Some of this has been discussed in this recent thread, regarding GAI and CPI:
http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/198131/1.htmlYour child's profile is consistent with cognitive ability just outside/on the border of the gifted range. The VCI and PRI have more to do with higher-level thinking and reasoning skills, and can be combined in the GAI (General Ability Index). The WMI and PSI have less to do with general intelligence, and more to do with efficiency, and can be combined in the CPI (Cognitive Proficiency Index). Your child's performance on these tasks was slightly below average, which suggests that, although thinking ability is good, efficiency may be vulnerable, which can lead to a significant amount both of frustration for the student, and of underestimation of ability on the part of educators. Given the profile, the examiner should also have computed a GAI.
The scores are reported as ranges (VCI ranging from 113 to 127) because of standard error of measurement. This is a term that statisticians use to refer to the minor variations in measurement that occur due to the exact circumstances at the moment of any given test administration. Any given person, on any given day, may score a little higher or a little lower than the "official" score obtained on an IQ or achievement test. In order to capture that small amount of uncertainty, confidence intervals are used to indicate that, if administered the same tasks on another occasion, the individual would be expected to score within the range reported on 95 out of 100 chances (if your conf. int is at the 95% level, which it usually is for the WISC-IV).
As to the area performances: Both verbal and perceptual reasoning skills appear to be equally well-developed, on the border of High Average and Superior, which is considered to be just at the bottom edge of the gifted range by some professionals. This is actually an excellent place to be when navigating the public school system, as it is usually somewhat easier to balance appropriate challenge with academic acknowledgement in this range. Were there any inconsistencies within the domains, or were the subtests all within about three points of each other?
Working memory is the ability to retain, mentally manipulate, and reproduce information--symbolic, in this case. This area appears to be a significant relative weakness for your child. A number of different factors may affect performance on these tasks. It is not unusual for high cognitive children with a deliberate, conscientious, perfectionistic style to score lower on this and PSI than on VCI and PRI, however, usually, they score in at least the average range, and frequently at least high average. Your child's low average performance is more concerning. Other possible explanations include fatigue, inattention, impulsivity, emotional interference (e.g., anxiety, depression), psychomotor retardation from medication side effects (such as those used in the treatment of anxiety/depression), and illicit substance use.
The processing speed index reflects the efficiency with which individuals complete rote visual-motor tasks--pencil-and-paper symbolic tasks, in this case. It is subject to many of the same issues as working memory, both with regard to the high cognitive population and the alternate explanations of low performance. In addition, processing speed may be affected by vision, visual tracking, fine-motor skills, and motor planning.
The kind of academic concerns that are often encountered in conjunction with low CPI (WMI and/or PSI) include difficulty with automaticity, such as reading, writing, or calculation fluency skills, and downstream effects on reading comprehension, written expression or multi-step math/math problem solving. When expectations are for short or mostly oral responses, these may not show up as much. As students progress into the higher grades, where the volume of reading and writing, and the complexity of reading comprehension, writing, and math reasoning becomes greater, these vulnerabilities may be exposed. This transition may feel particularly unexpected in a child with strong thinking and reasoning, as, up until then, they were able to compensate for any shortcomings in efficiency by employing cognition. Based on the cognitive profile alone (absent achievement testing), I would wonder about the possible presence of a learning disability/2e.
You don't mention why you wanted your child tested, and what you hoped your family would gain from the process. If you are comfortable sharing a little more, perhaps folks here will be able to focus their comments a bit.
