1. 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

2. 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

3. 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

4. 13th International Conference on Thinking

5. 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

6. 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

7. 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:
13th International Conference on Thinking

8. 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 (1998).
13th International Conference on Thinking

9. 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:
13th International Conference on Thinking

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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