Geometric prediction: A framework to gain insight into solvers’ geometrical reasoning

Anderson, 1990 Arzarello, 2006, Semiosis as a multimodal process, Revista Latinoamericana de Investigación en Matemática Educativa, 9, 267 Arzarello, 2009, Gestures as semiotic resources in the mathematics classroom, Educational Studies in Mathematics, 70, 97, 10.1007/s10649-008-9163-z Arzarello, 2015, Growth point and gestures: Looking inside mathematical meanings, Educational Studies in Mathematics, 90, 19, 10.1007/s10649-015-9611-5 Battista, 1999, Fifth graders’ enumeration of cubes of 3D arrays: Conceptual progress in an inquiry- based classroom, Journal for Research in Mathematics Education, 30, 417, 10.2307/749708 Boero, 2001, Transformation and anticipation as key processes in algebraic problem solving, 99 Boero, 1996, Some dynamic mental process underlying producing and proving conjectures, Vol. 2, 121 Carlson, 2005, The cyclic nature of problem solving: An emergent multidimensional problem-solving framework, Educational studies in Mathematics, 58, 45, 10.1007/s10649-005-0808-x Chen, 2013, The interplay among gestures, discourse and diagrams in students’ geometrical reasoning, Educational Studies in Mathematics, 83, 285, 10.1007/s10649-012-9454-2 Chinn, 2014, Microgenetic methods, 171 diSessa, 2007, An interactional analysis of clinical interviewing, Cognition and Instruction, 25, 523, 10.1080/07370000701632413 Fischbein, 1987 Fischbein, 1993, The theory of figural concepts, Educational Studies in Mathematics, 24, 139, 10.1007/BF01273689 Gal, 2010, To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception, Educational Studies in Mathematics, 74, 163, 10.1007/s10649-010-9232-y Gallese, 2005, The brain’s concepts: The role of the sensory-motor system in conceptual knowledge, Cognitive Neuropsychology, 22, 455, 10.1080/02643290442000310 Ginsburg, 1981, The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques, For the Learning of Mathematics, 1, 4 Goldin, 2000, A scientific perspective on structures, task-based interviews in mathematics education research, 517 Kasmer, 2012, The nature of student predictions and learning opportunities in middle school algebra, Educational Studies in Mathematics, 79, 175, 10.1007/s10649-011-9336-z Kim, 2007, Using prediction to promote mathematical reasoning, Mathematics Teaching in the Middle School, 12, 294, 10.5951/MTMS.12.6.0294 Koichu, 2015, Proving as problem solving: The role of cognitive decoupling, The Journal of Mathematical Behavior, 40, 233, 10.1016/j.jmathb.2015.10.005 Kosslyn, 1980 Lim, 2006, Characterizing students’ thinking: Algebraic inequalities and equations, Vol. 2, 102 Lim, 2010, The role of prediction in the teaching and learning of mathematics, International Journal of Mathematical Education in Science and Technology, 41, 595, 10.1080/00207391003605239 Maciejewski, 2016, Mathematical foresight: Thinking in the future to work in the present, For the Learning of Mathematics, 36, 25 Mariotti, 1992, Geometrical reasoning as a dialectic between the figural and the conceptual aspects Mariotti, 1995, Images and concepts in geometrical reasoning, 97 Mariotti, 2018, Developing geometrical exploration skills through dynamic geometry, 153 Mariotti, 1997, Defining in classroom activities, Educational Studies in Mathematics, 34, 219, 10.1023/A:1002985109323 Mariotti, 2019, Intuition and proof in the solution of conjecturing problems’, ZDM, 51, 759, 10.1007/s11858-019-01059-3 McNeill, 1992 McNeill, 2000, Growth points in thinking-for-speaking, 141 Miragliotta, 2020 Miragliotta, 2018, You see (mostly) what you predict: The power of geometric prediction, Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, 387 Mogetta, 1999, Providing the motivation to prove in a dynamic geometry environment, Proceedings of the British Society for Research into Learning Mathematics, 91 Noss, 1996 Novack, 2015, Learning from gesture: How our hands change our minds, Educational Psychology Review, 27, 405, 10.1007/s10648-015-9325-3 Palatnik, 2019, Students’ reasons for introducing auxiliary lines in proving situations, The Journal of Mathematical Behavior, 55, 10.1016/j.jmathb.2018.10.004 Pedemonte, 2007, How can the relationship between argumentation and proof be analysed?, Educational Studies in Mathematics, 66, 23, 10.1007/s10649-006-9057-x Rescher, 1958, On prediction and explanation, The British Journal for the Philosophy of Science, 8, 281, 10.1093/bjps/VIII.32.281 Schoenfeld, 2000, Purposes and methods of research in mathematics education, Notices of the AMS, 47, 641 Schoenfeld, 1993, Learning: The microgenetic analysis of one student’s evolving understanding of a complex subject matter domain, 4, 55 Vygotsky, 1978 White, 2014