Instructional Science 19:29-52 (1990) 29 Kluwer Academic Publishers, Dordrecht - Printed in the Netherlands
Concept maps and Vee diagrams: two metacognitive tools to facilitate meaningful learning
JOSEPH D. N O V A K Department of Education, Cornetl University, Ithaca, NY 14853, U.S.A.
Abstract. This paper describes two metacognilive tools, concept mapping and Vce diagramming, and reports on research utilizing these tools from grades one through university instruction. The psycho- logical and epistemological foundations underlying these tools is presented briefly. The issues of the dominantly rote-mode nature of much school learning and the resistance of students (and teachers) to move to meaningful learning strategies fostered by concept mapping and Vet diagramming are dis- cussed. The data available to date from a variety of qualitative and quantitative research studies strongly support the value of these metacognifive tools both for cognitive and affective gains.
In the past decade, there has been a rapid increase in instruction that helps students "learn how to learn". This activity derived in part from advances in cognitive learning psychology (see Mayer, 1981) and the increase in cognitive learning research in school settings. Flavell (1985) defines metacognition as "cognition about cognition" (p. 104). Metacognitive learning occurs whenever a person acquires some general strategy that facilitates learning or understanding of know- ledge. Weinstein (1987) has described strategies that can be used for reading comprehension. Ideally, the most powerful metacognitive learning would be acquisition of strategies that apply at any grade level and to any subject matter. The intelligent construction and use of concept maps and Vee diagrams are two widely applicable metacognitive strategies we have developed at Cornell University, and world-wide use of these strategies is being reported increasingly in the literature since publication of Learning how to learn, (Novak and Gowin, 1984; 1988).
Concept maps as we have have developed them are a representation of mean- ing or ideational frameworks specific to a domain of knowledge, for a given con- text of meaning. We define concept as a perceived regularity in events or objects, or records of events or objects, designated by a label. Most of the labels we use are words, but signs such as +, -, E and so forth may also be used. Two or more concepts can be linked together with words to form propositions and we see prop- ositions as the units of psychological meaning. The meaning of any concept for a person would be represented by all of the propositional linkages the person could construct that include that concept. Since individuals have unique sequences of experiences leading to unique total sets of propositions, all concept meanings are
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Figure 1. A concept map showing key concepLs and propositions involved in concept mapping. Linking words together with concepts forms propositions and these am shown in a hierarchical sl.t'uc~rc..
to some extent idiosyncratic. However, in a given culture, there is sufficient commonality in experience that persons in that culture share sufficient common meanings for their concepts that they can communicate ideas to one another using language or other symbols. For most of us, we only have to look at a blackboard filled with mathematical relationships expressed in symbols to realize that this represents a "different world", a world for which we have no meanings. Figure I shows a concept map on concept maps.
Over the past dozen years, our graduate students and other colleagues have found that all domains of knowledge can be represented by concept maps (con- cept/propositional structures). Figure 2 shows representations of knowledge struc- tures in basketball. There is no domain of knowledge (or "skills") for which concept maps cannot be used as a representational tool, in our experience.
Vee diagrams (see Figure 3) are a heuristic tool developed by my colleague, Bob Gowin, to represent the structure of knowledge and the epistemological ele- ments that are involved in new knowledge construction. Epistemology is that branch of philosophy that deals with the nature and structure of knowledge. Epistemological elements are those units that together from the structure of some segment of knowledge and are required to construct a new piece of knowledge. The Vee heuristic is based on a constructivist epistemology, as contrasted to the empiricist or positivist epistemology that has characterized popular views of "knowledge discovery" in most elementary textbooks of science and social sci- ences. Kuhn (1962), Toulmin (1972), Brown (1979), Popper (1982) and others have shown the inadequacies of positivistic (truth-falsity proving) epistemologies and most leading contemporary philosophers concerned with the nature of knowl- edge and knowledge construction are agreed upon some form of constructivist epistemology. Conslructivist epistemology sees production of new knowledge as a human construction, with all the power and weaknesses associated with the ideational frameworks, instrumentation used, and emotional vagaries of human beings. The Vee heuristic represents a constructivist view of knowledge and iUus- trates the dozen or so epistemological elements that interact in the process of new knowledge construction. The Vee heuristic can also be used to dissect an existing domain of knowledge and to see its structural elements. Figure 4 shows a repre- sentation of this for one area of biology.
My work and the work of my students has been based upon Ausubel's assimi- lation theory (1963, 1968) of cognitive learning for the past quarter century. In his epigraph to his 1968 book, Ausubel asserts: "If I had to reduce all of educa tional psychology to just one principle, I would say this: The most important sin- gle factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly." It is this fundamental principle that led our research group to search for better ways to represent "what the learner already knows" and to develop the tool of concept mapping in 1972. Although we developed this for
research purposes to represent student's knowledge slructures before and after instruction, we soon learned that concept maps could be a useful tool to help stu- dents move from learning by rote to learning meaningfully. We now see meaning- ful learning as the fundamental process that underlies useful knowledge acquisition and also new knowledge construction. I have argued that meaningful learning is the foundation for human constructivism which is both a psychological and an epistemological phenomenon. Figure 5 shows a concept map representa- tion of this union of psychological and epistemological meaning making (from Novak, 1987). This representation of meaning making draws upon and incorpo- rates ideas from many contemporary psychologists and philosophers including the work of Ausubel et al. (1978); Donaldson (1978); Flavell (1985); Gowin (1981); Johnson-Laird (1983); Kelley (1955); Kuhn (1962); Mathews (1980); Mayer (1981, 1983); MacNamara (1982); Piaget (numerous writings); Popper (1982); Steinberg (1985); Toulmin (1972); Vygotsky (1962) and many others.
Figure 2, Two concept maps prepared by a basketball player, one (above) early in training and the other (right) late in the season. Note the increased complexity and integration of concepts of team defense and communication, emphasized in coaching, which was accompanied by much-improved player performance. ('From Novak and Gowin. 1984, p. 44)
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World view: The general belief system motivating and guiding the inquiry.
Philosophy: The beliefs about the nature of knowledge and knowing guiding the inquiry.
Theory: The general principles guiding the inquiry that explain why events or objects exhbit what is observed.
Questions that serve to focus the inquiry about events and/or objects studied.
Value claims: Statements based on knowledge claims that declare the worth or value of the inquiry.
Knowledge claims: Statements that answer the focus questions and are reasonable interpretations of the records (or data) obtained.
Principles: Statements of relationships between concepts that explain how events or objects can be expected to appear or behave.
Concepts: Perceived regularity in events or objects (or records of events or objects) designated by a label.
Transformations: Tables, graphs, concept maps, statistics, or other forms of organization of records made.
Records The observations made and recorded from the events/objects studied.
Events and/or objects: Description of the event(s) and/or object(s)
to be studied in order to answer the focus questions.
Figure 3. Gowin's Vec hcurcstic invented to iUustratc the conceptual and methodological elements that interact in the process of knowledge construction or in thc analysis of lectures or dooamcnts presenting knowledge.
FOCUS QUESTION: Can we design an experiment to study some aspect of orientation behavior in an organism-its response to a particular stimuli, the classificelien of that response, and the posebls adaptive benefit of that behavior?
rt.~orr: Orientation behavior- stimulus-reaponse. Adaptalion and evolution of behavior.
Principles: 1). Orientation behavior is the act of turning or moving in a predictable way with respect to an external stimulus. 2). Orient. behavior can be classified as a kinesis (the speed or turning rate changes with no orientation of the body with respect to the stimulus) or a taxis (the body is directly orientated toward, away from, or at an angle to the stimulus). 3). Orient. behavior can be named based on three things: a. positive or negative (attracted or repulsed by the stimulus), b. stimulus type (chemo-, photo-, thermo-, etc), c, response of body - kinesis (tuming is klino-, speed is ortho-), or taxis (receptors used, at fixed angle to, memory based, sic). 4). Experiments to study orientation behavior should control for variablos, include replicates, and provide quantifiable data.
Concepta Orientation behavior, taxis, kinasis, stimulus, response, receptor, adaptation, orthokinosis, klinokinosls, humidity, schooling behavior, bilateral sense receptor, circus movements.
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I I Ve/ue /aine: I 1). Designing and conducting a study gives I students experience with sciantilic knowledge I constructkin. 2). This lab is valuable for providing
experience with orientation behaviors and their adaptive signifk~ nce.
Knawlmdge clakna: 1 ). Isepads exhibit a positive hygrokinesis and a negative phofotaxis, 2). Blowfly larvae usually show a negative phofokllnotaxis. 3). Daphnia usually have a negative phototaxis and a pasitlve geotaxls. 4). Fish species vary in the strength of their schooling behavior. Most tend to spend more time with conapecifios and with the larger group of conspeoifics. This behavior is considered Io be a telotaxis.
TranJformationo: Total, average and graph data_ Compare observed turning or movement rates and time spent with various stimuli to definition of kinesis and taxis in order to decide on classification ol observed behavior.
Record=: Measurement of times spent near various stlmuit. Counts of Lures or numbers of organisms at specific time intervals. Measurement of distance traveled and time evolved.
Obji~~: Isepeds, petri dish experimental apparatus, desiccant, paper Iowels, black paper, lights, marking pens, map measurer, blowfly larvae, Daphnia, graduated cylinders, ring stands, black plastic, several species of fish, lost fish lank, jars. Events: Design a study using one of the experimental organisms to determine the type of orientation behavior used in response to a particular stimulus. Gather data, transform data, and present results. Consider adaptive significance of the observed behavior.
Figure 4. A Vee diagram produced by a student for laboratory work in a study by Robertson-Taylor (1985). A PC software program was used for the construction.
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Figure 5. A concept map showing key concepts and propositions involved in "human constructivism", uniting meanings from psychology and epistemology.
Classroom research using concept maps and vee diagrams
As noted above, the development of concept mapping derived from our research program wherein we sought to represent science concept meanings possessed by students before and after instruction. We were engaged in a twelve-year study of concept development and needed a tool to show simply but also explicitly the concept meanings a student possessed as indicated in modified Piagetian clinical interviews (see Pines et al., 1978). Figures 6 and 7 shows a representation of the concept/propositional framework held by a student in grade two and later in grade twelve. These maps were drawn from clinical interviews (see Novak and Gowin, 1984 and notedly Chapter 7) with the student They show growth in the number and relationships of concept meanings for this student over the ten-year span of schooling.
Our first use of concept maps to help students learn subject matter meaning- fully were in the areas of mathematics and science at the college level. Cardemone (1975) found that preparation of a "master" concept map for the topic of "ratio and proportion" helped him to plan instruction on this topic. Copies of his map were distributed to students but only a minority of students reported in their questionnaire responses that Cardemone's concept maps were helpful to them for learning of this topic. Similarly, Bogden (1977) found that concept maps prepared by him and a professor for each lecture in a genetics course were reported to be of value in learning genetics by a small minority of students. Some students indicated they were confused by concept maps prepared for them. Concept maps proved useful, however, in designing and interpreting answers for course examinations. The concept maps used by Cardemone and Bogden did not have words on the linking lines between concepts.
From the Cardemone and Bogden studies, we learned that the primary benefit of concept maps accrues to the person who constructs the maps. It was of little value to distribute teacher-prepared concept maps to students when the latter were not involved in constructing their own concept maps. In more recent work, we have found concept maps prepared by a teacher to be helpful to students, but only after they had practice in constructing their own concept maps. Also, w...