TAIWAN
Dynamic geometry, implication and abduction: a case studyIn this paper we illustrate the role of dynamic geometry as an environment that propitiates the use of empirical explorations to favor learning to prove. This is possible thanks to abductive processes, related to the establishment of implications that university students of a plane geometry course carry out when, supported by a dynamic geometry program, they solve a problem in which they must discover a geometric fact, formulate a conjecture and prove it. Camargo, L., Molina, Ó., Perry, P. y Samper, C. (2012). Dynamic geometry, implication and abduction: a case study [Ponencia]. 36th Conference of the International Group for the Psychology of Mathematics Education, Taipei, Taiwan. |
Assigning mathematics tasks versus providing pre-fabricated mathematics in order to support learning to proveWe present types of mathematics tasks that we propose to our students —future high school mathematics teachers— in a geometry course whose objective is learning to prove and whose enterprise is collectively building an axiomatic system for a portion of plane geometry. We pursue the achievement of the course objective by involving students in different types of tasks instead of providing them with pre-fabricated mathematics. Camargo, L., Echeverry, A., Molina, Ó., Perry, P. y Samper, C. (2009). Assigning mathematics tasks versus providing pre-fabricated mathematics in order to support learning to prove [Ponencia]. 19th ICMI Study Conference: Proof and proving in mathematics education, Taipei, Taiwán. |
Learning to prove: Enculturation or…?Empirical evidence coming from a curriculum innovation experience that we have been implementing in the Universidad Pedagógica Nacional (Colombia), in a plane geometry course for secondary mathematics pre-service teachers, allows us to affirm that learning to prove, more than enculturation into mathematicians’ practices, is participation in proving activity within the community of mathematical discourse Camargo, L., Echeverry, A., Molina, Ó., Perry, P. y Samper, C. (2009). Learning to prove: Enculturation or…? [Ponencia]. 19th ICMI Study Conference: Proof and proving in mathematics education, Taipei, Taiwán. |