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# Measuring and Calculating Student Growth 2014

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## Dave Moyer

on 8 April 2015

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#### Transcript of Measuring and Calculating Student Growth 2014

Measuring and Calculating Student Growth
What's a Median Again?
We use averages all the time, which also go by the name "mean." Medians are less common and are best understood as the "middle" value. So to calculate a median, we order all the values and take the middle one.
So how does this work?
More Resources
This is just the tip of the iceberg...if you want to get technical or ask questions specific to an accountability system you can find resources to suit your needs:
But what happens when we change tests?
The transition to Smarter Balanced will not prevent us from assigning SGPs. The scale does not matter, as we'll still be able to judge how similar students performed relative to each other.
Why Growth?
Here's a hypothetical classroom:

Which student(s) are the best performing in this hypothetical classroom?

If we could only pick two, which students would be most in need of extra help?
This axis represents the scaled score on the HSA exam. Each student gets an individual point value from 100-500 with 300 being the threshold to be labeled proficient.
We compare a student's performance to other students who scored like him or her in the past.

This gives us context into what we should expect.
3rd
4th
5th
6th
7th
Scale
Score
High SGP
Low SGP
SGP
of 50
To calculate a student growth percentile we compare our current student with students who had the same score history in the same grades.

We know where others with the same history scored in 7th grade and we compare our current student's 7th grade score with others like him. Each score dot corresponds with an SGP--so we just find which values match.
Students with the same score history
All possible scores
Hawaii Department of Education, 2015
Some Details on the Calculation
1) We use test scale scores from grades 3-8 and one high school grade to calculate SGPs

2) Students are compared to all students with the same test score history (and therefore the same age) in our system. As a result students are compared to their peers statewide.

3) We only calculate SGPs for students who have taken a test in our system once before. In other words, we need a starting point to measure their growth from (more on this later).

Let's imagine we have a class of 25 students, each with a student growth percentile. If we line them up according to their SGP (just as we might if we lined them up by height), we can find the median simply by choosing the 13th student.

In this case that student has an an SGP of 61, which would be the median for the class.
12 students below the median
12 students above the median
Why use a median?
Medians are more resistant to "outliers."
Imagine you're at a BBQ and someone decides to conduct a poll of everyone's salary:
Average salary: \$36,200
Median salary: \$31,000
\$22k
\$52k
\$29k
\$31k
\$47k
What if Bill Gates joins you...
\$1 million
Average salary: \$196,833
Median salary: \$39,000
3rd
4th
5th
6th
7th
HSA
Scale
Shared HSA score history
Recall that we compare similar students to one another.

The change in tests will not affect students' past scores, and we will still be able to see how students with similar test score histories performed on the new exam, which will allow us to assign an SGP.
Smarter
Balanced
Scale
Educator Effectiveness System: http://doeohr.weebly.com/
Strive HI Performance Index: hawaiipublicschools.org, click -> "Strive HI"
This is great, so how do I use the reports you gave me?
The "bubbles"
impress your nerdy friends by calling this a scatterplot
This axis tells us a student's scale score, which is the raw value that a student receives on an exam.
The white lines show the thresholds that determine the achievement categories of "proficient," exceeds," etc.
The horizontal axis shows a student's growth percentile. The further to the right, the more a student grew relative to her peers
Think about the difference between the two highlighted students. What do we know about their academic performance?
This is a view of an entire grade in an elementary school. Each circle represents a student and plots her growth against her scale score on the exam
The student view in SchoolView
This view appears in SchoolView when one drills all the way down to an individual student. Note how it resembles the fan chart, where there's a scale score and then a colored line shows whether the growth was high, typical or low.
Each dot is a scale score, and the color of the line shows growth.
The horizontal axis is time, and shows a student's testing career in Hawaii
This presentation: http://tinyurl.com/growthinhawaii
\$22k \$29k \$31k \$47k \$52k
How does a second dimension of performance change our understanding?
The Life Cycle of a
Student Growth Percentile

SBA
SGPs are created from student test scores on the Smarter Balanced Assessment (and formerly from the HSA). So the first step in creating one is for students to take the test and earn scores in the two tested subjects.
English/Language Arts

2467
Math
2184
We use a student's SGPs along with his scale scores to understand his performance and plan for his future education
Scale Scores
SGPs
24
52
(There's a lot to these arrows that we'll skip for now. More to come.)
ELA
Math
We also combine SGPs to understand how groups of students perform--often taking the median (or middle) student's performance as the summary.
Classroom
Educator Effectiveness
(Teacher)
School
Strive HI
Educator Effectiveness
(Principal)
Scale score: 2467 = Proficient
SGP: 24 = Low Growth
Scale score: 2184 = Approaches Proficiency
SGP: 52 = Normal Growth
Our student only performed better in English/Language Arts than 24% of students like him
In Math, our student performed better than 52% of students like him
A student's comparison group (or academic peers) are other students in the state of the same age who scored similarly in the past in a given content area. Academic
peers are not an actual set of students but are constructed using all the
state’s data
Each black line represents an academic peer group
High SGP
Low SGP
SGP
of 50
SBAC Score
100
300
500
2000
3000
2500
Click the play button to hear a narrated version!
Full transcript