There is no standard procedure required to be used in New Zealand schools for identifying students who are gifted in maths. Individual schools develop their own systems to ensure that they identify gifted students, including Māori, students from other cultures/ethnicities, students with learning difficulties or disabilities, underachievers, and those from low socio-economic backgrounds.
Gifted and Talented online provides information on a variety of ideas relating to the identification of gifted students, including guidelines for developing criteria, and available tools to use.
Twice exceptional students are gifted students whose performance is impaired, or high potential is masked, by a specific learning disability, physical impairment, disorder, or condition. They may experience extreme difficulty in developing their giftedness into talent. You can read more about twice exceptional students on Gifted and Talented Online.
The most important consideration in identifying gifted students is ensuring the use of multiple methods to assess students, including both formal and informal tools.
A list of some of the characteristics of highly able maths students is available on this website.