Recent progress in artificial intelligence (AI) has aroused interest in the growth and development of educational AI tools (EAITs). Teachers' adoption of EAITs in classrooms has helped in shaping instructional decisions taken by them in an attempt to promote intelligently and actively students' meaningful learning of contents areas. Nevertheless, science, technology and mathematics (STM) teachers in Nigeria are rarely adopting and incorporating EAITs in their classrooms pedagogical discourse, and their perceptions of EAITs are rarely assessed. To this end, this study identified human factors in acceptance of EAITs by STM teachers in Nigeria. The study proposed an extended technology acceptance model (TAM) integrating STM teachers' perceived trust and instructional beliefs in EAITs through a quantitative blueprint of a descriptive survey design. The sample for the study consisted of 345 STM teachers in the six education districts of Lagos State, Nigeria. A valid and reliable instrument tagged adoption of educational artificial intelligence tools questionnaire (AEAITQ, [alpha]=0.87) was used to collect survey data which, were analysed via structural equation modeling. The study results showed that STM teachers with constructivist beliefs had the tendency to adopt and incorporate EAITs into their instructional decisions than their counterparts with traditional beliefs. Traditional instructional beliefs (TIB) had a negative influence on perceived trust (PT), perceived ease of use (PEOU), and perceived usefulness (PU). In addition, PT, PEOU and PU were strong factors predicting STM teachers' adoption of EAITs. However, PEOU was the strongest factor that predicted STM teachers' adoption of EAITs in pedagogical discourse. Important inferences regarding the growth and adoption of EAITs for significant stakeholders in STM education were discussed.