The aim of this paper is to investigate the ethical and responsible use of AI chatbots in education in support of critical thinking, cognitive flexibility and self-regulation in terms of their potential to enhance and motivate teaching and learning in contemporary education environments. AI chatbots such as ChatGPT by OpenAI appear to be improving in conversational and other capabilities and this paper explores such advances using version 4. Based on a review of the research literature, a conceptual framework is formulated for responsible use of AI chatbots in education supporting cognitive flexibility in AI-rich learning environments. The framework is then operationalized for use in this paper through the development of exemplars for math, english language arts (ELA), and studying with ChatGPT to close learning gaps in an effort to foster more ethical and responsible approaches to the design and development of AI chatbots for application and use in teaching and learning environments. This paper extends earlier foundational work on cognitive flexibility and AI chatbots as well as work on cognitive flexibility in support of creativity and innovation with AI chatbots in urban civic spaces.