Solving Network Theory Problems
According to Barker and Kemp (2011), teaching network theory is one of the most challenging tasks in the education sector. Network theory refers to a study of complex graphs either as a representation of asymmetric or symmetric relations between discrete objects. In network theory, a network is referred as a graph in which the nodes or the edges have distinguishing characteristics like names. Network theory can be applied in many disciplines like finance, engineering, economics, biology, and operation research among others. Network theory provides various mechanisms for analyzing graphs and providing solutions to complex problems. In the education setup, students are frequently encountered with new networking and applications problems in their day to day experiences (Barker & Kemp, 2011),
As such, students studying these courses are expected to understand the concepts as well as the application of network theory so as to be able to solve the network theory problems. However, there are various difficulties or challenges that students face when solving network theory problems. This article will discuss the difficulties experienced by the students while solving network theory problems.
When solving network theory problems, students will be faced by the following difficulties;
Inadequate diagrammatic representation
Katz (2014) argues that use of diagrammatic representations play a significant role in solving network problems, Network theory educators strongly advocate for the use of diagrams or graphs when solving a network problem. Educators argue that use of graphs and diagram is an effective way of solving network theory problems because they meaningfully exploit spatial layout, thus enabling holistic representation of complex structures and processes. However, some students find difficulties in generating a diagrammatic representation of the problem. Additionally, in adequate diagrammatic representations can mislead students when solving the problems. As such, to ensure accurate solutions when solving network theory problems, students need to ensure that diagrammatic representations generated are accurate and complete.
Interpretation of the diagrammatic representations
The application of network theory largely depends on the accurate interpretation of diagrams and graphs prepared by the students. Poor interpretation of the diagrams and graphs will lead to students arriving at an inaccurate conclusion. Research shows that a majority of the students lack adequate knowledge and skills to interpret graphs and diagrams accurately when solving network theory problems. The inability of the students to accurately interpret diagrams and graphs when solving network theory problems is associated with their lack of mathematical knowledge and understanding (Granovetter, 2013). As such, knowledge and understanding of the mathematical concepts play a crucial role in overcoming difficulties experienced by students when applying network theory.
Practical application of the theory in real life cases
The purpose students being taught the concepts of the network theories is to be able to apply these concepts to solve practical problems they face in their day to day experiences (Granovetter, 2013). Granovetter (2013) argues that the ability to apply network theories in solving practical solutions is facilitated by the capability of the students to precisely understand the theory concepts and the understanding of these concepts in students own approach. It can be achieved by not only discussing the theoretical aspects and concepts of the theory but also through actual discussion of the practical cases and real-life examples. However, students find difficulties in relating and applying network theory concepts to solve practical problems because they were mostly taught the theoretical aspects and concepts of the theory and not how to apply the theory in real life situations. Therefore, to better equip students to apply network theory concepts in solving problems, educators need to ensure that more time is not spent in theoretical concepts at the expense of discussing practical application of the theory.
Analyzing relationships between units
According to Havlin and Kenett (2010), network theory is based on the relationship between different units in the network. As such, students need to be able to properly analyze the relationship that exists between different units in the network to accurately solve network problems. When using network theory to solve a problem, the focus ought to be on the relationship that exists between units rather than the unit's intrinsic characteristics or the specific units. It is not possible to properly understand the relationship between units in a diagram or graph in isolation and therefore, the ability of the students to analyze the relationship between units in the graph as a whole will lead to accurate results. As such, students usually find difficulties analyzing the relation between the units in the diagrammatic representation when solving network theory problems.
Predicting the results of the assumptions made and ensuring inaccurate assumptions do not affect the result's analysis
The complex nature of the network theory problems usually requires some diagrammatic representation or modeling. Various assumptions are made when constructing a graph or model. As such, the application of network theories relies on the exponential assumptions (Havlin & Kenett, 2010). Havlin and Kenett (2010) further claim that though these assumptions may be considered unrealistic, they are important for mathematical tractability. When applying these assumptions in the application of the network theories, students have the responsibility of ensuring that the inaccurate assumptions made do not affect the result of the analysis or ensure that the effect is justifiable as well as predictable. However, students find difficulties in determining the predictability of these assumptions and justifying the assumptions made.
The application of network theories plays a significant role in solving day to day problems people or organizations face, However when applying the network theories; there are certain difficulties and challenges that people and students face. Often, students face many challenges like inadequate diagrammatic representations, inability to practically apply the theory in practical situations, inability to analyze the relationship between units, inability to interpret graphs and models and the selection of the correct assumption when solving the network theory problems. These difficulties are associated with student's lack of practical application of the theoretical concepts as well as inadequate mathematical knowledge and skills. As such, network theory educators need to ensure students not only understand the theoretical aspects and concepts of the theories but also can apply these concepts to real-life problems. Therefore, educators should balance the time spent in teaching the theoretical concepts and time spent in analyzing practical situations, as well as help students, improve their mathematical knowledge and skills to help them overcome these difficulties.
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