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This paper looks at a data analysis method for analyzing longitudinal network data called MRQAP. We describe a dataset from a study on the development of peer networks of one cohort of pre-service mathematics trainees in the south of England and apply the MRQAP method to its four timepoints. We include attributes for gender, study programme, trust and self-efficacy. The analysis shows that MRQAP is a viable data analysis method for looking at the longitudinal development of networks. We conclude with a short discussion of further methodological challenges and limitations.

Christian BokhoveFollow

Associate Professor in Mathematics Education at University of SouthamptonAdvertisement

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- USING MRQAP TO ANALYSE THE DEVELOPMENT OF MATHEMATICS PRE- SERVICE TRAINEES’COMMUNICATION NETWORKS Christian Bokhove and Chris Downey University of Southampton Jasperina Brouwer University of Groningen
- Context Teacher training in UK • PGCE University Led (UL) • School Direct (SD) → Newly Qualified Teacher Secondary Maths and Science • cohort size (~35) • “sink or swim” • longevity of course Social (support)Networks play a role
- Social Network Analysis (SNA) as method
- Dynamic SNA From a previous project: networks change over time.
- Data collection • Longitudinal - 4 ‘waves’ of data collection (per 2 months) • Directed network question: “During the last month, to whom have you turned for support?” • Both instrumental and affective aspects of support • Online questionnaire instrument Network Related factors Peer (whole) External (ego) Trust Network intent Support views Self- efficacy 1 2 3 4 See Bokhove & Downey (2018) for more info on measures
- Longitudinal development • Visual representation of the development of mathematics trainees’ communication networks. • Red nodes trainees, arrows indicate communication • For every trainee, every red node, the attributes gender, program, trust and self-efficacy were collected • The figure shows a development from a tight knit community to a situation where some trainees go their own way.
- MRQAP • Studies have used multiple (logistic) regression or Quadratic Assignment Procedures (QAP) for a bivariate association between two networks. • But longitudinal data violate independence. • Multiple regression quadratic assignment procedures (MRQAP) • In our case we would be able to test whether gender, program, trust or self-efficacy predict the development of communication networks. • The interpretation of the standardised betas is similar to OLS regression analyses. • We use R statistical software with the asnipe package.
- Results The program (UL or SD) is a negative predictor in all final models. Trust only is a positive predictor from timepoints 3 to 4, perhaps indicating that by that time, towards the end of the year of training, it is trusted peers that are mainly sought. The table shows that the configuration of previous networks predict future networks.
- Other methods – other SNA • Teacher student interaction • Whole class, directionality • Student interactions • Groups and cliques • Individual behaviour • Help seeking • Disturbances • Central students • Perhaps, patterns over classes, schools, countries (analogue TIMSS video study) • Longitudinal: STERGM, RSIENA
- Conclusions • Social phenomena can be modelled with SNA. • Networks change; how can we describe this change? • Visualisations. • Descriptive statistics and inferential statistics. • MRQAP is one example of this. • Working on a comparison article of popular methods (Bokhove, Brouwer, & Downey, in preparation). • These methods can be complemented by rich qualitative data (and vice versa).
- QUESTIONS/DISCUSSION C.Bokhove@soton.ac.uk Twitter: @cbokhove
- Bibliography • Bokhove, C., & Downey, C. (2018). Mapping changes in support: a longitudinal analysis of networks of pre-service mathematics and science teachers, Oxford Review of Education, 44(3), 383–402. • Daly, A. J., & Chrispeels, J. (2008). A question of trust: Predictive conditions for adaptive and technical leadership in educational contexts. Leadership and Policy in Schools, 7(1), 30–63. • Dekker, D., Krackhard, D., Snijders, T.A.B (2007). Sensitivity of MRQAP tests to collinearity and autocorrelation conditions. Psychometrika, 72(4), 563–581. • Krackhardt, D. (1988). Predicting with networks: Nonparametric multiple regression analysis of dyadic data. Social Networks, 10(4), 359–381. • Krivitsky, P. N., & Handcock, M. S. (2014). A Separable Model for Dynamic Networks. Journal of the Royal Statistical Society. Series B, Statistical methodology, 76(1), 29–46. • Rienties, B., Héliot, Y. & Jindal-Snape, D. (2013). Understanding social learning relations of international students in a large classroom using social network analysis. Higher Education, 66(4), 489–504. • Rienties, B., & Nolan, E-M. (2014). Understanding friendship and learning networks of international and host students using longitudinal Social Network Analysis. International Journal of Intercultural Relations, 41, 165–180. • Snijders, T. A. B., Van der Bunt, G. G., & Steglich, C. E. G. (2010). Introduction to stochastic actor-based models for network dynamics. Social Networks, 32(1), 44-60. • Sweet, T.M. (2016) Social Network Methods for the Educational and Psychological Sciences. Educational Psychologist, 51(3-4), 381–394. • Tschannen-Moran, M., & Hoy, A. W. (2001). Teacher efficacy: Capturing an elusive construct. Teaching and Teacher Education, 17(7), 783–805.

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