Three  factors  that have been considered to influence mathematics learning outcomes are anxiety,

self-efficacy and positive attitudes. Those have correlation each other. The analysis between the three factors

is usually carried out using the pearson correlation concept where the data used is the crisp data. The fuzzy

correlation is an attempt to provide an alternative in analyzing the correlation between two variables and the

data used is fuzzy data. The data was collected from 1063 respondents through fuzzy instruments. The

advantage of this instrument is that crisp and fuzzy data can be obtained immediately. Data analysis is done

using pearson and fuzzy correlation. The results reveal several facts, those are: fuzzy data provides a more

flexible and real conception,  anxiety with self-efficacy has a negative correlation at a low level, anxiety with a

positive attitude of students have a negative correlation at a low level, self-efficacy with a positive attitude has

a moderate positive correlation, fuzzy correlation coefficients in the form of fuzzy interval numbers provide an

advantage in decision making

Anwar, Mallongi

Hafidah, A. S.

Muhith, Abdul

Susanto, H. P.

Sutarti, Tatik

English

University of Nahdlatul Ulama Surabaya Repository

Journal of Engineering and Applied Sciences 14 (7): 2340-2344, 2019ISSN: 1816-949X© Medwell Journals, 2019Corresponding Author: Tatik Sutarti, STIKIP PGRI, Keyen, Pacitan, Indonesia2340Evaluating Anxiety, Self-Efficacy and Positive Attitude CorrelationTowards Mathematics Through Fuzzy Correlation UtilizationTatik Sutarti, H.P. Susanto, A.S. Hafidah, Muhith Abdul and Mallongi Anwar1   1   2   3    4STIKIP PGRI Pacitan, Keyen, Indonesia1Department of Public Health,2Department of Nursing, STIKes Majapahit Mojokerto, Mojokerto, Indonesia3Department of Environmental Health, Faculty of Public Health,4Universitas Hasanudin, Makasar, IndonesiaAbstract: Three  factors  that have been considered to influence mathematics learning outcomes are anxiety,self-efficacy and positive attitudes. Those have correlation each other. The analysis between the three factorsis usually carried out using the pearson correlation concept where the data used is the crisp data. The fuzzycorrelation is an attempt to provide an alternative in analyzing the correlation between two variables and thedata used is fuzzy data. The data was collected from 1063 respondents through fuzzy instruments. Theadvantage of this instrument is that crisp and fuzzy data can be obtained immediately. Data analysis is doneusing pearson and fuzzy correlation. The results reveal several facts, those are: fuzzy data provides a moreflexible and real conception,  anxiety with self-efficacy has a negative correlation at a low level, anxiety with apositive attitude of students have a negative correlation at a low level, self-efficacy with a positive attitude hasa moderate positive correlation, fuzzy correlation coefficients in the form of fuzzy interval numbers provide anadvantage in decision making.Key words: Anxiety, self-efficacy, positive attitude, mathematics, fuzzy correlation, decisionINTRODUCTION researches  have  reached  the  conclusion that  theA marriage between psychological factors and and has positive attitudes towards mathematics as well asmathematics is still an inspired or even minor issue in a positive correlation to negative attitudes. Furthermore,education.   Some    of    the    psychological   factors self-efficacy has a positive correlation with a positivewhich   influence   mathematics   learning   are   first,  math attitude and has a negative correlation with a negativeanxiety  (Ashcraft and Kirk, 2001; Ashcraft,  2002). attitude. These three factors were analyzed usingFurther, the negative  effects  caused  by    the  anxiety analytical  pearson   correlation   (Recber   et   al., 2018;can result in a reduction of student’s memory. Then, it Akin and Kurbanoglu, 2011).effectuates the test they face. They  will  be  difficult  to Pearson  correlation  is  a  probability  concept baseduse the obtained information in completing the tests. statistical analysis. It is not able to explain the correlationSecondly, mathematics self-efficacy (Kundu and Aditi, between   detailly   analyzed  variables (Coppi, 2008).2016). Self-efficacy is an individual’s belief in the ability to Therefore, the fuzzy concepts provide an alternative to besolve problems faced. Good self efficacy can reduce the used in the process of data analysis because of its severalanxiety arising in students (McGrath  et al., 2015; Lee, advantages statistics do not have (Chi et al., 1996), those2009; Hoffman, 2010). Third, the  attitude  of  students are not dependent upon randomization, able to analyzetowards mathematics (Zan and Martino, 2007). The the crisp and fuzzy data able to explain in which statisticsattitudes toward mathematics can be either a positive or cannot, able to model problems easily, more flexible tonegative emotions towards mathematics (Zan and easify the use of expert knowledge.Martino, 2007). A positive attitude towards mathematics Fuzzy correlation develops as an alternative tohas a positive influence on mathematics learning pearson correlation analysis. Fuzzy correlation with theoutcomes while a negative attitude is vice versa. As such expected interval method (Hung and Wu, 2001) usesthese three factors have a close correlation to each other interval data. While fuzzy correlation with centroid(Recber et al., 2018; Akin and Kurbanoglu, 2011).  The method (Hanafy et al., 2013) uses fuzzy neutrosophicanxiety  has  a  negative  correlation with the self-efficacy*i 1i 2?ex [a a ].= +* 1i 1ii 1i 2ia ax a ,a .2+é ù= ê úë û[ ] [ ][ ] [ ][ ][ ] [ ][ ]* *1 11 21 2 12 22* x1 2 11 21 12 2211 12 21 22* *1 2 11 21 12 2211 12 21 22x a , a dan x a , a( ) a , a a , aa a , a , ax x a , a a , aa a , a a= =b + = ++- = -- -*i 1i 2ix [a , a ], i 1,2, ... , n=n n1i 2ii 1 i 1*a ax ,n n= =é ùê ú=ê úë ûå å*1 2 n 1 2 nMe [Me{a ,a , ... , a }, Me{b ,b , ... , b }]=1-3 n 1-3 nX {x , ... , x },Y X {y , ... , y }= = =n1 ii 1xy n n2 2i ii 1 i 1(x x)(y y)r , i 1, 2, 3, ... ,(x x) (y y)== =- -= =- -åå å* *ji 1j 2i i 1j, 2ix [a , a ], y [b b ],= =nji j ki ki 1jk2 2n nji j ki ki 1 i 1(a a )(b b )r ,(a a ) (b b )j 1, 2, 3 dan k 1, 2== =- -=- -= =åå ålow up[r , r ]with low r p rr r s and u r s= - = +J. Eng. Applied Sci., 14 (7): 2340-2344, 20192341data. Fuzzy correlation is developed by generalizing the fuzzy data  Addition operation andform of fuzzy pearson correlation (Cheng and Yang, 2013).The data used are fuzzy interval data, trapezoidal data,and triangle. Cheng and Yang (2013) fuzzy correlationseasify the data analysis practitioners to use themcompared to the two earlier mentioned fuzzy correlations.Pertaining to the background in what follows, we willdiscuss the main application of fuzzy correlation inevaluating the correlation among mathematical anxiety,mathematics self-efficacy and student’s positive attitudestowards mathematics using Cheng and Yang correlation(2014) as well as pearson correlation as a displayedcomparison. The data used is collected through fuzzycinstruments. The two types of data can be immediatelyobtained using this instrument, namely fuzzy interval dataand crisp data.MATERIALS AND METHODSParticipant: Participants were 1063 of high schoolstudents and vocational students, class 10 and 11. Theages of the participants were between 15 and 17 years old.Instrument: The instruments with fuzzy Likert scale areused to measure mathematical anxiety, self-efficacy andattitudes towards mathematics. Each scale consists of 15items. The choice of language terms on each item isstrongly disagree, disagree, neutral, agree and stronglyagree. This instrument is filled with two steps, first, therespondent chooses the answer as in the classic Likertscale and the two respondents determine the confidenceinterval for the choice in the first step. The crisp data isobtained from the first step and fuzzy data is obtainedfrom the second step of filling the instrument. The scoringon each language term on each item is by giving a scoreof 10 to strongly disagree, 20 to disagree, 30 to neutral, 40to agree and 50 to strongly agree.Correlation between two variables: The correlationbetween mathematical anxiety and self-efficacy as well asa positive attitude towards mathematics was determinedusing pearson correlation analysis for the crisp data.Meanwhile, the fuzzy data is determined using fuzzycorrelation analysis. Previously, the basic operation offuzzy interval data was given before applying the fuzzycorrelation formula.Fuzzy data: Fuzzy data in the form of interval data basedon the need to be able to use Cheng and Yang (2013).Fuzzy  interval  data  can  be  written  with Fuzzy interval data can be transformed into triangulardeviation in fuzzy interval data.  Let there be given twofuzzy data  dan:Fuzzy interval data  mean: Given  n  fuzzy  interval data, then the mean of these data can bewritten as follows:Fuzzy interval data medianPearson  correlation: Let,  bea sequence of paired data sample on populations S.  Lets:Pearson correlation coefficient has a correlation rxycoefficient located at intervals [1, -1]. the level ofcorrelation between variables is determined by thestandard in Table 1 and 2.Fuzzy    correlation:    Fuzzy    correlations    developedby Cheng and Yang (2013) use the following definitions: let  be a sequence of paired fuzzysample on populations S. Let: Then fuzzy correlation is where (Fig. 1):r2 2 2 2 2jkj 1 k 1 j 1 k 1 jkrr (r r)r and s4 4= = = = -=å å å åJ. Eng. Applied Sci., 14 (7): 2340-2344, 20192342Table 1: Descriptive statistic of fuzzy and crisp dataCrisp data Fuzzy interval data-------------------------------------------------------------------- -----------------------------------------------------------------------------------------Variables Anxiety Self-efficacy  Attitude Attitude Self-efficacy AnxietyMin data 160 150 150 [0 168] [0 140] [0 168]Max data 730 730 980 [617 766] [656 870] [816 900]Median data 470 450 490 [411 502] [403 494] [445 533]Mean data 464,5 450,3 494,2 [402, 54 500, 68] [399, 38 494, 63] [444, 33 539, 44]Table 2: Results of combined data fuzzy correlation analysisCorrelations betweenVariables Anxiety and self-efficacy Anxiety and attitude  Attitude and self efficacyPearson correlation -0.259 -0.160 0.710Fuzzy correlation [-0, 278 -0,275] [-0, 185 -0,183] [0,665 0, 663]N 1063 1063 1063The definition has a correlation coefficient value atintervals [-1, 1] and the correlation level betweenobserved variables can be determined by the followingdefinitions:C When [r , r ] 0 [-0.10, 0.10], the fuzzy correlations islow  upnot significantC When [r , r ] 0 [-0.39, 0.11] or [0.11, 0.39], the fuzzylow  upcorrelations is lowC When [r , r ] 0 [-0.69, 0.40] or [0.40, 0.69], the fuzzylow  upcorrelations is middle C When [r , r ] 0 [-0.99, 0.70] or [0.70, 0.99], the fuzzylow  upcorrelations is highRESULTS AND DISCUSSIONThe fuzzy data is required to use Cheng and Yangcorrelation which is fuzzy interval data. The data isobtained from the data collection process through thefuzzy anxiety and attitude scale. The score ofmathematical anxiety and attitudes toward mathematicsare the sum of fuzzy interval data scores using theformulas.Data analysis: Explaining the concept and the advantagesof fuzzy data (Table 2), it can be seen that each correlationmethod provides indifferent results pertaining to thecorrelation among anxiety and self-efficacy, anxiety witha positive attitude and self-efficacy with a positiveattitude. The fuzzy correlation coefficient is in the intervalform while the pearson correlation coefficient is a crispvalue.The three correlation coefficients are obtained fromthe results of data analysis, those are the correlationcoefficient between anxiety and  self-efficacy  in  Table  2Fig. 1: The correlation between anxiety, self-efficacy andpositive attitudeshows that these two variables have a negativecorrelation at a low level. In conformity with the theprevious research (Lee, 2009; Hoffman, 2010; Akin andKurbanoglu, 2011; McGrath et al., 2015; Recber et al.,2018), the higher the condition of student’s self-efficacyis the minimized student’s anxiety in learning mathematicsbecomes at a low effect the correlation coefficientbetween anxiety and positive attitudes towardsmathematics in Table 2 illustrates that the two variableshave a negative correlation at a low level. These resultsare in line with the previous research of Recber et al.(2018),  Akin  and Kurbanoglu (2011). The more positiveof the student’s positive attitude is the more reducedstudent’s anxiety in learning mathematics becomes witha low effect the correlation coefficient between self-efficacy and positive attitudes toward mathematics inTable 3 clarifies the results of the study (Recber et al.,2018; Akin and Kurbanoglu, 2011), namely that these twovariables have a moderate correlation each other. Thehigher the condition of self-efficacy is the higher thestudent’s positive attitude towards mathematics becomeswith a moderate effect. The correlation between thesethree factors is described as follows.Fuzzy data in the interval form has their ownuniqueness, namely, a student can have a level of anxiety,self-efficacy or a positive attitude at the same level or twoJ. Eng. Applied Sci., 14 (7): 2340-2344, 20192343levels immediately. For instance, the level of these factors positive attitudes towards mathematics at a low level andcan be high to very high or very low to low and so on.These characteristics prove that fuzzy interval numberscan indicate the transition level of the condition of eachvariable in students. Unfortunately, the crisp dataobtained from the classic instrument cannot reveal thetransition level of each variable because respondents areforced to choose options being closed to their conditions.Based on these findings, fuzzy numbers provide flexibleresults when compared to the crisp numbers. Further,fuzzy numbers are able to describe the more clearcondition of each variable when compared to the crispnumbers (Muhith et al., 2018; Mallongi et al., 2018). Thecorrelation coefficient in Table 2 conceptualizes that thethree variables have correlation each other. The possiblecorrelation level between two variables when usingpearson correlation analysis are having no correlation,low correlation, moderate correlation and high correlation.These levels are also very likely to occur when applyingfuzzy correlation. Like fuzzy interval numbers, fuzzycorrelation coefficients can be at several levelsimmediately, namely not significant until having a lowcorrelation, having a low to moderate correlation, havinga moderate to high correlation. These conditions areimpossible in the classical correlation analysis, eventhough contextually possible.The concept of fuzzy correlation was developed byCheng and Yang (2013) by adopting the Pearsoncorrelation the principle. It easifies practitioners to analyzecorrelation data using the fuzzy data. The advantage ofcorrelation coefficients in the form of intervals is thatresearchers or experts have a subjectivity in determiningthe correlation coefficient used from the analysis results.Whereas in the pearson correlation coefficient,researchers cannot determine the subjectivity of theobtained crisp coefficient.CONCLUSIONReturning to the question posed at the beginning ofthis research, it is now possible to state that the intervalnumbers provide a very large role in explaining obscuritywhich is not clarifiable from the crisp numbers. Fuzzynumbers can explain the psychological condition ofstudents, in this case, anxiety, self-efficacy and positiveattitudes of students with more flexible and tangiblecontexts. For instance, the students can be at a differentlevel at the same time.The analysis of pearson and fuzzy correlation in thisresearch provides the same conception, namely theanxiety has a negative correlation with self-efficacy at alow level anxiety has a negative correlation with student’sself-efficacy has a positive correlation at a moderate level.Both of these analyses are distinguished by the form ofthe correlation coefficient which is in the crisp and fuzzyinterval data.REFERENCES Akin, A. and I.N. Kurbanoglu, 2011. The relationshipsbetween math anxiety, math attitudes andself-efficacy: A structural equation model. Stud.Psychol., 53: 263-273.Ashcraft, M.H. and E.P. Kirk, 2001. The relationshipsamong working memory, math anxiety andperformance. J. Exp. Psychol. Gen., 130: 224-237.Ashcraft, M.H., 2002. Maths Anxiety: Personal,educational and cognitive consequences. Am.Psychol. Soc., 11: 181-185.Cheng, Y.T. and C.C. Yang, 2013. The application of fuzzycorrelation coefficient with fuzzy interval data. Intl. J.Innovative Manage. Inf. Prod., 4: 65-71.Chi, Z., H. Yan and T. Pham, 1996. Fuzzy Algorithms: WithApplications to image Processing and PatternRecognition. Vol. 10, World Scientific, Singapore,Asia, Pages: 221.Coppi, R., 2008. Management of uncertainty in statisticalreasoning: The case of regression analysis. Intl. J.Approximate Reasoning, 47: 284-305.Hanafy, I.M., A.A. Salama and K.M. Mahfouz, 2013.Correlation coefficients of neutrosophic sets bycentroid method. Int. J. Probab. Stat., 2: 9-12.Hoffman, B., 2010. I think I can, but I'm afraid to try: Therole of self-efficacy beliefs and mathematics anxietyin mathematics problem-solving efficiency. Learn.Individual Differences, 20: 276-283.Hung, W.L. and J.W. Wu, 2001. A note on the correlationof fuzzy numbers by expected interval. Intl. J.Uncertainty Fuzziness Knowl. Based Syst., 9: 517-523.Kundu, A. and G. Aditi, 2016. The relationship betweenattitude and self efficacy in mathematics amonghigher secondary students. IOSR. J. Humanities Soc.Sci., 21: 25-31.Lee, J., 2009. Universals and specifics of mathself-concept, math self-efficacy and math anxietyacross 41 PISA 2003 participating countries. Learn.Individual Differences, 19: 355-365.Mallongi, A., M. Selomo, S.A. Rahman, A. Mattangangand A. Muhith, 2018. The spatial pattern and riskfactors of leprosy occurrence in Barru, Indonesia.Indian J. Publ. Health Res. Dev., 9: 1489-1494.J. Eng. Applied Sci., 14 (7): 2340-2344, 20192344McGrath, A.L., A. Ferns, L. Greiner, K. Wanamaker and S. Recber,  S.,   M.   Isiksal   and   Y.   Koc, 2018.Brown, 2015. Reducing anxiety and increasingself-efficacy within an advanced graduatepsychology statistics course. Can. J. ScholarshipTeach. Learn., 6: 1-19.Muhith, A., M.H. Saputra, A. Fardiansyah and L. Andani,2018. Risk factor of rheumatoid arthritis among elderlyin UPT Panti Werdha Mojopahit Mojokerto DistrictIndonesia. Indian J. Publ. Health Res. Dev., 9:412-416.Investigating  self-efficacy,    anxiety,   attitudes  andmathematics  achievement regarding gender andschool  type.  Anal.  Psicol.   Ann.  Psychol., 34:41-51.Zan, R. and P. di Martino, 2007. Attitude towardmathematics: Overcoming the positive/negativedichotomy.   Montana    Math.   Enthusiast, 3:157-168.

Evaluating Anxiety, Self-Efficacy and Positive Attitude Correlation Towards Mathematics Through Fuzzy Correlation Utilization

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Evaluating Anxiety, Self-Efficacy and Positive Attitude Correlation Towards Mathematics Through Fuzzy Correlation Utilization

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