ABSTRACT
The paper presented by George Burket was intriguing, to say the least. His use of my model of school learning (Carroll, 1963) prompted me to see whether I could push that model further in studying his data and his interpretations. I perceived immediately that in view of the very large sample sizes represented, his data afforded a rare opportunity to attempt to fit a precise mathematical model to aptitude and achievement data over multiple grade levels. I am happy to report success beyond what I could have hoped for. Even though, as Burket remarked, I had suggested that longitudinal data would be more appropriate for exploring the usefulness of my model, the cross-sectional data he presented proved to be quite satisfactory for this purpose. (I would still hope that the longitudinal approach could be tried someday, but for now, the cross-sectional approach will suffice.)
It was apparently not without good reason that Burket chose to present, in his paper, the detailed regression data for the pair of aptitude and achievement tests represented by the SFTAA Memory Test and the CAT Arithmetic
Total score, for this pair of tests seemed to come closest to reflecting a true aptitude-achievement distinction. At least, this was the only pair of tests for which all four of Burket's conditions for an aptitude-achievement distinction were met in as many as three (out of 11) comparisons between adjacent grades. These data seemed appropriate, therefore, for fitting a school learning model concerned with aptitude-achievement relations. But it also seemed desirable to try to fit the model to a pair of tests which generally failed to meet Burket's criteria; for this purpose, Burket generously provided me with data on the SFTAA Vocabulary Test and the CAT Reading Total score. In the subsequent development, I will focus on the Memory/Arithmetic data for the exposition of my model, later applying it to the Vocabulary/Reading data.
