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Invited Symposium: Shaping the future learning of mathematics & science. Session Number: 4118 Presented In: American Association for the Advancement of Science, Authors: Kathleen M. Fisher, San Diego State University
PRE-PRINT VERSION KATHLEEN M. FISHER JAMES H. WANDERSEE GRAHAM WIDEMAN IntroductionThe desire to map what we know is natural, ancient, and pervasive. The oldest known fully-scaled geographic map was produced by a Chinese cartographer, Yu ji tu, in about 1100 AD (Tufte, 1997). Map-making has steadily advanced since this time. With the advent of computers, cartography has taken a quantum leap in its sophistication, visual expression of ideas, and eloquence. Cartography provides a concise means for representing large volumes of data in ways that are visually interesting and comprehensible, and that reveal important patterns and trends. Graphic visual-spatial representations tap into the power of human pattern recognition. We argue here that successful visual representation of large bodies of information is the key to success in the information and communication age. It can give us a sense of control rather than a feeling of being overwhelmed, much like having a good road map when we are driving across a state we have never seen before. Unfortunately, our ability to map what we know about a knowledge domain such as physics or medicine lags far behind our mappings of such things as territories, seas, heavens, chemical substances, and chromosomes. The massive volume and variable quality of information available on the World Wide Web (WWW) demonstrates persuasively the need for a good map. Instead of searching in the term-indexed but meaning-detached manner of most search engines, wouldn’t it be wonderful to log on, access a comprehensive, conceptually-organized map of all related sites, and then be able to choose the best route? And wouldn’t it be even better if it contained key indicators such as quality, level of intended audience, and so on for each site? Today’s knowledge explosion makes sophisticated, high-powered knowledge mapping an imperative. Yet a review of available knowledge-mapping strategies demonstrates that we have a long way to go. Knowledge mapping has been utterly neglected, in contrast to the great strides made in other forms of cartography. Most scientists and science education researchers are not enamored with the primitive forms of knowledge mapping currently available, and they have yet to recognize the need for powerful knowledge-mapping capabilities in the future. Thus funding, support, interest, and essential research are lacking. The will to move forward is absent. In the computer age, knowledge-mapping protocols and formats must develop in tandem with search strategies and search-engine design. High-quality and rapid knowledge transformations are paramount in the new millenium. To survive and thrive both economically and ecologically, we must be able to seamlessly transform scientific knowledge to meet the demands created by new and unexpected scientific and societal problems, issues, and needs. Such knowledge transformations necessarily should have options for layers of detail and levels of complexity. We predict that, in the future, computers will create maps of existing text without human guidance—that is, will automatically generate knowledge-distillation products. Reading linear text will simply be too time-consuming for making initial passes at knowledge sources. In thinking about mapping, it may be valuable to distinguish among data, information, knowledge, and wisdom. These represent increasingly well-developed ideas with the last two differing significantly in scope from the first two. Data and information are typically domain-centered and external, while knowledge and wisdom are largely integrated, multi-domain, and internal. We need tools to facilitate the transformation from data and information into knowledge and wisdom (Figure 1).
There is considerable research regarding knowledge mapping as a constructivist learning activity in which the external map provides a tangible arena for the manipulation and organization of ideas. In this paper we are proposing a relatively new and little understood but potentially extremely useful application, knowledge maps as road maps. Modern History of Knowledge MappingCultures have mapped their knowledge across the centuries, in various forms and styles. However, the knowledge mapping we discuss here is a 20th-century phenomenon. These maps are word-based and consist of networks of interconnected ideas. The maps attempt to capture and reflect the arrangement of these ideas in psychological space. Gordon Pask of Great Britain seems like the obvious one to begin this recent history. Pask straddled the dual worlds of artificial intelligence and education. He developed many different forms of cybernetic knowledge mapping in the 1950s–1970s. His research focused on such topics as the styles and strategies of learning (Pask, 1976a) and conversational techniques in the study and practice of education (Pask, 1976b). He developed maps to represent the ideas that emerged in student conversations and to show the connections between those ideas (Pask, 1975, 1977). In the same decade but on a different continent, science educator Joseph Novak and his graduate students invented concept mapping as a learning tool for K–12 students (Stewart, Van Kirk, & Rowell, 1979). Novakian concept maps grew out of Ausubelian learning theory (1963, 1968) with its emphasis on building connections between ideas. Novakian concept maps are widely used in science teaching today from elementary school through the university. With the advent of the Macintosh personal computer in the early 1980s, Fisher, Faletti, and their colleagues created the SemNet® knowledge mapping software as a learning tool for college biology students (Fisher, Faletti, Patterson, Thornton, Lipson, & Spring, 1990). The major objective was to help students shift from their prevailing rote learning methods to meaningful understanding of biology content. The design of this software grew directly out of cognitive science, especially Quillian’s semantic network theory (1967, 1968, 1969) for how we store information in long term memory. As Collins and Loftus (1975) described it, Quillian showed us how to capture human semantic structure and processing in a computer. Also in the 1980s, Wandersee (1987) developed concept circle diagrams for the purpose of helping students clarify their thinking about inclusive/exclusive relationships. This technique helps students learn to cluster and prioritize ideas into basic categories and to distinguish between similar and different entities. It is also intended to ease novices into the process of concept mapping by simplifying the mapping task and scope. In the late 1980s and early 1990s, Horn (1989) in the US and Buzan and Buzan (1993) in Great Britain took knowledge mapping into the business world. Buzan is interested in mapping as a means of promoting creativity and divergent thinking and has developed the MindMan software to support his style of mapping. Probably the greatest commercial success in knowledge mapping—at least in the US—is embodied in a concept mapping tool available for both IBM and Macintosh platforms called Inspiration®. Also in the 1990s, Wideman developed an IBM-based semantic networking program useful for mapping large organizational charts. The three authors have more than half a century of combined experience in the knowledge-mapping field. Of these various mapping forms, Novakian concept maps and SemNet have enjoyed the greatest benefits of ongoing research and iterative development. These two strategies have been products of design research before this name was even coined. In the old days, we called it product development with ongoing formative assessment. All forms of knowledge mapping have an emphasis on meaning-making achieved by building explicit connections among ideas. To promote creativity, the connections may remain unlabeled. To promote learning and communication, the connections are clearly labeled, preferably with unambiguous terms. It appears that knowledge mapping has originated independently many different times and in many different contexts. Neuropsychology is perhaps not yet at the stage where it can contribute effectively to the knowledge-mapping enterprise. Thus psychological and cognitive research and interpretations seem the most appropriate sources for informing tool design. Social learning theory must also be considered, since maps are often developed collaboratively. It appears that there have been three major steps forward in the historical course of cartographic development.
We’ve gone from mapping terra firma to mapping terra cognita. Knowledge Mapping in EducationEducational knowledge mapping is seen primarily as a tool to support the activities of learning, teaching, research, intellectual analysis, and organization of knowledge resources. In all fields using knowledge mapping, the idea is to tap into and mimic the workings of the brain, especially working memory and long-term memory. Educators want to use knowledge mapping to stimulate and support students’ intelligent use of their own innate resources and to leverage their own prior knowledge. Hand-drawn concept maps are by far the most common form of knowledge mapping currently being used in the classroom. In American schools, Novakian concept maps are favored (see Figure 2), while in Great Britain, Buzan’s mind-mapping is widely used.
The most powerful knowledge-mapping program currently available to educators is the SemNet® semantic networking software (Fisher et al., 1990) [see Figure 3]. This software allows a user to construct a large web of ideas with an unlimited number and types of links among them. For example, a knowledge network representing the main ideas in a quarter-long introductory biology course for majors contains about 2500 interlinked concepts. A Biology Resource network, useful for quickly looking up terms, contains about 4500 interconnected concepts. And a SemNet-based music course being offered via the internet contains about 20,000 concepts with about 1000 links to video and musical pieces. A SemNet user can represent descriptive knowledge in any domain. The content is as open-ended as it is in a word-processing program. Although estimation is difficult, this software is being used at approximately 10,000 sites world-wide. It can also be used by individuals of many ages, as illustrated by the dinosuar net created by John Yue, age 11, with 569 links among 110 concepts (Figure 3).
Knowledge maps provide skeletal representations of information. They strip away the minor connecting words and get at the essence of meaning. A map typically includes the most important concepts in a topic—usually expressed as noun-centered ideas. The concepts are drawn in boxes, ovals, or circles and are linked to one another by lines labeled with named relations (usually represented by verb or prepositional phrases). When students are engaged in creating such knowledge maps about topics they are learning and given feedback regarding their efforts, they tend to exhibit significant knowledge gains in learning, as indicated in the review of the literature that follows. It should be noted that a student-constructed map is not equal to all the student knows about the topic. It is a partial representation that can be skewed by the moment, the task at hand, the intent of its creator, and the time available for constructing the map. Yet it provides a better gauge of what the student knows than most other assessments because it is a free response, unaided by prompts. The map provides insights not only into what ideas the student knows but also how she or he organizes and links them. This is important because much of higher order learning derives from an individual’s structural knowledge (knowledge organization patterns). Also, a map is generally easier to understand and less ambiguous than an essay, another form of free response. Essays tend to reward linear thinking, be difficult to read, and can be loaded with poorly-connected jargon and buzzwords. In contrast, when constructing knowledge maps, students are compelled to reveal their naked thoughts, linked and unlinked, free of extraneous “fluff”. If these strategies have proven effectiveness, why aren’t they used more often? The simple answer is that they have not captured the hearts and minds of the people. One reason for this is that several key features are missing in all current knowledge representations. The first is scalability, the ability to zoom in and examine different levels of detail in selected areas of a map. In fact, some Novakian concept maps are now being scaled. Wandersee’s research group is exploring the use of high-level macromaps linked to a series of micromaps. This research can help pave the way to more sophisticated scaling. A second missing feature is the ability to generate high level overviews of large bodies of information in ways that allow discrimination of important patterns. Concept maps are too small to provide large-scale overviews. SemNet allows construction of large knowledge networks, but it is impossible to get a bird’s-eye view. A third missing feature is graphical differentiation of concepts and the links among them based upon the properties exhibited by these elements within the map. In hand-drawn concept maps and those drawn with Inspiration software, the user can place concepts in cloud-shaped figures, ellipses, rectangular boxes, or other arbitrarily chosen bounded containers. These add interest but at present are not systematically utilized to inform. On the other hand, if the software adjusted the size and appearance of concepts and links in a map based upon parameters of the knowledge structure that are easily and precisely assessed by the software, then the visual-spatial representation would be informative. Each map that is created would have distinct features and would look different from all other maps. This uniqueness of individual maps is essential to tap into the discriminatory powers of human pattern recognition. Important pathways through the knowledge map would leap out. Wandersee’s research group is investigating the use of various logical concept-enclosing shapes coding for different types of concepts. A fourth missing feature is the ability to choose among various strategies for knowledge representation and to automatically transform knowledge at will. For example, one should be able to generate a variety of concept maps from a semantic network and vice versa. The method of conversion should be the choice of the user—with manual and automatic options. Dr. Robert Abrams at the University of California—Santa Cruz, developer of the LifeMap software, has been working with Fisher to develop a prototype for concept map-Gowin’s Vee-SemNet conversions. Jack Park in Palo Alto is author of software called The Scholar’s Companion. This software allows users who are not trained in programming to develop expert systems and generate simulations (Trelease, Henderson, & Park, 1999). It can also automatically transform information between expert systems and concept maps. Park, Faletti, and Fisher are currently integrating semantic networking and The Scholar’s Companion to create a prototype for SemNet-simulation-concept map conversions. Rapid, easy, intelligent knowledge transformations will be extraordinarily empowering in tomorrow’s world, as managing scientific and technological information becomes our greatest challenge. The fifth and last missing feature we will mention is automatic language translation. Language translation with whole sentences continues to be problematic, but with the schematic representations used in knowledge maps, this should be quite manageable. There is still the problem of ambiguous words in all languages, but an intelligent translator can present choices to the user for final selection. Evidence that Using a Knowledge Map (like a road map) Can Promote LearningGood knowledge maps constructed by an expert are effective learning aids. Thus, the periodic table is a central feature of virtually every chemistry classroom. Chromosome maps are routinely used in teaching genetics, and pedigrees are important tools for analyzing inheritance patterns. Weather maps help students understand the movement of and interactions between air masses. Animal range maps help students and researchers understand the geographic extent of wildlife species. Maps of magnetic fields help physics students represent invisible forces. And schematic wiring diagrams help engineers understand how current flows in computer circuitry. Good knowledge maps are also important for researchers. The Human Genome Mapping Project illustrates the enormous value placed by scientists on the mapping of the entire human genome. This is an excellent example of a domain sector that doesn’t need to be stored in human memory but is extremely valuable on a look-up-as-needed basis. In spite of successes in many other areas, few people have used knowledge maps to help students find their way in a complex domain (although concept maps are gradually creeping into textbooks). The road map model for traversing a knowledge domain has yet to be implemented, primarily because the necessary software has yet to be invented. Reading a well-designed map is obviously a lot easier than constructing one. Thus, once this hypothetical tool is invented, perhaps an effective way to use it as a learning tool is to have students use a map to go into the science domain “woods” and then map their own way out, a “Hansel and Gretel” challenge. Designing Sophisticated Knowledge Mapping SoftwareWe need to develop the capability for constructing powerful knowledge maps before we can actually test them. Development requires iterative design research. We foresee tools that offer map search capabilities such as: concept proximity searches, thesaurus-based domain searches, Boolean search options, fuzzy logic-based searches, connection-pattern similarity searches, example matching, wildcard searching of concept attributes, linkouts to world-wide-web sites, and multiple knowledge transformation capabilities. These tools would be useful in synthesizing, analyzing, and comparing knowledge structures and in helping users make informed choices about where and how to apply the knowledge. The ability to automatically generate and maintain maps of information on the World Wide Web (WWW) represents a major priority for learners. “The Web, and the world, thrive on information which is accessible to all,” says W3C Director Tim Berners-Lee. The Internet began in 1983 and has grown from 1000 hosts in 1984 to 36 million hosts in 1998 (Griffiths, 2000). According to Griffiths, most of today’s search engines operate by selecting individual web-pages or documents. Many search engines use the same “spiders” to compile their indices, so the difference lies in the way they interpret the data and how they allow you to manipulate the results. The WWW originated in 1989–1991 and is a network of sites that can be searched and retrieved by a special protocol known as a Hypertext Transfer protocol (HTTP). The software or a closely related software application can hopefully support a much broader range of uses as well, so that it can be used by individuals and groups as a learning, teaching, and communication tool. In the meantime, to imagine what the effectiveness of knowledge maps as road maps might be, we must rely on inferences drawn from studies of knowledge mapping as a learning strategy. Evidence that the Process of Constructing a Knowledge Map Helps LearnersThere is an enormous body of research on semantic networks in cognitive science, psychology, and artificial intelligence (e.g, Sowa, 1983, 1990, 1998; Brachman & Levesque, 1985; Way, 1991; Brachman, Levesque, & Reiter, 1991; Jonassen, Beissner, & Yacci, 1993), as well as on spreading activation theory (e.g., Collins & Loftus, 1975). In this section we focus on the research on learning when learners are constructing maps. Knowledge mapping is consistent with the learning models proposed by theorists such as Ausubel (1963, 1968), Vygotsky (1978), and von Glasersfeld (1984, 1987, 1993). Constructing a knowledge network means actively engaging in the act of personal and social knowledge construction. Mapping is a simple strategy to promote desired mental activities. It promotes mindful learning (Langer, 1987, 1997), cognitive flexibility (Spiro, Coulson, Feltovich, & Anderson, 1991), and conceptual change (Strike & Posner, 1985). Student knowledge-mapping has fairly consistent positive effects on science and mathematics learning. Here is what one teacher says about mapping: “My students certainly had breakthrough successes with the quantity of ideas they could ‘web’. There was also a richer texture and personal detail to the ideas, and often a better final product, especially when balanced with instruction and with holistic scoring, group editing, and traditional writing techniques. As a teacher, I soon became enthralled by these simple tools because webbing opened new windows onto the mindscapes, the peaks and valleys, of my students’ unique patterns of thinking. I could see what and how each student was thinking about the content I was teaching.” (Jones, 1996). Knowledge mapping is more work than conventional learning, which is one reason why it is often more effective than conventional learning. People who choose the path of least resistance may tend to avoid mapping activities. On the other hand, students who love to learn often invent their own mapping strategies and gladly embrace more developed strategies when they encounter them. Here we summarize some representative research studies on the effects of concept mapping on science learning. The reason for doing this is to demonstrate that even in its currently primitive form, knowledge mapping generally promotes active, meaningful, mindful learning. Eighteen studies examined some aspect of student learning and achievement with concept mapping as a study tool. Seventeen of the eighteen reported positive or significantly positive results in favor of the concept-mapping students. Seven of these studies were conducted in biology classes (Trowbridge & Wandersee, 1996; Esiobu & Soyibo, 1995; Trowbridge & Wandersee, 1994; Okebukola, 1992a; Hegarty-Hazel & Prosser, 1991; Okebukola, 1990; Jegede et. al., 1990), especially in the areas of genetics, ecology and evolution. There were five concept-mapping studies in chemistry (Francisco, Nicoll, & Trautmann, 1998; Markow & Lonning, 1998; Wilson, 1996; Ross et al., 1991; Stensvold & Wilson, 1990). They examined the effects of concept mapping on learning within several subtopics in both chemistry lecture and laboratory. One used concept mapping to elicit students’ alternative conceptions. Three studies (Roth & Roychoudhury, 1993a, 1993b; Pankratius, 1990) examined the effects of concept mapping on learning in high school physics courses. Three international papers from Australia, Arabia, and Israel, respectively, examined overall science learning with concept mapping (Wilkes, Cooper, Lewin, & Batts, 1999; Elhelou, 1997; Barenholz & Tamir, 1992). Eight studies used concept mapping to examine conceptual change (Wilson, 1998; Jones, Rua, & Carter, 1998; Van Boxtel, Van Der Linden, & Kanselaar, 1997; Pearsall et al., 1997; Demastes et al., 1995; Hegarty-Hazel, 1991; Heinze-Fry & Novak, 1990; Wallace, 1990). These studies examined students’ knowledge restructuring and progress toward more meaningful understanding. This group of conceptual change studies spanned all the sciences mentioned above. Five studies investigated concept mapping as an assessment tool. McGinn & Roth (1998) assessed learning about levers. Botton (1995) used concept maps to assess understanding of acids and bases. Rice, Ryan, & Samson (1998) and Barenholz & Tamir (1992) assessed science learning with concept maps. Gaffney (1992) was interested in using multiple assessments for multiple learning styles. Three additional studies didn’t fit into the categories above. Rye and Rubba (1998) used concept mapping as an interview tool to elicit students’ understandings of global atmospheric change. Willerman and MacHarg (1991) used concept maps as advanced organizers for science learning. Anderson-Inman and Zeitz (1993) examined concept mapping as an active study tool. Similar positive results are seen in studies in which students engage in semantic networking as a means of mathematics and science learning. Several studies ranging from 7th grade to college found that biology students using SemNet learned more declarative knowledge and learned the topics more deeply than comparison groups (Gorodetsky & Fisher, 1996; Jay, Alldredge, & Peters, 1990; Christianson & Fisher, 1999). Gordon & Gill (1989) observed that when students have well-organized declarative knowledge about a topic (they looked at two topics, use of mathematical vectors and use of VCRs), the students are able to perform relevant problem-solving procedures. Furthermore, by identifying gaps in the students’ declarative knowledge, Gordon and Gill were able to predict the individual students’ performance errors with 85% and 93% accuracy, respectively. Thus these findings suggest that the construction of knowledge representations is likely to have a positive influence not only on acquisition of declarative knowledge but also on performance related to that knowledge base. In addition, when learners construct maps of their knowledge, they acquire greater mastery over concept discrimination, category formation, and hierarchy construction. Further, their enhanced cognitive skills transfer to other domains (Gorodetsky & Fisher, 1996; Chmielewski & Dansereau, 1998). Amer (1994) found that concept-mapping Egyptian students studying science in English wrote significantly better summaries than both an experimental group that underlined text and the control group with no specified study method. Garvie (1994) explored the use of semantic networks in the geosciences, to support learning about the classification of minerals. In sum, when students engage in the activity of mapping knowledge, they generally tend to learn more and reflect more upon their own learning than with other study methods. We think that the more powerful the mapping system and the more consistently it is used, the greater the gains in understanding tend to be. We also view institutions and corporations as learning “organisms,” and we predict that in the future, those without knowledge mapping units will become unviable and extinct. In another interesting development, Project 2061 of the American Association for the Advancement of Science is soon to release an "Atlas of Science Literacy." This contains a set of interconnected knowledge maps of a form that was developed exclusively for this association and which is as yet unresearched. These maps are based on Benchmarks for Science Literacy (AAAS, 1993). They aim to capture the way in which ideas arise in K–12 development and how these ideas are interrelated. These are some of the conclusions about knowledge mapping drawn by investigators in the field. Knowledge mapping is the representation of detailed, interconnected, non-linear thought (Fisher & Kibby, 1996). A knowledge map is an external mirror of your own radiant thinking, and it gives you access to your vast thinking powerhouse (Buzan & Buzan, 1993). Knowledge mapping is an external extension of working memory, which especially supports reflective thinking (McAleese, Grabinger, & Fisher, 1999). Knowledge mapping can capture both the learner’s prior knowledge (Jonassen & Wang, 1993) and the acquisition of new knowledge (West & Pines, 1985). Knowledge mapping can also capture concept elaboration, concept discrimination, and conceptual change (West & Pines, 1985; West, Fensham, & Garrard, 1985). It promotes comprehension skills well beyond simple decoding (Lehman, 1992). What Makes the Activity of Knowledge Mapping an Effective Learning Tool?There are numerous theoretical reasons why knowledge representation is a good learning strategy. We’ll mention four of the most powerful ideas: 1) chunking of information, 2) dual coding theory, 3) making relations between ideas explicit, and 4) broadcasting to the subconscious. 1) Chunking of Information. A SemNet frame or concept map has the advantage of providing not only a coherent graphic representation about a concept or group of concepts, but it also provides a manageable chunk of information which is easily assimilated (see Figure 4).
Chunks were first described by Chase and Simon (1973) in studying chess players. What Chase and Simon discovered was that master chess players have well-developed pattern-recognition abilities. The researchers found that chess players quickly recognize the arrangement of pieces on a chess board and associate certain outcomes with each arrangement. The pieces on the chess board comprise a chunk of information, which is perceived as an image and converted into a mental schema. Simon (1974) estimated that a class A player has a repertoire of about 1,000 such schemata, while a master chess player has between 25,000 and 100,000 chess board schemata stored in memory. By extension, a similar situation may apply in math and science—a knowledge-mapping student in an introductory class may develop 1,000 schemata, while an expert may have between 25,000 and 100,000 domain-specific schemata. 2) Dual-Coding Theory. According to dual-coding theory (Paivio, 1986; Mayer & Sims, 1994), the learner can encode information in two distinct information processing systems, one that represents information verbally and one that represents information visually. Dual coding facilitates ability to both retrieve and apply ideas (Mayer & Sims, 1994). A knowledge map presents a visual image as well as verbal information and therefore presumably taps into this dual-coding system. Knowledge-mapping conventions place bigger ideas above the central concept, smaller ideas below, with moving materials or event sequences on a horizontal plane reading from left to right. These consistent spatial patterns serve as memory prompts, much as in any landscape. 3) Making Relations Among Ideas Explicit. In knowledge mapping, students are required to make each relation between two concepts explicit. These links often remain implicit in text and lecture, and thinking about the nature of the link is something students easily overlook without a support tool such as SemNet or concept mapping. Luoma-Overstreet’s (1990) research is instructive with respect to the importance of relations. She kept a journal as she used SemNet to map the information in John Anderson’s (1983) book, The Architecture of Cognition. One of her goals was to determine if there is such a thing as a “perfect set” of relations. She found that the “perfect set” of ten relations she began with only lasted a few pages into the first chapter. In fact, different relations were required for every single chapter. She concludes: “It’s obvious to me now that content drives relations.” (italics added). Thus, identifying relations is intrinsic in learning a new domain of knowledge. Further, relations are generally more difficult to comprehend than concepts—children and second-language learners learn nouns before verbs (Gentner, 1978, 1981a, 1981b, 1982). Three relations seem to be universal and are used in about 50% of all links in biology (Fisher, 1988; Hoffman, 1991). These are set/subset, whole/part, and has characteristi/characteristic of, suggesting that these three relations are key elements to understanding. The cause/effect relation is also widely shared (Hoffman, 1991). Many of the remaining relations that are used are unique to a given field of study. Cooke and McDonald (1986) studied the Pathfinder software (Schvaneveldt, 1990) as a tool for eliciting expert knowledge. With Pathfinder, users identify the distance between ideas. The software then mathematically analyzes the input to generate a web of ideas linked by unlabeled lines. It is not possible, however, to name the links in Pathfinder. Cooke and McDonald (1986) conclude that Pathfinder is not suitable for eliciting expert knowledge because identifications of each link is critical in knowledge engineering. These varied studies demonstrate the importance of making relations explicit in mathematics and science learning. In sum, each domain is characterized by its own unique relations, meaning is captured in the relations, relations are more difficult to master than concepts, and understanding is facilitated by explicitly identifying each relation among important ideas. 4) Broadcasting to the Subconscious. Baars (1988) sees the conscious mind as the tip of the iceberg, resting on and supported by a vast array of subconscious modules which work more or less independently from one another and in parallel. These subconscious modules account for the solutions that pop out of your head when you put things “on the back burner.” According to Baars (1988), each concept pair that is brought into working memory and joined by a relation is broadcast to every subconscious module in the mind. This is one of the more potent “effects of” benefits described by Perkins (1993) that result from constructing a semantic network. 5) Time on Task. When they are constructing maps of their knowledge, learners typically engage in sustained and high-level thinking and conversation about the topic they are learning. The activity provides support for that thinking as well as for subsequent reflection and knowledge revision. Parameters for a Knowledge Mapping Tool for the New MilleniumCollaborative Thinking. As noted previously, concept modeling makes concepts explicit (notably including relationships), enabling individuals to comprehend and think about a topic far more powerfully and quickly. Equally significantly, it enables groups of participants to build and communicate a shared understanding of a domain and to efficiently collaborate on developing it further. Surfing the Wave of Understanding. The ability to model scientific systems and phenomena is an ongoing and growing challenge. Of significant interest is the status of the forefront of the concept-modeling area, as this is the area where domains of human endeavor are transitioning from “wallowing in narrative to surfing on a wave of understanding.” The Fifth Discipline (Senge, 1994) takes up the issues of modeling systems in the context of the business world. Systems Thinking in a Fast-Moving, Complex World. As rate of change increases, thinking and doing both involve increasing complexity traceable to the interdependencies inherent in the systems of interacting parts of an enterprise. It is exactly such systems (and especially their behaviors) that are particularly difficult to describe in narrative and discuss in words. If the intelligence of more than just individuals is to be brought to bear on such issues, then it is essential that the understanding and discussion be moved to a medium that allows collective construction and maintenance of knowledge. Diagrammatic Reasoning. The understanding of concepts and ideas by the use of diagrams and imagery, known as diagrammatic reasoning, differs in significant ways from understanding via linguistic or algebraic representations. A book on this topic by Glasgow, Narayanan, and Chandrasekaran (1995) brings together 23 recent investigations into the cognitive, the logical, and particularly the computational characteristics of diagrammatic representations and the reasoning that can be done with them. This book extends the underlying theory of diagrammatic representation and provides numerous examples of diagrammatic reasoning, both human and mechanical. Tufte (1983, 1990, 1997) and Horn (1989, 1998) also provide valuable insights into this important parameter of knowledge mapping. Some Sophisticated Concept Modeling Tools. Concept modeling can refer to a number of formal or informal techniques for capturing and manipulating concepts, and for using a vocabulary that provides more structure than simple narrative text. Currently available tools with significant semantic depth are primarily commercial engineering products such as: • Mechanical CAD (structure, and also behavior modeling, such as finite element analysis) Real-World Modeling. Of these, the developing UML initiative is particularly interesting, as its real-world-modeling capability expands in an attempt to model everything of interest to business and systems developers—which is an ever-increasing portion of the known universe. Although UML will by no means subsume all other modeling endeavors any time soon, the UML effort is very instructive regarding the kinds of modeling concepts that might be usefully applied in other domains. The Human Mind. There is some consensus that in the next few years the most evident feature on the cognitive landscape will be the limits on human capacity to deal with the escalating complexities of situations we are navigating. This will be characterized by potentially vast quantities of information available, yet little structure provided for distilling the detail into digestible aggregates and understandable relationships. Under such conditions, traditional management processes break down, and enterprises carry out courses of action that have a likelihood of success that is no better than chance. In essence the problem may be stated as a shortcoming in the ability for the individual to acquire or develop sufficiently sophisticated models of a situation sufficiently rapidly. So it follows that a potential answer lies in improving that ability. This would entail developing a modeling vocabulary and environment that affords several needed characteristics: • Allows individuals to read and write models to/from their local model environment far more rapidly. Drawing extensively from Merlin Donald's Origins of the Modern Mind, Wideman (2000) has outlined the evolutionary relationships between knowledge and the human mind. Figure 5 captures where we are today.
The knowledge mapping tools provided by the external modeling environment will be crucial in facilitating both assimilation of relevant portions of the torrents of information available in the external world and communication with both machines and people. Taking the Metaphoric LeapWe are convinced that sophisticated knowledge mapping is essential for the information age. The internet demands it and the knowledge explosion requires it. The problem is that knowledge mapping needs to progress rapidly so that it is useful, accessible, and comprehensible, among other things. We need representations that people can relate to and make immediate sense of, and that offer options of different styles of representation and different cultural referents. Several key features are missing in all current knowledge representations. These include the ability to generate high level overviews of large bodies of information in ways that allow discrimination of important patterns, scalability, differentiation of concepts and the links among them based upon the properties exhibited by these elements within the map, and the ability to transform knowledge rapidly and easily from one representation to another. We believe a quantum jump is required in thinking about knowledge mapping. At a click of a button we want to see a knowledge map as a road map, as a topographical map, as a frequency map, etc. On a road map, we want to be able to trace a particular route, or ask for help in navigating between cities. One way to achieve this quantum leap is to borrow from cartographic methods already developed in other fields. Such models are potentially adaptable because concrete metaphors provide critical support for abstract thinking (Lakoff, 1987; Lakoff & Johnson, 1981). In addition, using familiar templates would promote transfer of existing map-reading skills. Figures 5 and 6 represent but two of the many concrete mapping metaphors that may be used in sophisticated knowledge mappings. SummaryMany science domains use content-specific maps as tangible supports for thinking such as metabolic pathways in biochemistry, the periodic table in chemistry, food webs in ecology, tectonic plate maps in geology, and chromosome maps in genetics. Even as we speak, the crew of the shuttle Endeavor is endeavoring to produce the most accurate map of the world ever made! Given the obvious value of a good map and our enthusiasm for mapping in so many fields, one must wonder why the commitment to develop knowledge-mapping strategies in science education is at such a low ebb? Why isn’t academia at the forefront of the knowledge-mapping enterprise, demonstrating important leadership in producing essential thinking tools for the classrooms of tomorrow? The situation is reminiscent of this story. American computer scientists and engineers turned their back on fuzzy logic when it was developed by Dr. Lofti Zadeh at Berkeley in the early sixties (Zadeh, 1963, 1973, 1976, 1979). NSF refused to fund fuzzy-logic projects (there are apparently few if any executive mechanisms at NSF to overcome bias within a peer-review field). Then Japan recognized the wisdom in fuzzy logic and embraced it. According to McNeill and Freiberger (1993), the Japanese were 5–7 years ahead of the U.S. in using this important design tool at the time their book was published. A similar lack of interest seems to prevail in this country with respect to the development of adequate knowledge-mapping tools, in spite of the fairly obvious fact that this will become a key to success in mastering and managing complex systems. Who will beat us to the punch this time? The success of classrooms of the 21st century as well as of the growing corps of lifelong learners may depend on appropriate investments now. Development of tools that can support sophisticated knowledge-mapping strategies is a nontrivial task, one that requires iterative rounds of development and assessment, otherwise known as design research. The sooner we get started, the sooner our students and teachers can work smarter, transitioning from wallowing in narrative to surfing on a wave of understanding. Today’s knowledge explosion makes sophisticated, high-powered knowledge mapping an imperative for tomorrow (Figure 6)!
AcknowledgementThe ideas expressed in this paper have been the product of extended design discussions with many people including Joseph Faletti of Antioch, CA; Brockenbrough Allen, James Hollon, Amos Jessup, Daly Jessup, Jack Logan, Elaine Parent, and William Root of San Diego; Jack Park of Palo Alto; Robert Abrams of Santa Cruz; and Roger Schvaneveldt of New Mexico; among others. ReferencesAmer, A.A. (1994). ‘The effect of knowledge-map and underlining training on the reading comprehension of scientific texts’, English for Specific Purposes 13(1), 35—45. Last modified on June 1, 2000.
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