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. Copyright © 2022 Springer.

The contribution of teacher knowledge to learning outcomes at the beginning stages of literacy acquisition is of growing concern because the ability to provide quality instruction is central to successful literacy acquisition, particularly for pupils with dyslexia. To date, the majority of research has focused on teachers of English as a first language. Yet, English is the most widely taught foreign language today. The present study extends the exploration of teacher knowledge by probing two heretofore unexamined groups of teachers who are responsible for teaching beginning stages of literacy in English as a foreign language: regular class teachers who are non-native English-speaking (N = 96) and native English-speaking teachers (N = 24) working in the kindergarten setting in Hong Kong. As these two teacher groups serve as gatekeepers of beginning English as a foreign language literacy for kindergarten children in Hong Kong, it is crucial to gather information about the depth and quality of their teacher knowledge. This information can be instrumental to improving the quality of beginning literacy instruction in English and assisting early identification of dyslexia. Both groups completed the basic language constructs survey (Binks-Cantrell, Joshi, & Washburn, Annals of Dyslexia, 62, 153–171, 2012a). Results showed while native English teachers performed significantly better than non-native English teachers, total percentage correct scores were below 50%, except for phonological awareness tasks. All teachers scored higher in items requiring syllable as opposed to phoneme manipulation. Only teacher type predicted teachers’ performance on the survey. The need for quality instruction, particularly for children at-risk for dyslexia or those struggling at the beginning stages of literacy acquisition, is addressed. Copyright © 2020 The International Dyslexia Association.