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CDE uses data to analyze student performance and inform educational improvements at the policy, state board and classroom level.

General Growth Model FAQs

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Colorado Growth Model FAQs (General)


General Questions

What is the Colorado Growth Model?

The Colorado Growth Model is a statistical model to calculate each student's progress on state assessments.

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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 CMAS PARCC in that subject area (i.e. Math or English Language Arts). Also, growth scores are calculated using the same methodology based on WIDA-ACCESS overall performance scores for English Language Learners.
  • 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).  *Not available for the 2016 school year.
  • 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.  It's important to recognize that a student growth percentile in isolation fails to tell us if the change is sufficient to reach benchmark.  Of course, the starting proficiency level has bearing on what would be considered sufficient growth to help the student reach or maintain benchmark.  For these determinations we need to use measures of adequate growth.

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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.

*Please note that adequate growth was not calculated as part of the 2016 student growth percentiles.

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What is an academic peer?

Academic peers are defined as students in a particular grade with a similar CMAS PARCC or WIDA ACCESS 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 CMAS PARCC scores (consistently at the Does Not Meet Expectations 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. It is important to recognize that relatively 'high' growth may not be sufficient to move students to proficiency.  The context of achievement is important when understanding the degree of growth for groups of students.

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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. It is important to recognize that relatively 'high' growth may not be sufficient to move students to proficiency.  The context of achievement is important when understanding the degree of growth for groups of students.

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

*Please note that adequate growth along with catch up, keep up and move up growth were not calculated as part of the 2016 student growth percentiles.

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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 Does not yet meet level of achievement than a student moving from 'does not yet meet' to 'partially meeting'. 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 below benchmark demonstrated enough growth in the past year to meet or exceed benchmark within three years or by 10th grade (to be on track to "catch up" to the state's proficiency goal).

*Please note that  catch up growth was not calculated as part of the 2016 student growth percentiles.

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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 benchmark achievement level demonstrated enough growth in the past year to maintain proficiency (i.e. meeting expectations) over three years or until 10th grade (to be on track to "keep up" with the state's proficiency goal over time).

*Please note that keep up growth was not calculated as part of the 2016 student growth percentiles.

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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 meeting expectations achievement level demonstrated enough growth in the past year to reach the level of Exceeding expectations within three years or by 10th grade (to be on track to "move up" to the state's highest proficiency goal).

*Please note that move up growth was not calculated as part of the 2016 student growth percentiles.

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What is the Colorado Growth Model interactive report?

The Colorado growth model interactive report provides median growth percentile data by the district/school level for disaggregated groups of interest.  The reports display data for the school, district, and state levels.  The reports can be accessed at:  http://www2.cde.state.co.us/schoolview/growth/growthvisualization.asp

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

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 School and District Growth Summary reports located at:   http://www.cde.state.co.us/schoolview/coloradogrowthmodel.  Also, historical data is available for comparison within Data Lab which is accessible via the School View web-site.

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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 for a group can be used for comparison purposes with that of other groups. These values can be accessed by using the School and District Growth Summary reports located at:   http://www.cde.state.co.us/schoolview/coloradogrowthmodel.  Also, historical data is available for comparison within Data Lab which is accessible via the School View web-site.

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How is the growth model included in School Accountability, District Accreditation, and the reauthorization of ESEA?

The Education Accountability Act of 2009 tasks CDE with creating a method for bringing state and federal accountability systems into alignment, and the Colorado Growth Model is an integral piece of this 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 school performance. In 2010, the State Board of Education adopted the rules necessary for full implementation of the Education Accountability Act of 2009. It is expected that the Colorado Growth Model will continue to be a key measure/metric in meeting requirements under the Every Student Succeeds Act.

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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, as well as the district/school performance frameworks, 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. In effect, the obtained growth percentiles tend to be less reliable when calculations are based on less than 20 student growth percentiles.  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?

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 School and District Growth Summary reports located at:   http://www.cde.state.co.us/schoolview/coloradogrowthmodel.  Also, historical data is available for comparison within Data Lab which is accessible via the School View web-site.

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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, for multiple years and content areas. These values can be accessed by using the School and District Growth Summary reports located at:   http://www.cde.state.co.us/schoolview/coloradogrowthmodel.  Also, historical data is available for comparison within Data Lab which is accessible via the School View web-site.

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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 by using the School and District Growth Summary reports located at:   http://www.cde.state.co.us/schoolview/coloradogrowthmodel.  Also, historical data is available for comparison within Data Lab which is accessible via the School View web-site.

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

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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 CMAS PARCC 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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What if I have a question that is not answered here or would like to request in-person training for my school, district, or organization?

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

For inquiries regarding training, please contact Dan Jorgensen, Ph.D. at:  Jorgensen_d@cde.state.co.us.

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