
06639330
j
2016f.01001
G\'omezChac\'on, In\'es M.
Romero Albaladejo, Isabel M.
Garc\'{\i}a L\'opez, M. del Mar
Zigzagging in geometrical reasoning in technological collaborative environments: a mathematical working spaceframed study concerning cognition and affect.
ZDM, Math. Educ. 48, No. 6, 909924 (2016).
2016
Springer, Berlin/Heidelberg
EN
G40
U70
E50
C70
geometry
mathematical working space
GeoGebra
cognitionaffect interplay
argumentation
secondary education
doi:10.1007/s1185801607552
Summary: This study highlights the importance of cognitionaffect interaction pathways in the construction of mathematical knowledge. Scientific output demands further research on the conceptual structure underlying such interaction aimed at coping with the high complexity of its interpretation. The paper discusses the effectiveness of using a dynamic model such as that outlined in the Mathematical Working Spaces (MWS) framework, in order to describe the interplay between cognition and affect in the transitions from instrumental to discursive geneses in geometrical reasoning. The results based on empirical data from a teaching experiment at a middle school show that the use of dynamic geometry software favours students' attitudinal and volitional dimensions and helps them to maintain productive affective pathways, affording greater intellectual independence in mathematical work and interaction with the context that impact learning opportunities in geometric proofs. The reflective and heuristic dimensions of teacher mediation in students' learning is crucial in the transition from instrumental to discursive genesis and working stability in the InstrumentalDiscursive plane of MWS.