Multiple levels of influence. Networks can also be extended beyond direct interactions. For example, one could construct a network term based on others whom a teacher observed, members of a teacher’s cohesive subgroup (where interactions are concentrated within cohesive subgroups, but not all members of subgroups have interactions with each other – see Figure 1), or her department. That is, the network can extend beyond direct ties with whom one is close colleagues. These network effects beyond those of direct relations will quickly become difficult to measure and differentiate, especially in the small closed communities of elementary schools or high school departments which feature extensive opportunities for casual interaction and observation of all in the system. One way to model the influence of the community is through multilevel models. For example we can extend equation (1) to a multilevel framework (e.g., Raudenbush & Bryk 2002) for teacher i nested within subgroup j: At Level 1 (teacher i in subgroup j): Skills-based instructionij =β0j + β1j previous skills-based instructional of formal leaders in the network of iij + β2j previous skills-based instructionij + eij , (3) At the subgroup level (level 2), β0j, the adjusted mean behavior for a subgroup is modeled as a function of the previous subgroup norm: Level 2 (subgroup level j): β0j =γ00 +γ01 subgroup average of previous skills-based instructionj + u0j , (4)
Finnigan, K. S. & Daly, A. J. (2012). Mind the gap: Organizational learning and improvement in an underperforming urban system. American Journal of Education, 119(1), 41–71. Frank. K. A. (1995). Identifying cohesive subgroups. Social Networks, 17, 27–56. K. A. (1996). Mapping interactions within and between cohesive subgroups. Social Networks, 18, 93–119. Frank, K. A. (1998). The social context of schooling: Quantitative methods. Review of Research in Education, 23, 171–216. Frank, K. A. (2009). Quasi-ties: Directing resources to members of a collective. American Behavioral Scientist, 52, 1613–1645. Frank, K. A. & Fahrbach, K. (1999). Organizational culture as a complex system: Balance and information in models of influence and selection. Organization Science, 10(3), 253–277. Frank, K. A., Kim, C. & Belman, D. (2010). Utility theory, social networks, and teacher decision making. In A. J. Daly (Ed.), Social network theory and educational change (pp. 223–242). Cambridge, MA: Harvard University Press. Frank, K. A., Muller, C., Schiller, K., Riegle-Crumb, C., Strassman-Muller, A., Crosnoe, R. & Pearson J. (2008). The social dynamics of mathematics course taking in high school. American Journal of Sociology, 113(6),
Basic Influence Model Multiple Sources of Influence Multiple levels of Influence Basic Selection Model Hypothesis H1: If teachers interacted with others with higher levels of skills-based instructional expertise, their own instructional practices would be positively influenced. What types of instructional practices most responsive to which types of leaders. For example, H21: Teachers’ general practices (e.g., setting ambitious goals, choosing assessment and curriculum) would be more likely to respond to the influence of formal leaders H22: Teachers’ specific pedagogical practices in classrooms are more likely to be influenced by informal leaders who are regular classroom teachers.. H3: Teachers’ practices of skills-based instruction were increased if they belonged to a subgroup with a higher level of skills-based instructional expertise. H41: Teachers who were close colleague were more likely to help each other in classroom instruction. H42: Teachers who taught in the same grade were more likely to help each other. Data Longitudinal data Longitudinal data Longitudinal data with teachers nested in subgroups Longitudinal aata with relationships between all possible pairs of teachers Model Regression Regression Multilevel modeling Logistic regression Dependent Variable Y1: Teacher’s instruction Y2: Teacher’s skills-based instruction Y3: Teacher’s skills-based instruction Y4: at pair one teacher helped
the other teacher Independent Variable X11: Teacher’s exposure to the instructional expertise of other teachers in her/his network X12: Teacher’s own previous skills-based instruction X21: Teacher’s exposure to the general practices of formal leaders in her/his network X22: Teacher’s exposure to the skills-based instructional expertise of informal leaders in her/his network X23: Teacher’s own previous skills-based instruction Level 1: X31: Teacher’s exposure to the skills-based instructional expertise of other teachers in her/his network X32: Teacher’s own previous instruction Level 2: X33: The averages of teachers’ skills-based instruction in the subgroups X41: The pair of teachers taught the same subject X42: The pair of teachers taught in the same grade Hypothesis Test If the coefficient of X11 is positive and significant, the hypothesis H1 is retained. If the coefficient of X21 is positive and significant, the hypothesis H21 is retained. If the coefficient of X22 is significant, the hypothesis H22 is retained. The comparison of coefficients between X21 and X22 implies the comparative influences on different types of instructional practices between formal If the coefficient of X33 is positive and significant, the hypothesis H3 is retained. If the coefficient of X41 and X42 are positive and significant, the hypotheses H41 and H42 are retained.