Thanks, aeh.
I laughed at the 11.7. We keep getting that number for this kid since before he started kindergarten - never valid, but certainly a recurring level.
So looking at that table more closely, an 838 (his minimum score) is found at the 54th percentile for 10th grade. Does that mean that the 838 number is meaningless as a standalone measure? A 10th grader starts taking the test at the 10th grade level, so is not limited to a 7th grade level of math.
I'm missing something basic. No bother - I'll ask for a retest. Sigh.
838 is a scaled score--actually a Rasch score, which means it's continuously scaled across the grade norms, and is supposed to be equal-interval, meaning the difference in difficulty level between an 838 and 638 is equivalent to the difference in difficulty between a 638 and a 438. Obviously, since academic skills don't really grow at a uniform rate, and who knows what "difficulty" really means anyway, this is approximate at best. Now this sounds fabulous as a means of assessing growth, and making scores more comparable across grade levels, but for the question of where 838 comes from. It's derived (like most standard scores and scaled scores) from a raw score, with its requisite basals and ceilings. This would work nicely, if children had nice solid basals and ceilings, with uniform success on all items below the basal, and a smooth, predictable pattern of failures just below the ceiling. Alas, children decline to fit comfortably into this idealized pattern of performance. Consequently, some students' 838 fit the ideal, and probably are better represented by the grade equivalent than others. Others have a lot of holes before the basal level, and receive an overestimate of their actual skill level. One could miss some easy items at an inopportune moment (say early in the item set), and be directed to a lower level set of items, receiving a lowered estimate of their true skills. If you have conceptual skills above your calculation skills, or skills that you figured out on your own, absent instruction, you might be able to do some problems above the level of your ceiling, but we won't know that, because you ceilinged before then. If you start from a higher basal (such as in the 10th grade), the floor of the test will effectively not be as low, which may overestimate skills.
A 10th grader starts at about the 8th or 9th grade level, so, yes, they won't be limited to 7th grade level, and can in fact top out the test, in terms of item difficulty. But the low end of the spectrum will also not be represented as accurately.
The scaled score is not meaningless as a stand-alone measure, it just comes with a collection of caveats, just as the age/grade-equivalent scores derived from it do. It's most useful as what it's designed for, which is a growth score (keeping in mind that, at the upper extreme, it is possible to run out of the pool of high-level items, if too-frequent multiple measurements are taken--even more true of MAP).
