Abstraction in concept map and coupled outline knowledge representations. Sherman R. Alpert.

Full Text: COPYRIGHT 2003 Association for the Advancement of Computing in Education (AACE)

Concept maps are used to graphically represent knowledge about a domain. As a knowledge representation tool, concept maps should attempt to incorporate representational mechanisms isomorphic to users' cognitive representations. This article describes a computer-based concept mapping tool that provides rich representational capabilities, including dynamic imagery (video, animated images, sound) and multiple levels of abstraction. The tool can automatically translate a concept map into an alternative representation--an outline--which contains all of the knowledge contained in a multilevel concept map. This concept map tool is accessible through any standard Web browser.

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A concept map is a visual representation of knowledge of a domain. A concept map consists of nodes representing concepts, objects, or actions connected by directional links defining the relationships between nodes. Together, nodes and links define propositions, statements about a topic, domain, or object. For example, Figure 1 portrays concept map elements that represent the proposition "birds can fly." Concept maps as a knowledge representation mechanism are essentially equivalent to the semantic network formalism from the cognitive science community (Quillian, 1968).

Concept maps have been, and are, widely used in educational settings, as both pedagogical and evaluation tools, in virtually every subject area: reading and story comprehension, science, engineering, math word problems, social studies, decision making (Fisher et al., 1990; Bromley, 1996; Novak, 1998; Chase & Jensen, 1999). Conceptual maps permit students to demonstrate what they have learned and know about a domain; encourage practice of the metacognitive skill of reflection as students examine their knowledge to reify that knowledge graphically; act as tools to aid comprehension of a domain or story; support idea generation and organization in preparation for prose composition; and are used as instructional materials for students learning the concepts and conceptual structure of new domains. There is considerable anecdotal and experimental evidence that the use of graphical knowledge visualization tools such as concept maps helps improve student comprehension and enhance learning. For example, Fisher et al. (1990) and others report that maps constructed by experts in a domain to present new information to learners, to illustrate how an expert organizes concepts of a domain, result in apparent pedagogical benefits. Dunston (1992), and Moore and Readance (1984) have shown that concept maps are educationally effective tools when students create their own maps to reflect on and demonstrate their own knowledge.

The use of concept maps in educational settings has evolved from paper-and-pencil to computer-based tools. A number of computer-based concept mapping tools have been reported by researchers and software developers (Fisher et al., 1990; Gorodetsky, Fisher, & Wyman, 1994; Flores-Mendez, 1997; Gaines & Shaw, 1995) and shareware programs and even commercial products exist for this activity. Concept mapping software offers the same sorts of benefits that word processors provide over composing written works on paper, that is, the facilitation of revision of existing work, including additions, deletions, modifications, or reorganizations. In fact, students often revisit their existing maps to revise them as their knowledge of a subject evolves (Anderson-Inman & Zeitz, 1993).

Because the purpose of concept maps is to visually represent knowledge, mapping tools should be able to represent various types of knowledge people possess, using the same or similar knowledge structures. Existing concept map tools are indeed quite good at visually representing simple propositional statements, but not necessarily other forms of information in people's heads. For example, these tools do not do a good job of representing dynamic visual and auditory information (Alpert & Grueneburg, 2000). More germane to this article, these tools additionally do not allow users to easily structure knowledge represented in a concept map in a manner that is isomorphic to cognitive representations. Specifically, concept maps ought to allow users--in a straightforward and usable fashion--to apply the idea of conceptual abstraction to the represented knowledge as well as the facile navigation among abstraction levels.

This article describes aspects of a computer-based concept mapping tool named Webster. Webster aims to extend the capabilities of existing concept map software by providing for more comprehensive representation of knowledge of a domain, making concept maps more effective tools for students using them to express their knowledge or learn new concepts. Webster offers a unique combination of features that attempt to achieve these desiderata. It provides for integral multimedia capabilities in concept maps, and is web-enabled, accessible from the Web through any standard web browser and providing access out to the Web by way of nodes that act as hyperlinks from concept maps to external sites. Webster further allows the facile representation of, and navigation among, multiple levels of abstraction. In doing so, Webster also supports formal collaboration among students in disparate locations in the construction of complex maps with multiple abstraction levels. In another article, we offered psychological and pedagog ical design rationales for the integration of multimedia in Webster's concept maps (Alpert & Grueneberg, 2000). This article similarly presents a cognitive rationale for the representation of knowledge abstraction in concept maps and describes the abstraction mechanisms provided by Webster. It also describes how Webster concept maps may be automatically converted to outline form and how a concept map's abstractions are portrayed in this alternative representation.

ABSTRACTION

A fundamental characteristic of human cognition is the ability--actually necessity--to exploit knowledge abstraction. Abstraction inherently implies the ability to represent a concept, action, or object by a single node at one level of detail while possessing the knowledge to "expand" that single node into an elaborated definition of its own. It is knowledge abstraction that Miller (1956) spoke of when describing how human memory (he was speaking particularly about working memory) exploits the notion of chunking. According to this seminal paper, while working memory is capable of containing approximately seven active elements, working memory can apparently have access to more than seven pieces of information or knowledge. This is because any of those seven active elements may be a chunk, a single knowledge component at one level of detail but one that can be expanded into multiple constituent knowledge elements at a more detailed abstraction level. "At one level, a chunk combines a number of (lower level elem ents). At another level, it is a basic unit in a larger structure" (Anderson, 2000, p. 123).

Concepts are grouped into, or are members of, higher order (that is, more abstract) conceptual categories. There is considerable debate over the cognitive mechanisms of forming categories but one assumption is that abstraction into conceptual categories can arise from experiences with multiple concrete instances or specific experiences that can be generalized (or abstracted) into an overarching category (Anderson, 2000). For example, different kinds of birds share many common characteristics, enough so that bird becomes its own category with its own set of features, represented by a high-order knowledge structure. Thus, if we are demonstrating our knowledge of birds, we might wish to represent the category bird while also wanting to represent information about a specific kind of bird, robins. There is further argument over what indeed defines a category (Eysenck, 1984), but a simple definition would be a generalized concept that possesses multiple attributes, and for which each instance of that category shar es some subset of those attributes.

Other higher level knowledge structures have also been proposed to represent abstractions in long term memory. For example, scripts combine the typical sub-events or actions that comprise an event, such as eating in a restaurant (Schank & Abelson, 1977; Bower, Black, & Turner, 1979). And any number of related knowledge elements may be combined into, or associated together in, a schema. Rumelbart offered the following definition for schemas:

A schema, then, is a data structure for representing the generic concepts stored in memory. There are schemata representing our knowledge about all concepts: those underlying objects, situations, events, sequences of events, actions and sequences of actions. A schema contains, as part of its specification, the network of interrelations that is believed to normally hold among the constituents of the concept in question. (1980, p. 34)

One can see from this description that conceptual categories, scripts, and schemas are closely related or even conflated. More importantly, we see once again that even in higher order knowledge structures, a single node--in this case, a single schema--comprises, and can be expanded to make explicit, an underlying network of concepts and the relationship links among them.

Abstraction allows people to maintain large amounts of information about concepts and objects in an efficient and economical fashion. Higher order conceptual structures organize themselves into hierarchies according to generality-specificity, superordinate-subordinate relationships. "... [M]ost of the objects in the external world can be categorized at each of several different hierarchical levels. Thus, for example, an easy chair is an easy chair, but it is also a chair and an article of furniture" (Eysenck, 1984, p. 317). Continuing our running example, a goose is a bird and a bird is an animal. So, we also have an animal category in addition to the category bird. One's knowledge of the myriad characteristics and features of animals is sufficiently large and complex that we would not want to associate every such characteristic directly with the bird concept in addition to storing each of them in the animal category. Instead, knowledge or attributes common to two (or more) conceptual categories involved in a superordinate-subordinate relationship may be stored once, with the most general applicable category or schema, and more specific (subordinate) concepts and categories can then inherit these characteristics. By simply asserting the proposition "a bird is an animal" we know certain things about birds because we know certain things about animals. So if, for example, the property "has skin" is stored directly with the animal concept (is attached directly to the animal node), we know, because a bird is an animal, that a bird has skin, even if this information is not stored directly with the bird concept. That is, we know that, unless explicitly contradicted locally in the bird conceptual category, those characteristics associated with animals also apply to birds.'

Just to round Out this discussion, it should be noted that not all cognitive theories agree on the nature of abstraction in cognition. There are those who support so-called instance theories tual knowledge. Instance theorists maintain that we store no central concept but only specific instances of that concept (Anderson, 2000). Deciding whether a goose is a bird is based on a judgment of how similar a goose is to other specific birds. For the purposes of our discussion of Webster, however, we will assume abstraction mechanisms essentially as already described.

ABSTRACTION IN WEBSTER

Many concept map and semantic network tools lack adequate visual or structural abstraction mechanisms. In many cases, maps or networks appear as a single diagram. That is, nodes and links representing all of the knowledge of a domain are drawn in a single network, which can be thought of as a single layer. In these networks, the (weak) notion of abstraction is represented simply through generality-specificity relationships between nodes in the single layer: a node representing a specific concept (say, bird) may have a link, labeled is a or a kind of, pointing to a more general, or abstract, concept (say, animal). In this same single layer, the more abstract node might have additional links connecting to further concept nodes (e.g., portraying attributes of animals, that is, representing propositions such as animals have skin and animals breathe oxygen). And then we would need to attach numerous relationship links and associated concepts directly to the bird node to represent, say, a bird has wings and a bird can fly. And this format can extend several levels of abstraction in either direction (e.g., a lizard is an animal, a goose is a bird, an animal is a living thing). Eventually, our map can become quite busy and confusing. Further, the map may not reflect the map author's own (cognitive) representation of this knowledge, which would exploit abstraction mechanisms to represent categories or concepts at differing abstraction levels. Hence, the problems with this representation scheme are, (a) it may lead to visual clutter in the single network when representing more than a trivial amount of information, making the network difficult for a person to understand; and (b) it is not the way psychological theory would have us believe people represent knowledge, in particular, how they represent conceptual abstractions.

As an alternative, we should be able to incorporate a bird abstraction into the animal map. That is, we should be able to include a single node, labeled bird, in the animal map, without cluttering this level of our concept map with details about birds. And we should then be able to expand that single bird node into a map of its own, containing the more detailed elements of our knowledge of birds. In this way, we not only portray the knowledge as a person might, but also garner the benefit of making our knowledge representation more graphically parsimonious.

Webster attempts to allow for the representation of various types of information, and in ways analogous to natural knowledge representation forms and mechanisms. For example, Webster provides for the inclusion of dynamic imagery and sound, types of knowledge people possess but which cannot be incorporated in the concept maps built with most map tools. Because abstraction is also assumed to be an intrinsic part of human knowledge representation, Webster also provides for the abstraction mechanism previously described, a perhaps more natural structural form of abstraction. In Webster concept maps, an abstraction may be represented by a submap node and associated submap. A submap node is visually represented by a single node at one specific level of a map. But this submap node represents a cluster of information and can be "expanded" into its fuller meaning and constituent parts at a more detailed level of the map--these more specific knowledge elements (conceptual nodes and relationship links) comprise a submap . Obviously this is similar to the notion of chunking. Note that this is not to say that concept maps literally represent knowledge and knowledge structures in ways identical to cognitive representations; nonetheless, it is appropriate to have a knowledge representation tool accommodate different types of knowledge that people possess (e.g., verbal propositions, imagery, and sound, rather than textual propositions alone) and structural mechanisms (such as chunking and other abstraction mechanisms) that are analogous to cognitive representations.

Of course the knowledge elements in a submap may include any number of additional submap nodes, representing further abstractions, and these submaps may have further submap nodes--that is, submaps may be recursively embedded. We can thereby have multiple layers of maps. For example, one layer of a concept map might represent the knowledge elements that are specific (or local) to animals, other layers specifically about birds and lizards, and possibly others for further abstractions. The end result is a "three dimensional" knowledge representational scheme: each level of a map contains knowledge elements (nodes and links) represented in two dimensions, and these individual submaps are "stacked" in the third dimension. This vertical stacking of submaps represents multiple levels of abstraction within the overall concept map.

To reify further the preceding notions in the context of Webster, Figure 2 shows the topmost level of a concept map about animals. This level contains a submap node labeled bird connected by way of an is a link to the main node labeled animal. This map layer also contains lizard and living thing submap nodes/abstractions (note that lizard is an animal and animal is a living thing). At the currently visible level of this concept map, the bird concept is a single node. A user may "enter" the bird submap associated with that single submap node, to view its constituent knowledge elements. Doing so entails visiting a different abstraction level of the overall concept map. Figure 3 shows Webster when the bird submap has been entered, thereby becoming the inview, active level map.

To facilitate the use of its abstraction capabilities, Webster also provides tools for the simple navigation among submaps. Incorporating multiple, dynamically navigable, levels of abstraction in Webster should offer advantages for both concept map authors and learners using maps as instructional resources. The inclusion of a richer set of representation mechanisms, such as the use of dynamic media and structural abstraction mechanisms, also offers broader expressive power to map authors.

Creating Abstractions (Submaps)

There are a number of ways of creating and fleshing out the details of submap abstractions. Users may simply select the submap tool from the tool palette on the left side of the interface and drop a new submap node onto a map. Then the user may "dive into" the newly created empty submap and manually populate it with new knowledge elements.

As a second method, a user may select a group of knowledge elements at one level of a map and "push" them down to a new, automatically created, subordinate map level, leaving a single submap node in their place. For example, in Figure 3, the bird submap contains information specific to geese: a goose is a bird, a goose flies in a V formation, and so forth. Already, the bird map is becoming somewhat cluttered visually; if we wish to add information about, say, eagles and parrots, the problem worsens. Plus, this level of the map really contains information at different levels of detail: information about the general category bird as well as about the more specific goose concept. One way to rectify this situation is to abstract the goose-related information out of this submap and into a submap of its own. The user can easily do so by selecting the goose-related knowledge elements and clicking on a single tool button to push them down into a new submap, leaving behind in the same location a single submap node. Fi gure 4 shows the bird submap once this user action has occurred and Figure 5 portrays the automatically created goose submap. Note that the hierarchical tree of submaps in the upper right Abstraction Levels Navigator changes to reflect that a new goose submap was added in the bird map.

A third submap creation method exists and that is to import an existing, saved concept map in it's entirety, as a submap into any level of a map-in-progress. That imported map may have been created by the same concept map author or another user, and may itself possess multiple layers of abstraction, all of which are imported at the appropriate new abstraction levels. Clearly, this facility opens the door to formal collaboration among students with respect to constructing complex, multi-layer concept maps. One student might create and save a bird map. At a later time, a second user might construct a animal concept map and import the bird map as a submap.

Navigating Among Abstraction Levels

With regard to navigating among submaps, users may move up or down a single abstraction level, or jump to any submap in a concept map. The user may select a submap node and click a button to "dive into" that submap to view and edit the more detailed information inside it. For example, when the user selects the bird submap node in Figure 2 and clicks the "dive into submap" button (Figure 6), the bird submap shown in Figure 3 becomes the active, visible map. While "in" a submap, that is, when a submap is the visible, in-focus map, users can return to the next higher level map by clicking another tool button. Alternatively users can navigate directly to any abstraction level (that is, to any submap) by simply clicking on the name of the submap in the Abstraction Levels Navigator (this widget appears in the upper right of the user interface; see Figure 6 for a detailed view).

The abstraction Levels Navigator also makes the hierarchical relationships among submaps-which reflects the superordinate-subordinate realtionships among abstraction levels-explicit at the interface on a constant basis. This provides semantic information to users that makes sensible the notion of navigating to a specific submap in the overall concept map rather than simply up or down a single abstraction level. Last, the Abstraction Levels Navigator always indicates which submap is currently visible, thereby helping users always to know "where" they are in the stack of submaps, supporting users in not becoming confused or "lost" in their three-dimensional navigation of multiple abstraction levels. As demonstrated in Figures 2 through 5, as different submaps are visited, the currently active submap name is highlighted in the Abstraction Levels Navigator.

Comparison to Other Concept Map Tools

Other concept mapping software has provided for the idea of submaps but involving more awkward interaction mechanisms, or incorporates the concept of multi-layered maps but with a very different meaning. For example, Inspiration[R], the best-known and bestselling concept mapping product, also provides for what it labels "child maps." Here individual nodes in a map may have a child map; however the fact that a node has a child is indicated to users in a rather obscure fashion. When a concept node is selected (and only when the node is selected), resizing "handles" appear on the node's corners and sides; if the node has a child map, the handle in the upper right corner of the node is filled-in (the handles on the corners and sides of the node are normally outlines of a square; if the node has a child, the northeast handle is a color-filled square). When a node is not selected, there is no evidence that a child node exists. Webster on the other hand clearly indicates the existence of submap nodes (and therefore submaps) by visually typing its nodes, that is, making each node's type evident by its appearance--a submap node looks different than a simple textual concept node, or a video, audio, or image node, and so forth. Also, the existence of multiple levels of abstraction is not expressed in the central Inspiration user interface, although a dialog box similar to Webster's Abstraction Levels Navigator may be made to appear by a menu selection; once a child map selection is made, the dialog showing the list of levels disappears. Overall then, Webster attempts to better support the user in identifying the existence of, and navigating among, different abstraction levels in a concept map. Webster's interface makes the existence of all submaps as well as map-submap relationships persistently explicit and scrutable, makes all submaps instantly accessible, and makes apparent which submap is currently active, through the Abstraction Levels Navigator.

SemNet[R] (Fisher et al., 1990; Gorodetsky, Fisher, & Wyman, 1994) also possesses a notion of multi-layer concept maps. Here, however, only a single concept node and those nodes to which it is f:directly linked may be viewed at any time. One concept appears in a central position of the view, and the relationship links from (but not to) this node are visible, along with the nodes to which the links connect. No other secondary, tertiary, and so forth links and nodes are visible. Hence, if one were viewing the bird node, the link and nodes defining the proposition a bird can fly (as portrayed, for example, in Figure 3) would be visible, but no linksfrom (that is, further defining, describing, or augmenting)fly would be in view. To see details about fly or a bird flying (such as what a bird in flight looks like, as shown in Figure 3), the user would have to open a view with fly as the central concept. It is thereby difficult to envision the entire set of knowledge about birds, particularly for young student user s, thus weakening the use of concept maps for learning about new domains. Each of these views is considered a layer in SemNet; hence the notion of a multi-layer concept map is quite different than Webster's. Further, there is no interface device portraying an overview of, or providing facile navigation among, the multiple layers of a map, as the Abstraction Levels Navigator offers.

Abstraction and Outlines

An important activity often associated with concept map usage is generating and organizing ideas and thoughts in preparation for writing a report, composition, or story. A commonly used tool for idea organization is an outline, and many students prefer or require this alternative representational format. Hence, Webster automates the conversion of concept maps to outlines by way of a single button press.

The Inspiration product also produces outlines from concept maps, but again there is much room for improvement from the perspective of the user's needs and the usefulness of the outlines. Webster incorporates in its outlines all of the knowledge, information, media, and links contained in a concept map. This implies that all of the information contained in all concept map abstractions (i.e., submaps) appears in a single outline, at the appropriate indentation levels. Contrarily, in the Inspiration tool, the knowledge elements in child maps are absent in the outline translation of a concept map--that is, only top-level nodes are shown as items in the outline. Users may access the "additional" information represented in child maps, but again in an awkward and not particularly usable fashion. If a node in a concept map has a child map, a square appears next to that node's name in the corresponding outline view. A separate outline for each child map may be then be viewed by double-clicking on those squares annota ting parent nodes. These sub-outlines again show only the top-level nodes of the child map, and so the process of viewing child maps must be performed on any parent nodes that appear in that level of the concept map, and so on recursively.

Obviously, the hierarchical relationships among all concepts is easily lost once several sub-outlines are thus opened, thereby defeating the very purpose for the outline view. From a usability perspective, this process is cumbersome and, worse, defeats the users' goals in using the alternative outline representation. On the other hand, Webster's inclusive outline presents, in a single view, the organization of all thoughts and concepts, including those at all abstraction (or submap) levels.

Webster's outline "flattens" the information contained in all levels of an overall concept map into the single outline. In a sense, the three-dimensional knowledge represented by the concept map is compressed into the two-dimensional outline representation. Abstractions represented in the concept map in the form of submaps are displayed at the appropriate indentation level in the outline translation. In Figure 7, the lizard, bird, goose, and living thing abstractions are all incorporated into the outline view along with their constituent knowledge elements, all at their appropriate indentation levels. For example, in Figure 2, we see that the map for animal contains a bird submap node. In the outline, this bird abstraction appears as a sub-item ("V.") below animal. The knowledge elements contained in the bird submap, as seen in Figure 4, appear at a subordinate indentation level below the bird entry. These items include the goose abstraction seen in Figure 4 as a submap node in the bird submap. In the outlin e, the goose item appears at a further subordinate level (item "V.E.") below bird.

Another bit of detail regarding the translation of abstractions/submaps relates to the readability of the outline. The portion of the outline representing each submap begins with the main concept node in that level of the map--the node surrounded by the gray three-dimensional border. When the name of a submap node in one map level exactly matches the label of the main concept of the corresponding submap, the two labels are collapsed into one item in the outline (and all subordinate outline items appear at the appropriate indentation level). This is seen, for instance, for the birds submap: the submap node in the top-level Animals map is labeled bird and the main concept node in the bird submap has precisely the same label Figure 3). Thus, the two become a single outline item (item "V." in Figure 7). On the other hand, outline items "I." (...living thing) and "I.A." (living things) demonstrate the outline translation when the label of the main concept in a submap does not match the name of the associated subm ap node.

In addition to the specifics regarding the translation of abstractions, it should also be noted that Webster's multimedia concept maps are translated into multimedia outlines, integrating the image, video, and audio elements that appear in the map (Alpert & Grueneberg, 2000). Further, whereas labels that appear on inter-node relationship links are elided in Inspiration's outlines (these labels appear nowhere in Inspiration's outline translation of a concept map), Webster uses these concept-to-concept relationships to embellish outlines with important semantic information. For example, for the bird map shown in Figure 3, if we were to disregard the link labels and include only the names of concept nodes, a portion of the outline might be:

I. bird

A. wings

1. feathers

B. fly

However, this is a rather anemic translation of the information contained in the map. Webster provides a more meaningful conversion of concepts and links:

I. bird

A. has: wings

1. have: feathers

B. can: fly

CONCLUSION

Having students construct their own concept maps is an exercise in knowledge elicitation and knowledge representation; we are asking students to demonstrate and communicate to others their knowledge of a domain. In doing so, we should not limit students by restricting the type or structure of the knowledge they are able to portray. The concept map tool we supply to students should be capable of representing knowledge in a variety of ways. Webster offers students greater expressiveness and broader representation capabilities by incorporating multimedia elements and multiple navigable levels of abstraction in concept maps.

The incorporation of such features also offers advantages to students using concept maps as tools for learning new information. When used as instructional materials, concept maps are intended to show not only the concepts intrinsic to a domain of study, but the structural relationships among those concepts as well. This ought to include not only the two-dimensional semantic relationships between and among concepts (as represented by links in a map) but the three-dimensional structure produced by the relationships among concepts and conceptual abstractions. Webster allows the portrayal and learning of both types of structures. Further, all of the conceptual and structural information represented in a concept map is also represented in a complete and appropriately structured fashion in outlines created by Webster's automatic translation.

Finally, Webster is implemented in Java[TM] and runs as an applet in standard web browsers. Thus students may access the concept mapping and outlining tools with fewer constraints on time or location than those imposed by standalone software installed on a specific computer at a single site. Since students need not own a copy of a standalone program, the logistical problems of distributing software to individual people or computers is also eliminated.

Acknowledgments

Thanks to Erich Gamma for providing the source code for JHotD raw, a Java graphical editor framework that formed the foundation for portions of Webster's implementation. Thanks to Keith Grueneberg, Dick Lam, Lei Kuang, and Cyndi Conway for their help with the integration of the Webster applet into the Wired for Learning community-based educational environment. Thanks as well to Dick Lam, Peter Fairweather, and Mike Sharples and his students for discussions and suggestions regarding Webster. Inspiration is a registered trademark of Inspiration Software, Inc. SemNet is a registered trademark of the SemNet Research Group. Java is a trademark of Sun Microsystems, Inc.

Note

(1.) This is a simplified view. For example, there are frequency effects that "break" this organization. So, if a fact about a particular concept is encountered frequently, it may be stored directly with that concept even if it could also be inferred from a superordinate category or concept (Anderson, 2000).

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