Prior to 2001 and NCLB, a school psychologist's primary responsibility was to "test and place" students into one of the many areas of special education and related services.
School psychologists were often called for assistance when it was time to evaluate a student for a possible educational disability under according to the Individuals with Disabilities Education Act. We were then asked to give psychoeducational assessments to students to determine things like: reading ability, cognitive functionality, level of social development, intelligence, and other functions related to a child's performance in school.
However, that role is changing. Since NCLB, school psychologists are rapidly becoming much more than simply a test administrator. Testing is no longer the #1 priority of school psychologists, although it is arguably the most well defined. No other field of professionals in the school system knows as much about psychological, educational, or psych-educational testing as school psychologists do. Period.
I would posit that if there were one skill that school psychologists were known to have, it would be the ability to "give IQ tests".
Yes, school psychologists do engage in individually administered intelligence assessment. No, they are not the same tests that can be taken online by asking you to solve riddles, word puzzles, and identify which pattern of shapes would come next in a sequence. Those silly tests are not designed to accurately portray your overall intelligence. They are designed to collect your personal data, entice you to pay money for the "complete results", then send you spam for your time. (FYI, you might take a look at my other post about password safety if you think you have been a victim of one of these scams.)
School psychologists are trained, credentialed, and experienced in giving several types of cognitive assessments. There are only a small handful of professionals who are authorized to even see these materials (testing companies are very tight-lipped about the content of their tests.) In a large percentage of schools, school psychologists are the only professionals who carry this distinction and responsibility.
There is a large movement of schools that are working toward phasing out the need for individualized assessment of students when they are being evaluated for certain types of exceptionalities. Depending on your state, school system, or implementation phase, your school may use one or more of the following models instead of individualized assessment: Response-to-Intervention/Multi-Tiered Systems of Support, or Patterns of Strengths and Weaknesses. When I conduct hiring interviews for school psychologists for, one of the questions I ask is about their opinion about the necessity of individualized assessments today.
Unfortunately, many educators and community members still see school psychologists as nothing more than test-givers. I look forward to the day when school psychologists are recognized for the wide variety of educational services that school psychologists can offer, not simply the ability to identify children for educational exceptionalities.