Cogn Process (2013) 14:255–272 DOI 10.1007/s10339-013-0547-3

RESEARCH REPORT

Cognitive tools shape thought: diagrams in design Jeffrey V. Nickerson • James E. Corter • Barbara Tversky • Yun-Jin Rho • Doris Zahner Lixiu Yu

•

Received: 8 October 2012 / Accepted: 25 January 2013 / Published online: 15 February 2013 Ó Marta Olivetti Belardinelli and Springer-Verlag Berlin Heidelberg 2013

Abstract Thinking often entails interacting with cognitive tools. In many cases, notably design, the predominant tool is the page. The page allows externalizing, organizing, and reorganizing thought. Yet, the page has its own properties that by expressing thought affect it: path, proximity, place, and permanence. The effects of these properties were evident in designs of information systems created by students Paths were interpreted as routes through components. Proximity was used to group subsystems. Horizontal position on the page was used to express temporal sequence and vertical position to reflect real-world spatial position. The permanence of designs on the page guided but also constrained generation of alternative designs. Cognitive tools both reflect and affect thought. J. V. Nickerson (&)  D. Zahner  L. Yu Center for Decision Technologies, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030, USA e-mail: [email protected] J. E. Corter  B. Tversky  Y.-J. Rho Department of Human Development, Teachers College, Columbia University, New York, NY 10027, USA Present Address: Y.-J. Rho Pearson Education, 75 Arlington Street, Boston, MA 02116, USA Present Address: D. Zahner Council for Aid to Education, 215 Lexington Avenue, New York, NY 10016, USA Present Address: L. Yu Human-Computer Interaction Institute, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA

Keywords Diagrammatic reasoning  Design  Creativity  Cognitive tool  Affordance  Spatial thinking  Information systems design

When thinking overwhelms the mind, the mind puts thought into the world. Externalizations of thought are ancient and ubiquitous (e.g., Donald 1991; Kirsh 2010; Norman 1993; Tversky 1995, 2001, 2011b). A flat surface of a size convenient to eyes and hands, which we will call a page, provides a convenient place to put thoughts. A page can be viewed and reviewed, drawn and redrawn, construed and reconstrued by its creator and by others. All manners of thought, concrete and abstract, spatial and nonspatial, can readily be mapped to the page. Topics of thought can be mapped to marks on the page, and relations among topics mapped to marks and to spatial relations among marks. Ideas can be mapped to icons, like picnic tables on road signs or trashcans in computer displays, or mapped more abstractly to dots or nodes in an associative network or decision tree. Relations between ideas can be mapped to lines connecting them or frames containing them. Orderings of ideas can be mapped along lines on the page and distances between ideas to distances on the page. This enables the page to represent the inherently spatial, like maps and molecules, as well as the metaphorically spatial, like timelines, decision trees, and social networks (Tversky 2001, 2011a, b). Language also serves to organize and externalize thought as well as to make it accessible to others. However, unless it is written, language lacks the permanence of the page. Language is sequential and structured by syntax and semantics, all of which shape meaning. Language is (almost) purely symbolic and does not carry the spatial correspondences to meaning that the page and its marks

123

256

have [signed languages, which can and do use space to convey space, are an exception (Emmorey 2001; Liddell 2003; Talmy 2003)]. Yet, language makes abundant use of space to express abstract thought, evident in ways that people talk (e.g., Lackoff and Johnson 1980; Talmy 2000; 2003; 2005) as well as the way they gesture (e g., GoldinMeadow 2003; Tversky et al. 2009). Talk about time borrows spatial language: we look forward to celebrations, we arrive on time, or we extend the deadline (e.g., Clark 1973; Lackoff and Johnson 1980; Talmy 2000). So does talk about quantity, value, affect, social relations, and more: the stock market goes up when unemployment goes down; a movie was over the top; a friend is in a quandary and another has grown apart. If such a range of human thought is fundamentally spatial, then arraying it spatially is bound to promote thought, and indeed, it does (e.g., Mayer 2001; Tversky 2001, 2011b). Visualizing thought on a page has advantages beyond transparency of meaning. Arraying thought on a page allows using everyday spatial reasoning skills—about distance, direction, size, shape, position, connectedness, inclusion, and more—for abstract as well as spatial reasoning. Maps, architectural plans, and product designs all selectively represent real spaces. They allow viewers to estimate distances, to determine routes, to assess behavior, and to evaluate functionality. Diagrams, charts, and graphs selectively represent concepts and relations that may be abstract, but allow spatial reasoning. Things that are farther from each other on the page are farther apart on some abstract dimension. Things higher on a page have larger values on some abstract dimension. Larger things have more of some attribute than smaller ones. Things clustered together or within the same frame share a feature or features. Things along a line share an underlying dimension, but have different values on that dimension. These examples of spatial reasoning are neutral, applicable to any domain. But there are spatial meanings that are value-laden and can confer meanings that may be unintended or even unwanted. Direction in space has strong shared value. Upwards is associated with power, strength, health, money, quantity, and more. This association of upwards with all things good is at least in part the influence of gravity, an inescapable force in the world that can take power, strength, health, and energy to counteract. The association of upwards with power, strength, health, and the like rests not only in the world, but also in nature of the human body, to grow taller, stronger, wealthier, and wiser with age, barring infirmity which bends the body (e.g., Clark 1973; Cooper and Ross 1975; Lackoff and Johnson 1980; Tversky et al. 1991). Thus, people whose images are incidentally located higher in space are regarded as more powerful than people whose images are lower (e.g., Schubert 2005). In the absence of any shared strongly

123

Cogn Process (2013) 14:255–272

asymmetric horizontal force in the world, reading direction, handedness, and cultural associations confer order and asymmetry along the horizontal dimension. For readers of left-to-right languages, things on the left are perceived as earlier, more agentive, powerful, and beautiful. Movement in the direction of reading order is regarded as more powerful and smooth (e.g., Chatterjee 2001; Kranjec et al. 2010; Maass and Russo 2003; Maass et al. 2007). Righthanders tend to put things they like on the right, and lefthanders on the left, though the directional asymmetry is stronger vertically than horizontally (Casasanto and Henetz 2012). Leaning to the left leads to endorsing left ideas (Oppenheimer and Trail 2010). The multitude of associations to direction in space inevitably leads to ambiguities and confusions, and to connotations both intended and unintended. Is someone at top because of IQ or health or wealth or height? To the left because of primacy or power or politics? Marks on the page, notably words and pictures, carry meaning. But simple geometric forms, like dots, lines, arrows, and boxes, also carry shared meanings, often abstract ones (e.g., Tversky 2001, 2011a, b; Tversky et al. 2000). Lines are paths, connecting one thing to another, like streets in a city. Lines suggest a relationship, spatial or otherwise, linking the things along it. Arrows are asymmetric lines, suggesting asymmetric relationships. Frames contain enclosing a set of related things and separating them from things that are not related. Spatial grouping does the same, but frames make the inclusion and separation more explicit. These simple forms are readily understood and produced in context, suggesting shared meanings (e.g., Tversky et al. 2000). Nevertheless, the forms have ambiguity, just like their linguistic counterparts. Does the arrow mean time or motion or cause? Is the line or relationship romantic or mathematic? Context can, but does not always, reduce ambiguity. Thought needs expression, whether for self or for others, and cognitive tools provide expressive media. The thought and the tool together provide situated representations, representations that are external and a joint product of the thought and the tool. Cognitive tools such as the page and language have their own qualities. Language is largely sequential, often aural, and symbolic. The page, as we have seen, has an orientation, with horizontal and vertical axes, and various marks with various associated meanings. Ideally, the qualities of the tool align with the qualities of thought, but not always. When thought and tool are aligned, thought is enhanced. When they are not aligned, thought may be shaped by the tool. We have found both effects in diagrams for design. Design encompasses many domains, buildings, products, information systems, interfaces, games, websites, experiences, and more. It has been argued that we are all

Cogn Process (2013) 14:255–272

designers, from our desks and desktops to our days and the days of our lives. Whatever the domain, diagrams and sketches are an integral part of the design process. Designers involve their sketches in a kind of conversation (e.g., Schon 1983). They put tentative ideas on paper and reflect on them, reconfigure them in their minds, sketch, and reflect again. By this iterative process, designers see new relationships in their designs, draw new implications, and get new insights (e.g., Fish and Scrivener 1990; Goldschmidt 1991, 1994; Schon 1983; Suwa and Tversky 1997, 2001, 2003; Suwa et al. 2001; Tversky and Suwa 2009). Experienced designers use a process called constructive perception (Suwa and Tversky 2001, 2003; Tversky and Suwa 2009) to get new ideas. They mentally reconfigure, regroup, and reorganize the elements of their design sketch; then, they reinterpret the reorganized configuration. Constructive perception has a perceptual side, reconfiguring the design sketch, and a conceptual side, reinterpreting the reconfiguration. The configuration of marks on the page, because it is serves as an expression of ideas, a starting point for a conversation about the ideas, and an anchor for varying designs, is fundamental to successful design. Experienced designers pay attention to physical placement, as it provides a secondary notation that augments the information contained in the connectivity of a diagram (Oberlander 1996; Petre and Green 1993; Schrepfer et al. 2009). Because information systems combine the concrete and the abstract, the design of information systems is an especially interesting domain for studying the effects of the medium on the expression of thought and on thought itself. Information systems manage the flow of information among the components involved in accomplishing specific transactions. The transactions and the organizations that perform them are diverse, and can be quite complex, for example, the operations of a large bank, an on-line store, or a hospital. The components can be human, machine, or artifact, in varying roles, individually and in groups (cf. Avital et al. 2006; Hevner et al. 2004; March et al. 2000; Winograd 1996). The concrete aspects of information system design may include familiar entities, clients, places, computers, products, familiar transactions, purchasing products, depositing checks, and applying for college. The abstract aspect is the flow of information, and even that can take different forms. At an abstract level of design, information systems can be represented as networks of interconnected components with constraints. At this level, place does not matter, nor does proximity. The physical instantiation does not matter. What matters are the components and their interconnectivity, and for that, dots and lines suffice. Although dots and lines suffice to represent the design of information systems, they do not capture considerations

257

central to the typical design process, which pays attention to specificities of content. In a popular design method, system requirements are first expressed through narratives of specific situations (Booch et al. 2005; Carroll 2000); for example, ‘‘The customer sent an electronic coupon to the nearby cash register, which gave her a discount on her purchase.’’ These narratives are referred to as use-cases, or scenarios. They contrast with more abstract requirements such as ‘‘The system interfaces with the cash register.’’ Scenarios enumerate the major actors of the system and at the same time suggest the dynamic interactions of systems. These narratives are then converted by designers into diagrammatic sketches that show the structure of the system, abstracting away all but the most important relations. The narratives highlight aspects of the situation, some abstract, some concrete, that are relevant to creating a good design, even if they are not directly representable by formal properties of the diagram, the nodes, and the links. For one thing, the scenarios incorporate accumulated pragmatic and heuristic wisdom underlying good design. For another, numerous studies have shown that problem solving uses both concrete examples and a process of abstraction (e.g., Gick and Holyoak 1980, 1983; Kaminiski et al. 2006; Novick 1990), and design is no different. Do designers’ diagrams go beyond nodes and links as designers find ways to represent the other information central to the design? The page, the cognitive tool for design, whether on paper or a screen, has its own properties, constraints, and affordances. These properties, constraints, and affordances affect the ways that ideas can be expressed and interpreted, and thereby the thoughts themselves. The page is flat, with a specific orientation and a particular shape and dimensions. Parts of the page are directly associated with meanings, in context. There are concrete associations with the landscape, where ground is at the bottom and sky at the top of a page. There are also abstract associations, for example, upwards with increased quantity, power, and goodness (e.g., Clark 1973; Chatterjee 2001; Lackoff and Johnson 1980; Schubert 2005; Schubert et al. 2008; Talmy 2000; Tversky 2011b). Proximity on the page is associated with proximity on both concrete and abstract dimensions. The pencil or drawing program makes marks, including a rich variety of shapes, as well as dots and lines. The present analyses of information design show that designers take advantage of four different affordances of the page and the marks: paths and points, proximity, position, and permanence. The first three of these properties of marks and the page may be termed conceptual affordances, as they are visuospatial features directly associated with meanings, in contexts. Lines, for example, are interpreted as paths or links or relationships, points as intersections of paths, and arrows as asymmetric relationships. In languages that read left to right, left is interpreted as earlier than right (e.g.,

123

258

Tversky 2001, 2011a, b; Tversky et al. 2000), illustrating an effect of relative position on the page. Illuminating how such affordances affect the creation and interpretation of designs is the goal of the present project. These analyses of the design process and the properties of the page and marks on it have implications for information design diagrams. Points and paths are necessary as they are the nodes representing components and the lines connecting them that are the primary means of conveying the connectivity that structures information systems. The other affordances, proximity, position, and permanence are not necessary, but we expected that designers would use these conceptual affordances to amplify their design diagrams, sometimes to good effect, sometimes not. In particular, we expected that designers would use proximity to group conceptually related components and separate them from conceptually different ones, horizontal position to represent temporal order, and vertical position to represent location in the real world. We also expected the permanence of diagrams to constrain and guide the generation of alternative designs. In order to test these hypotheses, we created new tools in order to schematize, summarize, compare, and analyze sketches. These tools have general applicability to analyses of diagrams and sketches.

Study 1: Characterizing design sketches A Master’s level class in information systems architecture served as our laboratory. The majority of the students were practicing information technology professionals with several years of experience. Throughout the semester, the students were asked to solve a series of open-ended high-level systems architecture problems, and were exposed to, and critiqued, the other students’ designs. Students were instructed in methods of idea generation; every assignment and test asked them to generate several alternatives, and they understood from the instruction, and from in-class critiques of student examples that the alternatives should differ substantially from each other; Nickerson (2006) describes the pedagogy of the course in detail. This particular study examined in detail a design project mid-way through the semester. Method Participants Twenty-nine students in a class in information systems architecture participated as part of a classroom exercise. Twenty-four of these students were male, five female. Twenty of the students were full-time students, and nine were part-time students. All but one student reported experience writing software, with 11 students claiming

123

Cogn Process (2013) 14:255–272

they had written more than 100,000 lines of code. Eight students claimed no design experience. Stimulus and procedure The students were given a design problem that asked them to serve as a consultant for a client, a bookstore chain that wanted to take advantage of mobile technology in order to increase business. Specifically, they were told that the client bookstore wanted to insure that the system would enable the scenario below. Each student was given 1 h to respond with diagrams to this written prompt: Read the following solution scenario, and then draw three alternative spatial diagrams: deployment diagrams, or any form of spatial diagram that portrays the system that would support the solution scenario. As Jenny approaches 57th Street and 8th Avenue she inputs ‘‘books’’ on her Google-enabled phone. She vaguely remembers there is a bookstore in the area: she gets back a hit: Borders – and an arrow pointing her North towards Columbus Circle. Along with it she sees an ad – 10 % off any purchase within the next hour. She saves the coupon, and lets her phone guide her into Borders. While there, she finds a present for a friend, and electronically transfers the discount coupon to the cash register. Results Data and analyses Typical diagrams appear in Figs. 1, 2, and 3, all from the same participant. Diagrams were primarily an array of nodes (dots) and edges (links), often labeled and/or depicted. We coded the diagrams into nodes and edges, converting them into formal graph structures, and performed a series of calculations. Three measures were needed to test our hypotheses. First, the positions of the components were used to determine whether their placement on the page is arbitrary, or determined by the type of the component or the spatial or temporal properties of the problem and the design. Second, the links between components in the system were used to assess formal differences in design. That is, the edges connecting or not connecting specific components were used to determine the structural similarity between diagrams. Third, the metric distance between components in a diagram was computed to determine whether designers used proximity to represent extra information about the system that was not needed to convey connectivity. In order to apply these metrics uniformly, the handdrawn diagrams needed to be normalized into a common

Cogn Process (2013) 14:255–272

259

Fig. 2 The second alternative from participant one

Fig. 1 The first alternative from participant one

form. For a particular design problem, there are many ‘‘actors’’ (including system components) that can appear in a collection of diagrams. The master set of actors was constructed from the union of all distinct actors mentioned in the individual solutions. As a result, the components in an individual diagram formed a subset of this master set of actors. Diagrammatic representations of network infrastructure technologies, such as local area networks and hub-and-spoke architectures (cf. Peterson and Davie 2011), were normalized into an underlying relation structure that established which components could talk directly to other components. Thus, the underlying structure of the diagrams was extracted and compared in order to learn how the diagrams vary with respect to structure. Position and proximity, elements of the surface depiction of the structure, were examined separately to determine whether they were informative. Coding processes were performed in order to extract features for later analysis. We relied primarily on simple graph theory, seeking to form a representation that reflected the underlying intended structure of the designer. A summary of the diagram coding process and analysis process is shown in Table 1. The first five steps in the process entail human coding. Step 1 measured the locations of graphical elements. We accomplished this by overlaying a transparent grid on the sketched diagram to record the locations of the centers of

Fig. 3 The third alternative from Participant 1

all nodes. In step 2, the node labels made by the participants were collected from the diagrams in order to build up a complete set of node labels L. Then, in step 3, the names were standardized so that obviously identical items in different graphs were given the same names. For example, a phone might be labeled ‘‘phone’’ by some and ‘‘device’’ by others—‘‘device’’ would be chosen as the standard term. Next, in step 4, each node was classified as being either a network component, such as a router, or a computational component. In step 5, an edge was coded between two nodes if there was a line connecting the nodes, or if an icon for a person was placed directly next to a computer of some kind. The result of these steps was the creation of an adjacency matrix of each diagram (cf. Pemmaraju and Skienna 2003) augmented by a list of vertex locations. From this information, a set of transformations was performed automatically. In step 6, an abstract graph structure was built from the adjacency matrix, augmented

123

260 Table 1 Methods of coding, comparing, and integrating diagrams Manual steps in coding a diagram 1. Record the locations of nodes on the diagram 2. Build a list of all nodes used in all diagrams, L 3. Standardize a set of node names (e.g., ‘‘phone’’ is mapped to ‘‘device’’) 4. Classify each node as either an individual component or a network 5. Record the edges that are incident between nodes on the diagram Automated steps in coding a diagram 6. Build a graph, G = {V, E}, of nodes and edges, for each diagram. Full labels, types of nodes, and positions are recorded 7. Remove the network nodes, and take all the individual component nodes that were connected through each network node and connect them directly, yielding a new graph, G0 8. Compute Euclidean distances between the directly connected nodes using their spatial positions, thus building a Euclidean Network 9. Compute path distances between nodes using the topology of G0 . That is, distances between indirectly connected nodes will consist of the sum of the Euclidean distances of the directly connected segments in the path Automated steps to compare and aggregate diagrams 10. Using the frequency of occurrence of each edge, create a consensus graph based on edges that occur above a threshold. Then compute the median length of these edges. Use multidimensional scaling to embed the graph in the plane 11. Compute the graph edit distance between graphs: the amount of edge addition and deletion that will transform one graph into another 12. Based on graph edit distances between the design solutions, project all design solutions into the plane using multidimensional scaling

by lookup functions that provide node names, node locations, and node types. Two graphs of the above type were still hard to compare, because superficial differences in the network structure may disguise the equivalence of the graphs at a deeper level. For example, some participants may have directly connected three nodes, and others may have indicated all nodes were connected through a network hub. The effective topology of these graphs was the same, in that in both cases all nodes could talk to each other without going through another computer component. In order to normalize the topology, a new graph was created, which we call the logical graph, in which the specialized network nodes were removed, and all computational nodes that previously had been connected through each network node were connected directly to each other. To do this, all neighboring nodes of a network node were found, and then completely connected to each other, forming a clique. Thus, in step 7, the network nodes and all their incident

123

Cogn Process (2013) 14:255–272

edges were dropped, and a new set of edges substituted to form the canonical-form logical graph, G0 . From these structures, we derived the needed metrics. The locations of the nodes were used to see, for example, where the phone was usually put. In step 8, proximity was analyzed by computing the Euclidean distance between directly connected nodes—for example, the distance between the phone and its user. And in step 9, the shortest paths between each node were calculated using the distances calculated in step 8. This type of graph has been described as a Euclidean Network (Golden and Ball 1978) or a Spatial Network (Barthe´lemy 2011): networks of nodes are embedded in space, and directly connected nodes have an edge weight corresponding to the Euclidean distance between the pair. We were interested also in the consensus of the designers. In step 10, all edges were examined in all graphs, and edges that occur ten or more times in the entire set of designs (a threshold that guarantees at least three individuals have included the same edge) were retained. The median length of these retained edges was found. A new graph, a consensus graph, was then constructed using multidimensional scaling based upon the median distances. How much variation was there in the solutions of the different designers? All graphs were compared in step 11 by computing the graph edit distance (Sanfeliu and Fu 1983). This abstract distance is the number of edges that must be either removed or added to convert one graph into another: Because there was a bounded set of nodes, L, each participant diagram graph could be described as a subset of edges of the complete graph formed on L, and every participant graph could be transformed into another by the addition and/or removal of edges. In step 12, this graph was drawn using multidimensional scaling to locate the nodes. Findings Before turning to the general statistics, we discuss the successive graphs of a single participant, in order to show how the analysis methods described above can be used to extract information contained in the diagrams. In Fig. 1, the diagram is split into roughly three sections, corresponding to three subsystems—the customer/device/ GPS, the store, and Google. We notice that the satellite is positioned at the top in the diagram, the store on the bottom, the person on the far left, and Google up in the air. These locations are in some sense superfluous, because they do not affect the structure of the proposed system, but nonetheless they are not chosen arbitrarily, as we will show in the next section. Position information in the diagrams The first type of information that designers consistently use in creating deployment diagrams is position information,

Cogn Process (2013) 14:255–272

that is, location of nodes in the two-dimensional plane of the paper. We have observed certain implicit conventions regarding node placement that are remarkably consistent across designers. For example, student designers usually place the node representing ‘‘person,’’ the user of the system (often the customer in these examples) to the left of the page. The GPS device is often placed near the top of the diagram, evoking the role of earth satellites in these systems, but sometimes near the person, reflecting the conveyance of the information to the hand-held device. We analyzed the use of position in the Store problem diagrams by taking the median X and Y coordinates for each of five critical nodes (Fig. 4). The locations of the points in Fig. 4 are consistent with preferences of diagram designers documented in our previous studies. First, the person node is located at the left of the diagram—the person node is often the starting point in constructing a diagram, and it has been documented that people often start at the left side in drawing diagrams (Taylor and Tversky 1992). The device node is located just to the right of Person, illustrating our earlier observation that interactions between people and devices are often notated by proximity in diagrams. The GPS and Google nodes are both located up and to the right, while the store node is at the bottom of the figure. In cognitive linguistics, both proximity and a related concept, distality is used to indicate the degree of remove between cognitive entities (Talmy 2005). In the diagrams of this study, the close proximity of the person and the device indicates an implicit connection, whereas in other parts of the diagrams, the distance between explicitly connected entities indicates the degree of connection or association. In addition, there are other inter-individual consistencies in how designers locate specific objects in the Euclidean plane: calculating the medians of the designers’ X and Y coordinates results in node positions that appear to reflect

Fig. 4 Median locations of five critical nodes

261 Table 2 Relative positions of actors Person

Device

Store

GPS

Google

Person

–

0.41

0.24*

0.70*

0.58

Device

0.85*

–

0.26*

0.74*

0.64

Store

0.86*

0.77*

–

0.72*

0.84*

GPS

0.63

0.52

0.23*

–

0.29

Google

0.83*

0.87*

0.61

0.71

–

Entries below the diagonal report the proportion of diagrams for which the column node is placed to the left of the row node in the diagram. Entries above the diagonal report the proportion of diagrams for which the column node is placed above the row node

the structure of the problem. This is remarkable because left–right/up–down placement is completely arbitrary in the designer’s diagrams, in the sense that the placement does not affect topological connectivity, nor is it determined by the spatial proximity relations among nodes. Consistency is also apparent within individuals; individual designers show strong consistency in their use of positional information. This position consistency is documented in Table 2, which reports the proportion of diagrams for which node x is placed to the left of (or above) node y for all pairs of nodes. The asterisks and bold type denote proportions that significantly differ (p \ .05) from 0.5, although these results should be viewed as descriptive rather than inferential since the reported tests are not independent, and the observational units are individual diagrams, not participants. It is clear that store is generally positioned to the left of the other nodes, and Google to the right. In the vertical dimension, GPS is consistently positioned at the top and store at the bottom. Proximity to represent hierarchy It appears from the diagrams shown in Figs. 1, 2, and 3 that the designer has separated the problem into subsystems. However, there is no direct indication of this in the diagram—we believe that subsystem structure is implicitly coded by proximity. In order to discover hierarchical information in a designer’s diagrams, we must augment topological information with spatial information. Specifically, we can infer hierarchical structure through spatial location information by using a clustering methodology that takes as input both the connectivity and the physical distances between nodes in the diagram. In accordance with step 8 of Table 1, we computed the distances between all directly connected nodes in the canonical-form logical graph G0 (see Fig. 5a–c) as the Euclidean distance between nodes. In step 9, we determined distances between indirectly connected nodes based on the shortest paths in the graph (Floyd 1962). We then

123

262

Cogn Process (2013) 14:255–272

7

9

8

4

9

8 2

2 1

1

10

1

10

8

2 10

9 5

3

3

7

11

12

3

6

2

7 10 4

4

5

5

6

1

6 4

9

8

5

3

6

1

2

10

8

9

4

5

3

6

1 2 7 8 9 10 12 4 5 6 3 11

Fig. 5 Graphs and their associated dendrograms. The top diagrams a–c show the logical structure of the diagrams in Figs. 1, 2, and 3. The bottom diagrams d–f show the corresponding dendrograms. The number key for nodes in this and the following diagrams is as follows:

(1) person, (2) handheld device, (3) store, (4) coupon, (5) item, (6) cash register, (7) GPS satellite, (8) store information, (9) map, (10) Google, (11) computer, and (12) retail application

performed hierarchical agglomerative clustering (Jain and Dubes 1988) on this distance matrix among all pairs of nodes. The resulting clustering dendrograms—tree structures based on the distance matrix—(Fig. 5d–f) match our intuitions about the closeness of the items (cf. Sokal and Rohlf 1962). For example, in Fig. 5d, the closest pair is the interface between the user and the handheld device (nodes 1 and 2). These elements link to the satellite. Then, there is a cluster of Google-related nodes, followed by a cluster of store-related nodes. In the dendrogram representing the second design alternative (Fig. 5e), node 4 has moved from one cluster to another. And in 5f, there is an additional node added to the store cluster—a computer that handles communication with the device. The designer was running out of space on the page—so some of the LANs are rotated 90 degrees, and the GPS bends down, forced by the diagrams on top. The dendrograms suggest that there is hierarchical information embedded in the Euclidean distances between connected nodes. Furthermore, we found that agglomerative clustering will not produce such a clear dendrogram

when run on the topological distances between nodes, because the distances are too quantized, and thus there is no way to differentiate many nodes from each other. We also found that biconnected component analysis, another topological technique, does not capture the separation between the major subsystems.

123

Proximity and the consensus design diagram The clusters in Fig. 5 suggested the use of space to organize structure by one designer. But how prevalent is this strategy? To answer this, we examined the collective view of structure that emerges from a set of designers. We took as our basic data the Euclidean distances for all edges in 86 graphs drawn by 29 students. We worked from a master set of nodes. Not all students picked the same nodes, so some edges are very common and other edges are rare or idiosyncratic. In order to eliminate the idiosyncratic edges, we analyzed only edges that occurred in at least 10 graphs. Because most students provided three diagrams, this threshold guaranteed that more than three students used the

Cogn Process (2013) 14:255–272

edge in a diagram. We call this the consensus edge set. Note that the consensus edge set defines a subset of the nodes of the graph corresponding to the most important actors or components in the network. We then took the median length of each of the edges in this set, and formed a new graph, the consensus graph. In order to create a display of the consensus graph that uses spatial proximity effectively to convey information about the median distances in the student diagrams, we also performed nonmetric multidimensional scaling (MDS) (Kruskal 1964) on the distance matrix to find a configuration of point locations in the plane that approximate the distance constraints. The resulting graph, embedded in the plane according to the MDS solution, is shown in Fig. 6. The plot shows the consensus edge set, and also shows boxes drawn around three prominent high-level clusters evident. In order to confirm the clusters of components (subsystems) apparent in Fig. 6, a matrix of distances among nodes was created using shortest paths in the consensus graph; this matrix was used as input for a hierarchical clustering of the nodes or components (Fig. 7). The result can be viewed as representing the collective wisdom of the class. The dendrogram suggests three major clusters: {1, 2, 7}, {12, 4, 3, 5, 6}, and {9, 10, 8}, or, in words, {person,

263

device, GPS}, {store, cash register, retail application, computer}, and {Google, map, store information}. The consensus clustering is similar to the third graph of the first participant, shown in Fig. 5f. This consensus solution for the Store problem clearly delineates subsystems. Because this solution is based on a composite data matrix comprised of median diagram edge lengths, we cannot be sure if the individual graphs exhibit the same degree of hierarchical structure. To find out, we compared within- and between-cluster edge lengths in the individual graphs. We considered all those edges in each individual graph that correspond to edges in the consensus graph; this has the effect of filtering out idiosyncratic edges. Recall the lengths of these edges in the individual graphs were determined by the Euclidean distance between the two nodes in the individual diagram. Specifically, for each individual graph, we compared the mean length of the edges between clusters to the mean length of the edges within clusters, where the clusters are those identified in the consensus graph. If the proximity information in an individual graph exhibits strong hierarchical structure, then the edge lengths within a cluster should be smaller than between-cluster edge lengths. Out of 86 graphs, 12 did not contain pairs of edges that allow comparisons. Of the remaining 74, in 62 graphs, the mean edge length between

Fig. 6 Consensus graph, with salient clusters based on the median distance matrix, embedded with MDS into the plane

123

264

Cogn Process (2013) 14:255–272

Fig. 7 Clustering of the median distances between nodes

1

2

7

nodes within subsystems is less than the mean edge length between nodes across subsystems, and in 12, the mean between-subsystem edge length is less. The proportion of graphs that exhibit smaller within-subsystem edge lengths than between-subsystem edge lengths is significantly greater than chance by a sign test, z = 5.93, p \ .05. This result suggests that the use of Euclidean space to delineate hierarchy is a common tendency among this study’s participants. To summarize, students largely agreed on how to cluster nodes into subsystems, and manifest this by separating the clusters from each other in space. Permanence in the creative process Another affordance observable in the way designers use the page to create solutions is one we term ‘‘permanence’’ (it could be labeled ‘‘persistence’’ as well). The phenomenon we have in mind is the way designers create new designs by scavenging, recycling, and modifying ideas and structures from their previous attempts. These practices can lead to similarities between subsequent designs that we can discover and analyze using the tools we have developed. Specifically, each alternative diagram for a problem by a single participant may be represented as a node in a topological space. The alternatives are different from each other, as measured by the additions and deletions needed to transform one alternative into another. Tools that allow visualization and formalization of these edit operations may provide insight into the mental operations and transformations that designers use in producing these alternative designs. A graphical analysis can help convey the overall range of the alternatives designers generate. In Fig. 8, the distances in edit space among all the graphs are mapped into Euclidean space using nonmetric multidimensional scaling

123

12

4

3

5

6

9

10

8

(Kruskal 1964). The figure shows a clear center of mass. Each of the points represents one diagram—for example, 1.2 represents Participant 1’s second alternative (the graph shown in Fig. 2). Thus, by looking closely, we can see that all of Participant 1’s graphs are close to each other, but that the third alternative is actually closer to Participant 8’s second alternative. One might have reasonably expected that participants would start from very different places and make small modifications, so that all their alternatives will be mutual nearest neighbors. However, this was not the general case. This was true for only five participants—three of these participants made superficial rather than structural changes to their designs, so that their alternatives were identical at the graph level. For 24 participants, at least one alternative was closer to another participant’s graph than to their own other graphs. What about the average behavior? The mean distance to another graph of the same participant was 9.00, with SD 7.78, and the mean distance to a graph of a different participant was 13.72, with SD 3.5. So alternatives within participant are generally closer to each other than to other participants’ alternatives, but as can be seen from Fig. 8, there is a good chance another participant has a similar idea. We thought that designers may be more likely to explore a theme, create an alternative, and then modify that alternative. We therefore looked at which of the first two alternatives our participants based their third alternative on. By comparing the graph edit distances between alternatives 1, 2, and 3, for every participant, we could tell whether the third diagram was closer to the second diagram or to the first diagram. The mean edit distances among alternatives were the following: from alternative 1 to 2, X ¼ 9:62, s = 8.30, from alternative 2 to 3: X ¼ 9:00, s = 9.64, and from

Cogn Process (2013) 14:255–272

265

Fig. 8 Edit distances between graphs mapped into 2D using multidimensional scaling. The axes are not important, the result of fitting the distance matrix two-dimensional space, but the distances between variations are, as they express the closeness of the topologies in the diagrams

alternative 1 to 3, X ¼ 11:67, s = 11.24. Clearly, the mean edit distances from alternative 1 to alternative 2 and from alternative 2 to 3 are smaller than the mean distance from alternative 1 to 3. To test this difference, we took only the first diagram produced by each student, then compared the average of the edit distance from alternative 1 to 2 and from 2 to 3 with the edit distance from alternative 1 to 3. This difference was significant by a dependent groups t test, t(20) = 2.36, p \ .05. This result is consistent with the hypothesis that most participants worked from the second alternative to create the third alternative. This apparent ‘‘chaining’’ of designs, in which the designer modifies the most recent version of the design rather than the original, might be unsurprising in the field, where each new version of a solution may fix a problem with the original design, or be made in response to late-arriving information on requirements. However, in this study, where participants were asked, rather arbitrarily, to generate three designs, there was a ‘‘recency bias’’ in the sequential creation of alternative solutions. This bias may be related to fixation, in that participants may be constrained by the ideas they just generated (cf. Jansson and Smith 1991; Smith and Blankenship 1991). It may be useful for designers to know this—it is sometimes hard to determine where ideas have come from, and which parts of a design space still need exploring. In addition, such tools that provide the ability to search for the nearest possible match based on structural characteristics would be a boon for designers looking for alternative architectures for common problems. These matches might come from databases of old designs, or, as in our case, from the work of other designers working simultaneously.

Study 2: Replication The results described above, and our analyses using the new tools we have developed, show that systems designers use the affordances of the page, particularly position, proximity, and permanence, to convey important information about the problem and the proposed design beyond that needed to specify the formal solution (i.e., the systems diagram). Is it possible that the results from our first study were due to a set of participants who were exceptional in some way? To assess the stability and generalizability of our conclusions, we replicated the first study with a new class of students who participated 1 year later. Method Participants Forty students in a class in information systems architecture participated in the experiment. The class was taught by the same instructor using the same set of notes as in the previous experiment, but 1 year later. Twenty-eight of these students were male, 12 female. Thirty-two of the students were full-time students, and eight were part-time students. All but four students reported experience writing software, with 11 students claiming they had written more than 100,000 lines of code. Twenty students reported no design experience. Materials and procedures The materials and procedures were the same as used in the first experiment.

123

266

Results

Cogn Process (2013) 14:255–272

Participants produced similar diagrams as in the previous experiment: Fig. 9 shows three variations from one student. The last variation shows in one diagram the topology of the network, a map of the area, and a stack of the protocols. We analyzed all the student diagrams as we had in the first study.

median X and Y coordinates for each of five critical nodes (Fig. 10). Similar to the original study, the positions of the nodes fall in approximately the same positions, except that the GPS satellite is closer to the device in the replicated study than in the original study. The distances between these five critical nodes were compared to the distances between the same five critical nodes for the original study; the correlation was r = .88, indicating a high degree of correspondence in the use of distance in the solutions by these two populations.

Position

Proximity to represent hierarchy

The first analysis we conducted in this replication study looked at the median position of the nodes, where we calculated the

Figure 11 shows the hierarchical clustering of the nodes of the diagrams, based on median shortest-path distances

Example diagrams

Fig. 9 Three alternative diagrams from a student in the replication study

123

Cogn Process (2013) 14:255–272

267

Fig. 10 Median locations of five critical nodes in the replication study

between nodes in the diagrams. The results are similar to the original study (Fig. 8), with a few minor differences. Nodes 1, 2, and 7 {person, device, and GPS} cluster together as is seen in the first study. Nodes 9 and 10 are clustered together {map and Google}; however, instead of node 8, the store information, we see that node 36 {Borders’ website} is clustered with nodes 9 and 10. Upon further investigation, we noticed that nodes 36 and 8 represented a similar idea—information about the store accessed through the Internet—but were coded differently in the two studies. Finally, the last cluster of nodes 3, 4, 5, and 6 {store, coupon, item, and cash register} are all clustered together in the replication study as they were in the first study. The only node present in the first study that is missing here is the systems application node (node 12), probably a result of a different population of designers who described their designs with different vocabulary. Thus, we see some minor variations from the first to the second study, but the clustering is essentially the same. Proximity and the consensus design diagram

1

2

7

36

10

9

3

4

5

6

Fig. 11 Clustering of the median distances between nodes in the replication study

When we calculated the consensus solution for the diagrams, using the same method and thresholds as before, we found the resulting diagram to be very similar to the one created in the original study. Figure 12 shows the consensus diagram of the student solutions.

map

google

Borders’ website

item

store

device

cashRegister

coupon person

GPSsatellite

Fig. 12 Consensus graph, based on the median distance matrix in the replication study

123

268

As in the first study, there are three clusters {person, device, and GPS}, {map, Google, and Borders’ website}, and {item, store, cash register, and coupon}. The one major difference between the two studies is that a particular node, ‘‘point of sale,’’ drops out of this diagram. This is because very few participants used that particular description of the node in their sketches in the second study, instead focusing on the cash register. In order to confirm the prevalence across designers and designs of this hierarchical structure, we compared the mean distance of the edges between clusters to the mean distance of the edges within clusters. Out of 120 graphs, 36 did not contain pairs of edges that allow comparisons. Of the remaining 84, in 68 graphs, the mean distance between nodes within subsystems is less than the mean distance between nodes across subsystems, and in 16, the mean between-subsystem distance is less. The proportion of graphs that exhibit smaller within-subsystem distances than between-subsystem distances is significantly greater than chance by a sign test, z = 5.57, p \ .001. This result suggests again that the use of Euclidean space to delineate hierarchy is a common tendency and students largely agreed on how to cluster nodes into subsystems, and manifest this by separating the clusters from each other in space. Discussion The replication study confirmed the important findings from the first experiment. Even with a different participant pool, 1 year later, use of affordances of the page was similar, supporting the hypotheses.

General discussion: the affordances of marks and the page Designers routinely create diagrams to express and revise their designs. Diagrams serve as designers’ thinking tools. Diagrams for information systems provide an especially interesting platform for studying features of diagrams for design because information systems combine people, machines, and various kinds of information processing. They require representing both the concrete and the abstract. Here, we analyzed in detail the diagrams created by experienced information systems designers. The analyses of their diagrams showed that properties of the page and the marks on the page (see Tversky 2011a, b), notably paths, points, proximity, and position, were used to create meaning and affect interpretations, concrete, and abstract. The richness of the findings detailed above and described below was made possible by the tools we developed for summarizing and comparing network-like diagrams. The

123

Cogn Process (2013) 14:255–272

prevalence of network-like diagrams in communication and design should make these tools widely applicable, and the findings have implications for use of diagrams in design and in communication in general. Paths and points Two basic marks on the page are essential for network diagrams in general and for information design in particular, paths and points, corresponding to nodes and edges in networks and intersections and streets in maps. In information systems, points represent the components and paths represent the links among them. In fact, paths and points are the only essential affordance of the marks on the page, the means by which the long and complicated process of design negotiation is finally represented. Points represent individual system components by a single location, a dot that is in some sense the minimal representation of a physical object, thus a bridge between the physical and the abstract. Paths are afforded by the lines created by the instrument acting on the page. Because a line resembles a path, it is a natural way to express a link or connection or relationship between entities (Tversky et al. 2000). Paths are a common feature of diagrams, from diagrams of real spaces such as maps to diagrams of virtual or abstract spaces, such as information systems, organization charts, and social networks. Paths are the primary means of showing links, relationships, connections, real, or metaphoric. Proximity Interestingly, the other affordances of the page, proximity, position, and permanence, although not essential to the formal specification of a systems design, are routinely used by designers to capture the semantics of the situation to be designed. Those semantic features of the design problem seem to be represented in the diagrams because they capture essential characteristics of the design problem that make it easier for designers to think. For example, designers went beyond indicating the relations among components in their diagrams using points and paths. They also grouped sets of components into subsystems. The affordance of proximity was used by designers to chunk the system into subsystems. Grouping-related components expresses an important process in design, hierarchical organization (e.g., Egan and Schwartz 1979; Simon 1969; Wand and Weber 1993). Hierarchical organization is a basic feature of all cognition, not just design, for example, categorization (Rosch 1978), memory (Miller 1956), stories (Rumelhart 1980), and events (Zacks and Tversky 2001). When a conceptual space grows large, it is partitioned and grouped, partitioned into subcategories and grouped into larger ones. The designers’ diagrams

Cogn Process (2013) 14:255–272

demonstrate clearly that their categorization processes use diagrammatic space to separate categories. Grouping and subgrouping reduce memory load by reducing the number of units the thinker must keep in mind. Designers can and do manipulate each group as a unit, ignoring the subunits for the moment. Hierarchical organization is one of the abstraction processes in design so critical to becoming expert. The physical separation of clusters facilitates grouping and abstraction. Proximity is prevalent in many kinds of diagrams. Things that are conceptually closer are represented as spatially closer. Proximity is a basic feature of graph production and understanding, even in children (e.g., Tversky et al. 1991). Proximity affects reasoning even when it is not relevant; for example, in solving algebra problems, students operate on close units prior to distant ones even when the order of operation in no ways affects solution accuracy (Landy and Goldstone 2007). Proximity also affected reasoning in the case of information design presented here, especially in the creation of design variations. Moving a component from one subsystem to another sometimes corresponded to changing ownership of an important asset, changing the business model in profound ways. The properties of diagrams, then, may have deep links to the pragmatics of the system. Expert designers are likely to be adept at sensing which components can shift, and how the shift impacts the system. Position Although the positions of entities in systems diagrams are not constrained, designers located system components systematically, and in two dimensions. The vertical orderings served concrete organization, and horizontal orderings served abstract organization. For the most part, vertical location corresponded to vertical spatial location in the world and horizontal location corresponded left-to-right to temporal sequence in the information system, a fascinating combination of concrete aspects of the structure of the situation and abstract aspects of the performance of the system. Time is frequently represented linearly in graphs, diagrams, language, and gesture. For readers of Western languages, time is ordered horizontally left-to-right (Tversky 2011a, b). In both comprehension and production of diagrams of varying content, reading order provides a default ordering when no other ordering is present (e.g., Taylor and Tversky 1992; Tversky 2011a, b). Permanence Finally, the diagrams provided evidence for the influence of a fourth affordance of the page on design thinking, permanence. The persistence of a design on paper serves

269

several roles in design cognition. Permanence reduces memory load; the critical aspects of memory are abstracted and externalized relieving limited capacity working memory. This allows designers to use working memory for inferences and mental revisions. Permanence encourages reinspection, reconstrual, and redesign (e.g., Goldschmidt 1991; Scho¨n 1983; Tversky and Suwa 2009), all beneficial to design. But permanence, like many cognitive processes, also has a detrimental side. Permanence constrains the alternative designs that will be produced. Early design sketches can act as anchors that can potentially lead to fixation (e.g., Smith and Blankenship 1991). In fact, designers’ second designs were rooted in their first designs and their third designs rooted in their second. Given that most real-world design problems entail creating progressive design versions, the affordance of permanence is bound to affect the design process. Indeed, it has been observed that designers in the world tend to work a theme (Akin 2001). If designers do not stray far from their original designs, then their designs should cluster rather than being distributed more evenly in a design space, and the data also supported that. The aggregate graph showing the distances between all diagrams (Fig. 5) shows that collectively the designs of groups of designers tended to cluster around sets of solutions. A few designers did make extreme shifts, making it difficult to understand their work, but most designers generated only a moderate degree of change between alternatives. Would providing designers with designs of others promote a broader, and perhaps better, range of solutions? While recent experiments suggest that harnessing the wisdom of crowds can increase both the range and the quality of designs (Dontcheva et al. 2011; Dow et al. 2011; Maher 2010; Nickerson and Sakamoto 2010; Yu and Nickerson 2011, 2013), it remains an open question whether individual designers, shown the designs of others, might explore a design space more effectively. The aggregate design space highlights the behavior of crowds. It makes apparent that the crowd can generate more variations than an individual, and these variations might be of use to the solo designer or design teams. The results suggest the possibility of designing aids to promote reflective design and relieve fixation (cf. Redmiles and Nakakoji 2004) by combining human evaluative skills with the search and combinatorial skills of the computer. Such tools are different in nature from the typical Computer Aided Software Engineering (CASE) tool, because CASE tools tend to generate systems from requirements, removing designer choice, whereas reflective tools provide feedback on already-created designs. The reflective tool we envision could detect patterns of design, and evaluate distances between components and subsystems. The

123

270

evaluation of the effects of a design would remain with the human designer. Thus, the design tool would help the designer generate alternatives and see implicit similarities and differences, and the designer would evaluate the results. Each subsystem, human and computational, would take advantage of the affordances of the other. Tools of thought Design is an interaction between minds and the tools used to express the design. Designers use properties of the page and marks on the page: paths, points, proximity, position, and permanence, to work through their ideas. The design process is iterative, progressing from internal representations to external ones and back again. It seems inevitable that the external expression of thought affects the internal representations; in the case of design, that the affordances of the pencil on page affect design ideas. It is not that the page and its marks determine the design, but rather that the designer’s choices are guided by what is on the page, much the way that a hiker’s choices are influenced by the terrain. Design is perhaps inherently spatial, but spatial thought permeates abstract thought as well. Time is mapped onto space in language, diagram, and thought (e.g., Clark 1973; Lackoff and Johnson 1980; Talmy 2000; Tversky et al. 1991; Boroditsky 2000). Response time to judge the pleasantness or ferocity of animals depends on proximity and position (e.g., Banks and Flora 1977; Moyer 1973). Gestures, which have many of the same properties as diagrams, also use space to express ideas, spatial, and abstract (e.g., Goldin-Meadow 2003; Tversky et al. 2009). From birth, and perhaps earlier, people act in space and learn its properties, yielding rich knowledge of space. This knowledge can serve, in language, in gesture, and on the page, as a metaphoric base for abstract. Diagrams are the tools of design in general, and for information systems design in particular. Designers translate their internal representations to external representations on a page. They can then contemplate what they have produced and revise. Systems diagrams are topological, but they are embedded in a Euclidean space, a page. The qualities of the page provide affordances that are used to promote design thinking and serve to make designs clearer. These qualities can also constrain design. Designers use paths and points to express the essential core of information systems. Using other affordances of the page, they add information that is not critical to the design but that may aid designers in the creation and interpretation of their design diagrams. Here, designers used proximity on the page to group components into subsystems and separate clusters from each other. They used vertical position to reflect the spatial arrangement of components in the real world and horizontal position to reflect the temporal

123

Cogn Process (2013) 14:255–272

sequence of the components. Finally, they used the permanence of marks on a page to guide design of alternative configurations. Design is a product of the interaction of representations in the mind with representations on the page. Thus, the affordances and constraints of the page cannot help but shape the designs themselves. Cognitive tools, like diagrams and models, words, and gestures, are just that: tools. They both effect and affect thought. Whether they benefit or detract depends on how they are used. Acknowledgments This work has been supported by awards IIS0725223, HHC-0905417, IIS-0855995, and IIS-0968561 from the National Science Foundation, and by the Stanford Regional Visualization and Analysis Center.

References ¨ (2001) Variants in design cognition. In: Eastman C, Akin O McCracken M, Newstetter W (eds) Design knowing and learning: cognition in design education. Elsevier, Amsterdam, pp 105–124 Avital M, Lyytinen K, Boland R, Butler B, Dougherty D, Fineout M, Jansen W, Levina N, Rifkin W, Venable J (2006) Design with a positive lens: an affirmative approach to designing information and organizations. Commun Assoc Inf Syst 18:519–545 Banks WP, Flora J (1977) Semantic and perceptual processes in symbolic comparisons. J Exp Psychol Hum Percept Perform 3(2):278 Barthe´lemy M (2011) Spatial networks. Phys Rep 499(1):1–101 Booch G, Rumbaugh J, Jacobson I (2005) The unified modeling language user guide, 2nd edn. Addison-Wesley, Upper Saddle River, NJ Boroditsky L (2000) Metaphoric structuring: understanding time through spatial metaphors. Cognition 75(1):1–28 Carroll JM (2000) Making use: scenario-based design of human computer interactions. MIT Press, Cambridge, MA Casasanto D, Henetz T (2012) Handedness shapes children’s abstract concepts. Cogn Sci 36:359–372 Chatterjee A (2001) Language and space: some interactions. Trends Cogn Sci 5:55–61 Clark HH (1973) Space, time, semantics, and the child. In: Moore TE (ed) Cognitive development and the acquisition of language. Academic Press, NY, pp 27–63 Cooper WE, Ross JR (1975) World order. In: Grossman RE, San LJ, Vances TJ (eds) Papers from the parasession on functionalism. Chicago Linguistic Society, Chicago, pp 63–111 Donald M (1991) Origins of the modern mind. Harvard University Press, Cambridge Dontcheva M, Gerber E, Lewis S (2011) Crowdsourcing and creativity. CHI 2011: Crowdsourcing Workshop Dow S, Kulkarni A, Bunge B, Nguyen T, Klemmer S, Hartmann B (2011) Shepherding the crowd: managing and providing feedback to crowd workers. In: Proceedings of the 2011 annual conference on human factors in computing systems (CHI) Egan DE, Schwartz BJ (1979) Chunking in recall of symbolic drawings. Mem Cogn 7:149–158 Emmorey K (2001) Language, cognition, and the brain: insights from sign language research. Erlbaum, Mahwah, NJ Fish J, Scrivener S (1990) Amplifying the mind’s eye: sketching and visual cognition. Leonardo 23(1):117–126

Cogn Process (2013) 14:255–272 Floyd RW (1962) Algorithm 97: shortest path. Commun ACM 5(6): 345 Gick ML, Holyoak KJ (1980) Analogical problem solving. Cogn Psychol 12(3):306–355 Gick ML, Holyoak KJ (1983) Schema induction and analogical transfer. Cogn Psychol 15(1):1–38 Golden BL, Ball M (1978) Shortest paths with euclidean distances: an explanatory model. Networks 8(4):297–314 Goldin-Meadow S (2003) Hearing gesture: how our hands help us think. Belknap Press, Cambridge, MA Goldschmidt G (1991) The dialectics of sketching. Creat Res J 4(2):123–143 Goldschmidt G (1994) On visual design thinking: the vis kids of architecture. Des Stud 15(2):158–174 Hevner AR, March ST, Park J, Ram S (2004) Design science in information systems research. MIS Q 28(1):75–105 Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice Hall, Upper Saddle River, NJ Jansson DG, Smith SM (1991) Design fixation. Des Stud 12:3–11 Kaminiski JA, Sloutsky VM, Heckler AF, Sun R, Miyake N (2006) Effects of concreteness on representation: an explanation for differential transfer. In: Proceedings of the 28th annual conference of the Cognitive Science Society. Lawrence Erlbaum Associates, Hillsdale, NJ, pp 1581–1586 Kirsh D (2010) Explaining artifact evolution. In: Malafouris L and Renfrew C (eds) The cognitive life of things: recasting the boundaries of the mind. McDonald Institute for Archaeological Research, Cambridge pp 121–144 Kranjec A, Lehet M, Bromberger B, Chatterjee A (2010) A sinister bias for calling fouls in soccer. PLoS One 5(7). doi: 10.1371/journal.pone.0011667 Kruskal JB (1964) Nonmetric multidimensional scaling: a numerical method. Psychometrika 29:115–129 Lackoff G, Johnson M (1980) Metaphors we live by. University of Chicago Press, Chicago Landy D, Goldstone RL (2007) The alignment of order and space in arithmetic computation. In: Proceedings of the twenty-eighth annual conference of the Cognitive Science Society. Lawrence Erlbaum Associates, Hillsdale, NJ, pp 382–387 Liddell S (2003) Sources of meaning in ASL classifier predicates. In: Emmorey K (ed) Perspectives on classifier constructions in sign language. Lawrence Erlbaum, Mahwah, NJ, pp 199–220 Maass A, Russo A (2003) Directional bias in the mental representation of spatial events: nature or culture? Psychol Sci 14:296– 301 Maass A, Pagani D, Berta E (2007) How beautiful is the goal and how violent is the fistfight? Spatial bias in the interpretation of human behavior. Soc Cogn 25:833–852 Maher ML (2010) Design creativity research: from the individual to the crowd. In: Taura T, Nagai Y (eds) Design creativity 2010. Springer, London, pp 41–47 March S, Hevner A, Ram S (2000) Research commentary: an agenda for information technology research in heterogeneous and distributed environments. Inf Syst Res 11(4):327–341 Mayer RE (2001) Multimedia learning. Cambridge University Press, Cambridge Miller GA (1956) The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol Rev 63:81–97 Moyer R (1973) Comparing objects in memory: evidence suggesting an internal psychophysics. Percept Psychophys 13:180–184 Nickerson JV (2006) Teaching the integration of information systems technologies. IEEE Trans Educ 49:271–277 Nickerson JV, Sakamoto Y (2010) Crowdsourcing creativity: combining ideas in networks. Workshop on Information in Networks

271 Norman DA (1993) Things that make us smart. Addison-Wesley, Reading, MA Novick LR (1990) Representational transfer in problem solving. Psychol Sci 1(2):128 Oberlander J (1996) Grice for graphics: pragmatic implicature in network diagrams. Inf Des J 8(6):163–179 Oppenheimer DM, Trail TE (2010) Why leaning to the left makes you lean to the left: effect of spatial orientation on political attitudes. Soc Cogn 28:651–661 Pemmaraju S, Skienna S (2003) Computational discrete mathematics: combinatorics and graph theory with mathematica. Cambridge University Press, New York Peterson LL, Davie BS (2011) Computer networks: a systems approach. Morgan Kaufmann, Los Altos, CA Petre M, Green TRG (1993) Learning to read graphics: some evidence that ‘seeing’ an information display is an acquired skill. J Vis Lang Comput 4:55–70 Redmiles D, Nakakoji K (2004) Supporting reflective practitioners. In: Proceedings of the 26th international conference on software engineering (ICSE’04), pp 688–690 Rosch E (1978) Principles of categorization. In: Rosch E, Lloyd BB (eds) Cognition and categorization. Lawrence Erlbaum Associates, Hillsdale, NJ, pp 27–48 Rumelhart D (1980) On evaluating story grammars. Cogn Sci 4:313–316 Sanfeliu A, Fu KS (1983) A distance measure between attributed relational graphs for pattern recognition. IEEE Trans Syst Man Cybern 13(3):353–362 Scho¨n DA (1983) The reflective practitioner: how professionals think in action. Basic Books, Jackson, TN Schrepfer M, Wolf J, Mendling J, Reijers HA (2009) The impact of secondary notation on process model understanding. Lecture Notes in Business Information Processing, 39, part 5. Springer, pp 161–175 Schubert T (2005) Your highness: vertical positions as perceptual symbols of power. J Pers Soc Psychol 89(1):1–21 Schubert TW, Waldzus S, Seibt B (2008) The embodiment of power and communalism in space and bodily contact. In: Semin GR, Smith ER (eds) Embodied grounding: social, cognitive, affective, and neuroscientific approaches. Cambridge University Press, New York, pp 160–183 Simon HA (1969) The sciences of the artificial. MIT Press, Cambridge, MA Smith SM, Blankenship E (1991) Incubation and the persistence of fixation in problem solving. Am J Psychol 104:61–87 Sokal RR, Rohlf FJ (1962) The comparison of dendrograms by objective methods. Taxon 11:33–40 Suwa M, Tversky B (1997) What do architects and students perceive in their design sketches? A protocol analysis. Des Stud 18:385–403 Suwa M, Tversky B (2001) Constructive perception in design. In: Gero JS, Maher ML (eds) Computational and cognitive models of creative design. University of Sydney, Sydney, pp 227–239 Suwa M, Tversky B (2003) Constructive perception: a skill for coordinating perception and conception. In: Alterman R, Kirsh D (eds) Proceedings of the 25 annual meeting of the Cognitive Science Society. Cognitive Science Society, Boston, pp 1140– 1145 Suwa M, Tversky B, Gero J, Purcell T (2001) Seeing into sketches: regrouping parts encourages new interpretations. In: Gero JS, Tversky B, Purcell T (eds) Visual and spatial reasoning in design Sydney. Key Centre of Design Computing and Cognition, Australia, pp 207–219 Talmy L (2000) Toward a cognitive semantics. MIT Press, Cambridge, MA

123

272 Talmy L (2003) The representation of spatial structure in spoken and signed language. In: Emmorey K (ed) Perspectives on classifier constructions in sign language. Lawrence Erlbaum, Mahwah, NJ, pp 311–332 Talmy L (2005) The fundamental system of spatial schemas in language. In: Hampe B, Grady JE (eds) From perception to meaning: Image schemas in cognitive linguistics, Cognitive Linguistics Research 29. Mouton de Gruyter, Berlin/New York, pp 199–234 Taylor HA, Tversky B (1992) Descriptions and depictions of environments. Mem Cogn 20:483–496 Tversky B (1995) Cognitive origins of graphic conventions. In: Marchese FT (ed) Understanding images. Springer, New York, pp 29–53 Tversky B (2001) Spatial schemas in depictions. In: Gattis M (ed) Spatial schemas and abstract thought. MIT Press, Cambridge, MA, pp 79–111 Tversky B (2011a) Spatial thought, social thought. In: Schubert T, Maass A (eds) Spatial dimensions of social thought. Mouton de Gruyter, Berlin, pp 17–38 Tversky B (2011b) Visualizations of thought. Top Cogn Sci 3:499–535 Tversky B, Suwa M (2009) Thinking with sketches. In: Markman AB, Wood KL (eds) Tools for innovation. Oxford University Press, Oxford, pp 75–84

123

Cogn Process (2013) 14:255–272 Tversky B, Kugelmass S, Winter A (1991) Cross-cultural and developmental trends in graphic productions. Cogn Psychol 23:515–557 Tversky B, Zacks J, Lee PU, Heiser J (2000) Lines, blobs, crosses, and arrows: diagrammatic communication with schematic figures. In: Anderson M, Cheng P, Haarslev V (eds) Theory and application of diagrams. Springer, Berlin, pp 221–230 Tversky B, Heiser J, Lee P, Daniel MP (2009) Explanations in gesture, diagram, and word. In: Coventry KR, Tenbrink T, Bateman J (eds) Spatial language and dialogue. Oxford University Press, Oxford, pp 119–131 Wand Y, Weber R (1993) On the ontological expressiveness of information systems analysis and design grammars. Inf Syst J 3(4):217–237 Winograd T (1996) Bringing design to software. Addison-Wesley, Boston Yu L, Nickerson JV (2011) Cooks or cobblers? Crowd creativity through combination. In: Proceedings of the 2011 annual conference on human factors in computing systems (CHI) Yu L, Nickerson JV (2013) An Internet scale idea generation system. ACM Trans Interact Intell Syst 3(1). Art 2 Zacks J, Tversky B (2001) Event structure in perception and conception. Psychol Bull 127(1):3–21