Divergent and Convergent Knowledge Processes on Wikipedia

Abstract: The paper presents a new theoretical consideration of knowledge processes bridging the individual and the collective level. Building on a differentiation between accommodation and assimilation of knowledge in wikis, we derive divergence and convergence from intelligence and creativity research and reconstruct their impact on the open-ended development of knowledge. The distinction from related CSCL constructs is elaborated. Using examples from Wikipedia, the definition of divergence and convergence is illustrated in the dynamic context of article development. p. 1

Artifacts such as explicit ideas at the same time mediate and coordinate the interaction between collaborators. The exact knowledge processes between individuals and mediating collaborative artifacts are addressed by the co- evolution model (Cress & Kimmerle, 2008) transferring some of Piaget’s (1983) ideas to the context of social software and wikis in particular. Knowledge incongruities between the mediating artifact system of a wiki and the cognitive systems of its users are suggested to create a cognitive conflict that is resolved through the processes of assimilation and accommodation. Assimilation means that new information is received and customized to fit the prior knowledge. Accommodation, accordingly, means that new information leads to structural changes of the prior knowledge. The predicted outcome of the model is individual learning – internalization – or a change of the information in the wiki – externalization. p. 1

“Knowledge creation” models deal, compared to the other two metaphors, in the most explicit way with the interaction between individual and collective knowledge. They are best suited to give a more accurate account of how collective knowledge emerges from the collaboration of a large number of individuals. This form of collaboration has become more common as a result of the emergence of Web 2.0 technologies, with Wikipedia being the most remarkable example (Halatchliyski, Moskaliuk, Kimmerle, & Cress, 2010). We consider the postulated equivalence of assimilation and accommodation processes at individual and collective level as a very interesting research question for CSCL. In this paper, we will elaborate on the equivalence, introducing the processes of divergence and convergence as complementary to the assimilation-accommodation perspective. We will explain the origins of the concepts and differentiate our understanding against other usages of these terms in the field of learning sciences. p. 1

Regarding the perspective of an individual, the convergence and divergence opposites were first described by Guilford (1950). He later included them as dimensions of thinking into his model of intelligence (Guilford, 1967) contrasting the identification of a single correct solution to a problem with the generation of many different possible alternatives. At about the same time, Hudson (1966) described the opposites as different cognitive styles, correlating with the different abilities of students in science and arts. This started a controversy about the connection of both styles with intelligence and creativity. Convergers were described as people who tend to analyze systematically, evaluate critically and deduce logically one feasible solution. Divergers were supposed to be intuitive explorers of ideas in multiple frames. Later it was concluded that these styles were not a stable personal characteristic and better seen as modes of thinking (Robertson, 1985). Creativity researchers also p. 1

acknowledged the need to achieve a balance between both complementary modes in order to obtain relevant and, at the same time, original solutions or products (Levine & Moreland, 2004). p. 2

Convergence and divergence have also been discussed in the context of group creativity and decision making. Brainstorming and other creativity techniques are widely applied and aim at facilitating divergent thinking and development of innovative ideas. Otherwise, the full solution to a problem often demands the choice and implementation of a single best idea. Janis (1982) has shown that this process of convergence in groups may be very erroneous, coining the term groupthink. p. 2

Creative processes in groups have a long tradition of being divided into divergent and convergent phases (Finke, 1992). In the context of CSCL, Onrubia and Engel (2009) noted that many researchers have also defined various numbers of stages of the joint creation of knowledge. Convergence is supposed to occur at a later moment after people have shared knowledge, identified differences and negotiated common understanding. Fischer and Mandl (2005) found that convergence is beneficial to learning. p. 2

The reason why more attention is paid to convergence than divergence is the view that constructing shared understanding is the main goal of collaborative learning (cf. Roschelle, 1992). A knowledge building discourse is not an argumentative debate, where people try to defend different opinions, but it aims at collaboratively advancing ideas and reaching commonly accepted solutions to problems (Scardamalia & Bereiter, 2006). p. 2

The above results apply best in those settings in which small groups of people collaborate on solving a restricted problem with constraints on time, goals, or solution approaches. Observations in different settings (cf. Liu & Wang, 2010) show that convergence and divergence can repeatedly occur and complement each other during different stages of group interaction. Jorczak (in press) also challenged the idea that convergence alone is beneficial for learning. He emphasized the need for cognitive conflict within and among group members based on divergence, so that improved learning and knowledge can be achieved upon conflict resolution. Another recent analysis of knowledge building in school classes (Zhang & Messina, 2010) confirms the equivalent importance of both the accumulation of variable ideas as well as their critical examination. p. 2

The co-evolution model (Cress & Kimmerle, 2008) offers a good theoretical starting point, as it is geared to the learning context of wikis. It describes assimilation and accommodation as two processes of adaptation of an individual or a wiki, following the experience of a cognitive conflict. Referring to wikis, assimilation is defined as the addition of information at a suitable place, without establishing new connections that would change the structure of the wiki. Accommodation means a distinct change of the knowledge organization through rearrangement of paragraphs and pages, which results in a new focus. Both processes are compatible, often appear together and concern the question of structural changes in the wiki (Moskaliuk, Kimmerle, & Cress, 2009). p. 2

Divergence and convergence, the processes in the focus of the current discussion, are not derived from Piaget’s theory, and represent a different categorization of knowledge creation. So the essence of divergence and convergence shows itself not in the way how new information is integrated – as in the case of assimilation and accommodation –, but in the qualities of this new information, compared to the available knowledge. So we see these two categorizations of processes as independent from each other. p. 2

We define the characteristics of the new processes in a wiki on the lines of the definition of divergent and convergent thinking at an individual level. Divergence is present when a new idea is added that opens a new direction for addressing the problem of a specific article page. This may be new information that cannot be categorized under the available viewpoints, an alternative explanation, or it may be a new way of describing the issue. Convergence refers to acts based on critical evaluation and logical reasoning. Here, the result is not so much the addition of new aspects as the establishment of a coherent structure of the presentation. This may be done by subsuming some of the new or already available major points under a common category, through abstracting a model or principle, or through eliminating a conflicting issue. Some actions, like corrections of simple mistakes, may not be categorized in this schema, and some other actions may contain elements of both processes. The categorization may also be applied to analyses with different granularity, for example, at the level of an article, at the level of a connected group of articles like a wiki category, or at the level of a whole knowledge domain like a network of categories and articles. Complex actions may be both converging and diverging at different levels at the same time. For example, the movement of a section from an existing article into a new article would represent a convergence for the old article and a divergence for the set of articles that both the old and the new article belong to. This new categorization schema is not a substitute for the accommodation-assimilation perspective. A single change may, for example, be a case of accommodative restructuring that resolves a conflict in a wiki, and at the same time it may be classified as divergence or convergence or neither of these. Using dynamic social network analysis, Kimmerle, Moskaliuk, Harrer und Cress (2010) have given an example of high level processes concerning a set of articles about schizophrenia. The researchers identified accommodative p. 2

reorganization of clusters of article on different explanatory approaches to the mental disorder. Articles on two of the approaches merged into one tightly interconnected cluster – in our view another example of a higher- order convergence process. As with the assimilation-accommodation dichotomy, we describe here two complementary processes regulating the development of both individual and collective knowledge. In the following section we will provide an illustration of the differentiation between assimilation, accommodation, divergence and convergence, using the edit history of the English Wikipedia article on Knowledge (1). p. 3

The following examples are reported chronologically and reflect the starting period of the article Knowledge. Each case is chosen to show one of the eight possible occurrences of the independent categories, assimilation, accommodation, divergence, convergence, and their combinations. p. 3

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