Research on Mathematical Proof

Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method

“…This method is a well-articulated combination of collaborative learning (Davidson, 1998), scientific debate (Alibert & Thomas, 1991;Legrand, 2001), and self-reflection (Hadamard, 1945(Hadamard, /1975. This method of teaching is named ACODESA, which in French stands for "collaborative learning, scientific debate and self-reflection", and it is in continuous process of development and refinement (see Hitt, 2007).…”

“…However, it is true that in the phase of debate, especially if there is the possibility of promoting a scientific debate (Alibert & Thomas, 1991;Legrand, 2001), the teacher must be prepared to react accordingly when the students are ready to engage in an in-depth discussion. We believe that this issue requires more research in order to develop specific tools that will enable researchers to study this phase.…”

Mathematicians’ perspectives on the teaching and learning of proof

“…It certainly seems reasonable to claim that collaborative classroom environments, in which students investigate, refine, and prove mathematical conjectures, address both of these issues reasonably well. Indeed, such environments may directly impact a number of the failings cited by the professors here because research indicates that in such situations students will find meaningful ways to understand statements and to check their own and others' assertions (Alibert & Thomas, 1991;Blanton & Stylianou, 2003;Rasmussen, Zandieh, King, & Teppo, 2005;Yackel, Rasmussen, & King, 2000). However, this does not mean that the potential is always maximized in such classrooms.…”

“…With a similar focus on structure, empirical studies have specified skills students need to produce simple proofs in a given area (Gholamazad, Lijedahl, & Zazkis, 2003;Weber, 2006), and have investigated technological environments that can focus students' attention on the axiomatic development of a mathematical theory (Cerulli & Mariotti, 2003). Suggestions and research in keeping with the "natural" route to proof tend to focus on classroom environments in which students and teacher work collaboratively, investigating problems, formulating conjectures, debating the validity of arguments and so forth (Alibert & Thomas, 1991;Blanton & Stylianou, 2003;Rasmussen, Zandieh, King, & Teppo, 2005;Yackel, Rasmussen, & King, 2000).…”

Development of Electronic Learning Tools to Improve the Quality of Elementary Linear Algebra Course

“…Similarly, Lakatos (1976) argued that a learning approach involving experiments can provide students with an intuition in understanding a theorem. Classroom discussion activities give students the opportunity to pose ways or strategies that may be more efficient than those found by other students, arguing in class discussions will be an invaluable exercise in an effort to improve students' ability to reason deductively, eventually improving students' ability in making mathematical proofs [8]. So, class discussions can foster creativity in students.…”