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This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators.

Mathematics. --- Mathematics Education. --- Learning & Instruction. --- Teaching and Teacher Education. --- Math --- Science --- Mathematics—Study and teaching . --- Learning. --- Instruction. --- Teaching. --- Didactics --- Instruction --- Pedagogy --- School teaching --- Schoolteaching --- Education --- Instructional systems --- Pedagogical content knowledge --- Training --- Learning process --- Comprehension --- Mathematics Education --- Learning & Instruction --- Teaching and Teacher Education --- Pedagogical issues of integration into classroom practice --- assessment of modelling competencies --- teachers as learners of mathematical modelling --- technological influences on modelling education --- managing group interactions in modelling --- mathematical model --- modelling problems --- heuristic strategies --- teaching mathematical modelling --- modelling competencies --- learning mathematics modelling --- interpretations modelling --- pedagogical practice and research --- modelling perspective --- teaching practices in mathematical modelling --- Open Access --- Teaching of a specific subject --- Mathematics --- Teaching skills & techniques --- Cognition & cognitive psychology --- Teacher training