Embodied Learning Environments for Graphing Motion: a Systematic Literature Review

Duijzer, Carolien; Heuvel–Panhuizen, Marja van den; Veldhuis, Michiel; Doorman, Michiel; Leseman, Paul

doi:10.1007/s10648-019-09471-7

Cited by 50 publications

(35 citation statements)

References 105 publications

(192 reference statements)

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“…Students may have encountered many graphs that share observable characteristics with the motion of physical objects, even though graphs do not need to share such characteristics. Students demonstrating MO conceptions could benefit from embodied tasks for graphing motion (Duijzer et al 2019), so that they could have opportunities to form links between their own movements and the appearance of graphs they sketch. Task sequences could begin with a background of invariance, and different kinds of motion, and then incorporate variation in both backgrounds and motion.…”

Section: Shifts In Students' Conceptions Of Graphsmentioning

confidence: 99%

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

Johnson

McClintock

Gardner

2020

Digit Exp Math Educ

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We posit a dual approach to digital task design: to engineer opportunities for students to conceive of graphs as representing relationships between quantities and to foreground students' reasoning and exploration, rather than their answer-finding. Locally integrating Ference Marton's variation theory and Patrick Thompson's theory of quantitative reasoning, we designed digital task sequences, in which students were to create different graphs linked to the same video animations. We report results of a qualitative study of thirteen secondary students (aged 15-17), who participated in digital, taskbased, individual interviews. We investigated two questions: (1) How do students conceive of what graphs represent when engaging with digital task sequences? (2) How do student conceptions of graphs shift when working within and across digital task sequences? Two conceptions were particularly stablerelationships between quantities and literal motion of an object. When students demonstrated conceptions of graphs as representing change in a single quantity, they shifted to conceptions of relationships between quantities. We explain how a critical aspect: What graphs should represent, intertwined with students' graph-sketching. Finally, we discuss implications for digital task design to promote students' conceptions of mathematical representations, such as graphs. Keywords Digital task design. Variation theory. Quantitative reasoning. Graphs By means of digital technology, students have opportunities to sketch and interpret dynamic graphs linked to video animations (Kaput 1994; Kaput and Roschelle 1999; Schorr and Goldin 2008). Yet, such opportunities are only a starting point. Instead of promoting reasoning, student interactions with digital technology may focus on skills and recall (Kitchen and Berk 2016). We developed digital task sequences that center on Digital Experiences in Mathematics Education

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Section: Shifts In Students' Conceptions Of Graphsmentioning

confidence: 99%

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

Johnson

McClintock

Gardner

2020

Digit Exp Math Educ

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“…In these embodied learning environments, bodily experiences are an essential part of the learning activities (e.g., Johnson-Glenberg et al 2014;Skulmowski and Rey 2018). In the context of graphing motion these bodily experiences can be manifold and range from making whole-, or part-bodily movements, to observing someone, or something else, moving (Duijzer et al 2019). In some studies, the focus has (inter alia) been on students' use of gestures and their supportive role in expressing ideas and supporting learning graphical reasoning with motion sensor technology (e.g., Radford 2009a, b;Robutti 2006).…”

Section: Embodied Learning Environmentsmentioning

confidence: 99%

Supporting primary school students’ reasoning about motion graphs through physical experiences

Duijzer

Heuvel–Panhuizen

Veldhuis

et al. 2019

ZDM Mathematics Education

Self Cite

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Reasoning about graphical representations representing dynamic data (e.g., distance changing over time), including interpreting, creating, changing, combining, and comparing graphs, can be considered a domain-specific operationalization of the general twenty-first century skills of creative, critical thinking and solving problems. This paper addresses the issue of how these 21st century skills of interpreting and creating graphs can be supported in a six-lesson teaching sequence about graphing motion. In this teaching sequence, we focused on the potential of an embodied learning environment to facilitate the development of primary school students' reasoning about motion graphs by having primary school students (9-11 years) 'walk' graphs in front of a motion sensor to generate distance-time graphs. We asked: How does students' reasoning about graphing motion develop over a six-lesson teaching sequence within an embodied learning environment? Based on the collected data, we examined changes in students' level of reasoning on graph interpretation and graph construction tasks using a repeated measurement design. Additionally, we present two teaching episodes showing instances of how perceptual-motor experiences during the lessons aided students' reasoning about graphical representations of motion. Results show that students went from iconic understanding towards understanding in which they reasoned based on one or two variables when interpreting and constructing graphical representations of motion events. At these higher levels of reasoning these students showed understanding of modelling motion in line with the intended 21st century skills of generating, refining, and evaluating graphs.

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“…Findings from recent studies reiterated the effectiveness of employing a composite framework integrating the three worlds of mathematics (embodied, symbolic, and formal world), and the actions, processes, objects, and schemas (APOS) theory (Hong & Thomas, 2015). There appears a positive and long-lasting impact of designing an embodied learning environment (Duijzer, Heuvel-Panhuizen, Veldhuis, Doorman, & Leseman, 2019). When it comes to the teaching and learning of calculus, designing problem-based learning that focuses on the infinite concept that promotes capability of the students to think calculus conceptually (Zerr, 2010); and the importance of balanced emphasis among the algebraic, numeric, and graphic representations of functions under investigation (Çetin, 2009) is the emphasis for a meaningful learning process.…”

Section: Introductionmentioning

confidence: 99%

“…The tool designed is named Graph Puzzle (GP) (Liew, Chen, Tuh, Ling & Ahmad Bakri, 2019). GP is a type of board-game tool innovated for an embodied learning environment with a balanced emphasis among the algebraic, numeric and graphic presentations of functions and their derivatives so that capability of the students to think calculus conceptually could be promoted (Duijzer et al, 2019;Hong & Thomas, 2015;Zerr, 2010;Çetin, 2009). On top of this, the power of technology is also exploited to expand the capacity of the amount of content that could be included in it.…”

Section: Introductionmentioning

confidence: 99%

Bridging the Gap Between the Derivatives And Graph Sketching in Calculus

Bakri

Liew

Chen

et al. 2021

AJUE

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Sketching the graph of mathematical functions using derivatives is a challenging task for undergraduate students who enrol for the first level of calculus course. Before graph plotting, students are required to perform a thorough function analysis using the concepts learned in differentiation. They are then expected to solicit the results obtained to sketch the graph. Nevertheless, the students face great difficulties in achieving this goal; and fail to relate the results obtained in the analysis and their representation in a graph. Their performance is thus negatively affected eventually. To overcome this cognitive gap, an innovative board game named Graph Puzzle (GP) is developed. It is intended to function as a manipulator to facilitate students in comprehending the inter-related algebraic, symbolic, and graphic representation of a function under the applications of derivatives, forming the corresponding procedural and conceptual knowledge. To measure the effectiveness of this board game, 84 undergraduate students who took this calculus course were given pre- and post-test before and after the learning session. An ANCOVA test conducted reveals a significant difference (F (1, 81) = 12.182, p = 0.001) between pre and post-test score in solving polynomial functions, whereas students’ performance in solving rational functions indicates no meaningful difference (F (1, 81) = 0.04, p = 0.841) of post-scores between control and treatment groups. From this standpoint, it is shown that GP has the potential to serve as a solution to the difficulties faced on graph sketching in calculus, particularly when dealing with polynomial functions. Keywords: Visualization, Calculus, Embodied learning, Game-Based Learning, Graph Sketching

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Embodied Learning Environments for Graphing Motion: a Systematic Literature Review

Cited by 50 publications

References 105 publications

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

Supporting primary school students’ reasoning about motion graphs through physical experiences

Bridging the Gap Between the Derivatives And Graph Sketching in Calculus

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