Can interaction among students act as a proxy to their grades?

Motivation:

Understanding the interaction among students have always been an area of interest among the educators who want to improve the overall productivity of students and reduce the drop-outs from schools and colleges by identifying the "groups at risk". There have been several works upon who the student interacts with, how and when they do it and outcome of the interactions. An interesting study on such temporal network was performed by Luis Vaquero and M. Cebrian in the paper where they identified the interaction among high and low performing students at academics. They did their experiments on dataset involving 80k online interactions among 290 students in Basic Computer Skill Course at Spanish University.

Results:

1. Diversity and Assortativity analysis :
 The social diversity, the interactions among individuals among different groups, was found to be negatively co-related to the performance. This tells us that high performing students do not have much diverse interactions as can be realized in our own class-room. Secondly, the assortative missing was observed where students have a preference to bind to similar students.

Figure shows a graph of one of the analysed courses including 82 students at the end of the last week of the course. Continuous thick blue edges indicate persistent interactions while dotted thin grey edges indicate transient interactions. High performing students are shown in dark blue, mid performing ones in red and low performing ones in green. As can be observed, high performance students form a ‘‘core’’ where the highest density of persistent interactions can be observed. Low performance students remain in the periphery of the graph, mainly holding transient interactions. 

Granovetter's proposed 'strength of weak ties' phenomenon is observed in this case in which isolated ties by poor performing students offer limited access to external prospect while heterogeneous ties formed by better performing students allow them to diversify their opportunities. We can also observe this effect in social sites like LinkedIn where people rely upon weak connections to increase their opportunities.
2. Persistent Interaction Analysis :
 This method involved analysis of persistent interaction( the interactions that continue above a threshold time) to transient ones involving fewer exchanges. The authors used Pearson correlation among grades and the persistent interaction to form a conclusion that the number of interaction and the number of connections are positively correlated to one another. This tells us that high performing students are involved more in persistent interaction as opposed to low performing ones who seldom interact and interact for shorted durations.

3. Information Cascade :

There information flow in social network is analysed to understand the small subcomponents of graph that influence its dissemination. For the interaction network the underlying cascades for A) low and B) high performing students was found to be remarkably different being more complex in high performing students as one could intuitively expect.
4. Temporal Analysis :

Probability density distribution of the number of iterations (A) and connections (B) per group in one of the courses being analysed. 



As expected the number of iterations and connections among low performing student declines with time. This can be attributed to lack of interest or extra -academic activities among such students.

Inference :

The most prominent results of the above analysis was the formation of rich club (set of nodes with degree larger than k that tend to be more densely connected among themselves than the nodes with degree smaller than k) among high students performing students during the initial weeks and persistent interactions among them over the time and involves complex cascades for sharing the information among them. However, low performing students generally tend to form transient/ temporary interactions and have large social diversity. They start their interactions late and hence are not reciprocated well from the rich club members already formed. This can give an insight to educationalist to identify these groups and modify their curriculum or course structure to ensure that such students do not fall apart during the most important initial weeks. In conclusion, we can use simple observations of network to solve some of the greatest problems of our lives.

Sources:
Paper : Luis M. Vaquero & Manuel Cebrian, Rich club phenomenon in classrooms.
Paper : Mark S. Granovetter, the strength of weak ties.
Blog : Online social networking, the strength of weak ties. 
Some other sources from internet.