Introductory Map Theory

Introduction to Karnaugh Mapping
Free download. Book file PDF easily for everyone and every device. You can download and read online Introductory Map Theory file PDF Book only if you are registered here. And also you can download or read online all Book PDF file that related with Introductory Map Theory book. Happy reading Introductory Map Theory Bookeveryone. Download file Free Book PDF Introductory Map Theory at Complete PDF Library. This Book have some digital formats such us :paperbook, ebook, kindle, epub, fb2 and another formats. Here is The CompletePDF Book Library. It's free to register here to get Book file PDF Introductory Map Theory Pocket Guide.

The editorial selection of fifty-four theoretical and thought provoking texts demonstrates how cartography works as a powerful representational form and explores how different mapping practices have been conceptualised in particular scholarly contexts. Themes covered include paradigms, politics, people, aesthetics and technology. Original interpretative essays set the literature into intellectual context within these themes. Excerpts are drawn from leading scholars and researchers in a range of cognate fields including: The Map Reader provides a new unique single source reference to the essential literature in the cartographic field:.

Request permission to reuse content from this site. Robinson and Barbara B. Advancing the Agenda Alan M. MacEachren and Menno-Jan Kraak. Jensen and Dave C. Process and Products Roger M. Downs and David Stea. Obviously, our brains store more than concepts and propositions. While the latter are the principal elements that make up our knowledge structures and form our cognitive structure in the brain, we pause briefly to discuss other forms of learning.

Iconic learning involves the storage of images of scenes we encounter, people we meet, photos, and a host of other images. These are also referred to as iconic memories Sperling, ; While the alphanumeric images Sperling used in his studies were quickly forgotten, other kinds of images are retained much longer. Our brains have a remarkable capacity for acquiring and retaining visual images of people or photos. For example, in one study Shepard, presented pictures of common scenes to subjects, and later asked which of two similar pictures shown was one of the seen earlier?

This and many other studies have shown that humans have a remarkable ability to recall images, although they soon forget many of the details in the images. Considering how often we look at pennies, it is interesting that the subjects asked to draw a penny in a study by Nickerson and Adams omitted more than half of the features or located them in the wrong place. We believe that integrating various kind of images into a conceptual framework using concept mapping software like CmapTools described below could enhance iconic memory, and we hope research on this will be done.

The learning and recall of sounds is also referred to as archic memory. Consider the musician who can play hundreds of songs without reading any music. Again we are dealing with memories that are not coded as concepts or propositions. Studies by Penfield and Perot , among others, indicate that regions of our brain that are activated when we hear sounds are the same regions that are active when we recall sounds. While we can locate regions of the brain that are active in learning or recall of information using positron emission tomography PET scans, the specific mechanisms by which neurons store this information is not known.

A full discussion of memory mechanisms is beyond the scope of this document. He has proposed a Theory of Multiple Intelligences. His work has received much attention in education and has served to draw attention to the broad range of differences in human abilities for various kinds of learning and performance. It is good that schools are recognizing that there are important human capabilities other than the recall of specific cognitive information so often the only form of learning represented in multiple-choice tests used commonly in schools and corporations.

One reason we encourage the integration of the broad range of activities represented in our New Model for Education is to provide opportunities for these other abilities to be represented and expressed. Nevertheless, we seen the organizing opportunities afforded by associating the various activities with an explicit knowledge structure as very beneficial. Time will tell if future research studies will support this claim. While it is true that some students have difficulty building concept maps and using these, at least early in their experience, this appears to result primarily from years of rote-mode learning practice in school settings rather than as a result of brain structure differences per se.

It is not easy to help students in the former condition move to patterns of learning of the latter type. While concept maps can help, students also need to be taught something about brain mechanisms and knowledge organization, and this instruction should accompany the use of concept maps. The information in the above paragraphs should become part on the instructional program for skillful use of concept maps. The information provided in this document could be part of this instruction. Other ideas for improving instruction to achieve understanding of the subject is available elsewhere Mintzes et al.

To illustrate how difficult it can be for individuals to modify their ideas, especially if they learn primarily by rote, we cite the example of interviews done by the Private Universe Project PUP at Harvard University Schneps, The PUP interviewers found that 21 of the 23 interviewed could not explain why we have seasons, a topic that is taught repeatedly in school. Included in this group was a graduate who had recently taken a course in the Physics of Planetary Motion, who also believed erroneously that seasons were caused by the earth moving closer to the sun in summer and further away in the winter.

In fact, the earth is slightly closer to the sun when it is winter in Massachusetts, rather than in summer. The primary reason we have seasons in latitudes away from the equator is due to the tilt of the earth on its axis toward the sun in summer resulting in longer days and more direct radiation, thus greater heating. In winter, the axis of the earth points away from the sun, thus resulting in shorter days and less intense radiation. What is interfering with these 21 Harvard people is confusion with the common experience that when we are closer to a fire or lamp, the heat is more intense than when we are further away.

Thus, these people have failed to recognize that this same phenomenon is not operating to give seasons on Earth. They are transferring knowledge from one context to another, but incorrectly. The only solution to the problem of overcoming misconceptions is to help learners learn meaningfully, and using concept maps can be very helpful. For more information on misconceptions in science and mathematics see Novak , and: One representation of the knowledge structure required required for understanding why we have seasons.

As indicated earlier, we defined concept as a perceived regularity or pattern in events or objects, or records of events or objects, designated by label. It is coming to be generally recognized now that the meaningful learning processes described above are the same processes used by scientists and mathematicians, or experts in any discipline, to construct new knowledge. In fact, Novak has argued that new knowledge creation is nothing more than a relatively high level of meaningful learning accomplished by individuals who have a well organized knowledge structure in the particular area of knowledge, and also a strong emotional commitment to persist in finding new meanings Novak, , , Epistemology is that branch of philosophy that deals with the nature of knowledge and new knowledge creation.

There is an important relationship between the psychology of learning, as we understand it today, and the growing consensus among philosophers and epistemologists that new knowledge creation is a constructive process involving both our knowledge and our emotions or the drive to create new meanings and new ways to represent these meanings. Learners struggling to create good concept maps are themselves engaged in a creative process, and this can be challenging, especially to learners who have spent most of their life learning by rote.

Rote learning contributes very little at best to our knowledge structures, and therefore cannot underlie creative thinking or novel problem solving. As defined above, concepts and propositions are the building blocks for knowledge in any domain. We can use the analogy that concepts are like the atoms of matter and propositions are like the molecules of matter.

There are only around different kinds of atoms, and these make up an infinite number of different kinds of molecules. There are now about , words in the English language most of which are concept labels , and these can be combined to form an infinite number of propositions. Although most combinations of words might be nonsense, there is still the possibility of creating an infinite number of valid and meaningful propositions. Poets and novelists will never run out of new ideas to express in new ways. We shall never run out of opportunities to create new knowledge!

As people create and observe new or existing objects or events, the creative people will continue to create new concents and new knowledge. Creating new methods of observing or recording events usually opens up new opportunities for new knowledge creation. While there is value in studying more extensively the process of human learning and human knowledge creation, this is beyond the scope of this document.

The reader is invited to peruse some of the references cited. Some important considerations for construction of better concept maps and facilitation of learning will be discussed further below. In learning to construct a concept map, it is important to begin with a domain of knowledge that is very familiar to the person constructing the map. Since concept map structures are dependent on the context in which they will be used, it is best to identify a segment of a text, a laboratory or field activity, or a particular problem or question that one is trying to understand.

This creates a context that will help to determine the hierarchical structure of the concept map. It is also helpful to select a limited domain of knowledge for the first concept maps. A good way to define the context for a concept map is to construct a Focus Question , that is, a question that clearly specifies the problem or issue the concept map should help to resolve.

Every concept map responds to a focus question, and a good focus question can lead to a much richer concept map.

  1. The Way Of Shadows: Book 1 of the Night Angel!
  2. !
  3. .
  4. .
  5. Chaos theory.
  6. Kill Fish Jones!

When learning to construct concept maps, learners tend to deviate from the focus question and build a concept map that may be related to the domain, but which does not answer the question. It is often stated that the first step to learning about something is to ask the right questions. Given a selected domain and a defined question or problem in this domain, the next step is to identify the key concepts that apply to this domain. Usually 15 to 25 concepts will suffice. These concepts could be listed, and then from this list a rank ordered list should be established from the most general, most inclusive concept, for this particular problem or situation at the top of the list, to the most specific, least general concept at the bottom of the list.

Although this rank order may be only approximate, it helps to begin the process of map construction. We refer to the list of concepts as a parking lot , since we will move these concepts into the concept map as we determine where they fit in. Some concepts may remain in the parking lot as the map is completed if the mapmaker sees no good connection for these with other concepts in the map.

The next step is to construct a preliminary concept map. Post-its allow a group to work on a whiteboard or butcher paper and to move concepts around easily. This is necessary as one begins to struggle with the process of building a good hierarchical organization. Computer software programs are even better in that they allow moving of concepts together with linking statements and the moving of groups of concepts and links to restructure the map.

When CmapTools is used in conjunction with a computer projector, two or more individuals can easily collaborate in building a concept map and see changes as they progress in their work. It is important to recognize that a concept map is never finished. After a preliminary map is constructed, it is always necessary to revise this map. Other concepts can be added. Good maps usually result from three to many revisions.

This is one reason why using computer software is helpful. Once the preliminary map is built , cross-links should be sought. These are links between concepts in different segments or domains of knowledge on the map that help to illustrate how these domains are related to one another. Cross-links are important in order to show that the learner understands the relationships between the sub-domains in the map.

The class identified concepts in the parking lot on the left, but this student was not successful in using many of these and her map makes little sense. After a preliminary map is constructed, cross-links should be sought. Cross-links are key to show that the learner understands the relationships between the sub-domains in the map. It is important to help students recognize that all concepts are in some way related to one another. Therefore, it is necessary to be selective in identifying cross-links, and to be as precise as possible in identifying linking words that connect concepts.

Figure 6 shows an example of a string map. This is because they poorly understand the relationship between the concepts, or the meanings of the concepts, and it is the linking words that specify this relationship. Once students begin to focus-in on good linking words, and on the identification of good cross-links, they can see that every concept could be related to every other concept. This also produces some frustration, and they must choose to identify the most prominent and most useful cross-links.

This process involves what Bloom identified as high levels of cognitive performance, namely evaluation and synthesis of knowledge. Concept mapping is an easy way to encourage very high levels of cognitive performance, when the process is done well.

  1. .
  2. Babyernährung gesund & richtig (German Edition).
  3. Women Who Kill.
  4. .
  5. ;

This is one reason concept mapping can also be a very powerful evaluation tool Edmondson, Thus, we see that concept maps are not only a powerful tool for capturing, representing, and archiving knowledge of individuals, but also a powerful tool to create new knowledge. The software not only makes it easy for users of all ages to construct and modify concept maps in a similar way that a word processor makes it easy to write text, it allows users to collaborate at a distance in the construction in their maps, publish their concept maps so anybody on the Internet can access them, link resources to their maps to further explain their contents, and search the WWW for information related to the map.

The software allows the user to link resources photos, images, graphs, videos, charts, tables, texts, WWW pages or other concept maps located anywhere on the Internet or in personal files to concepts or linking words in a concept map through a simple drag-and-drop operation. Links to these resources are displayed as icons underneath the concepts, as shown in Figure 7. Clicking on one of these icons will display a list of links from which the user can select to open the linked resource.

Using CmapTools, it is possible to use concept maps to access any material that can be presented digitally, including materials prepared by the mapmaker. In this way, concept maps can serve as the indexing and navigational tools for complex domains of knowledge, as will be illustrated later with NASA materials on Mars Briggs et al. A concept map about birds constructed by a high-school student. Icons under the concepts provide links to resources e. There is a growing body of research that shows that when students work in small groups and cooperate in striving to learn subject matter, positive cognitive and affective outcomes result Johnson et al.

Vygotsky introduced the idea that language and social dialogue can support learning, especially when members of the social group are at about the same Zone of Proximal Development ZPD. When students work cooperatively in groups and use concept maps to guide their learning, significantly greater learning occurs Preszler, In our work with both teachers and students, small groups working cooperatively to construct concept maps have proven to be useful in many contexts.

In our own classes and workshops, and in classes taught by our students and colleagues, small groups of students working collectively to construct concept maps can produce some remarkably good maps. CmapTools provides extensive support for collaborative work during concept map construction. The concept maps built using CmapTools can be stored on servers CmapServers, see: Through CmapServers, users of all ages and working in many disciplines have published thousands of maps on all topics and domains.

While concept maps on these public servers are only a sample of concept maps submitted by persons using CmapTools, and some do not meet our criteria of good concept maps, they nevertheless serve to illustrate diverse applications. Through the storing of concept maps in CmapServers, CmapTools encourages collaboration among users constructing the maps. The high degree of explicitness of concept maps makes them an ideal vehicle for exchange of ideas or for the collaborative construction of new knowledge. We have also found that the obstacles deriving from personal insecurities and fear of embarrassment are largely circumvented, since critical comments are directed at the concept map, not at the person s building the map.

The extensive support that CmapTools provides for the collaborative construction of concept maps by groups, whether they are at the same location or in distant locations, has encouraged the increasing use of collaboration during map building. In a variety of educational settings, concept mapping in small groups has served us well in tasks as diverse as understanding ideas in assimilation learning theory to clarifying job conflicts for conflict resolution in profit and non-profit corporations e. Concept maps are now beginning to be used in corporations to help teams clarify and articulate the knowledge needed to solve problems ranging from the design of new products to marketing to administrative problem resolution.

In addition to a network environment that fosters collaboration and the possibility of constructing knowledge models, the software allows users, among other features, to a search for information based on a concept map Carvalho et al. The concept map can thus become an artifact around which the various activities of the learning process can be centered, as shown in Figure 8.

A concept map-centered learning environment implies that concept maps are used throughout the development of a learning unit or module. Concept maps within this environment are likely to be used as the mechanism to determine the level of understanding students have about the topic being studied before the topic is introduced.

The maps are then developed, extended and refined as the students develop other activities on the topic and increase their understanding, possibly concluding with complex knowledge models that link resources, results, experiments, etc. The whole spectrum of learning activities can be integrated using CmapTools, incorporating various learning activities recorded via the software creating a digital portfolio as a product of the learning. Each student can construct the initial concept map individually, giving the teacher feedback on the level of understanding of every student.

The concept map can be constructed by students working in couples or small groups, where the teacher must pay attention to the level of participation of every student. CmapTools has a recorder feature tht allows recording and playback of steps in map construction, including identification of each contributor.

The concept map can also be a class effort, using a projector, where all students give their opinion and participate in the construction of the map. Teachers must be alert to evaluate the individual participation of every student. Concept map that is part of a collaborative Knowledge Soup. The lower right window shows propositions from other participants in Soup, some of which have discussion threads attached questioning or commenting on the proposition.

The starting point for constructing a concept map can consist of only the focus question. The type of focus question makes a difference in the type of concept maps that the student builds. Originally, we used an oblique principle components factor analysis approach to hierarchical cluster analysis where the input for the analysis consisted of the similarity matrix. The problem with this approach was that it often led to results which did not visually correspond with the way in which multidimensional scaling mapped the points.

This is because differences in the two algorithms i. These results were hard to interpret and seemed to give equal weight to multidimensional scaling and cluster analysis. Instead, it makes sense to view the mathematical basis for multidimensional scaling as stronger than basis for cluster analysis and, accordingly, to rely on the multidimensional scaling rather than cluster analysis to depict the basic inter-statement conceptual similarities.

The Map Reader: Theories of Mapping Practice and Cartographic Representation

What we wanted was a cluster analysis which grouped or partitioned the statements on the map as they were placed by multidimensional scaling. We found that this could be accomplished by using the X-Y multidimensional scaling coordinate values for each point rather than the original similarity matrix as input to the cluster analysis. In addition, we also found that Ward's algorithm for cluster analysis generally gave more sensible and interpretable solutions than other approaches e. Therefore we have moved to an approach which uses Ward's hierarchical cluster analysis on the X-Y coordinate data obtained from multidimensional scaling as the standard procedure.

This in effect partitions the multidimensional scaling map into any number of clusters. Just as deciding on the number of dimensions is an essential issue for multidimensional scaling analysis, deciding on the number of clusters is essential for cluster analysis.

All hierarchical cluster analysis procedures give as many possible cluster solutions as there are statements. In principle, these clustering methods begin by considering each statement to be its own cluster i. At each stage in the analysis, the algorithm combines two clusters until, at the end, all of the statements are in a single cluster.

The task for the analyst is to decide how many clusters the statements should be grouped into for the final solution. There is no simple way to accomplish this task. Essentially, the analyst must use discretion in examining different cluster solutions to decide on which makes sense for the case at hand. Usually, assuming a set of a hundred or fewer statements, we begin by looking at all cluster solutions from about 20 to 3 clusters. Each time the analysis moves from one cluster level to the next lowest e.

In examining different cluster solutions we have found it useful to use a cluster tree which shows pictorially all possible cluster solutions and mergers.

In general, we attempt to decide on a cluster solution which, if anything, errs on the side of more clusters than fewer. Clearly this is a task which requires discretion on the part of the analyst and it would be ideal if we could involve the participants directly in this decision making process, but as of yet we have not determined an easy way to accomplish this kind of task within a group process. Our experience shows that, in general, the cluster analysis results are less interpretable than the results from multidimensional scaling.

The cluster analysis is viewed as suggestive and, in some cases, one may want to "visually adjust" the clusters into more sensibly interpretable partitions of the multidimensional space. The key operative rule here would be to maintain the integrity of the multidimensional scaling results, that is, try to achieve a clustering solution which does not allow any overlapping clusters e. Once we have conducted the multidimensional scaling and cluster analysis, we are able to generate a point and a cluster map.

The final analysis involves obtaining average ratings across participants for each statement and for each cluster. These can then be overlayed graphically on the maps to produce the point rating map and the cluster rating map as will be shown later. We have several products at the end of the representation step.

First, we have the two-dimensional point or statement map which locates each of the brainstormed statements as a point. Next to each point we place the number of the statement so that participants can identify each point as a statement. Second, we have a cluster map which shows how the cluster analysis grouped the points. Third, we have the point rating map which shows the average ratings for each statement on the point map.

Finally, we also have the cluster rating map which shows the average rating for each cluster on the cluster map. This information forms the basis of the interpretation in the next step.

Abstract. Map theory (MT) is a foundation of mathematics. MT is slightly more powerful than ZFC set theory, but its merit is that it builds on top. As an introductory book, this book contains the elementary materials in map theory, including embeddings of a graph, abstract maps, duality, orientable and.

To interpret the conceptualization, we usually assemble a specific set of materials and follow a specific sequence of steps -- a process which has been worked out largely on the basis of our experiences on many different projects. The materials consist of:. Notice that there are four different types of maps here. Which of them is the concept map? In fact, they are all concept maps.

Each of these maps tells us something about the major ideas and how they are interrelated. Each of them emphasizes a different part of the conceptual information. While the maps are distinctly different ways of portraying or representing the conceptual structure and consequently, different names are used to distinguish them , it is important to remember that they are all related to each other and are simply reflecting different sides of the same underlying conceptual phenomenon.

In the remainder of this paper, if the type of concept map is not specified, it is usually fair to assume that the discussion pertains to the cluster map because that is usually the most directly interpretable map. The facilitator begins by giving the group the original set of brainstormed statements for the York County example, the statement list is shown in Table 1 above and recalling that the statements were generated by the them in the brainstorming session. Participants are then reminded that they grouped these statements into piles and told that the individual sortings were combined for the entire group.

The statements as they were grouped by the cluster analysis the cluster list are then presented. For the York County study, the cluster listing is given in Table 2. Each participant is asked to read through the set of statements for each cluster and come up with a short phrase or word which seems to describe or name the set of statements as a cluster. This is analogous to naming factors in factor analysis. When each person has a tentative name for each cluster, the group works cluster-by-cluster in an attempt to achieve group agreement on an acceptable name for each cluster.

This is an often interesting negotiating task. When each person in turn gives their name for a certain cluster, the group can often readily see a consensus which exists. For some clusters, the group may have difficulty in arriving at a single name. This is because the statements in that cluster might actually contain several different ideas and, had a higher cluster solution been selected, the statements would have been subdivided into subclusters.

In these cases, the facilitator might suggest that the group use a hybrid name, perhaps by combining titles from several individuals. In any event, the group is told that these names are tentative and may be revised later. When the group has reached consensus on the names for each cluster, they are presented with the numbered point map. The York County map is shown in Figure 3.

Navigation menu

They are told that the analysis placed all of the statements on the map in such a way that statements which were piled together frequently should be closer to each other on the map than statements which were not piled together frequently. Usually it is a good idea to give them a few minutes to identify a few statements on the map which are close together and examine the wording of those statements on the original brainstormed statement list as a way to reinforce the notion that the analysis is placing the statements sensibly.

When they have become familiar with this numbered point map, they are told that the analysis also organized the points into groups as shown on the list of clustered statements which they just named. The cluster map is presented and participants are shown that the map portrays visually the exact same clustering which they just looked at on the cluster list. They are then asked to write the cluster names which the group arrived at next to the appropriate cluster on the cluster map. They are then asked to examine this named cluster map to see whether it makes any sense.

The facilitator should remind participants that in general, clusters which are closer together on the cluster map should be more similar conceptually than clusters which are farther apart and ask them to assess whether this seems to be true or not. Participants might even begin at some point on the map and, thinking of a geographic map, "take a trip" across the map reading each cluster in turn to see whether or not the visual structure makes any sense.

For the York County example, the named cluster map is given in Figure 4. The participants are then asked to see whether there are any sensible groups or clusters of clusters. Usually, the group is able to perceive several major regions. These are discussed and partitions are drawn on the map to indicate the different regions. Just as in naming the clusters, the group then attempts to arrive at a consensus concerning names for these regions.

In the York County study, people were satisfied with the clustering arrangement and did not wish to define any regions. This final named cluster map constitutes the conceptual framework and the basic result of the concept mapping process. The facilitator should remind the participants that this final map is their own product. It was entirely based on statements which they generated in their own words and which they grouped.

The labels on the map represent categories which they named. While in general the computer analysis will yield sensible final maps, the group should feel free to change or rearrange the final map until it makes sense for them and for the conceptualization task at hand. At this point it is useful for the facilitator to engage the participants in a general discussion about what the map tells them about their ideas for evaluation or planning.

If ratings were done in the structuring step, the facilitator then presents the point rating and cluster rating maps. The point rating map for the York County Study is given in Figure 5. Participants examine these and attempt to determine whether they make sense and what they imply about the ideas which underlie their evaluation or planning task.

In the York County study some interesting insights arose from the interpretation process. If we look at either of the cluster maps Figures 4 or 6 we can see that the clusters on the right side of the map -- Personal Growth and Education, Stereotyping, Socialization Needs, and Political Strength and Advocacy -- tend to be the types of issues of most concern to the "well elderly", people who are not ill or institutionalized. The group perceived this counter-clockwise cycle as a good description of their implicit theory of the aging process.

Furthermore, they believed that most of the political strength and advocacy work that is exists around aging issues tends to be done by the "well elderly" as the map implies. This led them to discuss the desirability of working within the community to encourage the well elderly to perceive their position within the entire aging cycle and begin to engage in more active advocacy for the full range of concerns which the map describes.

Thus, the map provided a foundation for an approach to the elderly which addresses major concerns and emphasizes the more active involvement especially of the well elderly.

Description

The CmapTools Network may serve as a clearinghouse for some of these efforts through its Public servers in Italy and other countries. This is a phenomenal ability that is part of the evolutionary heritage of all normal human beings. This feedback should help us to rapidly refine concept maps, techniques and approaches for improving practice of the New Model for Education. First, we conduct an analysis which locates each statement as a separate point on a map i. Again, one could use virtually any word processing program for entering the statements e. Charles University Karolinum Press. If the words are unfamiliar, such as technical terms introduced for the first time, the learner may do well to recall correctly two or three of these.

At this point in the process we turn our attention back to the original reason for conducting the structured conceptualization. The group discusses how the final concept map might be used to enhance either the planning or evaluation effort. The uses of the map are limited only by the creativity and motivation of the group. A number of straightforward applications suggest themselves. For instance, if the conceptualization was done as the basis for planning, the final map might be used for structuring the subsequent planning effort.

The planning group might use it for dividing up into subgroups or task forces, each of which is assigned a specific cluster or region. Each task group could then examine issues like: The task forces can use the individual statements within a cluster as cues or prompts concerning what they should consider specifically within each cluster.

One major advantage to having the concept map is that the results of these task force investigations can often be usefully displayed directly on the concept map as were the priority ratings for the York County example in Figures 5 or 6. For planning purposes, the concept map can also be used as the framework for an outline of a planning report. Regional headings would constitute the highest level of indentation for the outline, clusters would be subheaded within their appropriate regions, individual statements could be subheadings within clusters, and any statement-level information relevant to planning could be subheaded within this structure.

Thus for planning, the concept map provides a framework for understanding important issues in a way which enables sensible pictorial and outline representations. The concept map is also extremely useful in evaluation contexts. Here, its utilization depends on what the focus was for the conceptualization.

Latent Learning & Cognitive Maps (Intro Psych Tutorial #68)

If the focus was on planning a program or service which would then be evaluated, the concept map can act as an organizing device for operationalizing and implementing the program. For instance, if the program is a training program in a human service agency, the training can be constructed based on the concept map with different training sessions designed to address each cluster and the individual brainstormed statements acting as cues for what kinds of information should be covered in each session. The concept map is the framework for the program construct and can form the basis of a process evaluation of the program.

In this case or in the case where the focus of the conceptualization was on the outcomes of some program, the concept map can guide measurement development. Each cluster can be viewed as a measurement construct and the individual statements can suggest specific operationalizations of measures within constructs. For instance, if the group wished to develop a questionnaire, they could use the concept map by having each cluster represented with questions on the questionnaire. Furthermore, the original brainstormed statements might provide question prompts which either directly or with some revision could be included on the questionnaire along with some rating response format.

Alternatively, if a more multimethod approach to measurement was desired, the group could make sure that within each cluster several different types of measures were constructed to reflect the cluster. The exciting prospect here is that the concept map provides a useful way to operationalize the multitrait-multimethod approach to measurement which was outlined by Campbell and Fiske and is described in greater detail in the paper by Davis this volume.

In this example, the concept map represents the group's theoretical expectations about how the major measurement constructs are conceptually interrelated. From the concept map we can predict the rank order which we expect in the correlations between measures. These expectations the theoretical pattern could then be directly compared with a matrix of correlations as obtained in the study the observed pattern and the degree to which the two match can constitute evidence for the construct validity of the measures.

This "pattern matching" approach to construct validity is discussed in detail in Trochim ; in press. A number of papers in this volume illustrate the use of structured conceptualization for evaluation. For instance, Valentine this volume used concept mapping to construct an instrument which could be used to assess caring in a nursing context.

An introduction to concept mapping would be incomplete without some consideration of the computer programs which can be used to accomplish this process. Essentially, there are two options: Each is discussed in turn. When using available general-purpose software packages, the analyst will have to be prepared to experiment with different processing options until a suitable procedure can be constructed.

Minimally, it is desirable to have a good word processing program; a statistics package which has routines for multidimensional scaling and cluster analysis, and which has fairly flexible data manipulation capabilities; and, a graphics program to plot the final maps. On a mainframe computer, brainstormed statements can be entered into any standard editor.

They would then need to be formatted and printed onto cards, labels, or sheets in a manner which allows the analyst to assemble them into sorting decks. In addition, the statements would need some minor formatting in order to produce an instrument for the rating task.