![](media/image1.jpeg){width="1.2902777777777779in"
height="1.2833333333333334in"}

Tom Horne

Superintendent of Public Instruction

Arizona Department of Education

Submitted by the , November 1, 2006. Revised January 5, 2007

Revised with Addendum July 2, 2007

Research & Policy

Arizona Department of Education

Robert Franciosi, Deputy Associate Superintendent

Achieve@azed.gov

The Arizona Department of Education of the State of Arizona does not
discriminate on the basis of race, religion, color, national origin,
sex, disability or age in its programs, activities or in its hiring and
employment practices. If you have questions or grievances related to
this policy, please contact the Administrative Services DAS at
(602)542-3186.

**Summary**

The Arizona Department of Education (ADE) is submitting this proposal
requesting the opportunity to incorporate a model of individual student
growth into the adequate yearly progress (AYP) evaluations of districts
and schools. If approved, the model can be implemented in the AYP
evaluations for the 2006-07 school year.

The purpose of including a growth model in AYP evaluations is to
recognize the success of schools in improving student achievement, even
though that achievement may fall short of proficiency. With recognition
comes the incentive for schools to concentrate further effort toward
assisting students who fall short of proficiency. Increased attention
toward the lowest performing students will keep them from falling
further behind their peers. Educators in successive grades will find
more of their students within striking distance of proficiency, allowing
the achievement gap to be closed more quickly.

Arizona has publicly reported its measure of student growth for schools,
the Measure of Academic Progress (MAP), for seven years. It is included
on school report cards and used by third party information sources like
GreatSchools.net. It is also used as a performance pay indicator for
teachers. Parents, the public, school administrators, and teachers are
all familiar with the specific measure and the concept of growth in
general. With increasing emphasis on state standards, the old MAP based
on the norm-referenced test was starting to be deemphasized. With the
introduction of a new growth measure based on state standards, we expect
additional use of the growth measure to develop state and local policy
and treat the instructional needs of individual students. Including
growth as part of the AYP determination will bring the various
accountability measures in the state into greater congruence, increasing
the effectiveness and validity of the state's overall school
accountability system.

**Components in Place**

Arizona has in place all the necessary elements for a student-level
growth model:

-   The state's Student Accountability Information System (SAIS) has
    been in place since 2002. Each student of a public (including
    charter) school in the state is assigned a unique SAIS ID that
    follows her through her career from kindergarten to high school
    graduation. The SAIS system also contains demographic and program
    membership information for all students.

-   All students are tested in both reading and math in grades three
    through eight. The state's assessment system has been approved by
    the NCLB peer review. The AIMS test is vertically scaled for grades
    three through eight. Arizona has vertically aligned, articulated
    standards for all grades.

The growth model submitted in this proposal will be calculated for all
subgroups of students and used as a parallel AYP evaluation for both
schools and districts. Schools and districts will be identified for
school improvement if they miss AYP both via the growth model and the
via traditional status model of determining AYP.

The model looks at the progress individual students make toward
proficiency from one year to the next. The goal is proficiency within
three years or by the eighth grade, whichever comes first. Annual growth
targets are set that measure each student's progress toward that goal.
Students are deemed to have made sufficient progress if they meet their
annual growth target. Scores for individual students are aggregated by
the relevant subgroups. If the percentage of students in a subgroup that
meets the target for growth is equal to or greater than the AMO, then
the subgroup is considered to have met AYP.

**Details of Model**

**NOTE: The addendum of July 2, 2007 supersedes the description given
below for determining if a student meets his or her growth target.**

The proposed model calculates the annual progress made by each student
toward proficiency in state standards. Progress is measured against the
goal of proficiency within three years or by eighth grade, whichever
comes first. This represents a horizon of no more than three years, and
less for students in higher grades. The steps for calculating it are:

1.  For each student an **annual growth target** is set for each
    subject: reading and math. The growth target is how much improvement
    measured by scale score points a student would have to make over her
    previous year's score in equal intervals in order to achieve
    proficiency within three years or by the eighth grade. The growth
    target is set by subtracting the student's previous year scale score
    from the scale score for proficiency in the target grade and
    dividing by the number of remaining grades. Since Arizona's
    vertically scaled series of tests ends at eighth grade, the scale
    score for eighth grade will be used for grades five through seven.
    The targets are rounded to the nearest whole number. Demographic
    factors are not used to set the target.

> [Example:]{.underline} A student scores 402 on the 3^rd^ grade math
> test in 2005. The passing score on the 6^th^ grade math test is 496.
> The student's math score must improve 31 points each year---(496 --
> 402)/(6-3) = 94/3 = 31---for him to reach proficiency by 6^th^ grade.
>
> [Example.]{.underline} A student scores 469 on the 6^th^ grade reading
> test in 2005. The passing score on the 8^th^ grade reading test is
> 499. The student's reading score must improve 15 points each
> year---(499-469)/(8-6) = 30/2 = 15---for her to reach proficiency by
> 8^th^ grade.

2.  For each student **actual growth** is measured for each subject.

> [Example:]{.underline} A student scores 402 on the 3^rd^ grade math
> test in 2005 and 442 on the 4^th^ grade math test in 2006. The
> student's actual growth is 40 points (442 -- 402).

3.  For each student **actual growth** is compared to the **annual
    growth target**. If actual growth is greater than or equal to the
    annual growth target, the student is deemed to have made adequate
    growth.

> [Example.]{.underline} A student's growth target is 31. The actual
> growth shown is 40. The student is considered to have made adequate
> growth.

To determine if a subgroup met the AMO, the following percentage is
calculated:

$$\frac{\text{ Students }(\text{proficient and non-proficient})\text{ meeting growth target}}{\text{Number of students in analysis}}$$

If this percentage is greater than or equal to the AMO, then the group
is deemed to have made AYP. Because the AMOs increase over time, the
growth targets increase over time as well. In 2014, all students will
either have to be proficient or be on the road to achieving proficiency
within three years or less. This is consistent with the NCLB goal.

**Conclusion**

Arizona is well qualified to incorporate a growth model into its AYP
evaluations for schools and districts.

1.  Arizona has in place all the necessary elements for a growth model.
    The SAIS database assigns each student a unique identifier that
    tracks students across grades, schools, and districts. It also holds
    student demographic information, allowing growth to be measured for
    all the subgroups required by NCLB. The AIMS test has been
    administered operationally in all grades three through eight, is
    vertically scaled, and will remain stable for the next four years.

2.  Arizona has experience with growth measures. Student growth has been
    a part of Arizona's school accountability system since the previous
    century. Growth measures have been reported publicly and used by
    administrators. We will continue to do so regardless of the status
    of this proposal.

3.  Arizona's growth model provides a more valid measure of school
    effectiveness than the current status-only evaluation. It recognizes
    and gives schools the incentive to improve student performance at
    all levels.

4.  Arizona sets ambitious growth targets for all students in all
    schools. Expected growth is not dependent on students' demographic
    characteristics. It sets the ultimate goal of all students being
    proficient or on track to proficiency by 2014.

If approved, the Arizona growth model would lessen the possibility that
students would fall behind. It will increase the number of students who
move on to higher grades that are ready to learn. Consequently, adding
the growth model to the AYP determination will help close the
achievement gap more rapidly.

**Table of Contents**

[1 Overview 6](#overview)

[1.1 A Growth Model Will Improve School Accountability in Arizona
6](#a-growth-model-will-improve-school-accountability-in-arizona)

[1.2 Arizona Meets the New Equation for Flexibility
7](#arizona-meets-the-new-equation-for-flexibility)

[1.3 Core Elements in Place for Growth Model
8](#core-elements-in-place-for-growth-model)

[1.4 Development and Implementation 8](#development-and-implementation)

[2 The Proposed Model 10](#the-proposed-model)

[2.1 The Current System for AYP Determination in Arizona
10](#the-current-system-for-ayp-determination-in-arizona)

[2.2 Incorporating the Growth Model into the AYP Evaluation
11](#incorporating-the-growth-model-into-the-ayp-evaluation)

[2.3 Calculation of Growth 11](#calculation-of-growth)

[2.4 Details of the Calculation 13](#details-of-the-calculation)

[2.5 Alternate Tests 16](#alternate-tests)

[2.6 K-2 Schools, High Schools, and Third Grade
17](#k-2-schools-high-schools-and-third-grade)

[3 Arizona's Growth Model Meets the Seven Core Principles
18](#arizonas-growth-model-meets-the-seven-core-principles)

[3.1 100 percent proficiency by 2014 and Incorporating Decisions about
Student Growth into School Accountability
18](#percent-proficiency-by-2014-and-incorporating-decisions-about-student-growth-into-school-accountability)

[3.2 Establishing Appropriate Growth Targets at the Student Level
19](#establishing-appropriate-growth-targets-at-the-student-level)

[3.3 Accountability for Reading/Language Arts and Mathematics Separately
20](#accountability-for-readinglanguage-arts-and-mathematics-separately)

[3.4 Inclusion of All Students 20](#inclusion-of-all-students)

[3.5 State Assessment System and Methodology
21](#state-assessment-system-and-methodology)

[3.6 Tracking Student Progress 24](#tracking-student-progress)

[3.7 Participation Rates and Additional Academic Indicators
26](#participation-rates-and-additional-academic-indicators)

[4 Conclusion](#conclusion) 29

# Overview

The Arizona Department of Education (ADE) is submitting this proposal
requesting the opportunity to incorporate a model of individual student
growth into the adequate yearly progress evaluations (AYP) of districts
and schools.

Arizona has the components in place---a statewide student data system,
vertically scaled standards and tests---to implement a growth model.
Furthermore, Arizona meets the criteria set out in the New Equation for
providing flexibility in implementing NCLB.

Arizona's first model of school accountability, introduced in 1998-99,
was a growth model: the Measure of Academic Progress (MAP). The MAP was
based on growth measured by stanine to stanine movement on the state's
norm-referenced test. At the time it was the only test administered
statewide, and until the 2004-05 school year, the only test administered
in all grades three through eight. The ADE has reported MAP results by
school since 1999. Now that the state's criterion-referenced test, the
AIMS, is given at every grade three through eight, the ADE intends to
introduce a new growth measure based on growth measured against state
standards.

If approved, the model can be implemented in the AYP evaluations for the
2006-07 school year.

## A Growth Model Will Improve School Accountability in Arizona

The purpose of including a growth model in AYP evaluations is to
recognize the success of schools in improving student achievement, even
though that achievement may fall short of proficiency. With recognition
comes the incentive for schools to concentrate further effort toward
assisting students who fall short of proficiency. Increased attention
toward the lowest performing students will keep them from falling
further behind their peers. Educators in successive grades will find
more of their students within striking distance of proficiency. This
will allow the achievement gap to be closed more quickly.

Including a growth measure in the state's AYP determinations will raise
expectations by making explicit the goal that ***all*** students in
Arizona are to show improvement. It is widely recognized that a simple
status model of accountability that only looks at percent proficient
gives schools the incentive to focus on so-called "bubble"
students---those who fall just short of proficient. Arizona addressed
this problem when designing its state accountability system AZ LEARNS.
AZ LEARNS credits schools for improvement across all levels of student
achievement. The Measure of Academic Progress has also been included in
AZ LEARNS. By expecting improvement from students at all levels, schools
will not just focus on the bubble students and allow the lowest
performing to languish.

A growth model will make the state's AYP determinations a more valid
measure of school effectiveness. Arizona currently bases its AYP
determinations on percent proficient with the safe harbor provided for
in legislation. Because status models do not account for improvement
shown by all students, they can only imperfectly distinguish schools
that are truly effective. Schools that are highly successful in raising
student achievement can be falsely identified as ineffective and in need
of improvement if a proficiency target is not met. Using growth as a
component in the AYP determination will help ADE in identifying those
schools where student achievement is truly stagnant. This will allow ADE
to focus resources and assistance in helping those schools.

Arizona has publicly reported its measure of student growth for schools,
the MAP, for seven years. It is included on school report cards and used
by third party information sources like GreatSchools.net. It is also
used as performance pay indicator for teachers. Parents, the public,
school administrators, and teachers are all familiar with the specific
measure and the concept of growth in general. With increasing emphasis
on state standards, the old MAP based on the norm-referenced test was
starting to be deemphasized. With the introduction of a new growth
measure based on state standards, we expect additional use of the growth
measure to develop state and local policy and treat the instructional
needs of individual students. Including growth as part of the AYP
determination will bring the various accountability measures in the
state into greater congruence, increasing the effectiveness and validity
of the state's overall school accountability system.

## Arizona Meets the New Equation for Flexibility

Arizona has a history of commitment to educational reform and
accountability. Initiatives that have been in place since the 1990s
include school report cards, ratings of school effectiveness, statewide
assessment of proficiency in state standards, proficiency as a
graduation requirement, and school choice through charter schools and
open enrollment.

Our state accountability system, AZ LEARNS, allows schools only three
years to move out of the lowest performance category before they face
state intervention. The state has already put into place turnaround
principals in several of its failing schools as well as ATLAS teachers
who are teacher leaders/mentors that model best practices. Before this
happens, however, each year a school identified as underperforming must
still notify the public of its underperforming status and file a school
improvement plan. Meanwhile the state provides assistance through
solutions teams.

Arizona is meeting the key NCLB principles for school accountability:

-   It has in place an accountability system for all schools and
    districts that tests in all grades three through eight, and high
    school. The system holds entities accountable for subgroup
    performance in reading and mathematics.

-   School performance measures are made available to parents both in
    paper and electronically through school, district, and state report
    cards. The report cards include student proficiency by subgroup,
    teacher experience; the number of classes taught by highly qualified
    teachers; and attendance, promotion, dropout, and graduation rates.

-   Choice and supplemental services are available for students in
    underperforming schools, as well as the options for school choice
    available for all students in the state. Schools in school
    improvement receive visits from solutions teams made up of top
    educators. ADE also assigns a coach to monitor the implementation of
    their school improvement plan. Coaches also evaluate compliance with
    federal and state accountability. A school in improvement uses
    Arizona's Standards and Rubrics for School Improvement to identify
    the strengths and limitations of the school\'s overall program. The
    Standards and Rubrics are anchored in the scientifically
    research-based principles and indicators that consistently
    distinguish top-performing schools. ADE also provides a web resource
    guide to support the Standards and Rubrics.

-   Arizona has issued standards for qualified teachers and reports to
    parents the qualifications of teachers at their children's schools.
    Arizona has in place a career ladder program that encourages
    performance-based compensation plans to provide incentives to
    teachers to make career advancements without leaving the classroom
    or the profession. Arizona requires a proficiency assessment for
    most certifications, and will require a performance assessment for
    future teacher certifications. Arizona has also established a
    classroom site fund in which teachers are compensated for student
    performance and based on school improvement goals identified in the
    school\'s improvement plan.

## Core Elements in Place for Growth Model

Arizona has in place all the necessary elements for a student-level
growth model:

-   The state's Student Accountability Information System (SAIS) has
    been in place since 2002. Each student of a public (including
    charter) school in the state is assigned a unique SAIS ID that
    follows her through her career from kindergarten to high school
    graduation. The SAIS system also contains demographic and program
    membership information for all students.

-   All students are tested in both reading and math in grades three
    through eight. The state's assessment system has been approved by
    the peer review. The AIMS test is vertically scaled for grades three
    through eight. Arizona has vertically aligned, articulated standards
    for all grades.

## Development and Implementation 

The Arizona Department of Education developed the growth model presented
here with comments and suggestions from:

-   The State Assessment and Accountability Advisory Committee (SAAAC),
    a group of 40 members representing districts, charter schools, and
    other stakeholders statewide.

-   The National Assessment and Accountability Advisory Committee
    (NAAAC), a group of six university scholars with expertise in
    assessment and accountability.

-   Arizona's Title I Committee of Practitioners (COP)

-   The Accountability Systems and Reporting working group of CCSSO.

In general it was the recommendation of the groups that the growth model
used by ADE be fair, simple, and consistent across accountability
models.

The model also holds to the criteria set down by the U.S. ED,
especially:

1.  Demographic characteristics of students are not used to set
    different growth targets.

2.  Growth is measured toward the goal of proficiency.

3.  Growth by students above proficient does not compensate for the
    growth of less than proficient students.

Aggregate results and the results for subgroups will be reported
publicly and placed on school, district, and state report cards. The
proposed measure was chosen to be straightforward, intuitive, and easily
understood by principals, teachers, and parents. As always, ADE is ready
to offer supplementary material and training to further understanding.

It is the intent of the ADE to continue to monitor the validity of the
growth measure. The growth measure proposed here will be calculated in
parallel with the current status model. This will enable an easy
comparison of the results produced with the growth model to those that
would have been provided under the current model. The ADE will provide
the necessary information for the evaluation of the program by U.S. ED.

# The Proposed Model

The growth model submitted in this proposal will be calculated for all
subgroups for both schools and districts, parallel to the traditional
AYP evaluation. The model looks at progress individual students make
toward proficiency from one year to the next. The goal is proficiency
within three years for grades three and four, or by the eighth grade for
grades five through seven. Annual growth targets are set that measure
each student's progress toward that goal. Students are deemed to have
made sufficient progress if they meet the annual growth target. Scores
for individual students are aggregated by the relevant subgroups. If the
percentage of students in a subgroup that meets the target for growth or
who are proficient is equal to or greater than the annual measurable
objective (AMO), then the subgroup is considered to have met AYP.

## The Current System for AYP Determination in Arizona

The present method for AYP evaluation in Arizona examines student
performance in reading and math for each grade three through eight, and
high school (10^th^ grade). There are separate annual measurable
objectives (AMOs) for each grade. The approved AMOs for are given in
table 1.

  ------------ ----------- ----------- ----------- ----------- -----------
  **Table 1.                                                   
  AMOs**                                                       

  **Grade 3**  **Reading   **Math      **Grade 6** **Reading   **Math
               AMO**       AMO**                   AMO**       AMO**

  2005-07      53.3 %      43.3 %      2005-07     45%         43%

  2008-10      62.6 %      54.6 %      2008-10     56 %        54.4 %

  2011         71.9 %      65.9 %      2011        67 %        65.8 %

  2012         81.2 %      77.2 %      2012        78 %        77.2 %

  2013         90.5 %      88.5 %      2013        89 %        88.6 %

  2014         100 %       100 %       2014        100 %       100 %

  **Grade 4**  **Reading   **Math      **Grade 7** **Reading   **Math
               AMO**       AMO**                   AMO**       AMO**

  2005-07      45%         54%         2005-07     49%         48%

  2008-10      56 %        63.2 %      2008-10     59.2 %      58.4 %

  2011         67 %        72.4%       2011        69.4 %      68.8 %

  2012         78 %        81.6 %      2012        79.6 %      79.2 %

  2013         89 %        90.8 %      2013        89.8 %      89.6 %

  2014         100 %       100 %       2014        100 %       100 %

  **Grade 5**  **Reading   **Math      **Grade 8** **Reading   **Math
               AMO**       AMO**                   AMO**       AMO**

  2005-07      43.3 %      33.3 %      2005-07     42.5 %      22.5 %

  2008-10      54.6 %      46.6 %      2008-10     54 %        38 %

  2011         65.9 %      59.9 %      2011        65.5 %      53.5 %

  2012         77.2 %      73.2 %      2012        77 %        69 %

  2013         88.5 %      86.5 %      2013        88.5 %      84.5 %

  2014         100 %       100 %       2014        100 %       100 %
  ------------ ----------- ----------- ----------- ----------- -----------

The AYP evaluation does not average across grades or years when
determining if a subgroup met the AMO. The minimum group size is 40 and
a 99 percent confidence interval is used. Safe harbor is evaluated per
statute without a confidence interval.

## Incorporating the Growth Model into the AYP Evaluation 

The growth model will be incorporated into the AYP evaluation for each
subgroup as shown in the flow chart in figure 1. The growth model will
be calculated for all subgroups. If the subgroup meets the growth
target, then it is considered to have made AYP. Meeting the growth
target [does not]{.underline} overrule the requirement that 95 percent
of the subgroup be tested. If 95 percent of the subgroup is not tested,
then it fails to make AYP regardless of percent proficient, safe harbor,
or growth. Schools or districts that make AYP via the growth model will
be considered to have made AYP regardless of the traditional AYP
determination.

![](media/image1.pct)

## Calculation of Growth

**NOTE: The addendum of July 2, 2007 supersedes the description given
below for determining if a student meets his or her growth target.**

The proposed model calculates the annual progress made by each student
toward proficiency in state standards. Progress is measured against the
goal of proficiency within three years. Because Arizona's vertical scale
ends at eighth grade, a goal of proficiency by eighth grade will be used
for grades five through eight. The growth target represents a horizon
ranging from one to three years. The steps for calculating it are: For
each student an **annual growth target** is set for each subject:
reading and math. The growth target is how much improvement measured by
scale score points a student would have to make over her previous year's
score in equal intervals in order to achieve proficiency within three
years or by the eighth grade, whichever comes first. The growth target
is set by subtracting the student's previous year scale score from the
scale score for proficiency in the target grade and dividing by the
number of remaining grades. The targets are rounded to the nearest whole
number. Demographic factors are not used to set the target.

> [Example:]{.underline} A student scores 402 on the 3^rd^ grade math
> test in 2005. The passing score on the 6^th^ grade math test is 496.
> The student's math score must improve 31 points each year---(496 --
> 402)/(6-3) = 94/3 = 31---for him to reach proficiency by 6^th^ grade.
>
> [Example.]{.underline} A student scores 469 on the 6^th^ grade reading
> test in 2005. The passing score on the 8^th^ grade reading test is
> 499. The student's reading score must improve 15 points each
> year---(499-469)/(8-6) = 30/2 = 15---for her to reach proficiency by
> 8^th^ grade.

1.  For each student **actual growth** is measured for each subject.

> [Example:]{.underline} A student scores 402 on the 3^rd^ grade math
> test in 2005 and 442 on the 4^th^ grade math test in 2006. The
> student's actual growth is 40 points (442 -- 402).

2.  For each student **actual growth** is compared to the **annual
    growth target**. If actual growth is greater than or equal to the
    annual growth target, the student is deemed to have made adequate
    growth.

> [Example.]{.underline} A student's growth target is 31. The actual
> growth shown is 40. The student is considered to have made adequate
> growth.

To determine if a subgroup met the AMO, the following percentage is
calculated:

$$\frac{\text{ Students }(\text{proficient and non-proficient})\text{ meeting growth target}}{\text{Number of students in analysis}}$$

If this percentage is greater than or equal to the AMO, then the group
is deemed to have made AYP. Because the AMOs increase over time, the
growth targets increase over time as well. In 2014, all students will
either have to be proficient or be on the road to achieving proficiency
within three years or less. This is consistent with the NCLB goal.

## Details of the Calculation 

This section gives more details of the calculations, and provides
additional reasoning behind the model.

-   **Unmatched students.** Students without a score for the previous
    year will be counted at their current performance level. Proficient
    students will be considered to have met their growth target;
    non-proficient students will be considered to not have met their
    growth target.

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-   **Inclusion of students.** To be included in the growth measure a
    student must have been enrolled in his current school for the full
    academic year. However, to be included a student does not have to
    have been enrolled in the same school or district for two
    consecutive years. Furthermore, to be included, a student does not
    have to have been enrolled for a full academic year the previous
    year. ADE considers a student to have been enrolled for a full
    academic year if the student was continuously enrolled in a school
    from within the first ten school days through the testing date.

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```
-   **Minimum group size.** Only subgroups with 40 or more students who
    have been present the full academic year will be evaluated.

-   **The model sets ambitious growth targets.** The growth model sets a
    target of proficiency for students within three years or less,
    depending on the grade. This is a much more demanding expectation of
    non-proficient students than under the current AYP determination.
    Under the current status-only model, students who are not proficient
    may reach the 8^th^ grade without making any progress at all.

-   **New growth targets are set for each student, each year.** The
    model proposed here will set new individual growth targets for each
    student each year. Growth targets will be based on the grade at
    which a student first enrolls in an Arizona public school according
    to the table below.

  ------------------------------------- ---------------------------------
  **Table 2. Expected Grades to Reach   
  Proficiency**                         

  Student first enrolls in AZ public    Must be proficient by:
  school in this grade                  

  K-3^rd^                               6^th^ Grade

  4^th^                                 7^th^ Grade

  5^th^                                 8^th^ Grade

  6^th^                                 8^th^ Grade

  7th                                   8^th^ Grade
  ------------------------------------- ---------------------------------

> The growth target will expect a student to become proficient within
> three years of first enrolling in a grade between three and eight, or
> by eighth grade---whichever comes first. The clock will start over for
> students who leave and then return to the Arizona public school
> system.
>
> [Example.]{.underline} A student enrolls in school A in third grade.
> The next year she enrolls in school B. She must be proficient by sixth
> grade.
>
> [Example.]{.underline} A student enrolls in school A in third grade.
> The next two years she attends a private school. She re-enrolls in
> school A as a sixth grader. She must be proficient by eighth grade.
>
> Setting new growth targets each year addresses the situation shown in
> figure 2. The dark solid line shows the scale score considered
> proficient for each grade three through eight. Two students score
> below proficient in third grade. The lines labeled 'Student "X"
> Trajectory' show the amount of growth each student would need each
> year to reach proficiency within three years. Both score the same on
> the 4^th^ grade test. Student 2 exceeded her growth target but student
> 1 did not. The question is: What growth target should the school set
> for each student for the fifth grade? Under the model proposed here,
> the growth target would be a new, identical trajectory for both
> students starting from the fourth grade score. [Note that the original
> goal of proficiency by sixth grade is maintained.]{.underline}
>
> This rule has two advantages. First, it attempts to include as many
> students in the growth calculation as possible. Growth targets are set
> according to enrollment not test history, so a continuous test history
> is not required for a student to be included in the model. Second, it
> greatly eases planning and understanding for teachers, principals, and
> parents since it sets the same growth target for students scoring at
> the same level. Setting different growth targets based on a starting
> point that could be several years in the past would be confusing and
> perceived as unfair. Given the state's variation in grade
> configurations, student mobility, and the prevalence of charter
> schools, starting points could be in different schools and even
> unavailable to the school currently responsible for the student.

![](media/image2.pct){width="6.975694444444445in"
height="4.763888888888889in"}

-   **Average or expected growth.** The growth model proposed here sets
    growth targets that expect students to achieve proficiency in three
    years or less. It does [not]{.underline} make use of the concepts of
    average, expected, or one-year's growth as they have been typically
    used in growth models in the past. Growth expectations in this model
    are [not]{.underline} set by determining if growth is greater than a
    past average for the state or school. Growth expectations are
    [not]{.underline} set by determining if a student maintained a given
    performance level from year to year.

> Given that students below proficient may have up to three years to
> traverse the two performance levels below proficient, it necessarily
> follows that a student could meet the growth target and not change his
> performance level. This is even more likely given the relative scale
> score span of the lowest performance level (falls far below) compared
> to the next highest (approaches the standard).
>
> [Example 1.]{.underline} A student scores 200 on the third grade
> reading test. The scale score for proficiency in sixth grade is 478.
> The student's annual growth target is (478-200)/3 = 93. If the student
> met the growth target each year, her performance levels would be:

  ----------------------- ----------------------- -----------------------
  [Grade]{.underline}     [Scale                  [Performance
                          Score]{.underline}      Level]{.underline}

  3                       200                     Falls far below

  4                       293                     Falls far below

  5                       386                     Falls far below

  6                       479                     Meets the standard
                                                  (proficient)
  ----------------------- ----------------------- -----------------------

> [Example 2.]{.underline} A student scores 386 on the third grade math
> test. The scale score for proficiency in sixth grade is 496. The
> student's annual growth target is (496-386)/3 = 37. If the student met
> the growth target each year, her performance levels would be:

  ----------------------- ----------------------- -----------------------
  [Grade]{.underline}     [Scale                  [Performance
                          Score]{.underline}      Level]{.underline}

  3                       386                     Approaches

  4                       423                     Approaches

  5                       460                     Approaches

  6                       496                     Meets the standard
                                                  (proficient)
  ----------------------- ----------------------- -----------------------

## Alternate Tests

Arizona administers two alternate tests for the most significantly
cognitively disabled students: the AIMS-A and AIMS-A level II. Students
who take the AIMS-A will be included in the growth model. Like the AIMS,
the AIMS-A has four performance levels: falls far below (FFB),
approaches (A), meets (M), and exceeds (E). The last two levels are
considered proficient. Students who move up a performance level will be
considered as having met their growth target.

  --------------- --------------- -------------- -------------- --------------
  **Table 3. Met                                                
  Annual Growth                                                 
  Target for                                                    
  Alternate                                                     
  Assessment**                                                  

                  **Performance                                 
                  Level Current                                 
                  Year**                                        

  **Performance   **FFB**         **A**          **M**          **E**
  Level Previous                                                
  Year**                                                        

  **FFB**         N               Y              Y              Y

  **A**           N               N              Y              Y

  **M**           N               N              Y              Y

  **E**           N               N              N              Y
  --------------- --------------- -------------- -------------- --------------

The above table would also be used in the unlikely event that a student
would take the AIMS-A one year and the AIMS the next.

The AIMS-A and AIMS-A level II are not differentiated by grade: the same
tests are given to students regardless of grade. However, the scores
needed to attain a given performance level increase by grade.
Consequently, movement from one performance level to another does
represent an improvement in student performance.

## K-2 Schools, High Schools, and Third Grade

A growth model will not be used in the evaluation of K-2 or high
schools. Those schools will continue to be evaluated using the current
method. Third grade will continue to be evaluated using the current
status/safe harbor method as well.

# Arizona's Growth Model Meets the Seven Core Principles

## 100 percent proficiency by 2014 and Incorporating Decisions about Student Growth into School Accountability

### How does the state accountability model hold schools accountable for universal proficiency by 2013-14?

Arizona's growth model holds schools and districts accountable for the
academic growth of all students. This makes it an improvement over the
current status-only AYP evaluation, where schools have the incentive to
only focus on the students who are near proficiency.

Growth is measured as the change in scale score points in consecutive
years. A student's individual growth target is the growth necessary to
achieve proficiency by the time the student reaches eighth grade. The
growth measure for a subgroup is the percentage of students in the
subgroup meeting their growth targets. The percentage required for all
subgroups are the AMOs for proficiency (shown in table 1) for that
grade, subject, and year. As a result, the number of students required
to meet their growth target grows along with the AMOs. Thus, by 2013-14
the target is that all students will be on track to attain proficiency.

All students will be included in the growth model. It will be a parallel
evaluation of schools and districts. Consequently, status and safe
harbor will continue to be calculated and used for evaluation as before.
This will facilitate the monitoring and evaluation of the effectiveness
and validity of the growth model.

The growth model will be used for grades four through eight. Grade
three, high schools, and K-2 schools will be evaluated using the
current, approved method.

### Has the state proposed technically and educationally sound criteria for growth targets for schools and subgroups?

The Arizona growth model preserves the annual expectation that the goal
of all students in all grades and schools is to reach proficiency. The
model sets growth targets so that students will close the achievement
gap each year so that they will reach proficiency in three years or
less. (Refer to section 2.3 for the details of the calculation.) Thus
the growth target is the same for all subgroups in the relevant grade.

The AMOs provide challenging and continuously improving expectations for
student growth. They are goals familiar to schools that have already
been the focus of planning for the past four years. The AMOs have an
empirical basis in their starting point.

### Has the state proposed a technically and educationally sound method of making annual judgments about school performance using growth?

The growth measure will be applied in the same manner to all subgroups
for both subjects---reading and math---for all grades four through
eight. Its use will ensure that schools receive credit for, and hence
have the incentive to, improve student achievement over all performance
levels. This will help to see that as students advance up through the
grades some will not be left further behind. It will also help ensure
that there are no false negatives; that schools that are successful in
raising the performance of low-achieving students will not be mistakenly
identified as needing improvement.

The growth measure will include all students who have attended a school
for the full academic year that can be successfully matched from the
previous year---including students who take the alternate assessment.

The growth measure will not affect the other indicators of school
performance: the 95 percent assessment requirement, the graduation rate,
or the attendance rate.

The growth measure will be released to the public and placed on the
school, district, and state report cards. It is intuitive and
transparent and will be familiar to most parents, educators, and
policymakers in Arizona. Its use in AYP evaluations minimally disrupts
the formula.

The growth goals for subgroups will increase along with the AMOs so by
the year 2013-14 100 percent of students must either be proficient or on
track to be proficient within three years.

### Does the state-proposed growth model include a relationship between consequences and rate of student growth consistent with Section 1116 of ESEA?

The growth model submitted in this proposal will be calculated for all
subgroups of students and used as a parallel AYP evaluation for both
schools and districts. Schools and districts will be identified for
school improvement if they miss AYP both via the growth model and the
via traditional status model of determining AYP.

We anticipate the growth model being used by the state's school
improvement team and educators for diagnostic and planning purposes.
However, a school or district's performance measured by the growth model
will not mitigate, alter, or enhance the consequences of being
identified for improvement. Schools and districts identified for
improvement by the growth model will have to meet the consequences of
improvement---parental notification, choice, supplemental services---as
outlined in section 1116.

## Establishing Appropriate Growth Targets at the Student Level

A detailed description of the student level growth measure is given in
section 2.3. The annual growth target is the difference between the
student's previous year scale score and the proficient score for three
grades higher, divided by the number of intervening grades. This
individual growth measure provides an easily interpretable and
transparent measure of student progress. The simple calculation
facilitates its use in planning for students, classrooms, and schools.

The growth targets, the annual measurable objectives, and the rationale
for their use are described in section 3.1.2 above. We underscore that
we are setting expectations for growth that are not based on student
demographic characteristics.

The tests administered in 2007 represent the third year that Arizona has
tested at all grades three through eight. It is also the third
administration of the test with a vertical scale. As the data set for
the new test deepens, ADE intends to continually evaluate the growth
goals set for students. The growth goals proposed here represent
ambitious one-year targets for students. Additional years of data will
shed light on what growth trajectories are both necessary and feasible
for a student to reach proficiency.

## Accountability for Reading/Language Arts and Mathematics Separately 

As described in section 2.3 and section 3.1 the growth calculation
mirrors the AMO determination: it is done separately for reading and
math for each subgroup. It will also be reported by subject. Arizona
also assesses writing but does not include it in the AYP evaluation at
this time.

The growth model submitted ensures the validity and reliability of its
determinations by:

-   Placing a minimum group size of 40 to be considered in the AYP
    determination for a subgroup.

-   Using a dichotomous yes/no determination as to whether a student met
    her growth target. This will mitigate the impact of outliers and
    fluke results, and prevent growth above proficient from compensating
    for growth that will not cause a student to reach proficiency.

## Inclusion of All Students

The growth model will be applied to all students in all schools that
serve grades four through eight, subject to the rules regarding minimum
group sizes as outlined in section 2.6. Third grade, high schools, K-2
schools, and small schools will be evaluated using the current, approved
method (see section 2.7). Students taking the alternate assessment will
be included according to the rules outlined in section 2.5. Arizona law
requires that limited English proficient students take the English
language version of the AIMS. The students in this subgroup will be
evaluated using the same method for all students described above.
English language learners will not have extended time horizons to meet
proficiency.

Students who change program membership will be counted in the subgroup
to which they belong in the current year. Growth for promoted or
retained students will be measured by the change in scores for
consecutive tests, regardless of the grade level of the tests.

## State Assessment System and Methodology

### Has the state designed and implemented a statewide assessment system that measures all students annually in grades 3-8 and one high school grade in reading/language arts and mathematics in accordance with NCLB requirements for 2005-06, and have the annual assessments been in place since the 2004-05 school year?

Arizona's assessment system has received full approval with
recommendations from the assessment peer review.

Arizona's Instrument to Measure Standards Dual Purpose Assessment (AIMS
DPA) is used in grades three through eight, Arizona's Instrument to
Measure Standards High School (AIMS HS) is used in high school, and
Arizona's Instrument to Measure Standards-Alternate (AIMS-A) is used to
assess the competency and growth of students with significant cognitive
disabilities in grades three through eight and high school. AIMS DPA and
AIMS HS are selected response tests for all grade levels and AIMS-A uses
a performance evaluation, a parent interview and activity-based
evidence. Students are currently assessed in reading, mathematics, and
writing. A science test is under development.

Arizona tested all grades three through eight and high school
operationally in 2004-05. In 2005 the test underwent a standard setting
and a vertical scale was developed for grades three through eight.

AIMS DPA is a statewide assessment that is both standards-based,
measuring students knowledge against the Arizona Academic Standards, and
norm referenced, comparing student knowledge against students
nationwide. TerraNova, norm-referenced test items included in the test,
compare a student's performance to students nationwide. AIMS test items
measure a child's knowledge without comparison to other students based
on whether the child is proficient in accordance with the Arizona
Academic Standards.

The AIMS DPA provides a norm-referenced test score (NRT) and an AIMS
score. The results of the tests are used by classroom teachers to guide
instruction and improve student learning. The NRT compares a child's
performance on certain test items to the performance of students
nationwide based on percentile ranking. The AIMS score assesses a
child's knowledge of the Arizona State Standards. [Only the AIMS score
is used for accountability purposes.]{.underline} Each child will
receive one of the following scores for each of the three areas tested -
reading, writing, and mathematics:

**Exceeds the Standard --** denotes superior academic performance on
challenging subject matter reflected by the content standards

**Meets the Standard --** denotes solid academic performance and
understanding of the state content standards

**Approaches the Standard --** denotes partial understanding of the
skills and knowledge necessary for proficient work at grade level

**Falls Far Below the Standard --** denotes insufficient understanding
of the prerequisite skills. Students who achieve at this level have
serious gaps in knowledge and skills and may require remediation.

Performance levels of meets and exceeds are considered proficient.

**Arizona Academic Standards**

The Arizona Academic Standards are established academic expectations for
teaching and learning. They are statements of knowledge and skills that
every child is expected to learn. The standards were developed by the
state's educational community and adopted by the State Board of
Education to meet federal and state guidelines. Currently, academic
standards for grades three through eight have been developed in the
following content areas: reading, writing, mathematics, science, social
studies, foreign language, technology, arts, comprehensive health/PE,
and workplace skills.

Arizona's Instrument to Measure the Standards (AIMS) is aligned to the
grade-level Arizona Academic Standards in reading, writing and
mathematics. The test blueprints for AIMS DPA, AIMS HS and AIMS-A were
followed during item selection as test forms were developed. A committee
met in the spring of 2003 and developed assessment blueprints for
reading and mathematics that covered the content standards. The emphasis
that they placed on the number of items for future assessments reflected
both the content standards and classroom instruction across the state.
The blueprints were then reviewed by both the state (SAAAC) and national
(NAAAC) technical advisory committees. An external alignment study
confirming the degree of alignment of the assessments to the standards
was conducted July 25-27, 2005.

### How will the state report individual student growth to parents?

The Arizona Department of Education, in collaboration with
CTB/McGraw-Hill, developed paper reports that can be appropriately
interpreted for students, grade level groups, schools, districts,
counties and the state. Each year the student's growth target along with
her actual growth will be included on the report.

### Does the statewide assessment system produce comparable information on each student as he/she moves from one grade level to the next?

The criterion-referenced portions of the AIMS tests in grades three
through eight were placed on a vertical scale using TerraNova NRT items
as external anchors. Parameters for these items were obtained during
national standardization. The AIMS scale for grades three through eight
ranges from 200--800. The AIMS high school assessments were not placed
on the grades three through eight scale.

All items that made up the AIMS criterion referenced test (CRT) for each
subject and grade were calibrated in Pardux using the 3 PLM and placed
on the TerraNova scale using the TerraNova NRT standardization item
parameters as anchor estimates. Equating was done using the Stockard and
Lord procedure that matches the test characteristic curves of an anchor
test and the focal test. The mean and standard deviation of the Arizona
students' scores on the CRT were then calculated on the TerraNova scale
for each grade. The smoothed means of AIMS CRT on the TerraNova scale
fitted to a second degree polynomial was used to articulate the vertical
scale.

Transformation constants were calculated to convert the mean and
standard deviation for the third grade to a mean of 450 with a standard
deviation appropriate to the content area. The same constants were then
applied to the means and standard deviations for all other grades to
place the AIMS CRT on a scale of 200-800.

After transformation to the new scale, means, standard deviations, and
distributions were examined to ensure acceptable articulation. Minor
adjustments were made to eliminate overlap. Standard deviations were
adjusted slightly and the eighth grade observed mean was used instead of
the smoothed mean.

The lowest and highest obtainable scale scores were set for each grade
and subject using the following criteria:

The highest obtainable scale score (HOSS) had to be greater than the
scale score associated with one less than the maximum raw score;
increase monotonically; be high enough to prevent a ceiling effect; low
enough so that the Standard Error of Measurement (SEM) does not exceed
ten times the minimum SEM; and the scale score gap between the HOSS and
the scale score associated with one minus the raw score maximum had to
be similar to the scale score gap between the scale scores associated
with the raw score maximum minus one and the raw score maximum minus
two.

The lowest obtainable scale score (LOSS) also had to increase
monotonically; be low enough to prevent floor effects; and high enough
so that the SEM associated with the LOSS is less than ten times the
minimum SEM.

Grades four, six, and seven were tested for the first time in the
academic year 2004 -- 2005. ADE will provide evidence for equating test
scores between grades three through eight using the mean equating method
after the 2005-06 administration. A set of anchor items from the 2005
test has been reserved to control for drift in the scale.

The cut scores for each subject and grade are given in the tables below.

  ------------------ ----------- -------- -------- -------- -------- --------
  **Table 4.                                                         
  Mathematics Cut                                                    
  Scores for Grades                                                  
  3 Through 8**                                                      

                     **Grade**                                       

                     **3**       **4**    **5**    **6**    **7**    **8**

  Approaches         386         414      442      463      484      505

  Meets              420         448      476      496      517      537

  Exceeds            492         521      550      574      599      623
  ------------------ ----------- -------- -------- -------- -------- --------

  ------------------ -------- -------- -------- -------- -------- --------
  **Table 5. Reading                                              
  Cut Scores for                                                  
  Grades 3 Through                                                
  8**                                                             

  ** Grade**                                                      

                     **3**    **4**    **5**    **6**    **7**    **8**

  Approaches         379      402      424      433      443      452

  Meets              431      450      468      478      489      499

  Exceeds            516      536      556      571      587      602
  ------------------ -------- -------- -------- -------- -------- --------

### Is the statewide assessment system stable in its design?

There will be no changes to the grades assessed, content, instruments,
scoring, and cut-scores for the next four years.

## Tracking Student Progress

ADE has the ability to track students through their career kindergarten
through graduation in Arizona's public schools via its Student
Accountability Information System (SAIS). Since the 2001-2002 school
year, students enrolling in Arizona schools have been assigned a unique
identifier, the SAIS id that remains with them across grades, schools,
and districts until they graduate from high school. SAIS also contains
student demographic information---gender, ethnicity, etc.---and program
membership, whether the student is an English language learner, special
education, or eligible for a free/reduced lunch. Student testing data is
maintained in a separate database. Starting with the 2003-04 school
year, SAIS ids were attached to the state's testing data.

As mentioned before, Arizona has published a measure of student growth,
the MAP, since 1999. Matching for the MAP was based on student names,
birthdates, and other characteristics. ADE achieved a highly successful
match rate via these means. ADE intends to match students on their SAIS
ids to determine growth. The table below shows the results from matching
2005 to 2004 test data using student SAIS ids. The method achieves
nearly a 90 percent match rate that does not differ by program
membership or by proficiency level. As can be expected, the match rate
is lower for mobile students, those not enrolled in a school for the
full academic year.

  --------------------------------- -------------------------------------
  **Table 6. Match Rates**          

  Subgroup                          Match Rate

  Total                             89%

  English language learners         85%

  Free/Reduced lunch                89%

  Special Education                 89%

  Full academic year                93%

  Non-full academic year            63%

  Proficient                        94%

  Not-proficient                    91%
  --------------------------------- -------------------------------------

The key to having a high match rate is to make every effort to ensure
every test record has a valid student identifier attached. ADE takes
several steps, outlined in figure 3, to see that this is the case.

1.  ADE distributes pre-printed test labels for all students in the
    state containing students' unique identifiers. This minimizes errors
    due to students or administrators bubbling in student information on
    test answer documents.

2.  After the test is scored and ADE receives the test score results
    from the testing company, ADE matches the test scores back to its
    student database, SAIS, to update the student demographic
    information associated with the test scores.

3.  ADE then makes the test score data available to schools and
    districts. ADE has two online applications that allow schools to
    download a copy of their data as it exists in the ADE test database,
    make corrections, and upload corrected files to the database. At the
    same time schools may correct the student demographic and program
    information in SAIS. The only corrections schools may make directly
    to the test score database are test accommodations, school
    information, and the SAIS identification number associated with the
    test. All corrections to student demographic information must be
    made through SAIS. Demographic information associated with test
    scores is then corrected by repeated re-matching of the test score
    file to the student information file.

4.  ADE provides additional information to schools to help them identify
    test records with faulty student identifiers. First, it provides
    on-line reports that allow schools to view records in the test
    database with faulty ids. Second, it has added a field to the test
    score database that identifies records with invalid SAIS ids.
    Schools can then see those records when they download their data.

5.  ADE conducts an AYP appeals process during which schools are given a
    final opportunity to correct their data.

ADE also conducts trainings for administrators on both accountability
and use of the SAIS database, and has in place standard procedures to
maintain the integrity of the SAIS database.

![](media/image1.pct)

## Participation Rates and Additional Academic Indicators

The use of the growth model will not affect how participation rates or
the additional academic indicators are used in AYP evaluations.

# Conclusion

Arizona is well qualified to incorporate a growth model into its AYP
evaluations for schools and districts.

1.  Arizona has in place all the necessary elements for a growth model.
    The SAIS database assigns each student a unique identifier that
    tracks students across grades, schools, and districts. It also holds
    student demographic information. The AIMS test has been administered
    operationally in all grades three through eight, is vertically
    scaled, and will remain stable for the next four years.

2.  Arizona has experience with growth measures. Student growth has been
    a part of Arizona's school accountability system since the previous
    century. Growth measures have been reported publicly and are used by
    administrators. We will continue to do so regardless of the status
    of this proposal.

3.  Arizona's growth model provides a more valid measure of school
    effectiveness than the current status-only evaluation. It recognizes
    and gives schools the incentive to improve student performance at
    all levels.

4.  Arizona sets ambitious growth targets for all students in all
    schools. Expected growth is not dependent on students' demographic
    characteristics. It sets the ultimate goal of all students being
    proficient or on track to proficiency by 2014.

If approved, the Arizona growth model would lessen the possibility that
students would fall behind. It will increase the number of students who
move on to higher grades that are ready to learn. Consequently, adding
the growth model to the AYP determination will help close the
achievement gap more rapidly.

#   {#section .unnumbered}