[[abstract]]Student engagement has become a hot issue in education settings. Previous studies have provided a profound knowledge to tackle this issue from different perspectives. While engagement or not is an ambiguous question for student learning, it is not easy to reflect on a crisp answer in a traditional way. Similarly, the students’ interpersonal interactions among the teachers, classmates, and parents have shown uncertainly relationship with their engagement. This study aims to explore the issues by using self-designed fuzzy questionnaire as an example for high school teachers. Fuzzy means, centroids, variances, and fuzzy correlations have been transformed. The results reveal some indicators have negative tendency fuzzy relationships. The fuzzy correlation coefficients did not display their significant differences in this case study. This study has demonstrated that the fuzzy statistics can provide an example to tackle the similar issue on a class basis in education settings.[[sponsorship]]Tamkang University[[notice]]補正完

Chang, Dian-Fu

Student engagement has become a hot issue in education settings. Previous studies have provided a profound knowledge to tackle this issue from different perspectives. While engagement or not is an ambiguous question for student learning, it is not easy to reflect on a crisp answer in a traditional way. Similarly, the students’ interpersonal interactions among the teachers, classmates, and parents have shown uncertainly relationship with their engagement. This study aims to explore the issues by using self-designed fuzzy questionnaire as an example for high school teachers. Fuzzy means, centroids, variances, and fuzzy correlations have been transformed. The results reveal some indicators have negative tendency fuzzy relationships. The fuzzy correlation coefficients did not display their significant differences in this case study. This study has demonstrated that the fuzzy statistics can provide an example to tackle the similar issue on a class basis in education settings.Tamkang University補正完

Tamkang University Institutional Repository

ICIC Express LettersPart B: Applications ICIC International c2018 ISSN 2185-2766Volume 9, Number 1, January 2018 pp. 17{22FUZZY CORRELATION AMONG STUDENT ENGAGEMENTAND INTERPERSONAL INTERACTIONSDian-Fu Chang1, An Chen Chiu2; and Berlin Wu31Graduate Institute of Educational Policy and Leadership2Doctoral Program of Educational Leadership and Technology ManagementTamkang UniversityNo. 151, Yingzhuan Rd., Tamsui Dist., New Taipei City 25137, Taiwan140626@mail.tku.edu.tw; Corresponding author: anchen.912@gmail.com3Department of Applied StatisticsNational Chengchi UniversityNo. 64, Sec. 2, Zhinan Rd., Wenshan Dist., Taipei City 11605, Taiwanberlin@nccu.edu.twReceived July 2017; accepted October 2017Abstract. Student engagement has become a hot issue in education settings. Previousstudies have provided a profound knowledge to tackle this issue from dierent perspectives.While engagement or not is an ambiguous question for student learning, it is not easy toreect on a crisp answer in a traditional way. Similarly, the students' interpersonal inter-actions among the teachers, classmates, and parents have shown uncertainly relationshipwith their engagement. This study aims to explore the issues by using self-designed fuzzyquestionnaire as an example for high school teachers. Fuzzy means, centroids, variances,and fuzzy correlations have been transformed. The results reveal some indicators havenegative tendency fuzzy relationships. The fuzzy correlation coecients did not displaytheir signicant dierences in this case study. This study has demonstrated that the fuzzystatistics can provide an example to tackle the similar issue on a class basis in educationsettings.Keywords: Fuzzy correlation, Fuzzy questionnaire, Interpersonal interactions, Studentengagement, High school students1. Introduction. Previous studies indicated that college students' time and energy de-voted to purpose activities in campus have become one of the best predictors to explaintheir learning and personal development [1-4]. Student engagement is not conceptualizedas an attribute of the student, but rather a state of being that is highly inuenced bycontextual factors, like home, school, and peers, which will provide consistent support forstudent learning [5]. The related literature supports that student engagement is denedas a concept that requires psychological connections within the academic environment(e.g., positive relationships between adults and students and among peers) in addition tostudent's active behavior (e.g., attendance, eort, and behavior). Eective interventionshave also addressed student engagement comprehensively, not only focusing on academicor behavioral skill decits, but also on the social, interpersonal aspects of schooling, par-ticularly the need for supportive connections to other adults and peers [6]. For example,a process model focusing on students' motivational resources was used to frame a studyexamining whether engagement in the classroom shapes students' academic coping, andwhether coping in turn contributes to subsequent persistence on challenging tasks andlearning, which then feed back into ongoing engagement [7]. Various studies agreed thatstudent engagement refers to a relevant and multidimensional construction that integratesstudents' thoughts, feelings, and behaviors [8,9]. Based on previous studies, researchershave incorporated a three-part typology emphasizing aective, behavioral, and cognitive1718 D.-F. CHANG, A. C. CHIU AND B. WUdimensions of engagement [1-3,8]. In this study, the conceptual framework of studentengagement extended that students demonstrate their levels of engagement through avariety of emotional cognitive and behavioral engagement.Surveys play a prominent role in assessment and institutional research in this eld. Forexample, the NSSE College Student Report is one of the most popular surveys of enrolledundergraduates in the United States [10]. While engagement related studies in high schoollevel is relatively neglected in current educational settings. Moreover, students live in adigital society, where the information technology related devices have become necessarytools in their daily life. This study argues the interpersonal interaction pattern mighthave changed in the young generations because they are over depended smartphones orlaptops and lack of \face to face" with people. Therefore, realizing the relationshipsbetween student engagement and interpersonal interactions has become emergent issuein schools. For most of teachers, it is not possible to tackle the issues based on a largerscale survey, and then developing a small and practical way to realize the issue in theirclass is needed. Given this purpose, this study explores the status of student engagementand interpersonal interaction as an example in a selected class. This case study focuseson the relationship between student engagement and interpersonal interaction to developan alternative way to tackle the issue.This study begins with introduction to address the problem statement and purpose ofresearch. Then, this study displays the logics of data transformation with fuzzy statistics.The third section will report the result of fuzzy data transformation. Finally, we make aconclusion and provide some suggestions for enriching knowledge in the elds.2. Algorithm for Fuzzy Solution. The engagement issue includes theoretical conceptsand practical activities. This study reviews the related engagement literature and selectsthe target group in higher school level. The logic of fuzzy solution has been presented asfollows.1) Decide a research framework: We select two dierent concepts, student engagementand interpersonal interactions, in the research framework. Since the study focuses onfuzzy correlation solution, the related demographic variables will be neglected in thismodel. The concept of student engagement has been dened as emotion engagement,cognitive engagement, and behavioral engagement.2) Design a fuzzy questionnaire: The self-designed fuzzy questionnaire for student en-gagement includes 19 indicators, in which eight indicators belong to behavioral engage-ment, six indicators belong to emotional engagement, and the other ve belong to activecognitive engagement. The interpersonal interaction refers to the relationships that stu-dents are interactive with teachers, classmates, and family. The selected indicators havebeen veried by the invited ve experts in this eld. Each indicator of the questionnairehas been designed by using 1 (minimum weight) to 5 (maximum weight) scale to t thefuzzy interval data format. For example, if N student's cognitive engagement is from 2to 4, s/he needs to circle 2 and 4 to represent the range of perception based on the scaleof the questionnaire.3) Select a target group: The target group has been selected from a high school as anexample to verify the relationship with fuzzy formats. The samples are 46 high schoolstudents in this case study.4) Transform fuzzy data: The fuzzy interval data were collected by using self-desig-ned fuzzy questionnaire. The data were transformed by fuzzy mean, center, variance,and fuzzy correlation. The related denitions will be addressed in the fuzzy correlationcoecient transformation and calculation of the fuzzy correlation coecient section.5) Report the results and draw conclusions: In the stage, the fuzzy correlation coe-cients will be displayed by using the rule to dene the fuzzy relevant interval. The ndingswill be reported in this section.ICIC EXPRESS LETTERS, PART B: APPLICATIONS, VOL.9, NO.1, 2018 193. Fuzzy Statistics.3.1. Fuzzy correlation coecient transformation. Each indicator of the fuzzy ques-tionnaire was designed by using a scale of 1 (minima) to 5 (maxima) for collecting fuzzyinterval data. For example, if the nth student believed that the weighting for the kthindicator was 2-4, the student would circle \2" and \4" on the scale. The data havebeen transformed by following fuzzy formats of student engagement and the interpersonalinteractions. We judge the selected indicators by using fuzzy means their centers and vari-ances. We assume the centers as the points that might take the highest fuzzy membershipfunction with the students' opinions. Considered the existing information constraint, theinterval fuzzy numbers have been dened as follows [11,12].The concept of interval fuzzy data can be dened as a well-distributed membershipfunction with fuzzy numbers. The symbol of \[ ]" means a closed interval. If a; b 2 R anda < b, then [a; b] is interval fuzzy data. It can be named \a" as the lower bound of [a; b]and \b" as the upper bound of [a; b]; if a = b, then [a; b] = [a; a] = [b; b] = a = b, and it isa real number a (or b). Similarly, a real number k can be dened as [k; k]. If [a; b] is aninterval fuzzy set, we can dene co =a+b2, so =b a2, and they represent the \center" and\radius" or \variance" respectively. This study also dened an interval fuzzy number asthe following format:[co; so]) [co + so; co   so] = [a; b]In this case, the ` = b  a is the length of the fuzzy interval measurement. For example,when we consider (xi; yi) as the rst i sample value, i = 1; 2; : : : ; n; xi, yi are interval fuzzynumbers; x, y represent its sample mean respectively. If we deal with both variables xi,yi as fuzzy numbers, we will obtain interval fuzzy distribution between the two variablesIx and Iy. The idea of interval distribution has displayed as Figure 1 [12].Figure 1. The distribution of xi, yi with fuzzy formats3.2. Calculation of the fuzzy correlation coecient. This study applied Formula(1) to calculating the upper bound correlation coecient and used  to adjust fuzzycorrelation coecient for a reasonable format [11-13]. Let lxi be the length of continuousinterval sample xi, lyi be the length of the sample interval yi, and then the correctedlength of correlation coecient isrl =Pni=1 lxi   lx  lyi   lyqPni=1 lxi   lx2qPni=1 lyi   ly2 (1)Similarly, the center's fuzzy coecient can be calculated by using the center related fuzzydata. We considered the  as a lter to adjust the length of correlation coecient. Formula20 D.-F. CHANG, A. C. CHIU AND B. WU(2) for  transformation is: = 1  ln(1 + jrlj)jrlj (2)Since 0 < rl < 1, the range of  is 0 <  < 0:3069.3.3. Redening the fuzzy relevant interval. In the nal stage, this study dened therules for taking the center and the length of fuzzy correlation coecients. Let Cxi , Cyi besamples from the interval fuzzy matrix central point, lxi , lyi for the interval length. The ris the center of the correlation coecient,  is the tter which can be used to correct thelength of the correlation coecient. The relevant interval with lower and upper boundshas been dened as follows [12,14]:(i) r  0, rl  0, (r;min(1; r + ))(ii) r  0, rl < 0, (r   ; r)(iii) r < 0, rl  0, (r; r + )(iv) r < 0, rl < 0, (max( 1; r   ); r)Finally, the meanings of correlation coecients can be justied following the rules: r > :65belongs to the high correlation, :35 < r < :65 is the moderate correlation, and r < :35means the low correlation. Similarly, r >  :35 is low degree of negative correlation, :65 < r <  :35 can be classied in moderate negative correlation, and r <  :65 can beclassied into high negative correlation.4. Results.4.1. Fuzzy means, centers and fuzzy variances for related indicators. Table 1shows the results of fuzzy transformation for student engagement (SE) and interpersonalinteractions. In regard to student engagement, the fuzzy center of cognitive engagementdomain (Co = 2:71) has shown higher than others. Referred to relationships, the fuzzycenter of relationship with family (Co = 3:09) is higher than others. The results of fuzzyvariances reveal the interpersonal interactions with higher So than that of engagementindicators. It implies the interpersonal interactions demonstrated wider dierences amongthese samples.Table 1. Fuzzy means, fuzzy centers and variances for selected indicatorsIndicators Fuzzy means Co SoStudent Engagement (SE) [1:50; 3:38] 2.44 0.94Emotion engagement (EE) [1:42; 3:58] 2.50 1.08Cognitive engagement (CE) [1:69; 3:73] 2.71 1.02Behavior engagement (BE) [1:32; 3:02] 2.17 0.85Relationship with teachers [1:59; 3:89] 2.74 1.15Relationship with classmates [1:26; 4:70] 3.01 1.73Relationship with family [1:53; 4:57] 3.09 1.524.2. The result of fuzzy correlation coecient transformation. Table 2 demon-strates the results of fuzzy r, rl and  between student engagement and interpersonalinteractions. The fuzzy transformation has followed the denition in Formulas (1) and(2). The r and rl are original fuzzy correlation coecients. Both r and rl will be justiedby their attribution of correlation in terms of negative or positive. The  is the tter forcorrecting the length of the correlation coecient for more reasonable fuzzy correlationformat. The range of tter () for relationship with teachers is from .001 to .041. Therange of tter () for relationship with classmates is from .003 to .048. The range of t-ter () for relationship with family is from .019 to .138. Negative correlation coecientsimply the r or rl needed to be adjusted to t the fuzzy correlation coecient format.ICIC EXPRESS LETTERS, PART B: APPLICATIONS, VOL.9, NO.1, 2018 21Table 2. Fuzzy correlation transformation with r, rl and Fuzzy RRelationshipwith teachersRelationshipwith classmatesRelationshipwith familyr rl  r rl  r rl SE  0:040  0:070 0.033  0:013  0:044 0.021 0.066  0:076 0.036EE  0:269  0:087 0.041 0.169  0:007 0.003  0:016  0:039 0.019CE 0.041 0.003 0.001 0.116 0.022 0.021 0.049 0.100 0.047BE 0.268 0.061 0.029  0:120  0:079 0.048 0.134 0.307 0.1384.3. Determining the fuzzy correlation. Table 3 displays the fuzzy correlation co-ecients between engagement and personal interaction. Based on the rule of judgmentfor the correlation coecients, r > :65 belongs to the high correlation, :35 < r < :65 isthe moderate correlation, and r < :35 means the low correlation. Similarly, r >  :35is low degree of negative correlation,  :65 < r <  :35 has been classied in moderatenegative correlation, and r <  :65 is specied to high negative correlation. This studyfound the fuzzy correlation coecients did not t these scopes, because the result revealsthat transformed fuzzy correlation coecients located in the range from  :035 to .035.However, the results reveal student engagement has negative tendency in interaction withteachers and classmates. Emotional engagement indicators also show negative tendencywith teachers and family. While behavior engagement has shown negative correlation withclassmates. The relationship between student engagement and its sub-domain indicatorsis relative low. The ndings may provide school teachers meaningful messages for theirstudents' learning conditions.Table 3. Fuzzy correlation between student engagement and interpersonal interactionsFuzzy correlation With teachers With classmates With familySE ( 0:074; 0:040) ( 0:034; 0:013) (0:030; 0:066)EE ( 0:300; 0:269) (0:166; 0:169) ( 0:035; 0:016)CE (0:041; 0:042) (0:116; 0:132) (0:049; 0:096)BE (0:268; 0:297) ( 0:168; 0:120) (0:134; 0:272)5. Conclusions. This study proposes a fuzzy format survey to explore the engagementand interpersonal interaction issue in schools. Even the result did not demonstrate thesignicant fuzzy correlations among these selected variables, this study provides a prac-tical example for high school teachers to realize their students' problem and prompt toselect better strategies for improvement. The self-designed fuzzy questionnaire with con-ceptual indicators can provide a strong theoretical support for the target issues. Fuzzystatistics has demonstrated which can be used to transform the interval data with reason-able formats in this study. The relationships among variables can be determined by fuzzydata transformation with means, centers, and variances. The study provides an exampleto transform fuzzy correlation coecients and interpret their meanings in practices. Forfurther studies, the fuzzy survey and data transformation can be used to tackle similarissues in the other settings.REFERENCES[1] J. A. Fredericks, P. C. Blumenfeld and A. H. Paris, School engagement: Potential of the concept,state of the evidence, Review of Educational Research, vol.74, pp.59-109, 2004.[2] M. J. Furlong and S. L. Christenson, Engaging students at school and with learning: A relevantconstruct for all students, Psychology in the Schools, vol.45, no.5, pp.365-368, 2008.22 D.-F. CHANG, A. C. CHIU AND B. WU[3] M. J. Furlong, A. D. Whipple, G. St. Jean, J. Simental, A. Soliz and S. Punthuna, Multiple contextsof school engagement: Moving toward a unifying framework for educational research and practice,California School Psychologist, vol.8, pp.99-114, 2003.[4] G. D. Kuh, Assessing what really matters to student learning: Inside the national survey of studentengagement, Change, vol.33, no.3, pp.10-17, 2001.[5] J. Brophy, Motivating Students to Learn, 2nd Edition, Mahwah, New Jersey, Lawrence Erlbaum,2004.[6] K. R. Wentzel, Social relationships and motivation in middle school: The role of parents, teachers,and peers, Journal of Educational Psychology, vol.90, pp.202-209, 2009.[7] E. A. Skinner, J. R. Pitzer and J. S. Steele, Can student engagement serve as a motivational resourcefor academic coping, persistence, and learning during late elementary and early middle school?,Developmental Psychology, vol.52, no.12, pp.2099-2117, 2016.[8] E. Chapman, Alternative approaches to assessing student engagement rates, Practical Assessment,Research and Evaluation, vol.13, no.8, pp.1-7, 2003.[9] S. R. Jimerson, E. Campos and J. L. Greif, Toward an understanding of denitions and measures ofschool engagement and related terms, California School Psychologist, vol.8, pp.7-27, 2003.[10] G. R. Pike, NSSE benchmarks and institutional outcomes: A note on the importance of consideringthe intended uses of a measure in validity studies, Research in Higher Education, vol.54, no.2, pp.149-170, 2013.[11] D.-F. Chang and H.-M. Wang, Colleagues' perception on servant leadership explained by fuzzymeasurement, ICIC Express Letters, vol.8, no.1, pp.165-171, 2014.[12] D.-F. Chang and W.-C. Chou, Detecting the linkage of time management and performance explainedby soft computing, ICIC Express Letters, vol.9, no.3, pp.721-727, 2015.[13] D.-F. Chang and W.-C. Chou, Fuzzy correlation with the issues of study in domestic campus orintent to study abroad, Lecture Notes in Information Technology, vol.10, pp.123-128, 2012.[14] D.-F. Chang, W.-C. Chou and C.-W. Yu, Fuzzy relationship between Facebook using and securityawareness, ICIC Express Letters, vol.8, no.1, pp.31-36, 2014.

Fuzzy Correlation among Student Engagement and Interpersonal Interactions

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Fuzzy Correlation among Student Engagement and Interpersonal Interactions

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