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explain Marston's (1988) finding that students' reading scores graphed on equal interval paper predicted outcome scores better than scores graphed on six-cycle paper. The related finding (i.e., when a linear relationship does not characterize progress, a negatively accelerating curve best approximates growth) also seriously questions the use of semilogarithmic graph paper to display progress --at least for use with a measurement approach, such as CBM, that samples material from the entire year's curriculum and focuses on student progress toward end-of-year goals.

Although a linear relationship adequately modeled reading and math growth within an academic year, a linear relationship did not adequately model academic growth across years in school. This was true for all measures in all academic areas, except the CBM maze measure for which weekly rates of growth were comparable regardless of time in school. Consequently, it appears that, over years in school, academic proficiency continues to increase (i.e., students exhibit positive slopes) -- at least when progress is indexed on measures of basic skills such as spelling words, reading aloud text, and conducting operations on numbers. The magnitude of that improvement, however, gradually decreases, probably as learning of the basics is acquired and attention becomes refocused on more complex domains of study not reflected in the measures employed in this study, except for the maze. This gradual deceleration may explain why, at Grade 6 for math and oral passage reading, but not for maze, the linear relationship applied to individual student regressions no longer modeled growth. Future research investigating the tenability of these hypotheses should not only enhance our understanding of models of human development but also contribute to a technology of measuring student change.


[1] All students within a class were monitored on the same, grade-appropriate materials. This uniform approach to measurement level frequently is adopted when CBM is used in general education to increase feasibility. Teachers did, however, set individual goals, specifying the desired performance by the end of the year on the grade-appropriate material and used the database to monitor student growth. They occasionally did make instructional adjustments based on the ongoing assessment information.

[2] The Harris-Jacobson word list includes high frequency vocabulary across reading curricula. This word list was selected because the participating school districts did not employ a spelling program. The computerized CBM spelling program can be adapted for use with any curriculum.

[3] When n exceeded 50 at a grade level, 50 cases were selected randomly for this analysis. When n < 50, all cases with at least seven measurements were employed.

[4] Although the use of a quadratic term in a polynomial regression is acceptable for evaluating the curvilinear nature of individual student progress within a year, please note that this would not be the procedure of choice for predicting performance beyond the range of data.


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