International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-12, October 2019 Graph Theory in the Analysis of Arithmophobia A. Uma Maheswari, A.S.Purnalakshimi Abstract: In this paper, Graph theoretical concepts are applied 2. Dizziness to analyze the reasons behind Arithmophobia commonly found 3. Excessive sweating . among the students.Bull graph is used to epitomize Mild 4. Palpitation Arithmophobia which occurs when the preparation of students to 5. Inability to think clearly face any test is deficient.Flower graph is used to represent Intense 6. Sensational detachment from reality Arithmophobia. Wheel graph is used to depict the factors which desensitize Arithmophobia. Inferring information from these 7. Passive behavior types of graphs is much more easier than inferring from a self 8. Unwillingness to try map. This analysis will help in treating Arithmophobia and 9. Chest pain in very rare cases improve the student’s performance in Mathematics progressively. 10. A fully blown anxiety attack The benefits of using interactive graphical interface, graphs and graph theory metrics for a client centered analysis is also C. Analytical Process Flow discussed. A questionnaire with 12 simple questions were Keywords : Phobia, Arithmophobia, Desensitize. prepared and survey was taken from nearly 120 students.The questionnaire was prepared keeping in mind the causes of I. INTRODUCTION Arithmophobia mentioned above.The fact that is inferred from the survey that 98% of the students have Arithmophobia Graph theory originated ,way back in 1736 is one of the most is appalling. As kids the students are interested in interesting branches of Mathematics and serves as a tool to mathematics since it deals with only four operations uncover the nature of physical reality .Graphs are used to (addition, subtraction, multiplication and division )and is model many types of relationships, physical,biological quite different from their other theory subjects. Whereas as ,social and in information systems. This paper enables the they grow up to learn the mathematical concepts and their graph theory application to the technique of mapping the applications their fear for mathematics gradually pops up. causes for a psychological problem and use the same for the The students do not express fear when some information can therapy. Today’s generation is phobia stricken that they are be by hearted and reproduced. However the uncertainty of the unknowingly muted from moving towards success. A solutions before solving the problems in Mathematics is the detailed analysis and exploration is needed to illustrate the one which causes fear. causes of phobias in the place of self mapping. The most Students who are interested in mathematics at a young age commonly found phobias in present generation is start hating the subject when the teacher is not upto their Arithmophobia-(fear of numbers )which leads to phobia for satisfaction or the concept is too difficult to understand. Mathematics. Many students are humiliated in the class which leads to the GRAPH THEORETICAL FORMULATION IN THE fear of getting embarrassed in public and start hating the ANALYSIS OF ARITHMOPHOBIA subject. A. Causes of Arithmophobia: It is universally accepted that diagrammatic representation of Early Egyptians were the first to start keeping time and a situation helps in solar calendar when other cultures marked seasons and days 1. simplifying a large volume of complex data based upon lunar calendars. Hindu scholar Aryabhata gave 2. quick grasping the concept of zero and further rised to the fact that numbers 3. revealing the hidden facts are infinite and never ending. This led to the myth that 4. inferring information for further case studies etc numbers and computation are complex, unknown, varying and also difficult to grasp. The following are the causes for So graphs can be used to compile the information Arithmophobia. gathered through the survey on Arithmophobia and utilized 1. Genetic factors – Parent’s Arithmophobia in treating the affected persons. inadvertently passed to their children As a first step we segregate the sufferers( diffident to 2. Hallucination about complexity in Mathematics use the word patients) into two categories one with Mild 3. Traumatic events Arithmophobia and another with Intense Arithmophobia. 4. Fear of public embarrassment after low performance D. Causes for Mild Arithmophobia 5. Approach of teachers Mild Arithmophobia occurs when the preparation of students prior to assessments is not sufficient(which results B. Top Ten Symptoms of Arithmophobia in low confidence), when the person has fixed his/her goal to 1. Unusual nervousness aroused soon after thinking get a specific percentage or to score more than his/her peers. about mathematics. These causes for mild Arithmophobia can be expressed as a Revised Manuscript Received on October 05, 2019 bull graph . A. Uma Maheswari, Associate Professor,PG & Research Department “The bull graph is a simple graph on 5 nodes and 5 edges of Mathematics, Quaid-E-Millath Govt College for Women, Chennai-002. whose name derives from its A.S.Purnalakshimi, PG & Research Department of Mathematics, Quaid-E-Millath Govt College for Women, Chennai-600002. resemblance to a schematic illustration of a bull or ram Published By: Retrieval Number: L3812081219/2019©BEIESP Blue Eyes Intelligence Engineering DOI: 10.35940/ijitee.L3812.1081219 3637 & Sciences Publication Graph Theory in the Analysis of Arithmophobia (whose face is the triangle and horns are the graph's two the helm. A person with Arithmophobia should be dealt on bridges)”. the basis of 2 parameters one being his/herfocus and another E. Directed Bull Graph Showing the Causes for Mild his/her physiology. Here a flower graph with 10 vertices are Arithmophobia used. So it is denoted as Fl10 . V3 Lack of preparation Aim to score more than the V2 peers Fixes the mark V4 V5 lack of confidence V1- Mild Arithmophobia Fig 1 The following table gives a clear picture of how we relate the mapping with the graph . Table 1 Figure 2 (Self Mapping to show the reasons for MAPPING GRAPH Arithmophobia ) Causes Vertex Figure 2 depicts various factors which causes the intense Relationship Edge Arithmophobia.It is quite obvious that the picture will not Impact of each cause on the other Edge line weight in percentage directly help in treating the sufferer because all are just Number of impacts Degree of the vertex clustered around the phobia without showing the weightages Path to Arithmophobia Path in the graph of each cause .So it becomes mandatory that every time we Relationship incident on the map Edge incident on the vertex treat a cause ,we need to refer to the questioner .Whereas Cycle in the map Cycle in the cyclic graph when we make use of the graphs in Graph theory ,it no doubt Adjacent facts Adjacent vertices enables us to see the weightages and gives scope to treat the V1,V2,V3,V4,V5,are the 5 vertices of the bull graph .Vertices sufferer meticulously .Hence the flower graph is used for V1 to V4 represents factors which influences Arithmophobia . depicting the same . V1 –Mild Arithmophobia Flower Graph showing the root causes of Intense V – Aim to score more than the peers 2 Arithmophobia V3 – Lack of preparation V4 – Fixing of marks V Lack of Confidence Genetic factors Lethargy 5 – 푉 In the treatment of mild Arithmophobia ,the percentage of the 6 푉7 influencing factors can be taken as the weightage of the edges 푉2 푉3 and try to remove each horn in the beginning and gradually treat the rest .Treating the horns first emphasis on the removal Lack of interest Lack of confidence of the most influencing/dangerous factors and then we move 푉1 on to the less influencing factors .As all of us know 푉1 diagrammatic representations are the best to make a common Arithmophobia man understand anything and leaves a long lasting impact on the minds .The benefit of using the Bull graph is to give a very clear picture of the reasons that lead to Arithmophobia. 푉4 F. Causes for Intense Arithmophobia . Humiliation Perceptions Consider the root causes for Arithmophobia already 푉5 discussed above. If these causes act forcefully on the sufferer The table below shows 푉8 the then it is assumed to be intense Arithmophobia and this 푉9 factors assigned to each vertex situation needs immediate attention .Otherwise it not only Parent’s arithmophobia Fear of public . leads to low performance in Mathematics ,but low embarassment performance in other subjects too which needs computational skills. Figure 2 is a mapping which shows all the root causes of intense Arithmophobia, enabling us to prioritize and treat In the above flower graph ,the factors which influence the with ease. But the figure is quite complicated that inferring intense Arithmophobia is shown as vertices .The factors details from it becomes mind-numbing. So to make the perception ,lack of interest ,lack of confidence ,humiliation is diagram simple in figure 3, the causes are expressed as a a cycle graph .The perception flower graph .A flower graph Fln is the graph obtained from a about mathematics by helm by joining each pendant vertex to the central vertex of Published By: Retrieval Number: L3812081219/2019©BEIESP Blue Eyes Intelligence Engineering DOI: 10.35940/ijitee.L3812.1081219 3638 & Sciences Publication International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-12, October 2019 parents/peers leads to lack of interest in the subject .Lack of • Mingling with students who are good in mathematics: interest in the subject leads to lack of confidence through low Peer learning always helps the students to learn better . performance .This lack of confidence in answering or solving • Regular practice listening to music : TABLE 2 Listening to mild music while practicising mathematics VERTICES FACTORS ASSIGNED TO THE enables them to learn in a relaxed (phobia free) manner.