This document describes a study that uses social network analysis to analyze the development of communication networks among mathematics pre-service teacher trainees over time. The study collected longitudinal network data on support networks from trainees in 4 waves over 8 months. It used multiple regression quadratic assignment procedures (MRQAP) to test whether attributes like gender, training program, trust, and self-efficacy predicted the development of networks. The results found that the training program was a negative predictor of network development, and that trust was a positive predictor later in the training period. Visualizing the network changes also showed networks shifting from tight-knit to some trainees going their own way.

1. 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

2. 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

3. Social Network Analysis (SNA) as method

4. Dynamic SNA
From a previous project: networks change over time.

5. 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

6. 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.

7. 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.

8. 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.

9. 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

10. 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).

11. QUESTIONS/DISCUSSION
C.Bokhove@soton.ac.uk
Twitter: @cbokhove

12. 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.