Student academic growth is a topic that almost everyone thinks they understand. Growth and change are familiar concepts to all parents, especially as they relate to increases in the height and weight of children. However, when details about the "growth model" emerge reactions often range from general confusion to frustration: Why does something so simple have to be made so complicated?
In reality, student academic growth is a little more complicated than most people think but much less complicated than what's written about it would lead one to believe. A simple 5th grade story problem helps to illustrate this point.
The story problem is drawn from a situation outside of education where we are asked to consider the improvement in personal best high jumps for two high jumpers, Anna and Judy.
<iframe height="700" class="full-width" src="https://rawgit.com/bclinkinbeard/a2fdce4d5b56d4563d4fef4292a90eda/raw/fbbaf7300a2131b604883b8e48a979b46bec56f9/index.html"> </iframe>Anna is a novice higher jumper and Judy is a world class competitor. In 2015 Anna’s best jump was 3 feet 6 inches whereas Judy's was 6 feet 7 inches. During following 2016 season Anna improved to 4 feet and Judy to 6 feet 9 inches.
- Whose high jump changed more? Explain your answer.
- Whose high jump change is more remarkable? Explain your answer.
- Which high jumper improved more? Explain your answer.
The first question is a familiar one in any arithmetic class. Simple subtraction tells us how much each changed: 6 inches for Anna and 2 inches for Judy. The second and third questions are more subtle.
One might simply answer those questions by saying that since Anna's best high jump changed more than Judy's, Anna's change is more remarkable. However comparing Anna’s 6 inch improvement to Judy’s 2 inch improvement requires care. Bigger isn't necessarily better when comparing changes in scores.
Though it is certainly true that 6 inches is more than 2 inches, a 6 inch improvement for a novice is not more remarkable than a 2 inch improvement for an expert. Novices generally improve a lot when starting--often referred to as beginners gains.
Understanding Anna’s and Judy’s improvement requires one to compare them to their peer’s: those whose high jumping ability is like theirs. A 2 inch increase for an elite high jumper is remarkable whereas 6 inches for a novice is typical.
A 6 inch improvement for a novice isn't that remarkable as most novices show at least that much improvement. By contrast, the 2 inch improvement for Judy puts her within striking distance of the world record. A bigger change isn't necessarily more remarkable.
This isn't unique to high jumping. Numerous events are like this: A 2 inch increase in height for a 60 year old is more remarkable than a 4 inch increase for a toddler. It is normal for toddlers to grow 4 inches from one year to the next but it is not normal for adults to grow 2 inches. The moral of the story problem is that context matters.
A common belief among users of Georgia Milestones data is that one can simply subtract a student's scores from one grade to the next and use the difference to evaluate student growth. Subtraction is what everyone learned to do in elementary school when asked to find how much a quantity had changed.
For the Georgia Milestones, there are two problems with subtracting a student's scores from one year to the next.
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The Georgia Milestones assessment scores from year to year are not meant to be subtracted. Even though the scores have the same range, subtracting them makes no sense: like subtracting your weight from your height.
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Even if scores could be subtracted, as the high jump story problem illustrated: Evaluating academic growth for students starting at different places is harder than just simple subtraction because academic growth varies based upon where a student starts. Students show beginner's gains in academics just like high jumping.
If subtraction doesn't work, what's the solution? The previous examples give a hint: Consider the and look at where the student currently is relative to students with the same starting point.
This is exactly what the Georgia Model of Student Growth does by looking at all students across the state that share the same achievement history as the student in the given grade and content area. Each student receives a student growth percentile (SGP) indicating how remarkable their progress is relative to their academic peers: those students with the same achievement history.
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