Análisis de errores en tareas sobre el concepto de derivada : una mirada desde la teoría APOE (Acción, Proceso, Objeto, y Esquema)

Funding Information: Este trabajo desarrollado gracias a la Agencia Nacional de Investigación y Desarrollo (ANID) por medio del proyecto N°11180899 y la colaboración de la Facultad de Ciencias de la Ingeniería de la UACh.Este estudio se enfoca en lo visible, es decir, en el análisis de errores que los estudiantes cometen a fin de identificar posibles dificultades. Se considera el marco propuesto por la teoría APOE (Acción, Proceso, Objeto, y Esquema), por medio de la definición de 27 variables en función de elementos matemáticos involucrados en tres tareas que conforman un cuestionario sobre el concepto de derivada. Los participantes son 103 estudiantes de primer año de ingeniería. Los datos corresponden a las producciones de los estudiantes, obtenidos de la aplicación del cuestionario y recolectados durante el primer semestre del año 2021. Los resultados muestran que existen dificultades asociadas a la construcción de la reversión de procesos que se manifiesta en el gran número de errores asociados al uso de las variables que se establecen a partir de las equivalencias lógicas. Se concluye que la encapsulación de la derivada como un objeto cognitivo, correspondiente a una función, es compleja de alcanzar.The present study focuses on the visible, that is, on analyzing errors that students make to identify possible causes. The framework proposed by the APOE (Action, Process, Object, and Schema) theory is applied through the definition of 27 variables based on mathematical elements involved in three tasks that conform a questionnaire on the concept of derivative. The participants are 103 first-year engineering students. The data gathered consist of students' answers to the questionnaire collected during the first semester of the year 2021. The results show that there are difficulties associated with the construction of the reversal of processes as revealed by the great number of errors associated with the use variables obtained from logical equivalences. It is concluded that encapsulating the derivative as a cognitive object, corresponding to its function, is difficult to achieve

Errores sobre subespacios vectoriales : un estudio exploratorio con estudiantes de primer año de ingeniería

Esta investigación exploratoria identifica y clasifica errores vinculados al concepto de subespacio vectorial que cometen estudiantes de ingeniería de primer año de universidad. Para ello, 210 estudiantes identifican y justifican por escrito por qué un conjunto no es un subespacio vectorial. Los resultados muestran que los estudiantes cometen tres tipos errores (E1, E2, E3): 1) procedimiento incorrecto para determinar si un conjunto es subespacio vectorial, 2) relaciones incoherentes entre conceptos y 3) representación errónea de los elementos de un subespacio vectorial. Esta tipología puede ser una guía para diseñar tareas que promuevan la comprensión de este concepto y gestionar la emergencia de estos errores en el aula. Se concluye que la clasificación de errores sobre subespacio vectorial puede ayudar a los profesores a la hora de planificar la enseñanza de este concepto.This exploratory research study identifies and classifies errors on the concept of vector subspace that are committed by first-year engineering students. Two-hundred and ten students identify and justify in writing why a set is not a vector subspace. The results show that students committed three types of errors (E1, E2, and E3): 1) conducting an incorrect procedure when determining whether a set is a vector subspace, 2) inferring incoherent correlations between concepts, and 3) misrepresenting vector subspace elements. This typology can be used as a guide to design tasks that enhance the understanding of the vector subspace concept. It can also serve to determine when these types of errors emerge in the classroom. It is concluded that classifying student errors on the concept of vector subspace can assist professors when planning on how to teach this concept

Relationship between social cognition and traditional cognitive impairment in progressive multiple sclerosis and possible implicated neuroanatomical regions

Background: Cognitive impairment is a relevant contributor of the medical and social burden in Progressive MS. Social Cognition, the neurocognitive processes underlying social interaction, has been explored mainly in European and North American cohorts, influencing social aspects of quality of life (QOI) of early MS patients and families. Few studies have studied Social Cognition in Progressive MS and the literature on its neuroanatomical bases or brain atrophy measurements is still scarce. Objectives: To explore the relationship between Social Cognition performance and its correlations with traditional cognitive domains, brain atrophy and QOL in primary and secondary Progressive MS patients. Methods: Cross-sectional analysis including: mini-Social-Cognition-and-Emotional-Assessment (mini-SEA), neuropsychological battery, disability, depression, fatigue, QOL, and brain volume. Results: Forty-three MS patients, 23 primary and 20 secondary Progressive, 65% women, mean age and disease duration of 57.2 and 15.7 years, respectively, with high levels of disability (median EDSS 6.0) and a widespread impairment in traditional domains (mostly episodic verbal/visual and working memories) were assessed. The Mini-SEA score was correlated with executive functions (cognitive shifts Rho: 0.55; p = 0.001) analyzing the whole group, and with visual episodic memory (Rho: 0.58, p = 0.009) in the primary Progressive MS group. Mini-SEA score was also correlated with total normalized grey matter volume (Rho: 0.48; p = 0.004). Particularly, atrophy within bilateral cortical regions of orbitofrontal, insula and cerebellum, and right regions of fusiform gyrus and precuneus were significantly associated with higher Social Cognition impairment. In this cohort, QOL was not correlated with Social Cognition, but with EDSS, fatigue and depression. Conclusions: In Progressive MS, Social Cognition is directly correlated with traditional cognitive domains such as executive function and episodic memory. It is also associated with global grey matter atrophy and regional atrophy within associative visual and executive cortical areas, but no correlations with QOL were found in this cohort. These findings may contribute to the understanding of the pathological bases behind Social Cognition in Progressive MS.CONICYT-PIA-Anillo ACT1416 CONICYT/Associative Research Program/Basal Funds Grant for Centers of Excellence FB 0003 CONICYT/FONDECYT 1160940 1140423 CORFO Innova Chile 14PIE-26946 CONICYT/FONDAP/1515001