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Learning coding during early childhood is an effective way for children to practice computational thinking. Aspects of children's motivation can increase the likelihood that children approach computational thinking activities with enthusiasm and deep engagement. Gender inequities may interfere with children's readiness to take advantage of opportunities to build computational thinking skills through activities such as coding. Societal stereotypes can reduce young girls' motivation to engage with computer science, preventing them from gaining benefits from coding activities designed to support computational thinking. This study examined children's gender stereotypes as well as children's own motivation for computer coding in 363 first- through third-grade children. We assessed gender differences in both stereotypes and motivation, as well as links between the stereotypes that individual children held and their own motivation. Children generally endorsed stereotypes about interest and ability for computer coding that favored their own-gender group, although third-grade girls reported gender-egalitarian beliefs about interest in coding. There were no gender differences in children's motivation for computer coding in terms of their own interest, sense of belonging, or ability self-concepts. Children's stereotypes about their own-gender group were significantly positively correlated with their own motivation for computer coding. These findings suggest that early childhood represents an excellent age for children to begin building computational thinking skills, before girls endorse negative stereotypes about their gender's interest in computer science.