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Universal and existential quantifiers revisited. (English)
Tso, Tai-Yih (ed.), Proceedings of the 36th conference of the International Group for the Psychology of Mathematics Education “Opportunities to learn in mathematics education", PME 36, Taipei, Taiwan, July 18‒22, 2012, Vol. 4. Taipei: National Taiwan Normal University. 235-242 (2012).
Summary: Investigation into students learning of logical quantifiers is extended to include both universal and existential quantifiers. The work confirms, in a spectacular fashion, the impact of natural language on the mathematical understanding of negation by identifying, during the student interview, a source of misconception initiated from incorrect French/English translation. The paper extends the analysis of the data into root causes of student difficulties and with the help of innovative teaching-research interviews, which identifies possible routes for the improvement of learning, when needed. This way, every research clinical interview of a student about mathematics can be enhanced, without loosing its scientific character, as it also becomes a carefully crafted, research-based tutoring session, exemplifying the reduction of time lag between research and practice to zero.
Classification: E30 D70 C50
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