Fowler-Final_Capstone

Running Header: POTENTIAL FOR QUALITY EDUCATION METRIC 1

Potential for Quality Education Metric

Jonathan Fowler

Adams State University

POTENTIAL FOR QUALITY EDUCATION METRIC 2

INTRODUCTION Education has long been seen by many societies to be the single most important social

program. Philosophers throughout history have debated the role of education and its access. The

concept of improving the quality of life for all through educational institutions has become a well

accepted philosophy in modern civilization. Therefore, it has also become important to analyze

the quality in which education is being provided.

To understand some of the issues plaguing developing educational system for large

societies, one only has to look as far the American education system. For decades this country

has attempted to provide quality education to all citizens, and spends the most per capita on

educational resources, yet it falls short at delivering the most well educated students. American

students often fall in the middle of the pack in a comparison of test scores across all subjects

among developed nations. Part of this continuing and growing issue is the prominence of the

Achievement Gap in various socio- economic and ethnic echelons.

To even begin understanding what causes American education to fail at closing the

Achievement Gap, we must first define what quality education is and how we can measure it.

There are many ways that we can define quality in education, of which Don Adams (1993)

narrows down to six different perspectives: quality as reputation, resources and inputs, process,

content, outputs and outcomes, and “value added”. The focus of this research mainly focuses on

the quality of process, defined by Adams as,

“Quality as process suggests that not only inputs or results

but also the nature of the intra-institutional interaction of

students, teachers and other educators, or ‘quality of life’ of

the program, school or system, is valued.”

POTENTIAL FOR QUALITY EDUCATION METRIC 3

This approach of understanding the process is essential, because this project proposes that is

equally essential to look at the results when determining quality as it is to look at initial potential

for such quality to have a propensity to prosper.

If we assume that the goal of education spending and reforms are to improve and

maintain the quality of education in schools, then it is equally important to understand the

propensity for quality education to be cultivated in a school or region. Though quantitative

metrics in educational research can be difficult to develop, I believe it will be possible to

measure the potential for education by measuring a limited number of key statistics in a

community, region, or district.

By developing this potential for quality education metric (PQE metric or PQEM), several

key uses can be concluded. The greatest advantage proposed is that the PQEM will allow

researches and policymakers to understand how to most effectively utilize educational resources.

For example, if the PQEM is calculated to be low for a school district, then it would be a “red

flag” for policymakers to investigate the causes for the lower metric, and possibly solve those

issues, instead of blindly giving resources to the district with little or no directive to solve the

issues inhibiting students to effectively be educated.

Once this PQE metric is refined, examined, and proven to be effective, further research

can be done to continue improving the quality of educational systems. Researching correlations

between incomes in a region and PQE can be investigated. Violence rates, quality of life,

property value, and a myriad of other statistics could also be opened up to correlated studies

surrounding the PQEM. The wealth of possible data is great and is worthy of investigating the

development of this new metric.

POTENTIAL FOR QUALITY EDUCATION METRIC 4

LITERATURE REVIEW Before a measure on potential educational quality can be made, it will be necessary to begin

defining education quality. This is a difficult task, but using the works of Adams (1993) and

Cheng (1997), an indication of how this definition can be boiled down is possible. Using these

documents as a backing, a clear indication of important quality indicators come from relative

teacher pay, pupil-teacher ratios, free and reduced lunch ratios, and density of gang and violent

criminal activity. Although these indicators are not alone, the literature provided shows their

strong correlation to educational quality and academic performance.

Teacher salary has been a contentious issue when it comes to academic performance

outcomes. Many economists have argued about whether raises base pay of works improves

productivity, effectiveness, and quality among candidates for positions. Eric Hanushek has

argued in many of his works about how direct increases of teacher salary does not correlate to

improve academic performance of students (1994; 1996; 2007). Yet, there are many researches

that show how important teacher pay is towards increasing the potential of high educational

quality. Jennifer Imazeki (2005) and Dolton & Marcenaro-Gutierrez (2011) show empirical

evidence of the importance of teacher salaries to the retention of both veteran and less

experienced teachers that show high potential as quality educators, while showing performance

gains in academic achievement. Lee & Barro (2001) also show how relative pay of teachers is an

important factor in developing higher academic performance.

Beyond teacher salary, the pupil-teacher ratio is also a controversial issue surrounding the

measurement of educational quality. Finn & Achilles (1999), Lee & Barro (2001), and Sequeira

& Robalo (2008) all show a high level of empirical evidence on the importance of the pupil-

teacher ratio in determining the quality of education a student receives. Despite many who

POTENTIAL FOR QUALITY EDUCATION METRIC 5

contradict this evidence, I believe the literature will provide a strong backing of the theory that

pupil-teacher ratios are important in this realm of educational quality. Furthermore, investigating

the educational philosophy of culturally relevant pedagogy (Ladson-Billings, 1995) is a strong

corollary indicator of need lower pupil-teacher ratios due to the necessity of developing strong

relationships with all students.

Along with understanding the economics of the teachers’ side of the equation, it may be

imperative to consider the economics of the community in which the students are immersed. A

significant amount of research has been done to show the importance of socioeconomics in the

achievement gap of students (Brooks-Gunn & Duncan, 1997; Lee, 2002; Reardon, 2011).

Research has also shown a strong correlation between socioeconomic statuses and the ratio of

free and reduced lunches in schools and districts (Caldas & Bankston, 1997; Harwell & LaBeau,

2010). Therefore, this ratio has the potential to be an important factor in measuring the potential

for quality of education in a region.

Finally, I came across the idea in my literature search of including criminal and gang

activity density as an indicator of educational quality. This is an important factor, as many

sociopsychological theorists have long claimed the importance of understanding “Broken

Window” theory and how our surrounds environments effect how we all behave (Wilson &

Kelling, 1982). Therefore, is a student is engulfed in a subculture of violence and crime then they

are more likely to be apart of that culture and thus have a lower chance of performing well

academically (Felson, Lisk, & South, 1994). This is also supported by research done by Case &

Katz (1991) on how family and communities interactions that are negative in nature will also

effect minors in a negative fashion as well. Through understanding these negative effects and

POTENTIAL FOR QUALITY EDUCATION METRIC 6

analyzing them, there should be some inclusion of them in any metric developed to measure

potential for quality education.

METHODOLOGY The mathematical model I propose to measure the potential for quality education revolves

around weighted normalized statistical measures. Researches and theorists in the educational

field have cited numerous indicators that effect the quality of education. To develop this model,

it seems prudent to start small and easily measureable. Complex indicators can always be

researched and added into the model if increased increased efficacy is deemed necessary.

Of all the statistics available, the pupil-teacher ratio (PTR) has come under scrutiny for

whether or not it is of importance to quality education. A larger body of evidence shows its

importance throughout the history of education research and most detractors are arguing against

the economics of reducing class-size. The educational philosophy of Culturally Relevant

Pedagogy (CRP) introduced formally by Ladson-Billings (1995), entrenches itself in the

importance of pupil-teacher relationships, which require reasonable class sizes. Therefore, the

PTR is included as an effective indicator in the PQE model. Collection of this data comes form

district statistics reporting, the Colorado Department of Education, or through the mathematics:

!"#$%&'( = +,-./01-2

+30'&4052

To normalize this metric, it will be compared to the national PTR average:

!"#$%&'( ≡Normalized Teacher-Pupil Ratio

!"# =!"#$%&'(

!"#7'-8%1'(

POTENTIAL FOR QUALITY EDUCATION METRIC 7

The average national pupil-teacher ratio reported by the National Center for Education Statistics

was 16.0 for the year 2013 (U.S. Department of Education, 2015), making the normalized

metric:

!"# =!"#$%&'(

16.0

This normalized metric can then be weighted into the overall model. A step that will be covered

at the end of this chapter.

The second indicator to be included in this model is the ratio of students eligible for free

and reduced lunch. Most schools public report their statistics on this ratio, as well as the

Colorado Department of Education and National Center for Educational Statistics.

Mathematically, the free and reduced lunch ratio can also be calculated:

=#>$%&'( =+?@$

+,-./01-2

The metric can then be normalized using the national average of the free and reduced lunch ratio:

=#> ≡ NormalizedFreeandReducedLunchRatio

=#> ==#>$%&'(

=#>7'-8%1'(

The national average ratio of students eligible for free and reduced lunch was reported by the

National Center for Educational Statistics as being 0.513 for the year 2013 (U.S. Department of

Education, 2014), making the normalized metric:

=#> ==#>$%&'(

0.513

POTENTIAL FOR QUALITY EDUCATION METRIC 8

With these redundant sources of data, it improves the potential for the free and reduced lunch

ratio to be a reliable statistic to be included in this model.

The final indicator that will be measured for this research is the violent crime density for

the region. Using the Federal Uniform Crime Reporting Statistics, the number of violent crimes

in a city with a population of 10,000 or a county with over 25,000 can easily be obtained on a

yearly basis. If we define this metric of per capita violent crimes as U$%&'( and compare it to the

national average, described as U7'-8%1'(, a normalized metric can be represented as:

U ≡U7'-8%1'(

U$%&'(

To account for natural fluctuations in these statistics in these statistics, an average of the violent

crimes per capita can be averaged for both local and national statistics over three years:

UV ≡U7'-8%1'(,V

U$%&'(,V

This normalized can then be weighted and added to the PQEM.

With the normalized statistics, !"#, X, and UV at hand, they can be weighted and summed

into the final PQEM. Since all the statistics are normalized, a value for each, greater than 1,

would indicate a higher than average statics in a positive manner. Lower than 1 would indicate a

lower than average statistic. Using a weight for each metric we can define three simplified

variables of the weighted metrics as:

YZ ≡ !"# ∗ \Z

Y] ≡ X ∗ \]

POTENTIAL FOR QUALITY EDUCATION METRIC 9

YV ≡ U ∗ \V

where \Z,\], and \V are the weighing variables, such that \Z + \] + \V = 1. With the

weighted metrics calculated, the PQEM can finally be defined as:

!_`a ≡ Y1

1

8bZ

!_`a = YZ +Y] +YV

The final hang-up is determining how to weigh these metrics accurately, and calibrate it

so that it is properly measuring potential for quality education. Using a Python script and the

linear regression analysis Application Programming Interfaces included from the Python libraries

NumPy and SciPy, calibrated weights will be calculated. Once the test sample of statistics are

collected, the matrix of results will be measured against average ACT scores for the district and

high school graduation rates, which are reported by the Colorado Department of Education. The

weight configuration that shows the strongest correlation will the be used for the final analysis.

The test sample with involve the school districts with student populations of 10,000 or

greater. Based on current statistics, this would include twenty school districts, providing a

statistically significant sample with a variety of demographics. This sample will make collected

data more accurate. To analyze the efficacy beyond this sample will require further research

beyond the initial scope of this project.

It should be noted that all the metrics provided in this chapter can also be zero normalized

to develop metrics that show positively correlating indicators as positive numbers and negatively

correlating indicators as negative numbers. The mathematics for this version of the model is

provided in the Appendix A.

POTENTIAL FOR QUALITY EDUCATION METRIC 10

Finally, during the literature review it was argued that teacher salary should be included

in this model. Unfortunately, due to the limitations of the Cost of Living Index accuracy that was

available at the time of this research, it was not included in this iteration of the model. An

argument and the mathematics behind using teacher salary in such a model is included in

Appendix B for reference.

RESULTS Using the methodology stated in the previous chapter, the PQEM statistics were collected

for the twenty Colorado school districts included in the study. Looking at the most basic results,

using equally weighted metrics, a moderate correlation can be observed using a coefficient of

determination in a linear fit to the data (Figure 1). Although this model with equally weighted

metrics does not show the perfect fit that one would hope for in a predictive model, it does show

that there is a correlation between the PQEM and the composite value of education quality for

each district.

Figure 1: A moderate (R² = 0.52) correlation can be found between the equally weighted PQEM and the composite quality of education values.

R² = 0.52

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2

PQ

EM

Composite Quality of Education

PQEM: Equal Weighted

\Z = 0.33\] = 0.33\V = 0.33

POTENTIAL FOR QUALITY EDUCATION METRIC 11

When the data is run through the Python weighting optimization script, a slightly stronger

correlation can be observed (R2 = 0.57) using the weighted metrics w1 = 0.03, w2 = 0.79, and

w3=0.79. This iteration can be seen in Figure 2. Also two strong outliers from Douglas County

Public Schools and Academy District 20 appear in this iteration.

Figure 2: A slightly stronger moderate correlation (R² = 0.59) can be observed when optimized weights are used for the metrics in the PQEM. The strong outliers from Douglas County Public Schools and Academy District 20 are circled.

If the two strong outliers are removed from the dataset and it is run through the script

once more, a pronounced increase in the correlation of the PQEM to composite quality of

education occurs (R2 = 0.87; Figure 3). The question then focuses on why Douglas County and

Academy District 20 are outliers in the first place. Both districts have uniquely high academic

outcomes overall. The demographics of these regions or the schools involved may also be more

complex than this model has been set up to account for. Unfortunately, these are purely

R² = 0.59

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2

PQ

EM

Composite Quality of Education

Weighted PQEM

\Z = 0.03\] = 0.79\V = 0.18

POTENTIAL FOR QUALITY EDUCATION METRIC 12

speculative reasons, and a more in-depth analysis is beyond the scope of this project.

Nevertheless, it indicates that for this model to be more successful, more factors may have to

taken into account or adjusted to increase its predictive abilities.

Figure 3: When the two strong outliers are removed, a strong correlation between the PQEM and quality of education can be observed.

Through all of these optimization weighted iterations, an interesting trend occurs with the

weighted metrics. As correlation increases, the violent crime density weight approaches zero.

The free and reduced lunch weight appears to have some use in producing a correlation. And the

pupil-teacher ratio weight appears to have the most relevancy in the optimization calculation by

far. These are all interesting outcomes and were not expected when this project began.

The violent crimes density is a large surprise in its possible irrelevancy to the PQEM

model. Due to the complexity of issues that go into the why and how violent crimes occur in a

R² = 0.87

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2

PQ

EM

Composite Quality of Education

Weighted PQEM

\Z = 0.00\] = 0.74\V = 0.26

POTENTIAL FOR QUALITY EDUCATION METRIC 13

region, it may be that they are too chaotic of a variable to be a reliable predictor towards

measuring quality of education. While research shows how there is a strong negative correlation

towards violent crimes versus academic outcomes, the current attempt made at modeling it in

this initial research may be flawed in an unknown manner. In future iterations of this model it

may be necessary to reevaluate the methodology in inclusion of violent crimes to the PQEM

model.

Another interesting standout is the high weight calculated for the pupil-teacher ratio

metric. One major possibility to this high weighted value is that pupil-teacher ratios fluctuate

much less than other predictive measurements. This would indicate that it would be

advantageous to seek out other stable variables that may predict the potential for quality

education in future iterations of this model. Another possibility is that the pupil-teacher ratio is

simply a reliable indicator of the potential for quality education. If this is the case it would be

another argument for the importance of keeping the pupil-teacher ratio low so that students have

the highest chance of success in the classroom.

The fact that reducing both the pupil-teacher ratio and free and reduced lunch ratio tend

to positively correlate to higher potential for quality education, it appears there is a strong

argument that improving both of these figures will increase the potential of high academic

outcomes. While some educational researches have begun to argue that pupil-teacher ratios and

economics do not inherently indicate that academic outcomes will be poor, this mathematical

model may lay the ground work to show the importance of economics and the number of teacher

in relation to students have significant effects on academic outcomes. Therefore, I believe this

research should be continued to improve the accuracy and predictive outcomes for the PQEM

model. With the knowledge this research has provided it should be argued that, at least in the

POTENTIAL FOR QUALITY EDUCATION METRIC 14

State of Colorado, that districts need to continue being considerate of the pupil-teacher ratio and

the economic viability of their region to understand how their students will perform

academically. Knowing this information may allow resources at all levels to be used more

effectively towards positive student academic outcomes.

CONCLUSION Educational reform to increase academic achievement has been an issue that has been

researched and discussed in the American system for decades. The purpose of this research was

to develop a new mathematical model in an attempt to understand the indicators of potential for

quality education in a region or district. Four indicators of quality education were considered

after studying years of previous research, including the pupil-teacher ratio, violent crimes

density, free and reduced lunch ratio, and teacher salaries. Unfortunately, the teacher salaries

statistics was not included in the final model for this project due to issues with the Cost of Living

Index. The results indicated a moderate to strong correlation between the weighted PQEM and

composite value measuring quality of education in the districts. Two strong outliers appeared to

effect the correlation and may indicate anomalies in the model that need to be researched further

to understand their importance in further iteration of this model. The model shows an indication

of strong importance on the pupil-teacher ratio in the ability to predict academic outcomes.

Further research may improve the understanding of this correlation, but it should be a note to

policymakers that the pupil-teacher ratio is still an important factor for academic performance.

POTENTIAL FOR QUALITY EDUCATION METRIC 15

APPENDIX A: ZERO NORMALIZATION MATHEMATICS The purpose of using zero normalized metrics is to show positively correlating indicators as

positive numbers and negatively correlating indicators as negative numbers. The mathematics for

this version of the model are include in this section.

PUPIL-TEACHER RATIO

!"# =

!"#7'-8%1'(

!"#$%&'(− 1for

!"#7'-8%1'(

!"#$%&'(≥ 1

1 −!"#$%&'(

!"#7'-8%1'(for

!"#7'-8%1'(

!"#$%&'(< 1

FREE AND REDUCED LUNCH RATIO

=#> =

=#>7'-8%1'(

=#>$%&'(− 1for

=#>7'-8%1'(

=#>$%&'(≥ 1

1 −=#>$%&'(

=#>7'-8%1'(for

=#>7'-8%1'(

=#>$%&'(< 1

VIOLENT CRIME DENSITY

U =

U7'-8%1'(

U$%&'(− 1for

U7'-8%1'(

!"#$%&'(≥ 1

1 −!"#$%&'(

U7'-8%1'(for

U7'-8%1'(

U$%&'(< 1

POTENTIAL FOR QUALITY EDUCATION METRIC 16

APPENDIX B: TEACHER SALARY METHODOLOGY Another easily measured indicator is teacher salary. This is a controversial statistic

because it has been argued that teacher salaries do not correlate to increased test scores. Basic

economic theory contradicts this notion fairly quickly (Dolton & Marcenaro-Gutierrez, 2011).

As you increase salary, within certain margins, you increase the pool of quality candidates for

the position. If teacher pay is low relative to the cost of living, then the propensity for teachers to

apply for positions in the region decreases. Therefore, despite detractors, relative teacher pay is

an important indicator for assessing the potential of quality education. There are several ways in

which relative teacher salary can be measured.

One method is to take the average of all teacher salaries in a region or district. This is a

difficult measurement because it usually requires districts to voluntarily release or report the

information. It is also a difficult measurement to verify independently. Another method simply

looks at the salary of the first year teachers. This method assumes a single-pay scale matrix,

often divided by years of experience and level of education. While this is often an easier

measurement, it may not point the most accurate picture of teacher salaries in the district.

Another possible measurement looks at the average pay-scale of masters-level educated teachers

for the first five years of experience. This method is slightly more complex than others, but looks

at an often publically published figure from teacher unions or district boards. Investigating

masters-level pay for these experience levels is important because they are the most important

when discussing quality teacher retention versus mobility and career exit from a district.

Although not all districts scale their pay on a single schedule, base-salary for this metric can be

used for all districts to simplify and unify the metric. Further investigation into modifying the

metric for more intricate complexities will be left for future research if deemed necessary.

POTENTIAL FOR QUALITY EDUCATION METRIC 17

From the mathematical standpoint the relative salary will have to be normalized. Using

the U.S. Bureau of Labor Statistics we will define a national average salary, X7'-8%1'(. Using the

Cost-of-Living Index (CLI; St Louis Robert, 1989), a relative average pay can be determined and

normalized:

X =X7'-8%1'( ∗ (m>n/100)

X$%&'(

This normalized value can then be weighted into the PQEM.

Running Header: POTENTIAL FOR QUALITY EDUCATION METRIC 18

APPENDIX C: DATA TABLES District NStudents NTeachers

Pupil-TeacherRatio

NFree&ReducedLunch RatioFRL

DenverPublicSchools 90,150 5,245 17.19 62,826 0.697

JeffCoPublicSchools 86,572 4,700 18.42 27,530 0.318

DouglasCountrySchoolDistrict 61,465 3,297 18.64 6,515 0.106

CherryCreekSchoolDistrict 54,228 2,983 18.18 14,099 0.260

Adams12FiveStarSchools 42,230 2,092 20.19 14,632 0.346

AuroraPublicSchools 40,877 2,083 19.62 29,145 0.713

BoulderValleySchoolDistrict 30,546 1,688 18.10 5,498 0.180

St.VrainValleySchoolDistrict 30,195 1,616 18.69 10,870 0.360

ColoradoSpringsSchoolDistrict11 28,407 1,686 16.85 16,334 0.575

PoudreSchoolDistrict 29,053 1,716 16.93 9,794 0.337

AcademyDistrict20 24,481 1,463 16.73 3,183 0.130MesaCountyValleySchoolDistrict51 21,906 1,263 17.34 9,201 0.420

Greely-EvansSchoolDistrict6 20,441 1,142 17.90 13,234 0.647

FalconSchoolDistrict49 18,880 914 20.66 5,664 0.300

PuebloCitySchools 18,034 1,048 17.21 12,966 0.719

SchoolDistrict27J 16,987 803 21.15 6,428 0.378

ThompsonSchoolDistrict 16,226 868 18.69 5,694 0.351

LittletonPublicSchools 15,830 843 18.78 3,324 0.210

HarrisonSchoolDistrictTwo 11,777 688 17.12 8,362 0.710

AdamsCountySchoolDistrict50 10,101 540 18.71 8,081 0.800

POTENTIAL FOR QUALITY EDUCATION METRIC 19

DistrictViolentCrimesper100k(2010)

ViolentCrimesper100k(2011)

ViolentCrimesper100k(2012)

MeanViolentCrimesper100k

DenverPublicSchools 564 607 616 596

JeffCoPublicSchools 227 231 234 231

DouglasCountrySchoolDistrict 119 138 92 116

CherryCreekSchoolDistrict 295 421 418 378

Adams12FiveStarSchools 701 476 263 480

AuroraPublicSchools 446 438 425 436

BoulderValleySchoolDistrict 216 278 248 247

St.VrainValleySchoolDistrict 599 538 564 567

ColoradoSpringsSchoolDistrict11 471 440 455 455

PoudreSchoolDistrict 182 168 172 174

AcademyDistrict20 471 440 455 455MesaCountyValleySchoolDistrict51 263 297 314 291

Greely-EvansSchoolDistrict6 397 397 433 409

FalconSchoolDistrict49 129 74 65 89

PuebloCitySchools 831 766 731 776

SchoolDistrict27J 207 259 345 270

ThompsonSchoolDistrict 191 157 210 186

LittletonPublicSchools 127 130 130 129

HarrisonSchoolDistrictTwo 471 440 455 455

AdamsCountySchoolDistrict50 220 227 260 236

POTENTIAL FOR QUALITY EDUCATION METRIC 20

DistrictNormalizedViolentCrimeDensity

NormalizedPupil-TeacherRatio

NormalizedFree&ReducedLunch

HSGraduationRate ACTAverage

DenverPublicSchools -0.517 -0.074 -0.358 0.628 17.6

JeffCoPublicSchools 0.703 -0.151 0.613 0.829 21.2

DouglasCountrySchoolDistrict 2.377 -0.165 3.840 0.914 21.7

CherryCreekSchoolDistrict 0.039 -0.136 0.973 0.871 21.4

Adams12FiveStarSchools -0.222 -0.262 0.481 0.74 19.5

AuroraPublicSchools -0.111 -0.227 -0.390 0.6 16.7

BoulderValleySchoolDistrict 0.588 -0.131 1.850 0.91 23.4

St.VrainValleySchoolDistrict -0.443 -0.168 0.425 0.83 20.2

ColoradoSpringsSchoolDistrict11 -0.159 -0.053 -0.121 0.784 18.9

PoudreSchoolDistrict 1.258 -0.058 0.522 0.84 22.1

AcademyDistrict20 -0.159 -0.046 2.946 0.91 22.1MesaCountyValleySchoolDistrict51 0.348 -0.084 0.221 0.78 19.5

Greely-EvansSchoolDistrict6 -0.041 -0.119 -0.262 0.78 17.4

FalconSchoolDistrict49 3.397 -0.291 0.710 0.9 19.1

PuebloCitySchools -0.975 -0.076 -0.402 0.719 18.3

SchoolDistrict27J 0.453 -0.322 0.356 0.79 18.6

ThompsonSchoolDistrict 1.112 -0.168 0.462 0.773 20.9

LittletonPublicSchools 2.045 -0.174 1.443 0.92 22.5

HarrisonSchoolDistrictTwo -0.159 -0.070 -0.384 0.776 18.8

AdamsCountySchoolDistrict50 0.667 -0.169 -0.559 0.64 16

POTENTIAL FOR QUALITY EDUCATION METRIC 21

REFERENCES Adams, D. (1993). Defining educational quality. Improving Educational Quality Project

Publication, 1.

Brooks-Gunn, J., & Duncan, G. J. (1997). The effects of poverty on children. The future of children, 55-71.

Case, A. C., & Katz, L. F. (1991). The company you keep: The effects of family and neighborhood on disadvantaged youths (No. w3705). National Bureau of Economic Research.

Caldas, S. J., & Bankston, C. (1997). Effect of school population socioeconomic status on individual academic achievement. The Journal of Educational Research, 90(5), 269-277.

Cheng, Y. C. (1997). A framework of indicators of education quality in Hong Kong primary schools: Development and application. Paper presented at the Asia-Pacific Economic Cooperation Education Forum on School-Based Indicators of Effectiveness, Quilin, China.

Corcoran, T. B. (2007). Teaching Matters: How State and Local Policymakers Can Improve the Quality of Teachers and Teaching. CPRE Policy Briefs RB-48. Consortium for Policy Research in Education.

Dolton, P., & Marcenaro-Gutierrez, O. D. (2011). If you pay peanuts do you get monkeys? A cross-country analysis of teacher pay and pupil performance. Economic Policy, 26(65), 5-55.

Felson, R. B., Liska, A. E., South, S. J., & McNulty, T. L. (1994). The subculture of violence and delinquency: Individual vs. school context effects. Social Forces, 73(1), 155-173.

Finn, J. D., & Achilles, C. M. (1999). Tennessee's class size study: Findings, implications, misconceptions. Educational Evaluation and Policy Analysis, 21(2), 97-109.

Hanushek, E. A. (1994). Making schools work: Improving performance and controlling costs. Brookings Institution Press.

Hanushek, E. A. (1996). School resources and student performance. Does money matter, 43-73.

Hanushek, E. A. (2007). The single salary schedule and other issues of teacher pay. Peabody Journal of Education, 82(4), 574-586.

Harwell, M., & LeBeau, B. (2010). Student eligibility for a free lunch as an SES measure in education research. Educational Researcher, 39(2), 120-131.

POTENTIAL FOR QUALITY EDUCATION METRIC 22

Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American educational research journal, 32(3), 465-491.

Lee, J. (2002). Racial and ethnic achievement gap trends: Reversing the progress toward equity?. Educational researcher, 31(1), 3-12.

Imazeki, J. (2005). Teacher salaries and teacher attrition. Economics of Education Review, 24(4), 431-449.

Lee, J. W., & Barro, R. J. (2001). Schooling quality in a cross–section of countries. Economica, 68(272), 465-488.

NumPy. (n.d.). Retrieved November 13, 2015, from http://www.numpy.org/

Python.org. (n.d.). Retrieved December 13, 2015, from https://www.python.org/

Reardon, S. F. (2011). The widening academic achievement gap between the rich and the poor: New evidence and possible explanations. Whither opportunity, 91-116.

SciPy. (n.d.). Retrieved November 13, 2015, from http://www.scipy.org/

Sequeira, T., & Robalo, P. (2008). Schooling quality in a cross section of countries: a replication exercise and additional results. Economics Bulletin, 9(9), 1-7.

St Louis Robert, A. (1989). The theory of the cost-of-living index. Oxford University Press.

Uniform Crime Reporting Statistics. (n.d.). Retrieved December 13, 2015, from http://www.ucrdatatool.gov/

U.S. Department of Education, National Center for Education Statistics. (2015). Digest of Education Statistics, 2013 (NCES 2015-011).

U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "Public Elementary/Secondary School Universe Survey," 2000-01, 2010-11, 2011-12, and 2012-13.

Wilson, J. Q., & Kelling, G. L. (1982). Broken windows. Atlantic monthly, 249(3), 29-38.