Math

As noted previously, fewer elements are significant in math than in reading, and those that are have a significance at the p<0.05 level or higher. There were no elements within the first block on faculty that showed a significant relationship to student gain scores. Additionally, in block 2, elements that pertained to candidate teaching experiences, only the variable for low number of courses with active teaching had a significant relationship. This element was only significant when

entered individually in the model with other student and teacher-classroom covariates at the p<0.1 level (0.61 SE=0.38).

There were more elements that were significant in block 3, required courses, than in other groupings for math gain scores. The first element to show a significant relationship was that of the number of courses on assessment of a student’s work. This was not significant when entered individually but was when entered with other variables in this block at the p<0.05 level with a coefficient of 0.70 (SE=0.28). The next element to show significance was the number of math only courses, though was also only significant when entered into the model in blocks with a negative relationship of -0.65 (SE=0.34), at the p<0.1 level. Finally, similarly to reading gain scores, the number of foundations in education courses saw a positive relationship in the blocked models, though at the p<0.1 level (0.43, SE=0.23) (Table 4.8).

The last two blocks with significant relationship between program elements and math gain scores was technology and techniques used to assess candidate teaching. For instance, in block 4 the number of courses that incorporated instructional technology, was significant both when entered individually and in blocks at the p<0.1 level. Unlike other variables, the size of the relationship barely changed between iterations as the coefficient was 0.28 (SE=0.15) when entered individually and 0.29 (SE=0.15) in blocked models. I further tested this element with a dichotomous variable to test whether a higher or lower number of courses made a difference and the variable for low number of courses with instructional technology was significant. When entered individually, low number of courses had a negative significant relationship of -0.38 (SE=0.21) at the p<0.1 level and a larger negative effect when entered in blocks with a coefficient of -0.51 (SE=0.25) at the p<0.05 level. Finally, for the assessment of a candidate’s teaching, programs with a formal teaching assessment had a significant effect in both the individual and

blocked models, at the p<0.1 level (0.36 SE=0.23 in the individual model increasing to 0.43 SE=0.27 in the blocked model.

Table 4.8. Exploratory Models of Achievement Gains by Program Elements and Subject Elements Assessed Individually (Reading) Elements Assessed in Blocks (Reading) Elements Assessed Individually (Math) Elements Assessed in Blocks (Math) β SE β SE β SE β SE Block 1: Faculty

Number FTE Faculty -0.00 0.00 -0.00 0.01 0.00 0.00 -0.00 0.01

Number Adjunct -0.00 0.00 -0.00 0.00 0.00 0.00 0.00 0.00

Percentage of Adjunct 0.29* 0.18 0.57** 0.24 -0.22 0.20 -0.17 0.27

Adjunct Teach all Course Types 0.01 0.02 0.05* 0.03 0.01 0.02 0.04 0.03

Faculty Incentives for Teaching -0.01 0.21 0.81** 0.40 0.23 0.22 0.49 0.39

Block 2 Candidate Teaching

Early Candidate Teaching Experience -0.17 0.17 0.18 0.39 -0.13 0.18 0.23 0.44 Classroom Experience in Intro Course -0.09 0.26 -0.04 0.37 0.29 0.26 0.53 0.39

Number of Active Teaching -0.04 0.18 0.11 0.20 -0.17 0.20 -0.11 0.23

High Number of Active Teaching 0.26 0.22 -0.03* 0.23 -0.04 0.256 0.03 0.27 Low Number of Active Teaching 0.83** 0.37 0.76* 0.40 0.61* 0.38 0.55 0.45

Computer Adaptive Teaching -0.18 0.20 -0.28 0.33 -0.00 0.22 -0.35 0.37

Hours of Student Teaching -0.00 0.00 -0.00 0.00 -0.00 0.00 -0.00 0.00

Block 3: Required Courses

Average SAT Score (University) -0.00** 0.00 -0.00 0.00 -0.00 0.00 0.00 0.00

High SAT University -0.07 0.17 0.57 0.43 -0.10 0.17 -0.28 0.48

Low SAT University 0.80** 0.26 0.66* 0.35 0.02 0.31 -0.54 0.49

Hours Prior to Student Teaching -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00

Method Courses -0.14* 0.10 -0.66** 0.23 -0.02 0.10 0.06 0.25

Assessment Courses 0.10 0.10 -0.05 0.24 0.09 0.11 0.70** 0.28

Math Only Courses 0.06 0.12 0.02 0.31 -0.00 0.13 -0.65* 0.34

Teaching Math Courses -0.01 0.13 0.93* 0.49 -0.02 0.12 -0.61 0.61

English Only Courses 0.21** 0.09 0.37* 0.24 0.04 0.10 0.11 0.27

***p<0.001 level, **p<0.05 level, p<0.1 level Table 4.8 Continued Elements Assessed Individually (Reading) Elements Assessed in Blocks (Reading) Elements Assessed Individually (Math) Elements Assessed in Blocks (Math) β SE β SE β SE β SE

Block 3: Required Courses (Cont.)

Diverse Learning Courses -0.01 0.09 -0.27 0.21 0.03 0.10 0.06 0.24

Foundation Courses 0.30** 0.13 0.38* 0.21 0.15 0.13 0.43* 0.23

Block 4: Technology

Number of Courses with Technology 0.07 0.14 0.32 0.14 0.28* 0.15 0.29* 0.15

High Number of Courses with Tech 0.12 0.26 0.34 0.29 0.32 0.29 -0.02 0.33

Low Number of Courses with Tech -0.08 0.20 0.20 0.25 -0.38* 0.21 -0.50** 0.25

Number of Technology Courses 0.18 0.13 0.31* 0.19 0.02 0.13 -0.16 0.22

Block 5: Assessment of Candidates

Number of Courses that Record Teaching -0.04 0.04 -0.00 0.04 0.03 0.05 0.02 0.05

High Number of Courses Record 0.16 0.20 0.74** 0.27 0.11 0.22 0.28 0.30

Low Number of Courses Record 0.41** 0.20 0.68** 0.27 0.08 0.23 0.20 0.31

Formal Teaching Assessment -0.05 0.22 -0.26 0.25 0.36* 0.23 0.43* 0.27

Course Based Assessment of Candidates 0.02 0.19 -0.11 0.21 0.25 0.21 0.37* 0.22

Pre-Post Student Tests 0.95*** 0.25 1.02*** 0.26 0.29 0.30 0.16 0.32

Block 6: Mentoring

Mentor in In-Service Training -0.26 0.21 -0.31 0.28 -0.04 0.22 -0.01 0.29

Mentor Review of Teaching Practice -0.13 0.19 0.07 0.26 -0.06 0.21 -0.05 0.27

Block 7: Noted Program Attributes

Student Teaching Experience -

1.24*** 0.31 -0.91** 0.36

-0.04 0.33 -0.15 0.38

Diversity 0.77*** 0.23 0.59** 0.24 -0.13 0.23 -0.16 0.25

Faculty 0.42 0.36 -0.08 0.39 -0.08 0.41 -0.09 0.45

After identifying elements that had a significant relationship in reading and/or math samples, I began to enter these into the full models, however, several elements showed a collinear relationship with one another. As a result, I examined a correlation plot to understand the relationship between these elements. From that review, I was then able to determine which elements should be added to the full model. A correlation plot for elements identified as having a significant effect above in Table 4.8, is shown below in Figure 4.1.

In the initial analysis of the correlation plot, I found that many of these elements were correlated with one another. Indeed, of the 25 elements originally tested, all have at least one variable with which it was positively or negatively correlated with a correlation of 0.50 or higher. The first block I assessed was that of faculty. In this block all 3 elements were strongly correlated with 3 other elements. After reviewing this, I assessed which elements were correlated with one another and determined which should remain in the full model. For instance, adjunct faculty variables were correlated with the elements of technology, formal assessment, teaching reading, teaching methods, intro teaching experiences, and math courses. Each of these elements were all necessary to include given their own significance in this study and prior literature when compared to that of adjunct variables. Whereas in the case of faculty incentives for teaching, this variable is strongly correlated with teaching experiences in the intro to teaching course, however, I have other variables that measure this element but no other variables that measure/assess faculty teaching. As such, I removed all variables in this block except for faculty incentives. For the second block of elements, candidate teaching experiences, courses with active teaching components were correlated with assessment courses, teaching math courses, and foundation in education courses, many of which tend to have an in-classroom experience. I reviewed relationships between these

elements and removed courses specific to student assessment as it was strongly correlated with other elements.

The correlation plot showed that many elements within block 3, required courses, were highly correlated with one another. For example, courses on teaching methods (that are not subject specific) were correlated with courses on teaching math as well as subject specific reading courses. Ultimately, I kept method courses in the full model given it is especially pertinent to the research question. However, I tested model changes with and without this element to better understand the relationship and changes were minimal. The only element that I removed from this section (other than assessment) was diverse learning courses as it was highly correlated with courses that taught math and reading methods. For courses in block 4, technology, I kept the number of courses that had lessons using instructional technology (instead of number of courses that focused solely on the use of instructional technology) as this was significant in the individual and blocked models and not highly correlated with other variables.

The last two blocks that I assessed were those in block 5 (assessment of candidate teaching) and block 7 (noted program attributes). As shown in the correlation plot, the program element of course based assessment of candidates (and not formal assessment outside of courses), was highly correlated with the notable attribute in block 7 unique/diverse student body. These two variables were both unique to this study, however when I entered them both into the full model, no element was significant. When I removed both elements there were variables that were significant. Furthermore, when either variable was in the model (together or separately), the model showed low power as several coefficients were very large compared to coefficients of other variables (above 5.00) yet were not significant. I therefore removed these elements in the full model. Finally, the variable for the candidate’s favorite program aspect was student teaching was strongly

correlated with pre and post-tests in candidate assessment. Given the significance of the relationship of the pre-post-test element, I excluded that element.