The "flat peer learning" agent-based model

Abstract

This paper deals with peer learning and, in particular, with the phenomena of exclusion; it proposes to model a group of learners where everyone has his own behaviour that expresses his way of following a curriculum. The focus is on individual motivations that avoid disadvantage certain individuals while optimising behaviour at the community level; in this context, the approach is based on the belief that the induced learning dynamics can be clarified by the contribution of agent-based modelling and its entry into the field of peer learning simulation. Flat learning means here that every learner features the same initial skill level, along with the same opportunities to learn both independently and with the help of peers. To address this topic the paper proposes the Flat Peer Learning agent-based computational model inspired by the Vygotsky's social and learning theory. The paper shows that even if strict equity could be guaranteed, educators would still be faced with the dilemma of having to choose between optimising the learning process for the group or preventing exclusion for some.

Keywords: Multi-agent-based modelling; Peer learning; Social exclusion.

Fig. 1

Independent learning alone: influence of the probability p $M=1024$; $L=50$ (mean over 1000 runs)

Fig. 2

Lattice network: learning-time distributions (Normal distribution in red). $M=1024$; $L=50$; $p=0.3$; $q=0.3$; $\delta \in \{1;4;7;10\}$ (significant runs)

Fig. 3

Lattice network: ZPD vs. MKO with $M=1024$; $L=50$; $p=0.3$; $q\in \{0;.1;.2;.3;.6\}$ (mean over 100 runs). The gain in learning-cost decreases with $\delta$ to reach a value close to zero; if $q<0.6$, the gain in exclusion-cost first increases with $\delta$ up to a maximum, then gradually decreases

Fig. 4

A scale-free network. $M=1024$; $\gamma \approx 2.4$; max-$degree=75$ (learner node-size is correlated to degree)

Fig. 5

Scale-free network: learning-time distributions (Normal distribution in red). $M=1024$; $L=50$; $p=0.3$; $q=0.3$; $\delta \in \{1;5;10;15\}$ (significant runs)

Fig. 6

Scale-free network: ZPD vs. MKO with $M=1024$; $L=50$; $p=0.3$; $q\in \{0;.3;.6;.8;.95\}$ (mean over 100 runs). The gain in learning-cost decreases with $\delta$ to reach a value close to zero for $\delta =20$; if $q<1$, the gain in exclusion-cost first increases with $\delta$ up to a maximum, then gradually decreases

Fig. 7

Scale-free network: learning-time vs. degree with $M=1024$; $L=50$; $p=0.3$; $q\in \{.3;.6;.8;.9\}$; $\delta ={\delta }_{\min }=1$ (Four significant runs). red line = mean learning-time; blue lines = mean + 0.99 $\times$ standard deviation and mean - 0.99 $\times$ standard deviation

Fig. 8

Scale-free network: learning-time vs. degree with $M=1024$; $L=50$; $p=0.3$; $q=0.6$; $\delta \in \{1;5;10;20\}$ (Four significant runs). red line = mean learning-time; blue lines = mean + 0.99 $\times$ standard deviation and mean - 0.99 $\times$ standard deviation

Fig. 9

Scale-free network: level vs. time for hubs (blue points; degree $\ge$ 30) and leaves (red points; degree = 1). $M=1024$; $L=50$; $p=0.3$; $q=0.6$; $\delta \in \{1;5;10;20\}$ (significant runs)

Fig. 10

3-D Snapshot of the scale-free population at a given time during the learning process (z-axis represents the level and node-size is correlated to degree). $M=500$; $p=0.3$; $q=0.95$ (Two significant runs)