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To make the best use of the projection data, it's important to understand how the projections are created, and therefore, what they can tell you about a student.
To begin, let's consider the idea of projections more broadly. We use projections in our everyday lives. Weather forecasts are projections of what the weather is likely to be in the days ahead. Meteorologists make these projections by building statistical models from weather data. This is similar to how we generate projections in TVAAS.
Consider how meteorologists project the path of a hurricane. As a storm begins forming in the Atlantic, meteorologists record and track data from the storm. To keep things simple for this example, let's just consider one type of data, the storm's position each day. Knowing only where the storm is today doesn't help the meteorologists much in projecting where the storm is headed several days from now. However, looking back at the storm's history does help. Knowing where the storm has been previously and what path it's followed to get to this point provides data for projecting where the storm is headed. The more data the meteorologists have, the better they understand this particular storm.
Meteorologists have been tracking and studying storms for many years, gathering a great deal of data, including the path each storm has followed. This information enables the meteorologists to build statistical models that not only describe how storms typically behave but also project where a storm is headed next.
The models generate a projected path for where the current storm will go. To generate the projection, the model considers what path other storms have followed, specifically storms that had histories like that of the current storm. If similar storms tended to follow a particular path, it's reasonable to project that the current storm will follow a similar path, assuming other atmospheric conditions are also similar.
We generate student projections using a similar type of statistical model. To generate a projection, the student's prior test scores are considered. How did the student perform on previous assessments in this subject? And how did the student perform on previous assessments in other subjects? TVAAS uses data across years, grades, and subjects to generate each projection. It can be helpful to think of it this way: how a student performs on a reading assessment affects how the student will perform on a math assessment. A natural relationship exists among subjects, and the projection model takes advantage of this relationship to generate more reliable projections.
To generate projections, we begin with the cohort of students who took the selected assessment in the most recent year. We use these students' scores, along with their testing histories, to build a statistical model. For the students who have not yet taken the selected assessment, we use the model to compare their testing histories across grades and subjects with the previous cohort's scores and testing histories. These relationships determine an individual student's projection that is based on their own personal testing history.
This approach is similar to the way teachers generate expectations for students in their classes at the beginning of the school year.
Let's consider an example.
Mrs. Sanchez, a seventh-grade math teacher, is trying to determine what her expectations are for Calvin, a student in her class. If she knows what Calvin scored on the sixth-grade math assessment, she can begin to set some expectations. However, she doesn't know if that one score is a good representation of Calvin's achievement level in math. What if that was a bad test day for Calvin? On the other hand, what if Calvin guessed at a number of questions and got them right? Because of the amount of measurement error associated with any single test score, knowing only what Calvin scored on last year's assessment isn't enough.
More information would help. What if Mrs. Sanchez also knew what Calvin had scored in reading? That would help her generate a clearer picture of Calvin as a student. Now imagine she knows what Calvin scored on all the assessments, across subjects, for the past few years. Having that much information would help her refine her expectations and ensure that they are reasonable.
For subjects or grades that are projected two years out, we only require two predictors in order to provide these projections.
Calvin is a high-achieving student who has scored well on state assessments for the past few years, especially in math. He completed reading and took the assessment. To provide a projection for Calvin, we:
- Determine the relationships between the testing histories of all students and their exiting achievement on this assessment in the previous year.
- Use these relationships to determine what the projection would be for Calvin, given his own personal testing history.
Based upon Calvin's testing history, a score at the 83rd percentile would be a reasonable expectation for him.
In conceptual terms, this is how the projection for a student is generated. A minimum of three prior scores is required for a student to have a projection. That doesn't mean three years of scores, or even three scores in the same subject. It simply means three scores across grades and subjects.
The model determines the relationships between all students' prior assessment scores. By considering how all other students performed on the assessment in relation to their testing histories, the model is able to calculate a projection for each student based on their individual testing history. In Calvin's case, the model would look at the students who took the seventh-grade math assessment in the most recent completed school year.
Remember that the projection is based on the assumption that Calvin will make average growth leading up to this assessment. If he makes less progress, he is likely to score lower than the projection suggests. Likewise, if he makes better than average growth , he will likely outperform the projection.