Results Summary

As mentioned in the Introduction, the data source for my research was the 2006 Illinois School Report Cards that every public school in Illinois must submit annually to the Illinois State Board of Education (ISBE).  I identified 18 environmental characteristics to study.  Conveniently, half of them were of the type I categorized as controllable and half were non-controllable.  For the purposes of this study, controllable factors are aspects of the school environment that the school's administration can exhibit partial or full control over.  By contrast, non-controllable factors are aspects of the school environment that the school's administration exhibits no control over.  Here are the controllable and non-controllable factors I examined in this study.

Controllable Factors

1. The pupil-to-teacher ratio
2. The 8th grade average class size
3. The 8th grade number of minutes of math instruction per day
4. The percentage of male teachers
5. The teachers' average years of experience
6. The percentage of teachers with M.A.s or higher
7. The average teachers' salary
8. The average administrators' salary
9. The 2005 expenditures per student on instruction 
Non-Controllable Factors

1. The percentage of white students
2. The percentage of black students
3. The percentage of Hispanic students
4. The percentage of Asian students
5. The percentage of native students
6. The percentage of multiracial students
7. The percentage of low-income students
8. The mobility rate 
9. The attendance rate 

To analyze the controllable and non-controllable factors I used Microsoft® Excel® 2003.  Excel has a data analysis package that contains several analysis tools including regression analysis.  Excel's regression analysis tool can analyze up to 16 independent variables simultaneously.  Since it was not possible to analyze all 18 factors at the same time, I decided to divide the analysis into two categories.  I separated them into controllable and non-controllable factors that might influence the 8th grade ISAT math passing percentage.  Analyzing the controllable and non-controllable factors separately allowed me to uncover the from each category that exhibited a link to the 8th grade ISAT math passing percentage. 

Controllable Factors
The controllable factors that had an influence on the 8th grade ISAT math passing percentage were:
1. The pupil-to-teacher ratio
2. The average class size
3. The minutes of math instruction per day
4. The percentage of teachers with M.A.s or higher
5. The average administrator salary

Results of the Controllable Factors Analysis

Factor Factor Coefficient
and Factor to Passing Percentage Relationship
Explanation
Pupil-to-teacher ratio (0.82)
+5 : 4%
Each additional student added to the pupil-to-teacher ratio REDUCES the 8th grade ISAT math passing percentage by 0.82%.
Increasing the pupil-to-teacher ratio by five students would reduce the passing percentage by 4%.
Average class size(+0.48)
+2 : +1%
Each additional student added to the average class size INCREASES the 8th grade ISAT math passing percentage by 0.48%.
Increasing the average class size by two students would increase the passing percentage by 1%.
Minutes of math instruction per day (0.28)
+10 : 3%
Each additional minute of math instruction per day REDUCES the 8th grade ISAT math passing percentage by 0.28%.
Increasing the minute of math instruction by 10 minutes would reduce the passing percentage by almost 3%.
Percentage of teachers with M.A.s or higher(+0.32)
+3 : +1%
Each additional percentage of teachers with M.A.s or higher INCREASES the 8th grade ISAT math passing percentage by 0.32%.
Increasing the percentage of teachers with M.A.s or higher by three percent would increase the passing percentage by 1%.
Average administrator salary(+0.18)
+6,000 : +1%
Each additional $1,000 of average administrator salary INCREASES the 8th grade ISAT math passing percentage by 0.18%.
Increasing the average administrator salary by $6,000 would increase the passing percentage by more than 1%.



Non-Controllable Factors
The non-controllable factors that had an influence on the 8th grade ISAT math passing percentage were:
1. The percentage of black students
2. The percentage of Hispanic students
3. The percentage of low-income students
4. The student mobility rate
5. The student attendance rate

Results of the Non-Controllable Factors Analysis

Factor Factor Coefficient
and Factor to Passing Percentage Relationship
Explanation
Percentage of black students (0.21)
+5% : 1%
Each additional 1% of black students REDUCES the 8th grade ISAT math passing percentage by 0.21%.
Increasing the percentage of black students by 5% would reduce the passing percentage by 1%.
Percentage of Hispanic students (0.12)
+8% : 1%
Each additional 1% of Hispanic students REDUCES the 8th grade ISAT math passing percentage by 0.12%.
Increasing the percentage of Hispanic students by 8% would reduce the passing percentage by about 1%.
Percentage of low-income students (0.11)
+8% : 1%
Each additional 1% of low-income students REDUCES the 8th grade ISAT math passing percentage by 0.11%.
Increasing the percentage of low-income students by 8% would reduce the passing percentage by about 1%.
Student mobility rate (0.17)
+6% : 1%
Each additional 1% increase in the mobility rate REDUCES the 8th grade ISAT math passing percentage by 0.17%.
Increasing the mobility rate by 6% would reduce the passing percentage by about 1%.
Student attendance rate (+2.25)
+1% : +2.25%
Each additional 1% increase in the attendance rate INCREASES the 8th grade ISAT math passing percentage by 2.25%.


After the first two analyses, five controllable and five non-controllable factors were flagged as having an influence on the 8th grade ISAT math passing percentage.  It is obvious however that the controllable and non-controllable factors are not isolated from each other.  To understand the real nature of the factors that affect a school's performance, we must analyze the school report cards with the influential controllable and non-controllable factors combined.  Thus the final analysis involved combining the influential controllable and non-controllable factors together to determine which one or ones truly influenced the 8th grade ISAT math passing percentage. And the winner is...The Pupil-to-Teacher Ratio.  Indeed, out of the 18 factors I examined the singular factor, pupil-to-teacher ratio, proved to be the only one that was significantly related to the 8th grade ISAT math passing percentage.

Pupil-to-Teacher Ratio
Before offering some suggestions as to why the pupil-to-teacher ratio shows a significant correlation to the 8th grade ISAT math passing percentage, it is important to understand what the pupil-to-teacher ratio is (and is not).  Persons not familiar with today's school systems might think of pupil-to-teacher ratio as meaning the same as class size.  These two metrics may or may not be the same.  For example, a classroom with one teacher and 24 students has a pupil-to-teacher ratio of 24-to-1 (24:1).  This same classroom has class size of 24.  However, if this class has a co-teacher, other certified staff, or paraprofessional, then the pupil-to-teacher ratio is 12-to-1 (12:1).  The class size is still 24.

In today's school systems it is not uncommon to have classrooms with more than one certified educator.  For various reasons, a classroom may have two or more certified educators and/or paraprofessionals.  Generally these additional educators are "assigned" to specific students on their caseload however, their expertise is rarely exclusive to their caseload.  These selfless professionals help were they are needed and make a huge difference in the classroom.

So why is pupil-to-teacher ratio a significant indicator of a school's 8th grade ISAT math passing percentage?
In itself, this may be a difficult question to answer.  Almost certainly there are numerous reasons supporting this postulated relationship.
Allow me to offer some possible reasons.

Family Structure
The number of single parent households is not an insignificant figure.  According to the US Census Bureau, the 1990 census showed that 23% of all family households were single-parent families.  Parents in single-parent households are almost certainly going to have less time to devote to their children, especially when it comes to helping them with homework.  Parents in single-parent households also tend to have lower educational levels themselves which is arguably a disadvantage to their children.

Home Study Time
The inexorable march of technology is, in many cases, the enemy of study time.  In the pre-cell phone and Internet days, parents might have admonished their kids to "turn the TV off and do your homework."  Today, kids have a plethora of tantalizing distractions they can choose from including video games, computer games, text and instant messaging, the Internet ala Facebook, music share websites, etc., and the ubiquity of cell phones.  Without unwaivering home study rules, kids are helpless to the allure of these time sappers.  Some teachers I have spoken to admit that they give less homework these days because an ever increasing percentage of students simply do not complete their homework assignments at home.  These teachers feel some students benefit more by completing at least some of the practice assignments while in the controlled, structured environment of the classroom. 

These are just a few of the reasons I believe that having more educators in the classroom is significantly correlated to 8th grade ISAT math passing percentages.  Because math is more procedural than most other curricular areas, success is largely dependent on practice and skill building.  It takes time to encourage, review, correct, and guide students to effectively practice and sharpen their skills.  One teacher with 24 students in a 45 minute class period will be able to offer less than one-minute-per-student once the classroom management issues are handled and the assignment is explained and demonstrated.  Adding one additional educator to this classroom can triple the time spent with each student.  Since the adjunct teacher's time is not used on classroom management or other issues, nearly 100% of their time can be devoted to one-on-one help with students.  And although three minutes of concentrated teacher time doesn't sound like a lot, it might be infinitely more than the student is likely to get at home.

Please feel free to contact me at jtomczak@ISATMathStudy.com.