Comprehension of Mathematical Relationships Expressed in Graphs

Curcio, Frances R.

doi:10.5951/jresematheduc.18.5.0382

Cited by 86 publications

(83 citation statements)

References 15 publications

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“…La propuesta del presente artículo se relaciona con estos constructos, aunque con más énfasis en el segundo y el tercero. El primer constructo (describir datos) se relaciona más con los niveles iniciales de lectura de gráficos (Arteaga et al, 2011;Curcio, 1987) y la identificación de la información fundamental en soporte gráfico (en auge a través de recientes sitios web de actividades ricas como What's going on in this graph (https://www.nytimes.com/column/whats-going-on-in-this-graph) o Slow reveal graphs (https://slowrevealgraphs.com/). El segundo constructo (organizar y reducir datos) se refiere a acciones como la ordenación, el agrupamiento y el resumen de los datos, reconociendo la pérdida de información que este pueda suponer.…”

Section: Las Alfabetizaciones Estadística Y Gráfica En La Educación Infantilunclassified

“…PNA 15(4) matemáticos en este nivel educativo se encaminaban al sentido numérico y, en menor medida, al sentido geométrico. Sin embargo, en el contexto internacional la introducción de la estadística y la probabilidad en los currículos de Primaria a partir de las reformas curriculares surgidas en los años 90 (Australian Education Council, 1994;National Council of Teachers of Mathematics [NCTM], 1989School Curriculum and Assessment Authority & Curriculum and Assessment Authority for Wales, 1996) y la investigación publicada a finales del XX y principios del XXI (Alsina, 2006;Baroody, 1987;Batanero, 2009Batanero, , 2013Cobb, 1999;Curcio, 1987;Franklin y Garfield, 2006;Lehrer y Schauble, 2007) han contribuido a introducir el embrión del sentido estadístico en el contexto español (Batanero, 2013;Batanero y Chernoff, 2018) en educación infantil.…”

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El recuento y las representaciones manipulativas: los primeros pasos de la alfabetización estadística

Muñiz

Muñiz-Rodríguez

Aguilar-González

2021

pna

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Los procesos estadísticos comienzan con la selección de la variable de estudio y la recogida de los datos. Para organizar los datos recogidos es esencial llevar a cabo un recuento de los valores observados. En este artículo se propone una aproximación al recuento mediante el análisis de las categorías observadas y se discuten distintas técnicas de recuento, sus formas de representación manipulativa o pictórica y su conexión con las tablas de frecuencias. Por último, se refiere un experimento didáctico llevado a cabo con estudiantes para maestros sobre el manejo de las representaciones manipulativas de los recuentos como paso previo a las gráficas estadísticas manipulativas.

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Section: Las Alfabetizaciones Estadística Y Gráfica En La Educación Infantilunclassified

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El recuento y las representaciones manipulativas: los primeros pasos de la alfabetización estadística

Muñiz

Muñiz-Rodríguez

Aguilar-González

2021

pna

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“…The difficulty that students often experience when first encountering graph tasks depends on the graphically represented concepts. Reading a point from a line graph with its coordinates, for example, presents a different challenge than interpolating between several data points or even predicting graph trends and extrapolation beyond the representation of a graph [4]. Especially in the field of physics education research, the determination of the slope of a graph vs. the area under a graph and the degree of mathematical requirements have been identified as determinants of the level of task difficulty [13,22,33].…”

Section: Eye-tracking Research On Students' Difficulties In Graph Understandingmentioning

confidence: 99%

“…Understanding graphs has been considered an essential skill both in everyday life (e.g., understanding newspapers) and in most academic disciplines [1][2][3]. Graphs serve to simplify the representation of complex concepts and can facilitate the development of conceptual knowledge in a domain [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Epistemic Network Analyses of Economics Students’ Graph Understanding: An Eye-Tracking Study

Brückner

Schneider

Zlatkin‐Troitschanskaia

et al. 2020

Sensors

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Learning to solve graph tasks is one of the key prerequisites of acquiring domain-specific knowledge in most study domains. Analyses of graph understanding often use eye-tracking and focus on analyzing how much time students spend gazing at particular areas of a graph—Areas of Interest (AOIs). To gain a deeper insight into students’ task-solving process, we argue that the gaze shifts between students’ fixations on different AOIs (so-termed transitions) also need to be included in holistic analyses of graph understanding that consider the importance of transitions for the task-solving process. Thus, we introduced Epistemic Network Analysis (ENA) as a novel approach to analyze eye-tracking data of 23 university students who solved eight multiple-choice graph tasks in physics and economics. ENA is a method for quantifying, visualizing, and interpreting network data allowing a weighted analysis of the gaze patterns of both correct and incorrect graph task solvers considering the interrelations between fixations and transitions. After an analysis of the differences in the number of fixations and the number of single transitions between correct and incorrect solvers, we conducted an ENA for each task. We demonstrate that an isolated analysis of fixations and transitions provides only a limited insight into graph solving behavior. In contrast, ENA identifies differences between the gaze patterns of students who solved the graph tasks correctly and incorrectly across the multiple graph tasks. For instance, incorrect solvers shifted their gaze from the graph to the x-axis and from the question to the graph comparatively more often than correct solvers. The results indicate that incorrect solvers often have problems transferring textual information into graphical information and rely more on partly irrelevant parts of a graph. Finally, we discuss how the findings can be used to design experimental studies and for innovative instructional procedures in higher education.

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“…The concept and use of graphs and diagrams are fundamental for learning and problem solving in all STEM disciplines [1]. Graphs are especially important for simplifying complex concepts [4], visualizing measurement data [3], for the exchange of information between individuals [13] and for online reasoning [15]. A convention strictly determines the way the data is visualized in a graph, and therefore, there is a clear procedure how to extract information from it [5,12].…”

Section: Introduction 1the Significance Of Graphsmentioning

confidence: 99%

The Predictive Power of Eye-Tracking Data in an Interactive AR Learning Environment

Dzsotjan

Ludwig-Petsch

Mukhametov

et al. 2021

Adjunct Proceedings of the 2021 ACM International Joint Conference on Pervasive and Ubiquitous Computing and Proceedings of The

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Learning through embodiment is a promising concept, potentially capable to remove many layers of abstraction hindering the learning process. Walk the Graph, our HoloLens2-based AR application, provides an inquiry-based learning setting for understanding graphs through the full-body movement of the user. In this paper, as part of our ongoing work to build an AI framework to quantify and predict the learning gain of the user, we examine the predictive potential of gaze data collected during the app usage. To classify users into groups with different learning gains, we construct a map of areas of interest (AOI) based on the gaze data itself. Subsequently, using a sliding window approach, we extract engineered features from the collected in-app as well as gaze data. Our experimental results have shown that a Support Vector Machine with selected features achieved the highest F1 score (0.658; baseline: 0.251) compared to other approaches including a K-Nearest Neighbor and a Random Forest Classifier although in each of the cases the lion's share of the predictive power is indeed provided by the gaze-based features. CCS CONCEPTS• Applied computing → Interactive learning environments.

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Comprehension of Mathematical Relationships Expressed in Graphs

Cited by 86 publications

References 15 publications

El recuento y las representaciones manipulativas: los primeros pasos de la alfabetización estadística

El recuento y las representaciones manipulativas: los primeros pasos de la alfabetización estadística

Epistemic Network Analyses of Economics Students’ Graph Understanding: An Eye-Tracking Study

The Predictive Power of Eye-Tracking Data in an Interactive AR Learning Environment

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