Hi momfor2,
Welcome!
WJ-III: there are actually two different tests: WJ-III-Cog (for cognitive IQ) and WJ-III-Ach (for achievement). Which one is the teacher referring to?
WPSSI-III is part of the Wechsler IQ tests. WPSSI is designed for age 2:6 to 7:3 years old. Then there is another Wechsler IQ test, WISC-IV, for age 6-16 yo. There are some overlap of age between these two Wechsler IQ test. I have heard the advice that if your child falls between 6 to 7:3 years old and is being tested for gifted program, consider WISC-IV (less likely to hit the ceiling, thus sometimes offer a better assessment.)
Which test to chose:
1. Depending on if your school is asking for an IQ or achievement test?
2. Depending on your child's age.
Here is a list of different tests with explanation.
http://www.hoagiesgifted.org/tests.htmHope this helps,
Mag