for it.
You concede if you express a proposition contrary to what you would like to or previously did believe.
You retract if you express that you no longer believe a proposition.
You assent if you express belief in a proposition already under discussion.
You dissent if you express disbelief in a proposition already under discussion.
You dispute if you express reason(s) not to believe a proposition already under discussion.
You respond if you express a proposition that has been inquired about.
You suggest if you express some, but insufficient, reason(s) to believe a proposition.
You suppose if you express that it is worth considering the consequences of a proposition.
 
Directives:
You request if you express that you desire your audience to act.
You ask if you express that you desire to know whether or not a proposition is true.
You command if you express that your authority is reason for your audience to act.
You forbid if you express that your authority is reason for your audience to refrain from acting.
You permit if you express that your audience‘s action is possible by virtue of your authority.
You recommend if you express the belief that there is good reason for your audience to act.
 
Commissives:
You promise if you express that you intend to act.
You offer if you express that you intend to act if and when your audience desires it.
 
Acknowledgments:
Apologies
Condolences
Congratulations
Greetings
Thanks
 
Source: Cooper 1984. Copyright © 1984 by the Guilford Press. Reprinted by permission.
Once students are aware of the various types of intentions, they can induce these intentions from information they read or hear. As students soon discover, inducing authors‘ intentions is an inexact process of identifying the driving force behind the form and content of a text. It involves analyzing why specific words were selected, why certain rhetorical devices were used, and so on. To illustrate, as a result of analyzing the Declaration of Independence, one group of 12th graders induced that one major intention of its authors was to ascribe specific highly negative characteristics to the reigning monarch of England. They cited as evidence for their induction the repeated use of a syntactic pattern beginning in the third paragraph of the Declaration:
He has refused his Assent to Laws....
He has forbidden his Governors to pass Laws....
He has refused to pass other Laws....
He has....
He has....
 
This "he has" pattern comprises thirteen consecutive one-sentence paragraphs and five additional paragraphs that together give the reader a strong impression of an unfair and uncompromising leader.
Students also found evidence that the authors of the Declaration were trying to permit their readers to act in ways counter to their natural inclination to submit to rule from England. According to Cooper (1984), the intention of permitting is a form of directive. Students believed the first paragraph of the Declaration was intended to establish a tone of permission by suggesting that the forthcoming Declaration was a necessary occurrence in the events of human history:
When in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with one another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature‘s God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
 
Finally, some students found evidence for the commissive intention of a promise. They perceived the last paragraph of the Declaration to be a promise to do whatever was necessary to effect the establishment of a free and independent United States of America. This promise was particularly evident in the closing line: "...we mutually pledge to each other our Lives, our Fortunes, and our Sacred Honor."
Deduction
There is a fair amount of confusion about the distinction between induction and deduction. Anderson (1990) clarifies the distinction with the following illustration.
The Abkhasian Republic of the USSR [in Georgia] has 10 men over 160. No other place in the world has a man over 160.
The oldest man in the world today is in the USSR.
The oldest man in the world tomorrow will be in the USSR.
 
 
He explains:
Conclusion 1 is deductively valid. If the premises are true,...then the conclusion must be true. However, conclusion 2 is only inductively valid, that is, it is a highly likely conclusion if the premises are true, but it is conceivable that all 10 men could die before tomorrow (Anderson 1990, p. 303).
 
As Anderson‘s example illustrates, deductive conclusions, given the validity of their premises, are absolute. Inductive conclusions, on the other hand, may be highly probable but they are never absolute. A common misconception is that deductive conclusions are used in mathematics but not in the humanities or social sciences. At a formal level, there is some truth to this, for mathematics is based on the use of axioms and theorems to generate deductive conclusions. In fact, one of the purest deductive activities is a mathematical proof (e.g., proving the validity of the Pythagorean theorem). Deductive reasoning is indigenous to mathematics, but why would anyone want to reinforce its use in other disciplines? First and foremost, much of our thinking, academic or otherwise, is deductive, though not consciously so. For instance, if someone says President Bush is going to veto the environmental bill because he‘s following standard Republican lines, that person would be reasoning deductively. His thought process breaks down to:
All Republican presidents vote against environmental bills.
George Bush is a Republican president.
Therefore he will vote against the environmental bill.
As we shall see, reorganizing the implicit deductive conclusions in a content area can be a very powerful tool in extending and refining content knowledge.
 
Another, albeit less important, reason for fostering deductive reasoning in the classroom is that many of the tests we call "reasoning tests" are highly deductive in nature. Take, for example, the New Jersey Test of Reasoning Skills (Shipman 1983), which is administered across the United States as a measure of general reasoning ability. The three items below are patterned after the items in that test. Take a moment to answer them.
Item 1
Martha said, "Rectangles always have four corners. Joe said, "That‘s no different from saying that all rectangles are four-cornered things.
Joe is wrong. Martha is saying that all four-cornered things are rectangles.
Joe is right.
Joe is wrong. Martha is saying that some four-cornered things are rectangles.
 
Item 2
The City Water Department says, "If the water has been treated, it is safe to drink." Since the water in our town has been found to be unsafe to drink, it follows that:
The water was treated.
The water was not treated.
The treatment made the water unsafe.
 
Item 3
Jack is older than Bill. Herb is also older than Bill. Therefore, it follows that:
You can‘t tell who is oldest.
Jack and Herb are both the same age.
You can‘t tell who is the youngest.
 
 
Would you expect to find these questions on a junior high school test? If not, you‘re in good company. I recently administered the New Jersey Test of Reasoning Skills to thirty adults, all of whom had advanced degrees in education. Although they did not do poorly on the test, more than 80 percent felt "unsure" of their answers because they weren‘t "used to the type of thinking involved." After administering the test, I analyzed the fifty items on the test and found that 84 percent were deductive in nature. The unease these educated people felt probably stemmed from their unfamiliarity with the rather formal type of deductive arguments used in the test. It has become my strong bias that if we, as educators, are going to use highly deductive tests to measure general reasoning ability, then we are duty bound to provide students with some practice in the types of reasoning they include.
Most textbooks on deductive reasoning (e.g., Klenk 1983) identify three basic types of deductive arguments: categorical, conditional, and linear. Items 1, 2, and 3 above represent respectively these three types. Categorical arguments are by far the arguments most commonly found in tests of reasoning that include deductive reasoning. Of the fifty items on the New Jersey Test of Reasoning that I administered, for instance, twenty-four (or 48 percent) involved categorical arguments.
Although there are many formal rules for properly using categorical arguments, the basic steps for using them as activities to extend and refine knowledge are quite simple. Categorical arguments are composed of two premises and a conclusion that stems from the premises. The syllogism is the typical form of a categorical argument:
All A are B.
All B are C.
Therefore all A are C.
 
The appearance of B in both premises enables a deductive conclusion to be drawn because B relates the information in the two premises. One of the first steps in using categorical arguments to extend and refine knowledge is to recognize what I call "hidden syllogisms" and state them in formal syllogistic form. This process is called standardization in the Philosophy for Children program (Lipman, Sharp, and Oscanyan 1980). Let‘s take the statement about George Bush and reword it into a more clearly syllogistic form:
Premise #1: All Republican presidents (A) are people who vote against environmental issues (B).
Premise #2: George Bush (C) is a Republican president (A).
Conclusion: Therefore, George Bush (C) is a person who votes against environmental issues (B).
It is the middle term, A, that appears in both premises and allows for a deduction to be made linking the term B with C.
 
Once students are aware of the form of categorical syllogisms and can standardize, or reword, statements so they reflect this syllogistic form, they can be asked to find syllogistic arguments in academic content. A junior high history teacher who had taught syllogisms to her students described to me what happened when she asked her students to analyze the Declaration of Independence for hidden syllogistic arguments. One group of students asserted that the logic underlying the Declaration could be stated in the following way:
Premise #1: Governments that should be supported and, consequently, not overthrown (A), protect the God-given rights of their people to life, liberty, and the pursuit of happiness. (B)
Premise #2: The Government of the present king of England (C) does not protect the God-given rights of the people to life, liberty, and the pursuit of happiness (B).
Conclusion: Therefore, the Government of the present king of England (C) is not one that should be supported and, consequently, not overthrown (A).
 
Stated in more abstract form, this syllogism might be written as follows:
All A are B.
C is not B.
Therefore C is not A.
 
All conclusions in syllogistic arguments are not valid. Once an argument has been stated in syllogistic form, its validity can be analyzed, though. A useful tool in helping students determine the validity of a syllogistic argument is the Euler diagram, named after Leonhard Euler, the 18th century mathematician who used this kind of diagram to teach logic to a German princess. The technique was, in fact, invented by Leibniz and is often confused with the quite different method of Venn diagrams (Johnson-Laird 1983). Euler diagrams use circles to represent set membership. We might use the following Euler diagram to represent the syllogism students found in the Declaration of Independence: Looking at this diagram, we can clearly see that set C (the present government of England) is not related to set A (governments that should be supported and, consequently, not overthrown). After using the Euler diagram, the junior high students concluded that the logic of the forgers of the Declaration was sound. But more important, they applied critical analysis to the reasoning behind a living document—a task that relatively few people have the tools to accomplish.
Recognizing and standardizing categorical syllogisms typically uncovers errors in logic. For example, I recently heard a television newscaster interview an individual who said, "Saddam Hussein is a dictator because he tortures people, and we know that all dictators are torturers." Standardized, the logic behind this statement might be written like this:
Premise #1: All dictators (A) are people who torture (B).
Premise #2: Saddam Hussein (C) is a person who tortures (B).
Conclusion: Therefore, Saddam Hussein (C) is a dictator (A).
 
Although there is certainly a great deal of evidence that Saddam Hussein is a dictator, this deductive argument does not prove it, as we can see by constructing Euler diagrams. We can represent the first premise with this diagram:
When you add the second premise, you can conclude only that C is a subset of B. C might not be related to A at all.
In fact, from the two premises given, we can draw no valid conclusion about the relationship between A and C.
The types of valid conclusions that can be drawn from syllogistic arguments are listed in Figure 4.5. What is perhaps most interesting about Figure 4.5 is that it reveals that only twenty-seven of the sixty-four possible forms of syllogistic arguments have valid conclusions.
Figure 4.5. Valid Conclusions from Syllogistic Arguments
First Premise
Second Premise
All A are B
Some A are B
No A are B
Some A are not B
All B are C
All A are C
Some A are C Some C are A
Some C are not A
Some B are C
Some C are not A
No B are C
No A are C No C are A
Some A are not C
Some B are not C
All C are B
No A are C No C are A
Some A are not C
Some C are B
Some C are not A
No C are B
No C are A No A are C
Some A are not C
Some C are not B
Some C are not A
First Premise
Second Premise
All B and A
Some B are A
No B are A
Some B are not A
All B are C
Some A are C Some C are A
Some A are C Some C are A
Some C are not A
Some C are not A
Some B are C
Some A are C Some C are A
Some C are not A
No B are C
Some A are not C
Some A are not C
Some B are not C
Some A are not C
All C are B
All C are A
No C are A No A are C
Some C are B
Some C are A Some A are C
Some C are not A
No C are B
Some A are not C
Some A are not C
Some C are not B
Another way students can use syllogisms to extend and refine their knowledge is to analyze their truth. Copi (1972) explains that the validity of a syllogism depends on whether the conclusion follows from the premises. As Figure 4.5 illustrates, 42 percent of all the possible forms of syllogistic arguments have valid conclusions. A syllogism that has a valid conclusion still may not be true, though, because truth depends on the accuracy of the premises. Take, for example, the earlier syllogism involving President Bush. The conclusion (President Bush is a person who votes against environmental issues) is logically valid, but the entire syllogism is not true because of the inaccuracy of the first premise (All Republican presidents are people who vote against environmental issues). Analyzing the truth of syllogisms represents an entirely different type of analytic thinking that in the Dimensions of Learning model is called error analysis.
Error Analysis
No matter how intelligent or educated we are, we make errors. Thomas Gilovich (1991) identifies numerous examples of erroneous conclusions in everyday reasoning, some of them drawn by otherwise academically rigorous thinkers. Francis Bacon, for example, believed that warts could be cured by rubbing them with pork. Aristotle thought that male babies were conceived in a strong north wind. Other reports of the types of errors reasonable people make in everyday situations have been compiled by Johnson-Laird (1985) and by Perkins, Allen, and Hafner (1983). As Gilovich notes, studying the types of errors we make enlightens us not only about our thinking, but also about the subject in which we make the errors. In keeping with this premise, the California State Department of Education uses error analysis as a testing and teaching tool. Figure 4.6 on page 90 is an example of one of the open-ended questions it administers to students as a strategy for enhancing mathematical competence.
Source: California State Department of Education 1989. Copyright © 1989 by the California State Department of Education. Reprinted by permission.
 
One of the most common types of errors made every day falls under the category of confirmatory bias, which is the tendency to seek out information that confirms our hypotheses. As Gilovich (1991) puts it:
When trying to assess whether a belief is valid, people tend to seek out information that would confirm the belief over information that might disconfirm it. In other words, people ask questions or seek information for which the equivalent of a "yes" response would lend credence to their hypothesis (p. 33).
 
Wason and Johnson-Laird (1972) conducted a study in which subjects were given the following rule: "If a card has a vowel, then it has an even number on the other side." The subjects were then given cards like these: The subjects were asked to turn over only those cards that had to be turned over to see if the rule was correct. Forty-six percent elected to turn over both the E and the 4. The E had to be turned over but the 4 did not. Only 4 percent elected to turn over the E and the 7, which is the correct choice of cards, since an odd number behind the E or a vowel behind the 7 would have broken the rule. Gilovich (1991) explains that the tendency for the subject not to turn over the 7 exemplifies the confirmative bias: we shy away from information that would prove a hypothesis false.
One of the most powerful ways I have seen this demonstrated in a classroom setting involved a teacher asking students to develop an argument against some strongly held belief. The teacher told me that she asked students to identify their position on the ban of fur sales and then work in cooperative groups to develop a strong argument supporting the position opposing their own. When the task was completed, few students had changed their opinion, but virtually all had identified the erroneous assumptions from which they had been operating. In fact, the culminating activity requested by students was to list all the incorrect assumptions and beliefs they discovered about their own thinking on the topic.
Informal fallacies are another type of error common in everyday reasoning, particularly when that reasoning is intended to "persuade." Lockwood and Harris (1985) assert that it is especially important to study these types of errors in a free society such as ours because much of the information we must process is persuasive in nature: someone is continually trying to get our vote, our money, or our agreement.
There are many descriptions of the kinds of informal fallacies that can be made in persuasive discourse, including those by Perkins, Allen, and Hafner (1983) and Toulmin (Toulmin 1958; Toulmin, Rieke, and Janik 1981). In the Dimensions of Learning model, informal fallacies are organized in three basic categories that are briefly described in Figure 4.7.
Figure 4.7. Informal Fallacies
Category I: Erros based on faulty logic
Errors that fall into this category use a type of reasoning that is flawed in some way or is simply not rigorous. Such errors include:
a. Contradiction: Someone presents information that is in direct opposition to other information within the same equipment.
b. Accident: Someone fails to recognize that an argument is based on an exception to a rule.
c. False cause: Someone confuses a temporal order of events with causality, or someone oversimplifies a complex causal network.
d. Begging the question (circularity): Someone makes a claim and then argues for it by advancing grounds whose meaning is simply equivalent to that of the original claim.
e. Evading the issue: Someone sidesteps an issue by changing the topic.
f. Arguing from ignorance: Someone argues that a claim is justified simply because its opposite cannot be proved.
g. Composition and division: Composition involves someone asserting about a whole something that is true of its parts. Division involves someone asserting about all of the parts something that is true about the whole.
Category II: Errors based on attack
Informal fallacies in this category all use the strategy of attacking a person or position.
h. Poisoning the well: Someone is committed to his position to such a degree that he explains away absolutely everything others offer in opposition to his position.
i. Arguing against the person: Someone rejects a claim on the basis of derogatory facts (real or alleged) about the person making the claim.
j. Appealing to force: Someone uses threats to establish the validity of a claim.
Category III: Errors based on weak references
Informal fallacies that fall into this category appeal to something other than reason to make their point; however, they are not based on attack.
k. Appealling to authority: Someone evokes authority as the last word on an issue.
l. Appealling to the people: Someone attempts to justify a claim on the basis of popularity.
m. Appealing to emotion: Someone uses an emotion-laden or "sob" story as proof for a claim.
After introducing students to a small subset of these fallacies, a teacher might ask students to look for them in persuasive information they encounter. One of my favorite examples of the use of informal fallacies in the classroom comes from a literature teacher. After presenting these fallacies to students before the presidential election in 1988, the teacher asked students to observe the debate between candidates George Bush and Michael Dukakis. Their task was to identify the informal fallacies used by each candidate. To their chagrin, many students found their favorite candidate frequently made recognizable errors. Their knowledge of informal fallacies affected the way students processed information as the campaign progressed. They were less likely to accept the opinion of their favorite candidate without question and delved more deeply into issues.
Constructing Support
The other side of analyzing a persuasive argument for errors is constructing a sound argument. Of course, one aspect of creating a sound persuasive argument is avoiding the errors described above, but persuasion also involves using certain conventions. The art of persuasion has its roots in classical rhetoric, which is built on four basic devices, commonly called the "four appeals" (Kinneavy 1991):
Appealing to an audience through personality.
Appealing through accepted beliefs and traditions.
Appealing through rhetorical style.
Appealing through the logic of one‘s argument.
 
When the appeal is through personality, the speaker or writer tries to get the audience to like him. The information presented is usually about the speaker or writer—anecdotes about his life intended to make you, the audience, identify with him. The speaker or writer also frequently compliments the audience in an attempt to be perceived as a friend or an ally.
When the appeal is through beliefs and tradition, the writer or speaker often refers to allegedly accepted principles based on tradition. For example, the writer or speaker may assert that the principles underlying his argument "have always been held as true." He is using beliefs and tradition to evoke the power of culture, the power of "the way things are done around here."
Appeal through rhetorical style aims to persuade through the beauty of language, including how ideas are phrased, the intonation used in their presentation, and the physical gestures that accompany them. Goldman, Berquist, and Coleman (1989) describe in detail the elaborate systems that have been created throughout the centuries to improve the persuasive power of appeal through rhetorical style.
The last of the four appeals is logic. Students of rhetoric used to be taught the formal rules of syllogistic reasoning to improve their ability to appeal through logic. In recent years, less formal and more flexible systems have been developed. The most common is that developed by Toulmin (Toulmin, Rieke, and Janik 1981). Although Toulmin‘s system has multiple aspects, his basic structure of an argument based on reason has four simple components:
Evidence. Information that leads to a claim. For example: Last night five crimes were committed within two blocks of one another.
Claim. The assertion that something is true: The crime rate in our city is escalating dramatically.
Elaboration. Examples of or explanations for the claim: The dramatic increase can be seen by examining the crime rates in the downtown area over the last twenty years.
Qualifier. A restriction on the claim or evidence counter to the claim: The crime rate has stabilized in some areas, however.
 
Once students understand the four types of appeals, they can analyze persuasive arguments. For example, a social studies teacher told me that he regularly asks students to analyze information from television, textbooks, and newspapers to determine which of the four types of appeals is being used. He attested to students‘ ability to perform such analyses with accuracy and enthusiasm.
Abstracting
The term abstracting is used frequently in conversations about learning and thinking. Webster‘s New Collegiate Dictionary says that to "abstract" is to remove, to separate, "to consider apart from application to or association with a particular instance." You would be abstracting if you looked at one situation and identified basic elements of the situation that occur in another situation. For instance, let‘s look at the situation below:
When C. L. Holes was inventing a typewriting machine in the early 1870s, he found that the machine jammed if he typed too fast. So he deliberately arranged the positions of the letters in a way that forced typists to work slowly. Nevertheless, Sholes‘ typewriter design was still a great improvement over earlier models, and it was soon in use all over the world.
Today, even though typewriters have been improved in many ways, nearly all of them have keyboards like the one Sholes devised in 1872. The letter arrangement is called QWERT, after the five left-hand keys in the top letter row. You can see QWERT keyboards on computer consoles as well as on typewriters. Unfortunately, the QWERT arrangement slows typing, encourages errors, and causes greater fatigue than another arrangement devised by August Dvorak in 1930, which has proved in several tests to be much faster and more accurate than QWERT.
Millions of people have learned the QWERT keyboard, however, and it is being taught to students in schools right now. So it seems that we will continue to live with this 19th century mistake.
 
Now think about how you might abstract this situation. You might first liken the history of the QWERT keyboard to that of the measuring system used in the United States. When asked to describe how they are alike, you would probably explain the connection in the following way: "In both situations, something was created that was initially very useful (QWERT and the British system of measurement). Then something better came along (the Dvorak system and the metric system), but the new invention was not used because everyone was so familiar with the old invention."
The psychological phenomenon that allows you to make the connection between the two seemingly unrelated events is the identification of a "general" or "abstract" pattern of information that applies to both situations. Here is the general pattern for the above example:
Something useful is created.
Something better comes along.
It is rejected because people resist change.
 
It is the identification of a general pattern that is central to the abstracting process. From this perspective, we might say that the process of abstracting is at the heart of metaphor. Ortony (1989) explains that a metaphor contains two basic components, a topic and a vehicle. The topic is the principal subject to which the vehicle (the metaphoric term) is applied. If we say that A is a B when A is not actually a B, then A would be the topic and B would be the vehicle. Consider the metaphor "Love is a rose." Here, love is the topic and rose is the vehicle. Love is not related to rose at a literal level but it is related at an abstract level, as shown in Figure 4.8. Speaking of the importance of metaphor, Ortony notes:
It is more than a linguistic or psychological curiosity. It is more than rhetorical flourish. It is also a means of conveying and acquiring new knowledge and of seeing things in new ways. It may well be that metaphors are closely related to insight (Ortony 1980, p. 361).
 
Figure 4.8. Abstractions in a Metaphor
Literal Attributes of Love
Shared Abstract Attributes
Literal Attributes of Rose
an emotion
a flower
sometimes pleasant
desirable
beautiful
can be associated with unpleasant experiences
double-edged
has thorns
often occurs in adolescence
comes in different colors
Teachers can use abstracting in the classroom in several ways. Comparing literary works is particularly suited to analysis by abstraction. After students have read a selection, they can be asked to identify the underlying abstract pattern of the content. For example, after reading The Old Man and the Sea students might first identify the key points of the novel:
The old man and boy had a close relationship.
The old man had a spell of bad luck in his fishing.
The boy had faith in the old man.
The old man hooked a large fish, and so on.
 
Once the key points or literal pattern of the novel are established, students then transform the ideas into a more abstract or general pattern:
Key Points
Abstract Pattern
Old man and boy had a close relationship.
Two people have a close relationship.
Old man had a spell of bad luck.
One of the partners experiences difficulties.
The young boy had faith in the old man.
The other partner is highly supportive.
The old man hooked a large fish.
The partner experiencing difficulty is faced with a difficult challenge that can bring him success.
The old man did not land the fish intact, but still resolved a basic conflict in his life.
The partner does not directly meet the challenge but still works out some basic issues in his life.
The abstract form identified, students then look for another piece of literature or another situation to which the abstract form applies. For example, using the abstracting process with The Lord of the Flies, one student described how the same abstract pattern in Golding‘s work also applied to a story she had seen on television about the birth of a street gang in east Los Angeles. Another student saw the abstract pattern in The Lord of the Flies applying to Mussolini‘s rise to power in pre-World War II Italy.
The abstracting process is well suited to many content areas. Here is an abstracting task that teachers might present to students in a history class:
Identify the generic elements or basic elements of the war in Vietnam. Then identify another situation that has nothing to do with wars between nations and describe how that situation fits the basic elements you have identified.
 
I have seen abstraction used by a science teacher who asked students to relate the functioning of a cell to the workings of a city and by a mathematics teacher who asked students to relate basic mathematical operations to relationships in nature.
Analyzing Perspectives
The final type of extending and refining activity in the Dimensions of Learning model is analyzing perspectives. Analyzing perspectives involves identifying your position or stance on an issue and the reasoning behind that stance. It also involves considering a perspective different from your own. Your perspective on an issue is usually related to some underlying value you hold. Value and affect are functionally related: you have a certain emotional response to a situation because you interpret your experiences partly through your values. For example, if you respond with anger to the treatment of Boo in To Kill A Mocking-bird, it is because one of your underlying values is that human beings should be respected regardless of their intellectual capabilities. Paul (1984, 1987) has noted that, given the complexity of our society, the ability to recognize our values and the reasons behind them and to acknowledge another system of reasoning that would yield a different value is one of the most important intellectual skills a person can develop. Fisher and Ury (1981) assert that this skill is at the heart of negotiation.
To practice the process of analyzing perspectives, students can systematically analyze their values as they are triggered by learning experiences; ultimately, this process will help them understand (though not necessarily agree with) other systems of values. At a basic level, the process involves:
Acknowledging your emotional responses.
Identifying the specific concept or statement that has triggered the responses.
Describing the specific value represented by the concept or statement.
Describing the reasoning or belief systems behind the value.
Articulating an opposing value.
Describing the reasoning behind that value.
 
This process is most commonly used in the context of an argument or conflict. For example, in a conversation about abortion, Person A might assert that abortion should be banned. In response, Person B might become angry. If person B were to stop and analyze perspectives, she would first acknowledge her strong emotional response (anger), and the specific concept or statement that triggered it (abortion should be banned). Then she would try to determine the underlying value represented by that statement, which in this case might be the idea that life should never be taken by another human being. At a much higher analytical level, she would try to discern the system of reasoning or beliefs underlying the value. Because systems of beliefs are invariably the foundation of values, identifying them is the very core of analyzing perspectives. In this case, Person B might discover that Person A‘s belief that life begins at conception is the underlying principle driving her value and consequent reaction to abortion. Person B would then articulate a value counter to this (abortion should not be banned) and a system of reasoning or beliefs that would logically support the value (life does not begin at conception).
This is an oversimplified example of a process that Paul (1984, 1987) and others assert has the power to create great personal insight and flexibility in dealing with others. As a tool for extending and refining knowledge it has wide application. For example, students might use the process with essays on the ethics of the U.S. invasion of Iraq in 1991. The teacher would present students with an editorial strongly in favor of (or against) the U.S. invasion of Iraq. Students would then try to identify their reaction to the editorial, the specific concept or statement they have reacted to, the value underlying their reaction, and the system of beliefs underlying that value. Students who have similar reactions might form a cooperative group. The group would then articulate an opposing value and a possible system of beliefs underlying it. Cooperative groups could present their findings orally or in writing, along with statements of the personal awareness the process created.
Teaching the Extending and Refining Processes
As you no doubt inferred from the previous discussion, the extending and refining operations can be rather complex processes that include steps or general rules. In short, they themselves are types of procedural knowledge. Within the thinking skills movement, there is some debate about whether these mental processes should be taught directly to students. On one side of the issue are theorists such as Beyer (1988), who assert that students need direct instruction and practice in these mental processes in a content-free environment. At the other end of the continuum are those who assert that these processes make sense only in the context of domain-specific content. Resnick (1987) and Glaser (1984, 1985) are perhaps the most widely recognized proponents of this perspective. Their position on the extending and refining operations described in this chapter would probably be that students should be given such tasks only to learn about content. The operations should not be taught as skills in themselves.
The Dimensions of Learning model combines the best of both views, although there is a strong bias toward the Resnick and Glaser end of the continuum. Because the extending and refining operations are intended as activities to help students deepen their knowledge of content, they should be presented to students as tasks that involve content-specific declarative and procedural information. There is, however, one situation in which it might be advantageous to teach the steps or heuristics involved in these operations: when students cannot perform or are having difficulty with a task for reasons other than their knowledge of the content involved. This might occur frequently in the lower elementary grades. I have witnessed situations where students were fully knowledgeable about the content involved, but had extreme difficulty with extending and refining tasks. The difficulty was alleviated when the teacher explained the processes involved and then demonstrated them for students.
One way of ensuring that students understand and can effectively use the extending and refining operations is to use Beyer‘s direct instruction approach with one important modification: the processes should not be presented in a content-free manner. That is, the teacher should outline the explicit steps in each process and use the subject being studied to give students practice in using the steps. In this way, students receive a detailed and clear demonstration of the processes without taking time or energy away from the curriculum.
Another way of increasing the probability that students can use the extending and refining processes is to initially use tasks that are structured in such a way as to make the process explicit. Here is an example of a "process explicit" abstraction task:
Bees, termites, and ants live in tightly structured social groups with strict rules governing behavior and roles within the group. Examine the rules that govern one of these societies, considering especially rules involving leadership and rank, work, living space, cooperation, competition, taking care of and educating the young, and continuation of the group. Relate the patterns that you have identified in the insect kingdom to the patterns that you see in human social groups (such as those in tribes, cities, small towns, or work in large companies or factories).
 
This task is structured so that students are presented with the literal information on which they are to focus (rules in a specific insect society regarding leadership, rank, work, and so on) and the general situation to which the information is to be abstracted (human societies). The part of the abstraction process left to students is to identify the abstract or general pattern. In short, the abstraction process is built into the task.
For some students in some situations, it is advantageous, if not necessary, to receive explicit guidance in the processes and general rules underlying the operations for extending and reigning knowledge. Theoretically, this guidance should help students transfer their use of these skills to other content areas, but it is common knowledge that the research on transfer is discouraging for people seeking to develop strategies that will help students transfer skills (Hayes 1981). After describing a study in which a subject was unable to transfer his skill in memorizing digits to the task of memorizing letters, Anderson (1990) noted that "this is an almost ridiculous extreme of what is becoming a depressing pattern in the development of cognitive skills. This is that these skills can be quite narrow and fail to transfer to other activities" (p. 284).
Even in light of these conclusions, there is some hope. Transfer appears to occur under two conditions, similar elements and explicit cueing. E. L. Thorndike, in a series of experiments, established the theory of similar elements, which states that the more two processes have in common the higher the probability of transfer (Thorndike 1906, Thorndike and Woodworth 1901). That is, the knowledge involved in process A would transfer to process B as long as process B had similar steps or component parts. Actually, Thorndike said that the processes had to have identical elements, but in later studies researchers showed that the elements simply had to be similar (Singly and Anderson 1989).
Even when processes contain similar elements, transfer usually doesn‘t occur without cueing. For example, Gick and Holyoak (1980, 1983) found that with a cue, 75 percent of students could transfer the process learned in one task to another. In contrast, only 30 percent of their subjects performed the transfer without the cue. In other words, students had to be explicitly reminded to use the strategies they had been taught.
In summary, for transfer to occur, the skill or process used in one task must be very similar to that in the transfer task and students must be reminded to use the strategy. Fortunately, these conditions are easily met by the extending and refining operations described in this chapter. For example, the process of comparison taught in science will be the same as the process of comparison taught in social studies except for the content used. The process of classification taught in mathematics will be the same as that taught in literature except for the content used. Once students learn the eight extending and refining operations, they can use them in any class, provided they are reminded to use them. Using the names of the processes—comparison, classification, induction, deduction, and so on—can be the cue for the processes that have been taught. Arthur Costa and I (1991) believe that teachers should regularly use the names of analytic skills in the classroom as part of a "language of thinking" shared by teacher and students. Carolyn Hughes, one of the initiators of the current emphasis on teaching thinking skills in American classrooms, has long asserted that from the primary grades on, students should be taught the names of the reasoning skills we want them to use.
Planning for Extending and Refining Knowledge
Just as a teacher plans activities to help students acquire and integrate declarative and procedural knowledge, so too must she plan to help students extend and refine their knowledge. Again, let‘s consider Ms. Conklin‘s planning for the unit on weather.
Ms. Conklin‘s Planning for Dimension 3
Ms. Conklin is pleased with the activities she has identified to help students acquire and integrate the information about weather. Surely all these different experiences will help students make the information about weather part of their knowledge base. But she wants them to go much further. She would like to help students think deeply about the content. First she has to consider which information to focus on. She soon finds that this isn‘t an easy decision. Even though she has been fairly specific about which information to emphasize in the various learning experiences, she must now be even more specific. She decides that three areas are good candidates for extending and refining activities:
The events leading up to a tornado
How we forecast the weather
Air pressure
 
In choosing extending and refining activities, she asks herself what kind of activities would suit the content. Her thinking goes something like this: "Let‘s see. I think it‘s important that they understand that the process of a tornado forming has some unique characteristics. Maybe comparing it with how a hurricane forms would bring out those unique characteristics. But what should I have them do to extend their knowledge about weather forecasting?" As she makes decisions about extending and refining activities, she records them in the unit planning guide (see Figure 4.9).
When Ms. Conklin is done, she pauses for a moment to reconsider her decisions. The more she thinks about the activities she has identified, the more excited she becomes. "There are some things here they can really get their teeth into. But I‘m going to have to give them a lot of guidance."
 
Figure 4.9. Unit Planning Guide for Dimension 3: Extending and Refining Knowledge
Information
Compare
Classify
Induce
Deduce
Analyze Errors
Support
Abstract
Analyze Perspective
Sequence of events of tornado
Compare tornado with hurricane
Forecasting Weather
Students will draw conclusions about weather people
Air Pressure Rise and Drop
Students will generate abstract pattern + relate to another process in nature
Ms. Conklin‘s planning illustrates two basic decisions involved in planning for Dimension 3:
1. What information will be extended and refined? Not all information must be analyzed in depth. The sheer amount of information available in most subjects makes that impossible. In 1982, John Naisbitt pointed out the futility of trying to keep up with the growth of information:
Between 6,000 and 7,000 scientific articles are written each day.
Scientific and technical information now increases 13 percent per year, which means it doubles every 5.5 years.
But the rate will soon jump to perhaps 40 percent per year because of new, more powerful information systems and an increasing population of scientists. That means that data will double every twenty months (Naisbitt 1982, p. 24).
 
 
Even though Naisbitt‘s predictions have not been entirely accurate, his essential message has proved true: Information continues to grow geometrically. It is impossible to know everything about a subject and even more foolhardy to try to teach everything about a subject. The renowned mathematician John von Neumann put it succinctly when he noted that a century ago it was possible to understand all of mathematics, but by 1950 even the most well-informed mathematician could have access to only 10 percent of the knowledge of this field (in Gardner, p. 149). The implication, then, is that educators must specify the information to be analyzed in depth. Of all the information covered in her unit on weather, Ms. Conklin has decided to focus on three basic pieces.
2. What activities will be used to help students extend and refine their knowledge? The important rule of thumb when selecting extending and refining tasks is to "let the content select the tasks"; that is, activities should naturally fall out of the content. For example, comparing the events leading up to a tornado with those leading up to a hurricane seems to be a natural way of extending and refining knowledge about tornadoes. The activity of comparison, then, fits well with that particular content, whereas the activity of analyzing errors or constructing support would not seem to fit as well. I have witnessed some disastrous results when teachers have tried to fit the content to the task, rather than the task to the content. Such tasks are usually clumsy, uninspiring, and not very effective. On the other hand, when teachers think of the eight categories of tasks described in this chapter as a menu from which to choose, the results can be very exciting. In some units, they use a little induction and analysis of perspectives because these go well with the content. In other units, comparison and abstraction may better complement the unit. What‘s most important is that the task help students better understand what they are learning.
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