Abstract
Using data provided by an empirical exploratory study with mathematics undergraduates, this paper discusses some key variables in the interaction between affective and cognitive dimensions in the perplexity state in problem solving. These variables are as follows: heuristics, mathematical processes, appraisal processes [pleasantness, attentional activity, control (self-other responsibility/control, situational control), certainty, goal-path obstacle, anticipated effort and mental flexibility], as well as the relationships these variables have with different emotions that make up perplexity. Fuzzy sets were introduced as a tool to capture and accurately reflect the diversity and subjectivity in the interplay between cognition and emotion. The descriptive analysis of the responses to a fuzzy rating scale-based questionnaire shows the interaction between variables linked to the dimensions of control and certainty and students’ ability to cope with perplexity in performance in mathematics. The study also adds novel considerations related to the function and interaction of mathematics cognitive processes that are linked to appraisal processes, namely, the perception of goal-path obstacle, attentional activity and mental flexibility that contributes to the ability to solve simpler problem components involved in mathematical performance.
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Notes
Based on the definitions of Diccionario de la Lengua Española de la Real Academia (DRAE), Diccionario María Moliner 3ª ed. 1988 and Diccionario del Español Actual (DEA) de Manuel Seco et al. 1999.
The Oxford English Dictionary defines perplexity as follows: “1. a. Inability to decide what to think or how to act owing to the involved, intricate, or complicated condition of circumstances or of the matters to be dealt with, generally also involving mental perturbation or anxiety…” (Oxford English Dictionary 2010, accessed September 2010).
Diccionario de la Lengua Española de la Real Academia (DRAE).
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Acknowledgements
This study was funded by the research grant Visiting Scholar Fellowship, University of California in Berkeley, Scholarship “Becas Complutense del Amo” 2015–16, Spain and by the Spanish Ministry of the Economy and Competitive Affairs under project EDU2013-44047-P.
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Gómez-Chacón, I.M. Emotions and heuristics: the state of perplexity in mathematics. ZDM Mathematics Education 49, 323–338 (2017). https://doi.org/10.1007/s11858-017-0854-8
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DOI: https://doi.org/10.1007/s11858-017-0854-8