JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 27. NO. 10. PP. 923-936 (1990)

CONCEPT MAPPING AND THE CARTOGRAPHY OF COGNITION

JAMES H. WANDERSEE

Graduate Studies in Curriculum and Instruction, Louisiana Stare University

Abstract

Since concept maps are designed to find out what the learner knows about a subject and are, in effect, maps of cognition, this article synthesizes relevant facts, concepts, and principles from cartography and applies them to concept mapping. The metaphor of the map and its applicability for representing scientific knowledge are discussed. The context of concept mapping IS presented and suggestions for successful application of the technique in the science classroom are offered. Finally, researchers are invited to conduct studies that investigate the graphic representation of scientiJic knowledge in order to create, evaluate, and improve the graphics and graphic metacognitive tools (such as concept mapping) which are used in science teaching.

Perspectives from Cartography

Mapping and Knowing

To map is to construct a bounded graphic representation that corresponds to a perceived reality. Cartography, the science of map making, has a long and noble history. The earliest known map was found inscribed on a bone artifact at Mezhirich. USSR and dates back to about 10,OOO BC (Hellemans & Bunch, 1988). It seems to show the geographic area immediately surrounding the site at which it was found. Not only ancient peoples, but also remote and isolated tribes living in modem times have developed mapping prowess. South Sea Islanders invented stick charts-palm sticks tied together in grid form with coconut fiber-to map the currents, prevailing winds, and islands they encountered in their journeys across hundreds of miles of open sea. The technique was fully developed even before they had any written language (Wman , 1989). In the early 1800s, Admirals Parry and Ross were startled to find that Eskimos whom they met on their expeditions to the Arctic were not only able to understand the explorers’ navigational maps but could even supply important information to hpmve them (Daly, 1879). From early on, humans have ventured forth to explore and then map their world of experience. Once mapped, it was no longer considered terra incognita but terra c0gnira-a region known to humankind. Thus, “to map” has always meant “to know.”

8 1990 by the National Association for Research in Science Teaching Published by John Wiley & Sons, Inc. CcC 0022-4308/90/100923- 14W.00

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The Signijcance of Mapping

The map was a signal innovation in human thought. Perhaps no one has captured its importance better than Arthur H. Robinson (1982), Lawrence Martin Professor Emeritus of Cartography at the University of Wisconsin:

The act of mapping was as profound as the invention of a number system. . . The combination of the reduction of reality and the construction of an analogical space is an attainment in abstract thinking of a very high order indeed, for it enables one to discover structures that would remain unknown if not mapped. (p. 1 )

The Cartographic Communication Process

There are two critical transformations which must occur if a map is to fulfill its role as an instrument of human communication (Dent, 1985). First, the mapmaker must encode the meaning, using appropriate graphic conventions. Only potentially meaningful, contextually appropriate information should be included on a map (Guelke, 1976). Second, the map reader must perform detection, recognition, discrimination, and estimation tasks in order to extract the meaning which was encoded.

Thus the cartographic design and interpretation processes involve complex cognitive transformations with both intellectual and visual components. Opportunities for creativity are also present at both transformation points and may serve (a) to challenge one’s assumptions, (b) to recognize new patterns, (c) to make new connections, and (d) to visualize the unknown. Thus, the real world yields the raw data of perception which are transformed by the map maker into a map that represents knowledge worth sharing; the map reader then extracts the relevant meaning and uses it for problem solving and decision making (Cuff C?Z Mattson, 1982).

In most commercial cartographic enterprises, there is little opportunity for two- way communication with or feedback from the map reader. The feedback which the map makers receive is usually indirect (e.g., the map’s sales document its value to the user). Most cartographers. however, admit that the solicitation and careful consideration of map readers’ evaluative responses are vital to improvement of map design (Dent, 1985).

Limiting Factors

Although all maps contain errors. the history of cartography shows that the accuracy of any map is highly dependent upon the quality and quantity of the data the map maker collects about the reality to be mapped. In addition, the cartographer’s prior knowledge influences hidher selection of and generalization about the data. The map maker’s aesthetic sense and artistry also affect the final product (Robinson, 1980). Thus, every map reflects both its data and its designer. Map making is a human exercise in “knowledge construction” or “meaning making,” and therefore has both inherent strengths and limitations.

Brown (1949) defends map makers with vigor in his classic work, The Story of Maps, when he writes

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criticized for its errors than cartographers . . . for every map and chart compiled by the pioneers in cartography, a thousand pages of adverse criticism have been written about them by men who were themselves incapable of being wrong because they would never think of exposing themselves to criticism, let alone failure. (p. 9)

Maps as Indicators of Change

It is interesting to peruse old world maps and compare them to modem ones; the older maps transport us to a strange perceived reality and help us to understand the thoughts of generations past. Where once dragons were believed to lurk, now new continents exist; when Once every civilization thought it was at the geographic center of the earth, now-on the surface of an oblate ellipsoid-no one is. Upon viewing a chronological sequence of world maps, we can see how knowledge about the natural world has changed over time. Changes in maps reflect changes in understanding.

The Influence of Prior Knowledge

It would be reasonable to assume that the parade of maps across time would show steady progress toward what we today consider greater understanding of the natural world. But that is not the historical reality. To give just one example, Boorstin (1983) writes:

Christian Europe did not carry on the work of Ptolemy [they replaced his detailed gridwork with caricature]. Instead the [medieval] leaders of orthodox Christendom built a grand barrier against the progress of knowledge about the earth . . . Designed to express what orthodox Christians were expected to believe, they were not so much maps of knowledge as maps of Scriptural dogma. (pp. 100- 101)

Jerusalem was placed at the center of the world because of the Bible verse Ezekiel 5 5 (“ . . . I have set it in the midst of the nations . . .”). More than 600 extant maps from this period in history reflect such medieval Christain thought. Thus, the prior (theological) knowledge of the medieval map makers affected their choice of data and, ultimately, the maps they constructed.

The Inherent Distortion of Maps

While technological advancements and cartographic algorithms give the impression that today’s maps are perfect representations of reality, every map (even a globe) still distorts reality. Various projections (e.g., cylindrical, conical, azimuthal) are employed to give alternate views of the perceived reality on a flat piece Of paper-views that are very useful for specific purposes, but distorted nevertheless. Why use a projection? Robinson (1980) observes, ‘“The projection Constitutes a systematic reference frame. . .” (p. 58). Commonly, factors such as the map’s intended intellectual function and desired visual structure are used to determine which projection is most appropriate for a given application. A single kind of graphic representation certainly does not meet the needs of all map makers and, even today. all maps are approximations of perceived reality. Monmonier (1977) goes so far as to contend that “distortion is necessary in order that the map reader be permitted to comprehend the meaning of the map” (p. 7).

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The Cognitive Power of Maps

In Chapter 3 (Mapping) of their stimulating book The Ring of Truth: How We Know What We Know ( 1987), Momson and Morrison point out that only in this century have humans been able to send astronauts and satellites into space to see what the world really looks like. Yet the space trips yielded no real surprises to change the world map; even before balloons and aircraft provided wider views, cartographers had already mapped the globe quite accurately “by crawling like ants” over its surface. We should never underestimate the cognitive power represented in the mapping process.

Using Maps to Integrate and Summarize Knowledge

The Great Trigonometrical Survey of India, finished in 1870, crisscrossed that country with huge sightline triangles using only the low technology of sighting towers (Momson & Momson, 1987). It was this survey and those triangles that identified Mount Everest as the highest mountain on earth-a mathematical discovery made by mapmakers doing calculations in an office in Calcutta-cartographers who never actually set foot on the mountain itself! From this historical account, it seems apparent that mapping-even using indirect methods-can be a valid and reliable way of integrating and summarizing a set of perceived units of reality.

The Generative Power of Maps

Another conclusion that one could draw from the same story is this: Not only do maps represent what we know, they suggest further explorations. When Sir Edrnund Percival Hillary and his native guide, Tenzing Norkay, reached the peak of Mount Everest on May 29, 1953, they provided direct verification of what the Indian map makers had predicted Some 80 years before (Asimov, 1972, pp. 758-759). There were other unclimbed peaks, but Sir Edmund wanted to conquer the one the mapmakers said was the highest of all. Just as an impetus for Columbus’ famous voyage was a map, so it was for Hillary’s momentous ascent.

The Metaphor of the Map

The Role of Metaphor

Metaphors are archetypes that can subsume difficult concepts and have heuristic value. For example, someone might say that the earth is an organism or the brain is a computer and then explore the implications of such a metaphor. Philosopher D. Bob Gowin once observed, “An apt metaphor is probably better than an arid and formally stated hypothesis in trying to find Out about something unknown. . . . Get thyself a metaphor to ride the unknown. All the rest is algebta” (Gowin, 1983, p. 39).

Scientific Knowledge and the Map Metaphor

If knowing is making a mental map of the concepts one has learned and if people think with concepts, then the better one’s map, the better one can think. Judson (1980) reminds us that “the map as metaphor for the network Of scientific knowledge has

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often been suggested . . .” (p. 191). Although maps are always somewhat inaccurate, approximate, and incomplete, so are the scientific theories which humans construct. Like a map, theories connect knowledge in many directions and are continually updated to incorporate new information. The act of theory building, like map making, exposes doubtful knowledge and calls for its replacement with more reliable knowledge. Ziman (1978) points out that the first maps of a new territory are usually naive, somewhat arbitrary, and asystematic. I t is only after innumerable expeditions have reported their findings that major discrepancies or ambiguities in the original map are resolved. But without that first map of the territory, subsequent explorers would have nothing to test and nothing to amend. Just as a map cannot be reduced to strings of text, scientific knowledge is fairly nonlinear, hierarchical, and weblike. Therefore, “the metaphor of the map” seems quite appropriate for holistic representation of scientific knowledge.

The Context of Concept Mapping

Theoretical Foundution

Concept mapping is a metalearning strategy based on the Ausubel-Novak-Gowin theory of meaningful learning (Ausubel, Novak & Hanesian, 1978; Gowin, 1981; Novak, 1977; Novak & Gowin, 1984). It relates directly to such theoretical principles as prior knowledge, subsumption, progressive differentiation, cognitive bridging, and integrative reconciliation. Unfortunately, some teachers master the technique because it is mentioned in their teacher’s manual, but are completely unaware that concept mapping is not just another “study strategy.” They do not realize that it is based upon a major psychological theory in science education and that it is designed to help students “learn how to learn” science.

Basic to making a concept map for a piece of scientific knowledge is the ability of the mapper to identify and relate its salient concepts to a general, superordinate concept. That requires an understanding of what constitutes a science concept. Concepts may be defined as regularities in objects or events designated by some label, usually a term. Whether a process (e.g., precipitation), a procedure (e.g., titration), or a product (e.g., carbohydrate), concepts are what we think with in science. Concepts can be connected with linking words to form propositions (e.g., turtles are classified as reptiles, sucrose tastes sweet, ontogeny recapitulates phylogeny). Therefore, a concept map may be defined as “. . . a schematic device for representing a set of concept meanings embedded in a framework of propositions” (Novak Lk Gowin. 1984, p. 15).

At first glance, a concept map looks like a flow chart without the arrows. However, it is not. Rather than representing a linear or branched sequence of steps in a process or procedure, concept maps are designed to parallel human cognitive structure, in that they show concepts organized hierarchically, whereas flowcharts do not. Instead of a representation that corresponds directly to a linear text or lecture and reflects the structure of knowledge (e.g., outlines), concept maps reflect the psvchologica/ structure of knowledge. A concept mapper must often transform the knowledge to be mapped from its current, linear form to a context-dependent hierarchical form. Before that can be done, the mapper must first identify the key concepts, arrange them from general to specific, and relate them to each other in a meaningful way.

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Graphic Conventions and Map tmprovement

A finished concept map, which has probably undergone numerous revisions, looks deceptively simple to someone who has never actually constructed one. It is visually efficient and easy to understand. Concepts are written using lowercase letters and are centered within circles or ellipses. From the superordinate concept at its top flow several cascades of subordinate concepts, each level of the case increasing in specificity as it approaches the bottom of the page. All of the lines connecting the concepts must be accompanied by linking words, so that each branch of the map can be read from the top down. Often, at the terminus of each branch, may be found examples of the terminal concept. Examples anchor the map, may be included anywhere in the map, and are not encircled as the concepts are; they may be enclosed by broken circles or ellipses, however. Where appropriate, cross-links labeled with linking words connect branches of the map like bridges link riverbanks. By convention, such cross-links may be represented by broken lines. Occasionally, an arrowhead is used at the end of a linking line to show that a proposition is not bidirectional. Despite their uncomplicated appearance, concept maps are, initially, difficult to construct. It may take as long as 8- 10 weeks for students to become fully accustomed to the technique and to realize its potential for improving their understanding of science.

One of the problems students initially encounter when constructing their own concept maps is how to formulate meaningful propositions so that they have appropriate linking words to write on the lines that connect the concepts. In their first attempts, often the maps students produce make heavy use of the linking verb be and the propositions they generate are less powerful because of it. Students need to see examples that use other verbs, as well as adverbs, adjectives, and prepositions so that the concept map reads like a graphic argument that uses data, claims, warrants, support, and reservations much like Toulmin’s (1964) system of argumentation.

This author also sees the recent discourse analysis conducted by Dagher and Cossman (1990). which seeks to analyze the verbal explanations which are often used in science teaching, as potentially invaluable as a heuristic for helping students word some of the key propositions which they place on their maps. That study’s organizational scheme would suggest that the following categories of propositions may be important to consider when making a Science concept map in that they are both useful for learning science and falsifiable: (a) practical: how to think about or do something (e.g., an instrument must be calibrated); (b) theoretical: analogical (e.g., the cell functions as if it were a factory); (c) theoretical: functional (e.g., together, the genetic program and the environment determine the phenotype); (d) theoretical: teleological (e.g., Salk wanted to find a polio vaccine); (el theoretical: genetic (antecedent event sequence) (e.g., the food chain biologically magnifies DDT); (f) theoretical: mechanical (e.g., new feathers that emerge following molting replace faded, brittle, or worn feathers); and (s) theoretical: rational (evidence-basPd) b g . , mammalian heart rate varies inversely with body size). As Robinson (1980) points out: “Cartography is a technique, just as scientific writing or the language of mathematics. by which intellectual concepts are displayed for consumption” (p. 19). Thus, the greater the clarity of the propositions, the more conceptually transparent one’s concept map Will be.

One of the best references on concept mapping and how it may be introduced to students at various grade levels is the book: Learning HOW to Learn (Novak & Gowin, 1984). Science educators should not attempt to teach others how to make a concept

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map unless they have mastered all of the graphic conventions and have constructed at least ten different maps by themselves. One can neither empathize with nor capably assist the beginning concept mapper without such experience. With such experience, it is also obvious that the educational benefit accrues chiefly to the mapper, not the person given another’s map.

Three Theory-Based Metacognitive Tools

If learners are empowered through instruction that promotes personal “meaning making” (Novak, 19891, and if “the world seems already firmly committed to a more visual than verbal learning mode. . .” (Hass, 1990, p. 61, and if “. . . meaning depends on context and ‘understanding’ requires a vast body of knowledge about the world” (Waldrop, 1984, p. 372), then new graphic tools and instructional strategies based on a theory of meaningful learning are needed.

At present, only three graphic metacognitive tools have been developed which are based solely upon the Ausubel-Novak-Gowin theory of meaningful learning. They are (a) concept circle diagrams, (b) concept maps, and (c) vee diagrams. See Appendixes A, B, and C. Each has a particular role to play in science instruction and each has its own growing research base.

The concept circle technique was invented at Cornell University in 1984 by Wandersee (1987a, 1987b) and was designed to conform explicitly to the Ausubel-Novak-Gowin theory of meaningful learning and to modern visual perception research. It is derived from mathematician Leonhard Euler’s (1707- 1783) system of logic diagrams and is especially useful for teaching bounded taxonomic concepts and depicting the categorical relationships of inclusion and exclusion.

Concept circle diagrams may be defined as two-dimensional geometric figures (circles) which are isomorphic with the conceptual structure of a particular piece of knowledge and are accompanied by a title, concept labels. and an explanatory sentence. Students use drawing templates (with experimentally determined, psychologically sized circle holes) in order to encode quantitative and categorical relationships between the concepts they wish to represent. The format of the concept circle diagram is based upon the scanning pattern of the human eye and the number of circles in a given diagram is intentionally limited to five or less, based upon research in information processing. visual perception, and science education (Wandersee, 1987b). Diagrams may be connected by a visual technique called “telescoping” and all diagrams are colored using principles of visual perception to guide color selection. The technique has been used successfully with life science classes from grade 4 through graduate school (Nobles & Wandersee, 1990) and it appears applicable to any science discipline. However, further research is both necessary and planned.

Initially, the author has found the technique eSpecidlY U s e f u l as a way of introducing students to graphic metacognitive tools, to the nature of a concept, and to the learning strategy of searching for simple exclusive/inclusive relationships between concepts. It appears to be the first graphic metacognitive tool to be designed using visual perception principles and it seems to be quite helpful in Preparing students to learn concept mapping.

Concept mapping was invented at COrnell University by Novak and the members of his research group (Stewart. Van Kirk & Rowell, 1979). It was

Concept circle diagrams.

Concept maps.

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described earlier in this article. Of the three, this tool has the largest research base and is quite widely used in textbooks, teacher’s guides, and science classrooms. For example, a recently completed major survey of the high school science teachers in the state of Louisiana showed that 50% of them were aware of the instructional technique of concept mapping (McCoy, Wandersee & Good, 1990). It is especially useful for helping students understand what meaningful learning is and showing them that learning is idiosyncratic and is therefore a responsibility which cannot be shared.

Vee diagramming was invented at Cornell University in 1977 by Gowin (1981). Although this technique is less widely known, it is ideally suited to improve science laboratory instruction, research design, and the writing of research papers. The same survey of Louisiana high school science teachers found that just 17% were aware of the vee diagramming technique (McCoy, Wandersee & Good, 1990). Nonetheless, it is especially useful in helping students understand the structure of knowledge and “how we know what we know” in science. This graphic has the form of a capital letter “V” and has a thinking (epistemological) and a doing (methodological) side. A central “telling question” points the vee at an object or event that can help to answer it. The method of extracting knowledge from the object or event of interest is informed by the conceptual side of the vee and the complex interplay of the vee’s elements produces knowledge and value claims. This tool is the most difficult of the three for students to grasp and therefore it should probably be the last one they learn to use. It may also be the most powerful of the three, and this author asserts that its use should be a part of every graduate program in science and science education.

Vee diagrams.

Applying Cartography to Metacognition

All three of the metacognitive tools discussed in this article are maplike, with concept mapping showing the closest relationship to cartography. The metaphor of the map seems quite appropriate for holistic representation of what we know in and through science. The following generalizations from cartography can inform our understanding of such graphic t‘epresentation of scientific knowledge: (a) mapping and knowing are closely intertwined; (b) maps are excellent heuristic devices; (c) both the map maker and the map reader have important responsibilities to fulfill if communication is to occur; (d) every map reflects both its data and its designer; (e) changes in maps reflect changes in understanding; (f) the Prior knowledge of the map maker can have a great influence on the maps he or she produces; (8) all maps distort reality, both because of the very nature of mapping and because map makers have learned how to exploit distortion to achieve their communicative goals; and (h) maps have great cognitive, integrative, summative, and generative Power.

Concept Mapping, Cartography, Cognition, and Future Research: Some personal Comments

Concept mapping, the subject of this Special issue of the Journal of Research in Science Teaching, is relatively new. Its long-term impact on science education cannot

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yet be determined. If research results remain promising, the technique will no doubt continue to be modified and improved.

With the reader’s forbearance, the following personal comments may be instructive. During the 11 years that I have been associated with Novak and his research group at Cornell University, I have used concept mapping (a) to teach undergraduate biology courses; (b) to teach science education methods courses to pre- and in-service primary, secondary, and university science teachers; and (c) to publish science education research papers based upon it (e.g., Abrams & Wandersee, 1990; McCoy, Wandersee, & Good, 1990; Wandersee, 1983; 1990).

I continue to be impressed by the potential of such graphic metacognitive tools to help science teachers and science educators improve science instruction. 1 invite all researchers with an interest in “the graphic representation of scientific knowledge” to join us in exploring this domain, since much more research is needed.

At Louisiana State University, a graduate course that I teach which is entitled “The Graphic Representation of Scientific Knowledge” attempts to integrate relevant principles and research from such domains of knowledge as epistemology, learning theory, visual perception, graphic design, computer visualization, information processing, scientific illustration, cartography, and even vexillology to create, evaluate, and improve the graphics and the graphic metacognitive tools used in science teaching. In addition to the instructor’s presentations, guest speakers from other units of the university, the city’s professional community, and neighboring universities offer students new per- spectives on what makes a scientific graphic effective.

At San Diego State University, Kathleen Fisher and the SemNet research group have also developed a promising new metacognitive tool, a course, and a research program in this field-all of which are described in an article appearing elsewhere in this issue.

In closing, perhaps a parallel can be drawn from the history of cartography. Up to the late 1600s, there were only general geographic maps. Then, a significant advance was made: Thematic maps were invented. Thematic maps portray variations within a single class of features rather than show an assemblage of features. A weather map, for example, is a thematic map, so is a bird species range map. Robinson (1982) contends that:

. . . the development of thematic mapping in the Western world ranks as a major revolution in the history of mapmaking. Its intellectual and conceptual consequences are comparable to those that followed upon the spread of the concepts in Ptolemy’s Geography some three centuries earlier. (p . 17)

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Appendix A

Two concept circle diagrams done by a student in a ninth-grade environmental science course, with annotation added to highlight key features of such diagrams and shading added to represent the original colors (redrawn). (Note: The technique can depict five basic qualitative relationships among concepts and two basic quantitive ones. This example shows only the inclusion and the relative importance relationships. It also shows how diagrams can be linked by “telescoping.”)

n

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Appendix B

Concept map on the design of the pencil, constructed to show most of the graphic conventions employed in concept mapping.

psnc 1 I Q

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Appendix C A Gowin’s vee diagram for a high school biology laboratory investigation of the

microscopic organisms in pondwater. (The original diagram was made by a preservice biology teacher.)

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Manuscript accepted August 21, 1990.