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Intuition and Proof in the Solution of Conjecturing Problems'
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Mariotti, Maria Alessandra; Pedemonte, Bettina – ZDM: The International Journal on Mathematics Education, 2019
The cognitive relationship between intuition and proof is complex and often students struggle when they need to find mathematical justifications to explain what appears as self-evident. In this paper, we address this complexity in the specific case of open geometrical problems that ask for a conjecture and its proof. We analyze four meaningful…
Descriptors: Mathematical Logic, Mathematics Instruction, Teaching Methods, Intuition
Reasoning by Contradiction in Dynamic Geometry
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Baccaglini-Frank, Anna; Antonini, Samuele; Leung, Allen; Mariotti, Maria Alessandra – PNA, 2013
This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…
Descriptors: Geometry, Thinking Skills, Mathematical Logic, Mathematical Concepts
Proof and Proving in the Classroom: Dynamic Geometry Systems as Tools of Semiotic Mediation
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Mariotti, Maria Alessandra – Research in Mathematics Education, 2012
The objective of this paper is to discuss the didactic potential offered by the use of a Dynamic Geometry System (DGS) in introducing students to theoretical thinking and specifically to the practice of proof. Starting from a discussion about what constitutes the general objective in developing students' sense of proof, the notion of Theorem is…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Geometry
Approaching Functions: Cabri Tools as Instruments of Semiotic Mediation
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Falcade, Rossana; Laborde, Colette; Mariotti, Maria Alessandra – Educational Studies in Mathematics, 2007
Assuming that dynamic features of Dynamic Geometry Software may provide a basic representation of both variation and functional dependency, and taking the Vygotskian perspective of semiotic mediation, a teaching experiment was designed with the aim of introducing students to the idea of function. This paper focuses on the use of the Trace tool and…
Descriptors: Semiotics, Computer Software, Mathematics Instruction, Geometry
Building Theories: Working in a Microworld and Writing the Mathematical Notebook
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Cerulli, Michele; Mariotti, Maria Alessandra – International Group for the Psychology of Mathematics Education, 2003
In the framework of a long term teaching experiment we present an Educational approach based on the use of a dynamic geometry software and a symbolic manipulator. Here we present the general ideas of the followed approach focusing on how meanings can originate from phenomenological experience and evolve under the guidance of the teacher. In…
Descriptors: Geometry, Teaching Methods, Experiments, Grade 9
Function and Graph in DGS Environment
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Mariotti, Maria Alessandra; Laborde, Colette; Falcade, Rossana – International Group for the Psychology of Mathematics Education, 2003
Assuming that dynamic features of Dynamic Geometry Software may provide a basic representation of both variation and functional dependency, and taking Vygotskian perspective of semiotic mediation, a teaching experiment has been designed with the aim of introducing pupils to the idea of function. First data coming from the observations in Italian…
Descriptors: Mathematics, Foreign Countries, Mathematics Instruction, Experiments