13th International Conference on Thinking

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:

a) 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

Knowledge

Mental

Structure

(Context

And

Organization)

Novice Expert

Routine Expertise

“Inert Knowledge”

Adaptive Expertise

“Flexible Thinking”

Adapted from John Bransford and the “Center for Learning in Formal and Informal Environments”.

The most powerful learning occurs when we move away from inert knowledge and towards flexible thinking.

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)

Num

ber

of

Nodes

(wit

h k

Lin

ks)

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

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

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

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

Number of Links (k)

Poisson Distribution

Num

ber

of

Nodes

(wit

h k

Lin

ks)

Many nodes have this number of links

A few nodes

have the min

A few nodes

have the max

13th International Conference on Thinking

Scale-free degree distribution

Number of Links (k)

Pareto Distribution

Num

ber

of

Nodes

(wit

h k

Lin

ks)

A large number of

nodes with few links

A small number of nodes with many links

the hubs

13th International Conference on Thinking

Some networks studies

Network SizeAverage Length

Cluster Coef.

Scale FreeCoef.

Movie Actors

225,226 3.65 0.79 2.3

Math. Co –

authorship70,975 9.5 0.59 2.5

WWW 3325,729 11.2 0.11 2.26

Silkwood Park Food

Web154 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 2.65 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

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

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

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 organizationNovice 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

Poisson degree distribution implies limits to number of links for any node

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

Structureless Clusters Hubs Bounded range Bounded RangeUnbounded Range

MiddleLearning

Novice Learning

Expert Learning

Small World Network

Scale Free Network

Random Network

Development of a knowledge network

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

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