A Network Model of Knowledge Acquisition Idea 1: a learner must thoughtfully develop a conceptual framework for their new knowledge. Idea 2: recent research in network science leads to an understanding of the structure and dynamics of networks. Networks for diverse systems share a set of common characteristics. If one assumes that acquired knowledge forms a network, then it should share these common characteristics 13th International Conference on Thinking

A key finding of “How People Learn” To develop competence in an area students must: have a deep foundation of factual knowledge, b) understand facts and ideas in a context of a conceptual framework and c) organize their knowledge in ways that facilitate retrieval and application.” 13th International Conference on Thinking

Transformation of students Adaptive Expertise “Flexible Thinking” The most powerful learning occurs when we move away from inert knowledge and towards flexible thinking. Mental Structure (Context And Organization) Routine Expertise “Inert Knowledge” Novice Expert Knowledge Adapted from John Bransford and the “Center for Learning in Formal and Informal Environments”. 13th International Conference on Thinking

13th International Conference on Thinking

Characteristics of networks What do you measure when you study a network? Average length (on connected components) Cluster coefficient Degree distribution Number of Links (k) Number of Nodes (with k Links) 13th International Conference on Thinking

Three important steps in the development of network science 1950’s Paul Erdös and Alfréd Rényi Random Network 1990’s Duncan Watts and Steve Strogatz Small World Systems 2000’s Albert-László Barabási, Reka Albert and Hawoong Jeong Scale-free Networks 13th International Conference on Thinking

13th International Conference on Thinking Random network Nodes are linked together at random. This figure has 300 nodes initially distributed around a circle and then connected in pairs at random This figure was generated using software developed by Uri Wilensky of Northwestern University and is incorporated in NetLogo: http://ccl.northwestern.edu/netlogo/models/. 13th International Conference on Thinking

13th International Conference on Thinking Small world network (a) (b) From D. J. Watts and S.H. Strogatz, “Collective dynamics of ‘small world’ networks”, Nature, Vol. 393, No. 4, pp 440-442 (1998). 13th International Conference on Thinking

13th International Conference on Thinking Scale-free network Network is formed by introducing new nodes connected with “preferential Attachment” This figure was generated using software developed by Uri Wilensky of Northwestern University and is incorporated in NetLogo: http://ccl.northwestern.edu/netlogo/models/. 13th International Conference on Thinking

Degree distribution Many nodes have this number of links Number of Links (k) Poisson Distribution Number of Nodes (with k Links) A few nodes have the min A few nodes have the max 13th International Conference on Thinking

Scale-free degree distribution A large number of nodes with few links Number of Links (k) Pareto Distribution Number of Nodes (with k Links) A small number of nodes with many links the hubs 13th International Conference on Thinking

13th International Conference on Thinking Some networks studies Network Size Average Length Cluster Coef. Scale Free Movie Actors 225,226 3.65 0.79 2.3 Math. Co – authorship 70,975 9.5 0.59 2.5 WWW 3325,729 11.2 0.11 2.26 Silkwood Park Food Web 154 3.4 0.15 1.13 C. Elegans 282 2.65 0.28 – Words: Synonyms 22,311 4.5 0.7 2.8 Power Grid 4,947 0.08 13th International Conference on Thinking

Network of acquired knowledge Knowledge Network – each “bit” of knowledge can be considered a node – bits are linked together in a network. – individual (like fingerprints) How does it develop? 13th International Conference on Thinking

13th International Conference on Thinking Novice learning Each bit of new knowledge is indistinguishable from others Joined at random to already existing bits Degree distribution is Poisson Distribution so there is a maximum number of links per node. 13th International Conference on Thinking

13th International Conference on Thinking Middle learning Some order begins to emerge but randomness remains Degree distribution is nearly a Poisson Distribution so there is a maximum number of links per node. 13th International Conference on Thinking

13th International Conference on Thinking Expert learning Hubs begin to appear as centers of organization Degree distribution is a Pareto Distribution so there is no limit to the number of links per node. 13th International Conference on Thinking

Evolution of knowledge organization Novice Learning stages flooding of independent and indistinguishable facts, linked at random network is featureless with no organization, Poisson degree distribution implies limits to number of links for any node Middle Learning stages as relationships among facts are observed information begins to cluster randomness is replaced with order, leading to a small world structure Expert Learning Stages thoughtful organization creates hubs and a scale free network Pareto distribution implies no limit to facts linked to a hub this is the transition advocated in “How People Learn” 13th International Conference on Thinking

Development of a knowledge network Middle Learning Novice Learning Expert Learning Small World Network Scale Free Network Random Network Structureless Clusters Hubs Bounded range Bounded Range Unbounded Range 13th International Conference on Thinking

How this influences learning ... Learners now – have a model of how the organization of knowledge evolves can assess their level of organization of knowledge can guide the improvement of their organization of concepts can discuss conceptual structures with others 13th International Conference on Thinking

13th International Conference on Thinking Understand the importance of learning for transfer the organization of acquired knowledge is a complex network which crosses disciplines Understand the importance of assessing learners prior knowledge new learning is linked to what is known 13th International Conference on Thinking