Founders of new schools and designers of new curricula often point to progress on standardized tests as evidence of their successful efforts to educate children. For this purpose, grade-level-equivalent scores have a fatal attraction. If we don't watch out, we find ourselves making claims like: "On the average, students gain more than two years in reading ability for every year at our school."

Likewise, if we don't watch out, we may find ourselves telling proud parents in a family conference that last year their child was reading at the third-grade level, but now she/he is reading at the middle of grade five. So she/he gained two and a half years in just one year.

But we can get into serious trouble by making such claims. The grade-level scores that are generated by standardized tests simply cannot be used that way. The logic doesn't work. Critics may rightfully say that we falsified our data, -- not purposefully, but because we fell into an intuitive trap .

What can we do instead? How can we portray individual progress on standardized tests in a clear and scientifically acceptable way? Expanded Standard Scores and Rasch Scale Scores provide more defensible ways to measure progress across grade levels. But these scores are not intuitively meaningful when taken by themselves. We have to put them in context. The purpose of this paper is to show how we can put such scores into graphic displays that are both intuitively clear and technically acceptable. The procedure can be used with any standardized test battery that provides Expanded Standard Scores or Rasch Scale Scores. Our examples are drawn from the Gates-MacGinitie Reading Tests and the Reading Section of the Wide Range Achievement Test .

The Gates-MacGinitie Tests

The dark-colored diamonds in Figure 1 show the "ESS Scores" (Expanded Standard Scores) that correspond to average student performance from Grade 1 through Grade 12, derived from the Gates-MacGinitie norms.

ESS Scores are marked along the vertical axis. Numbers along the horizontal axis mark the beginnings of each grade, and the grades are sub-divided into units according to the conventional scheme used by most standardized tests, i.e. 5.0 = September of Grade 5, 5.1 = October, and so on through 5.9 = June. Summer months are omitted. Then 6.0 = September of Grade 6, and so on.

Error bars around the ESS scores show their standard deviation. The curve rises rather steeply through the first four grades, then takes a more gradual slope through high school. This is a graph of expected, normal growth in reading competence, as measured by the Gates-MacGinitie tests, under ordinary conditions of American, public school instruction. One can think of it as analogous to a pediatrician’s chart of expected, normal growth in an infant’s weight, as measured by the clinic’s scale, under ordinary conditions of American nutrition and health care.

The Wide Range Achievement Test

Dark-colored diamonds in Figure 2 show the "Absolute Scores" (Rasch-Scale Scores) for the Wide Range Achievement Test, corresponding to each grade level for which the test manual provides data. (High-school grade levels are not distinguished by the Wide Range Achievement test.) As was the case with the Gates-MacGinitie Test, the curve rises rapidly over the first four grades. Then it takes a much lower slope through high school. This is normal growth in reading as measured by the WRAT.

Graphing Individual Progress

The triangles in Figures 1 and 2 show the progress of an individual student, Brendan, in comparison to the norms for the two tests. Brendan’s data were entered into the charts by determining his age-grade level at the time he took each test, and plotting his scores at each of those points. Age-grade level was calculated as follows:

1. Take Brendan’s year of birth and add six years. The result is his expected year of school entry according to his age.

2. Subtract the school year of entry from the school year in which he took the test. This is his age-grade.

3. Add decimal fractions of the school year until you get to the month in which he took the test. This is his age-grade level.

For example:

• Brendan was born on September 24, 1981
• Add 6 to get his expected entering school year, 1987/88
• Brendan was first tested in the summer of 1994, so subtract 1987/88 from 1993/94 to get his expected age-grade at that time, 6th grade
• Since he was first tested in the summer of 1994, his expected age-grade level was then 6.9
• Brendan was next tested in May 1995. His age-grade level was 7.8. In May 1996, it was 8.8.

With the analogy of the pediatrician’s growth chart, these displays are intuitively understandable by students, parents and teachers. Because the charts are straight-forwardly derived from the logic of the test construction, they should also be technically acceptable to the achievement testing community. We offer these charts as an alternative way to describe individual progress on standardized tests. (You can download copies of the Excel files that we used to create them.) Please let us know what you think. Write to wells@tli.com.