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Felix Klein's notion of "double discontinuity" between university mathematics and secondary school mathematics has persisted in mathematics teacher education. Situating this study in Hong Kong, we investigated three prospective secondary teachers' experiences in higher education and secondary mathematics classrooms, including their figured worlds, identities, and mathematical knowledge constructed through those experiences. Our analysis revealed their contrasting experiences in these two contexts, adding to our understanding of the phenomenon of "double discontinuity" in terms of not only how it is relevant to Hong Kong but also how it may manifest in the specific cultural context. Moreover, we found coherency and continuity during the prospective teachers' secondary-tertiary transition; their learning experiences in both environments served as critical resources upon which they reflected to envision their future mathematics teaching. We conclude with implications and suggestions for mathematics teacher education to support prospective teachers' (and their future students') transitions between high school and university mathematics.

Felix Klein's notion of "double discontinuity" between university mathematics and secondary school mathematics has persisted in mathematics teacher education. Situating this study in Hong Kong, we investigated three prospective secondary teachers' experiences in higher education and secondary mathematics classrooms, including their figured worlds, identities, and mathematical knowledge constructed through those experiences. Our analysis revealed their contrasting experiences in these two contexts, adding to our understanding of the phenomenon of "double discontinuity" in terms of not only how it is relevant to Hong Kong but also how it may manifest in the specific cultural context. Moreover, we found coherency and continuity during the prospective teachers' secondary–tertiary transition; their learning experiences in both environments served as critical resources upon which they reflected to envision their future mathematics teaching. We conclude with implications and suggestions for mathematics teacher education to support prospective teachers' (and their future students') transitions between high school and university mathematics. [ABSTRACT FROM AUTHOR]