The field of cognitive psychology is based on quantitative and qualitative data analysis of human intelligence. However, most of the inquiry that has been performed in this area has been prompted by theoretical frameworks. This means that theory, and not science, is what mainly drives the essential questions as to what exactly is human intelligence, how it is produced, and what is the most optimal way to use it.
Research in human intelligence is not that old, nor has it matured to perfection, as they say. Formal investigations did not start until the late XIX century. However, the results of over 100 years of research have determined that, indeed, intelligence cannot be measured comprehensively or under a general or generic perspective; it should be measured by skill and taking into consideration the cognitive level and ability of each test taker.This is why the field of education is moving away dramatically from standardized testing as a tool for formative assessment and, instead, only use it for only as a quantitative tool for summative assessment that seeks to analyze specific data.
Some of the theoretical frameworks most accepted in the field are, according to their impact in current best practices:
a) Howard Gardner's Multiple Intelligence theory (1989, 1990) - states that there are eight (sometimes up to thirteen) individual and independent types of intelligence. Some individuals may excel in all, or in only one; the latter variable does not entail that the individual has less intelligence than someone who succeeds in all. What it means is that such individual happens to be "intelligent" or "able" in a specific skill, rather than in a bunch of them.
b) Sternberg's Triarchic Model (1980-1990) - contends that intelligence is best acquired, developed, and applied when three steps are covered during the learning process: a) the capacity for analysis, b) the process to create with the analyzed data (sort of an extension of the tasks as Bloom would stay) and, c) the ability to apply knowledge to show understanding. KUD: Knowing, Understanding, Doing.
c) Prior to Sternberg and Gardner, intelligence was thought to be a general concept, as stated in the G-factor theory by C. Spearman. The problem with this theory is that it implied that everybody has the same skill and ability to learn and apply information, which is not the case.
In all, intelligence is not one general skill, nor one umbrella under which any learner can be covered. That would reduce intelligence down to a watered-down concept. Instead, intelligence is a combination of skills and modes of application that vary from people to people depending on their developmental levels.