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Colorado Growth Model FAQs (General)


General Questions


What is the Colorado Growth Model?

The Colorado Growth Model is both

  • A statistical model to calculate each student's progress on state assessments.
  • A tool for displaying student, school, and district results to educators and to the public.

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What does the Colorado Growth Model tell us?

The Colorado Growth Model shows us

  • how individual students (and groups of students) progress from year to year toward state standards. Each student's progress is compared to the progress of other students in the state with a similar score history on CSAP in that subject area.
  • the observed growth among different groups of students at the state, district, and school level.
  • the level of growth that we needed to observe in order to say that students were, on average, on track to catch up or keep up (Adequate Growth)
  • schools and districts that produce the highest rates of growth in academic achievement. These schools or districts may not be ones with the highest test scores every year - growth level is completely independent of achievement level for individual students.

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What is growth?

For an individual student, growth is a measure of progress in academic achievement. For some states, this measure might simply be a change (a gain or a loss) in test scores from one year to the next. For Colorado, growth is not expressed in test score point gains or losses, but in student growth percentiles. An individual's test scores are used as the basis for a growth calculation, using a statistical model called quantile regression. The calculations use all available test scores to estimate an individual growth score, or student growth percentile. The student growth percentile tells us how a student's current test score compares with that of other similar students (students across the state whose previous test scores are similar). This process can be understood as a comparison to members of a student's academic peer group. So, Colorado's measure of growth is a normative rather than an absolute one.

As an example, if I observe that my pet dog gains 20 number of pounds in its first year of life, that gain calculation indicates the amount of weight increase, but not whether the amount is low, typical, or high for a dog of this breed. In the same way, just seeing how much a student's test score went up or down in two consecutive years is not really a meaningful exercise. What does it really mean that my daughter's score was 357 last year and is now 398? Is 41 points a big or a small increase? How much did she really learn? Test score points are not in units that have a real world meaning, so we are not sure whether students gaining a certain number of points are showing typical or extraordinary academic growth.

Now, using the Colorado Growth Model, students with the same achievement history are compared to each other, helping us understand whether their growth is high, typical, or low. We are not stuck trying to understand what a 41-point increase really means, because we can understand how surprising or unsurprising the new score is on the basis of other students' scores, students that were similar in the first place. We use other students' scores to put the norm in normative, and to understand every student's academic progress.

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What is a student growth percentile?

A student growth percentile defines how much relative growth a student made. The Colorado Growth Model serves as a way for educators to understand how much growth a student makes relative to a student's "academic peers." More specifically, the Colorado Growth Model essentially compares each student's current achievement to students in the same grade throughout the state who had similar CSAP scores in past years. The model then produces a student growth percentile. This score has some things in common with the children's height and weight percentiles that pediatricians share with parents. Percentile scores have a relatively straightforward interpretation: A child that is in the 76th percentile in weight is as heavy or heavier than 76% of other children of the same age. But this is not a measure of growth, just a spot measurement of how much above or below the average a particular child is.

In terms of Colorado Growth Model, a student growth percentile of 60 indicates the student grew as well or better than 60% of her academic peers. It is not about how that recent test score compares to all the other test scores. Even students with test scores that are very low can receive high growth scores.

The test score data underlying these student growth percentiles are not perfectly precise, because they contain measurement error, so the growth percentiles themselves are in turn also not perfectly precise. A student with a growth percentile of 63 may not actually be growing significantly faster than another student with a 60. In a similar way, even though you might not be able to reliably discern a 63-decibel sound from a 60-decibel one, you can still easily categorize different sounds as soft, normal, or loud - finer-grained comparisons are hard to make. For this reason, student growth percentiles are categorized by "low," "typical," or "high" growth - we can be pretty sure about these large differences, even if small differences may not be reliable or meaningful.

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What is Adequate Growth?

Just as Observed Growth tells us what the level of growth was for a group of students, Adequate Growth tells us if that was enough growth or not.

More specifically, it tells us whether the observed level of growth was sufficient for those students to be, on average, on track to reach or maintain proficiency in that content area. It draws directly on the concepts of Catching Up and Keeping Up that you may already be familiar with. The Adequate Growth calculation combines Catch Up and Keep Up student data into a single number: for Catch Up students, it uses their Catch Up number, and for Keep Up students it uses their Keep Up number.

A student needing to Catch Up had a previous year score in that content area that was below proficient; the growth model tells us the amount of growth that would probably get this student scoring at the proficient level in the near future: his or her Catch Up number. Similarly, a student needing to KeepUp had a previous year score in that content area that was above the minimum required for a Proficient rating; the growth model tells us the amount of growth that would probably keep this student scoring at the proficient level in the near future: his or her Keep Up number. Combining all the Catch Up and Keep Up numbers for every student and taking the median (a kind of average) gives us the amount of growth that these students on the whole needed to be meeting state goals for student achievement.

If you go to the Terminology section of the following video tutorial, you will see a graphical discussion of adequate growth that will help you to understand more fully how it is calculated and what it means:

Tutorial

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What is an academic peer?

Academic peers are defined as students in a particular grade with a similar CSAP score history. The concept of similar score history is discussed in the Colorado Growth Model Technical Report available on CDE's website. The CSAP score history examined includes all past scores available for a given student. So, for a student who has had low CSAP scores (consistently at the Unsatisfactory level) for the last few years, his or her growth is compared to students who have scored similarly.

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What is a median growth percentile?

The median growth percentile summarizes student growth rates by district, school, grade level, or other group of interest. The median is calculated by taking the individual student growth percentiles of all the students in the group being analyzed, ordering them from lowest to highest, and identifying the middle score, the median. The median may not be as familiar to people as the average, but it is similar in interpretation it summarizes the group in a single number that is fairly calculated to reflect the group as a whole. (Medians are more appropriate to use than averages when summarizing a collection of percentile scores.)

So, the median growth percentile tells us how well a group of students is growing in comparison with other groups. These can be groups that actually consist of people in the same place at the same time, such as all the kids in a school, or they can be groupings that we create, such as all the Hispanic 7th graders across Colorado. The median growth percentile tells us how much growth that group as a whole is achieving. Knowing these growth levels helps Colorado understand what schools are doing a great job with their kids, no matter how high or low their test scores were when they started, as well as what schools are not really getting their students to grow as much as other schools are.

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What is considered low growth?

As defined by Colorado State Board of Education rule, a student growth percentile for a single child that falls below the 35th percentile reflects low growth. For example, a student growth percentile of 20 indicates that this student's growth was better than 20% his/her academic peers that is pretty low growth. In other words, 80% of similar students statewide made greater growth than this student in the current year. Put another way, this student's latest score is particularly low, considering the way that students with similar past scores also did.

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What is considered typical growth?

The answer depends on whether you are referring to student growth percentiles (individual-level scores) or median growth percentiles (group-level scores). As defined by Colorado State Board of Education rule, a student growth percentile for a single child that falls within the 35th-65th percentile range reflects Typical Growth. When referring to median Growth Percentiles, such as for a school or demographic group, the Colorado Department of Education (CDE) considers a median of 50 to be typical growth for school or group. The statewide median growth percentile in each subject and grade is the 50th percentile. When examining medians for schools, grades, subjects or groups, it is useful to look for differences from 50 when investigating growth. These data are particularly useful for benchmarking purposes and to understand how other schools or grades are doing in addressing problems in the educational system, such as the frequently observed achievement gap between poor and non-poor students. Comparing median growth percentiles for these two groups within a school or district can tell us whether existing achievement gaps might be closing. There is currently no single "rule of thumb" for deciding what are low, typical, or high growth median growth percentiles.

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What is considered high growth?

As defined by Colorado State Board of Education rule, a student growth percentile for a single child that is above the 65th percentile reflects High Growth. For example, a student growth percentile of 80 indicates that 20% of similar students made higher gains than this student. that is pretty high growth. In other words, 20% of similar students statewide made higher gains than this student in the current year.

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How much growth is necessary?

Colorado's goal, expressed in the Education Accountability Act of 2009, is for all children to be on track to proficiency within three years or by 10th grade, whichever comes first. We need to be able to clearly show how much progress would be necessary to reach this goal each year, and evaluate whether each student's progress is adequate or not.

CDE reports student growth percentiles for all Colorado's students, and a variety of related pieces of data, including whether the student is on track to catch up, keep up, or move up within the official time frame used by CDE.

A new calculation combining catch up and keep up numbers for schools and other student groups was developed in 2010, and is called Adequate Growth.

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Does successfully moving from one achievement level to a higher one necessarily produce a higher growth percentile than moving up within an achievement level?

No. student growth percentiles are calculated on the basis of overall growth using exact test scores, not with reference to movement between achievement levels. For example, a student can have a higher growth percentile and stay within the Unsatisfactory level of achievement than a student moving from Unsatisfactory to Partially Proficient. Growth percentiles describe growth anywhere along the score scale, not just as achievement levels are crossed.

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What does it mean for a student to be Catching Up?

Catching Up indicates that a student previously scoring at the Unsatisfactory or Partially Proficient achievement level demonstrated enough growth in the past year to reach Proficient or Advanced within three years or by 10th grade (to be on track to "catch up" to the state's proficiency goal).

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What does it mean for a student to be Keeping Up?

Keeping Up indicates that a student previously scoring at the Proficient or Advanced achievement level demonstrated enough growth in the past year to maintain proficiency over three years or until 10th grade (to be on track to "keep up" with the state's proficiency goal over time).

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What does it mean for a student to be Moving Up?

Moving Up indicates that a student previously scoring at the Proficient achievement level demonstrated enough growth in the past year to reach the level of Advanced within three years or by 10th grade (to be on track to "move up" to the state's highest proficiency goal).

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What are the Colorado Growth Model data display tools?

Colorado has invested a great deal of time and effort into providing informative and interactive internet-based data displays for parents, educators, and other stakeholders in the public education system. These web-based tools show student results from the Colorado Growth Model for use by educators and members of the general public. Interested parties can access the Colorado Growth Model software at http://www.schoolview.org

Additional information about the growth model is available on CDE's website here

Anyone can use the public-level Colorado Growth Model website. It provides a summary-level view of schools' and districts' growth and achievement results. Users simply need a relatively up-to-date version of a web browser, equipped with a plug-in to display Adobe "Flash" content, and an active internet connection. At this website users can explore and compare schools and districts on growth and achievement levels.

District and school users with a need for access to student-level data can use the more complete Colorado Growth Model website. This site allows educators to explore all the Colorado Growth Model data in their district or school. Access to this site is protected by a password so that confidential individual student data are not available to the general public. You can take the student-level website for a test drive, using demo data, by following the link and login instructions on http://www.schoolview.org/learningcenter.asp

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Which students get growth percentiles, and which student growth percentiles are included in a school or district median?

In order to receive a growth percentile score in a state assessment content area, a student needs to have valid scores in that content area from two consecutive years, following a normal grade progression. This is just for a growth percentile to be calculated. For that growth score to be reported in a school or district summary, there are a few rules that exclude students for reasons of fairness:

  • School Level: Growth percentile scores are included in school summary calculations for those students that do not have a 1 in the Oct. 1 New to School field, and who were not expelled in that academic year.
  • District Level: Growth percentile scores are included in district summary calculations for those students continuously enrolled in the same district in the current and prior year, OR who do not have a 1 in the Oct. 1 New to School field. Students in detention centers with districts as their LEAs are also not included.
  • State Level: All growth percentile scores are included in calculations.

In plain language, under the rules adopted in 2010, a school owns the growth data from every student tested in that school if s/he was enrolled there by Oct. 1 and was not subsequently expelled. A district owns the growth data from every student tested in that district if s/he was enrolled by Oct. 1 in one of the district's schools (not in a detention center), or if s/he was coded as continuous in district.

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How can I help my school get a higher median growth percentile?

For a school to have a higher median growth percentile, the students in the school need to have higher student growth percentiles. This means students' growth rates in that school need to rise. One of the overall goals of the effort to design and implement the Colorado Growth Model was to focus educators' attention on the improvement of all students' growth rates, not just those of students near the boundaries of achievement levels.

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How does student growth differ among groups of students?

The median growth percentile for a group can be used for comparison purposes with that of other groups. These values can be accessed by using the Colorado Growth Model web application here. You can currently compare students in different districts and schools in the public data Colorado Growth Model website, as well as compare students that belong to particular demographic groups by drilling down into the school and district data.

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How does student growth in our school compare with other schools, or how does student growth in our district compare with other districts?

The median growth percentile can be used for comparison purposes. These values are made publicly available by the Colorado Department of Education and can be accessed through the Colorado Growth Model software at SchoolView.org

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How is the growth model included in School Accountability, District Accreditation, and Adequate Yearly Progress under No Child Left Behind?

The Education Accountability Act of 2009 tasks CDE with creating a method for bringing these three accountability systems into alignment, and the Colorado Growth Model is an integral piece of this planned alignment. The state has already obtained approval from the U.S. Department of Education to use the data from its growth model for the calculation of Adequate Yearly Progress. In 2010, the State Board of Education adopted the rules necessary for full implementation of the Education Accountability Act of 2009.

You can visit a website dedicated to this implementation at http://www.cde.state.co.us/scripts/reforms/detail.asp?itemid=623952

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How will the growth ratings be reported in the SAR (School Accountability Report)?

The Education Accountability Act of 2009 did away with the SAR and replaced it with a new web portal called SchoolView.org, housing Colorado's school, district, and state growth and achievement data. The SAR is no longer produced, but much of the data previously reported on the SAR are or will be available on SchoolView.org

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Is there an established minimum group size for creating a median growth percentile for a school, disaggregated group, classroom, etc?

Yes - the District and School Growth Summary Reports available here, as well as the Colorado Growth Model, only display medians when data for a minimum of 20 students are available and should be included in this group's summary median. This is done for two reasons. First, the privacy of individual students must be protected at all times. It is very important not to release data to the public that are not adequately anonymous, and with small numbers of students in a given group, it might be possible to deduce exactly who each person is and what their test scores were.

Second, groups that have fewer than 20 members are not fairly characterized by a single number. The data for groups that have fewer than 20 members can be better understood by looking at the complete set of numbers, rather than by attempting to capture them in a single summary statistic. Districts and schools may need to do this as they evaluate their programs and plan for the future, but the general public has no educational need for such detailed private student-level information.

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Do we see especially high or low growth in certain grades, content areas, instructional programs or classrooms in our district or school?

Some of these comparisons can currently be made using the public data Colorado Growth Model website. Other comparisons can be explored behind the "District & School Diagnostic Performance Reports" link at http://www.schoolview.org/performance.asp

Some of this information is currently available to districts and schools through their password-protected Colorado Growth Model software, as well as in raw data provided by CDE.

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How are the different schools in our district doing? Are there any patterns?

The median growth percentile can be used for comparison purposes. Look at the schools' median growth percentiles, as shown in the public data Colorado Growth Model, for multiple years and content areas. The tutorial videos in the SchoolView Learning Center will be of great assistance to you in understanding and exploring the data presented in that display tool.

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What is the "average" student growth at our school or district?

The median growth percentile for the school or district summarizes the growth percentiles for all students in the school or district providing a measure of "average" student growth for a school or district. These values are made publicly available by the Colorado Department of Education and can be accessed at http://www.schoolview.org/, either by using the interactive Colorado Growth Model application, or by consulting data and reports on every school and district at http://www.schoolview.org/performance.asp

It is important to note that averages (means) cannot be calculated for student growth percentiles - medians must be used instead. Most computer programs for organizing data will have a median calculation function.

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What percentage of students are making growth adequate to reach proficiency? How much extra growth do our students need to reach proficiency?

You can find the percentage of students Catching Up, Keeping Up, and Moving Up within the district elementary, middle and high school levels behind the "District & School Diagnostic Performance Reports" link on http://www.schoolview.org/performance.asp

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How does the Colorado Growth Model account for demographic or regional differences among students in its calculations?

The Colorado Growth Model does not account for any demographic or context variables in the calculation phase itself. The calculations do not even know what school or district each student is in! The algorithms used only know students' grades in a set of calendar years and what scores they earned on CSAP in those years.

When growth data are reported for groups of students, the individual growth scores are grouped after the growth calculations have been performed. No adjustments are made to the calculations on the basis of any demographic or other group, so that all students are treated equally by the model.

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Does the transition to TCAP from CSAP break the growth model?

No, growth can be calculated without any problems. The Colorado Growth Model does not require identical tests or scales from year to year.

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What if I have a question that is not answered here?

Please send your question to growth.questions@cde.state.co.us

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