School Level Results

There was variability in the sampled schools on all of the demographic measures; for example, at an average school, 40% of students received

free/reduced priced lunch (SD = 0.26) and 23% of the students were minorities (SD = 0.39). The smallest school in the sample had 82 students whereas the largest had 676 (M = 377 students). In terms of student achievement, on average 77% of students in each school passed the math MEAP and about 80% passed the reading MEAP. Notably, the collective efficacy scores (not standardized) range

from a low of 2.85 to a high of 4.35 suggesting variability in collective efficacy across the sample (SD = 0.35). In sum, the schools in the sample represented the state of Michigan and illustrate variability on a range of measures.

Table 4.4 displays the school level correlations. At the school-level, generally the correlations have stronger coefficients (closer to 1 or -1) as

compared to the student-level correlations. Perhaps the most noteworthy findings are the strong negative correlations between collective efficacy and measures of social disadvantage. For example, there is a significant negative correlation between collective efficacy and proportion minority students (r = -0.66), and collective efficacy and proportion of students receiving free/reduced lunch (r = - 0.74). These strong correlations illustrate that collective efficacy, as it is measured in this dissertation, is more likely found in schools with lower proportions of minority students and students living in poverty. Collective efficacy also had a strong, positive, and significant correlation with student achievement at the school-level (r = 0.59 in math, r = 0.57 in reading).

This is an important issue to address – as the correlation between

collective efficacy and achievement is stronger than the correlation between social disadvantage and achievement. This suggests that the measure for collective efficacy captures something that while similar, differs importantly from the measures of social disadvantage. This piece of evidence provides a strong rationale for the qualitative component of this dissertation. Certainly, it is possible that teachers are, on average, are less efficacious as a collective group when students face social disadvantage. There is variability that remains

unexplained between collective efficacy and disadvantage, and the strength between these measures requires more exploration. It is possible that one outcome of my work could be improvement in the collective efficacy measure, such that it is not so highly correlated with social disadvantage. Furthermore, this supports the logic of studying collective efficacy in schools that serve low-income students.

4.4 Multilevel Analysis

To determine the extent of variation between schools in students‘ odds of passing the MEAP, I estimated two fully unconditional models (one for reading and one for mathematics). These initial estimates provided the basis for

determining the proportion of between-school variation explained by the full model. Table 4.5 illustrates these results. The chi-square statistics indicated students‘ odds of passing both the reading and mathematics assessment did vary significantly among schools. Therefore, I proceeded to the multilevel analysis to test whether collective efficacy predicted this variation.

The full models contained student-level demographic information and prior achievement controls. At level 2, I included the school-level variables that might be related to collective efficacy and achievement – school size, school demographic information, if the school is located in a MSA or not, and prior achievement.

At the student-level, all variables in both models were significantly related to students‘ achievement scores in reading and mathematics. Since the models only differed according to subject matter, I present the results of both models together; the math results can be found in table 4.6, and the reading results in table 4.7. I report all results as the change in odds for a particular group of students, ceteris paribus (other things being equal).

Both models concur with past research documenting the achievement gap across socio-demographic characteristics in the state of Michigan. On average, special education students were 76% and 84% less likely to pass the MEAP in

mathematics and reading respectively, as compared to students who did not have a special education designation. Students who received free or reduced lunch were 39% and 36% less likely to pass the MEAP in mathematics and reading respectively, as compared to their more advantaged counterparts. Minority students were 51% and 45% less likely to pass the MEAP in mathematics and reading respectively as compared to their non-minority peers. While the patterns were similar in both models for special education students, minorities and

students in poverty, there were two inconsistent patterns for females and ELLs present in the two models. Females were 18% less likely to pass the mathematics MEAP, but 30% more likely to pass the reading MEAP compared to males. Finally, ELLs were 65% less likely to pass the reading MEAP compared to native English speaking peers in reading; however ELLs did not perform significantly different in mathematics as compared to native English speakers. This might reflect that after accounting for SES, minority status, and special education, ELL did not add anything to a child‘s odds of passing16

. It is also plausible reading skills are not as critical to success on the mathematics section of the MEAP. In sum, these results concur with past research as several different achievement gaps were surfaced: gender, racial, linguistic, class, and special education.

This analysis concurs with past findings: there is a relationship between collective efficacy and student achievement in mathematics and reading.

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While it might seem that male, ELLs who are neither minorities nor receive free and reduced priced lunch are rare, this small group was represented in this study. This generally describes males who were more advantaged in the Springfield School District as will be elaborated in Chapter 5. Students in the case study schools were predominately Middle Eastern, which is classified as Caucasian, and nearly all were ELLs.

Specifically, at the school-level, after controlling for other variables, a 1 SD increase in collective efficacy was associated with a 35% increase in odds that students passed the mathematics MEAP and 42% increase in the odds of passing the reading MEAP. To further probe this relationship, the qualitative of this study is positioned to provide insight as to how and why collective efficacy has a

student achievement effect, through deliberately seeking cases with different configurations of poverty and levels of collective efficacy as elaborated in chapters six through eight.

Chapter 5