Research in educational psychology consistently finds a relationship between intelligence and academic performance. However, in recent decades, educational fields, including gifted education, have resisted intelligence research, and there are some experts who argue that intelligence tests should not be used in identifying giftedness. Hoping to better understand this resistance to intelligence research, we created a survey of beliefs about intelligence and administered it online to a sample of the general public and a sample of teachers. We found that there are conflicts between currently accepted intelligence theory and beliefs from the American public and teachers, which has important consequences on gifted education, educational policy and the effectiveness of interventions. A preprint of this article is available at https://psyarxiv.com/uctxp.