It may seem counterintuitive for gifted students to suffer from test anxiety, but these students are just as prone to struggle with test taking as any of their classmates. Pressure to perform in an expected manner can cause gifted students' brains to "shut down" during a test for which they have a thorough understanding of the subject matter. This article in Psychology Today discusses how test anxiety in gifted kids originates and why parents should not be surprised that gifted kids struggle with test anxiety considering the perfectionistic tendencies that many gifted students have.
Parents can work with their children on managing the stress that the student might encounter through a variety of methods. This post from Supporting the Emotional Needs of the Gifted discusses several tactics for coping with stress that gifted kids should use in an effort to curb text-taking anxiety. Additionally, this website offers tips on test taking, studying, and note taking; information on reducing test anxiety; and information for parents.