THE IRRELEVANCE OF VERTICAL SCALES TO
UNDERSTANDING STUDENT GROWTH
Damian W Betebenner
National Center for the Improvement of Educational Assessment
Dover, NH September 1st, 2015
“It is a common misconception
that to measure student growth
in education, the subject matter
and grades over which growth is
examined must be on the same
scale—referred to as a vertical
scale. Not only is a vertical scale
not necessary, but its existence
obscures fundamental concepts
necessary to understand growth.”
Me
Norm- and Criterion-Referenced Student Growth
“If you can’t solve a problem, then there is an
easier problem you can solve: find it.”
George Pólya
Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volume I
A Math Story Problem
• 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.
A Math Story Problem
Properties that don’t hold with simple examples will not hold in
complicated situations. This simple example illustrates how minimally
helpful a scale is to understanding change.
• A vertical scale allows one to answer a
very narrow question: Who changed
more?
• Remarkable & improvement need not be
synonymous with change.
• This example (ratio scale, no
measurement error) illustrates that a
vertical scale is of little help in answering
substantive questions.
“One Year’s Growth”
If “one year’s growth” is to be useful as a value
that makes points on the score scale
more meaningful, it would be useful to know if
the empirical average value of “one
year’s growth” is very different for students at
different levels of the score scale or
from different demographic backgrounds.
Because values for “one year’s growth”
are not currently available, the answers to these
questions are unknown.
David Thissen
Validity Issues Involved in Cross-Grade Statements About NAEP Results
About this copy
The Irrelevance of Vertical Scales to Understanding Student Growth — Center for Assessment staff meeting, September 1, 2015.
This is an image-based copy of the original PowerPoint slides; builds and animations are flattened.