How Multimodality Works in Mathematical Activity: Young Children Graphing Motion

Ferrara, Francesca

doi:10.1007/s10763-013-9438-4

Cited by 13 publications

(12 citation statements)

References 19 publications

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“…The current study focuses on research in the domain of proportional learning. Further research is also recommended on other topics, also beyond mathematics education (e.g., Nemirovsky et al, 1998; Ferrara, 2014). Last, it seems plausible that sub-populations of students benefit more from embodied design than others.…”

Section: Discussionmentioning

confidence: 99%

Touchscreen Tablets: Coordinating Action and Perception for Mathematical Cognition

et al. 2017

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Proportional reasoning is important and yet difficult for many students, who often use additive strategies, where multiplicative strategies are better suited. In our research we explore the potential of an interactive touchscreen tablet application to promote proportional reasoning by creating conditions that steer students toward multiplicative strategies. The design of this application (Mathematical Imagery Trainer) was inspired by arguments from embodied-cognition theory that mathematical understanding is grounded in sensorimotor schemes. This study draws on a corpus of previously treated data of 9–11 year-old students, who participated individually in semi-structured clinical interviews, in which they solved a manipulation task that required moving two vertical bars at a constant ratio of heights (1:2). Qualitative analyses revealed the frequent emergence of visual attention to the screen location halfway along the bar that was twice as high as the short bar. The hypothesis arose that students used so-called “attentional anchors” (AAs)—psychological constructions of new perceptual structures in the environment that people invent spontaneously as their heuristic means of guiding effective manual actions for managing an otherwise overwhelming task, in this case keeping vertical bars at the same proportion while moving them. We assumed that students’ AAs on the mathematically relevant points were crucial in progressing from additive to multiplicative strategies. Here we seek farther to promote this line of research by reanalyzing data from 38 students (aged 9–11). We ask: (1) What quantitative evidence is there for the emergence of AAs?; and (2) How does the transition from additive to multiplicative reasoning take place when solving embodied proportions tasks in interaction with the touchscreen tablet app? We found that: (a) AAs appeared for all students; (b) the AA-types were few across the students; (c) the AAs were mathematically relevant (top of the bars and halfway along the tall bar); (d) interacting with the tablet was crucial for the AAs’ emergence; and (e) the vast majority of students progressed from additive to multiplicative strategies (as corroborated with oral utterances). We conclude that touchscreen applications have the potential to create interaction conditions for coordinating action and perception into mathematical cognition.

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Section: Discussionmentioning

confidence: 99%

Touchscreen Tablets: Coordinating Action and Perception for Mathematical Cognition

et al. 2017

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“…The mathematicsoriented articles used motion to address the teaching and learning of graphs as visual representations of dynamic data (e.g., Boyd and Rubin 1996;Robutti 2006). Some of these articles also included more advanced topics like functions and the mathematics of change (calculus) (e.g., Ferrara 2014;Salinas et al 2016). Most of the articles in physics addressed the relation between distance traveled, velocity, and acceleration (kinematics) (e.g., Anderson and Wall 2016;Mitnik et al 2009).…”

Section: The Subject Matter Domains Addressed In the Articlesmentioning

confidence: 99%

“…Class I-Immediate Own Motion was the largest (34 learning environments). Brasell, 1987;Espinoza, 2015;Ferrara, 2014;Metcalf & Tinker, 2004;Nemirovsky, Tierney, & Wright, 1998;Radford, 2009;Robutti, 2006;Solomon, Bevan, Frost, Reynolds, Summers, & Zimmerman, 1991;Struck &Yerrick, 2008;Stylianou, Smith, & Kaput, 2005;Svec, Boone, & Olmer, 1995;Svec, 1999;Taylor, Hutson, Krawiec, Ebert, & Rubinstein, 1995;Thornton & Sokoloff, 1990;Wilhelm, & Confrey, 2015;Wilson & Brown, 1998;Zucker, Kay, & Staudt, 2014**** b Anastopolou, Sharples, & Baber, 2011Holbert & Wilensky, 2014;Noble, Nemirovsky, Wright, & Tierney, 2001;Russell, Lucas, & McRobbie, 2003 Class II-Non-immediate Own Motion was the smallest (4 learning environments). The other two classes contained the same amount of learning environments (12 learning environments each).…”

Section: Classes Of Embodied Learning Environmentsmentioning

confidence: 99%

Embodied Learning Environments for Graphing Motion: a Systematic Literature Review

et al. 2019

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Embodied learning environments have a substantial share in teaching interventions and research for enhancing learning in science, technology, engineering, and mathematics (STEM) education. In these learning environments, students' bodily experiences are an essential part of the learning activities and hence, of the learning. In this systematic review, we focused on embodied learning environments supporting students' understanding of graphing change in the context of modeling motion. Our goal was to deepen the theoretical understanding of what aspects of these embodied learning environments are important for teaching and learning. We specified four embodied configurations by juxtaposing embodied learning environments on the degree of bodily involvement (own and others/objects' motion) and immediacy (immediate and non-immediate) resulting in four classes of embodied learning environments. Our review included 44 articles (comprising 62 learning environments) and uncovered eight mediating factors, as described by the authors of the reviewed articles: realworld context, multimodality, linking motion to graph, multiple representations, semiotics, student control, attention capturing, and cognitive conflict. Different combinations of mediating factors were identified in each class of embodied learning environments. Additionally, we found that learning environments making use of students' own motion immediately linked to its representation were most effective in terms of learning outcomes. Implications of this review for future research and the design of embodied learning environments are discussed.

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“…Criticizing the platonic idealism and the Cartesian mindbody dualism, Lakoff and Núñez advocated that all kinds of ideas, including the most sophisticated mathematical ideas, are founded on our bodily experiences and develop through cognitive metaphorical mechanisms. The book aroused a great interest in mathematics education and prompted many research studies highlighting the role of bodily and kinesthetic experiences in mathematical learning (Arzarello and Robutti 2008;de Freitas and Sinclair 2014;Edwards 2009;Ferrara 2014;Nemirovsky 2003;Radford 2014;Roth 2009; for an overview, see Gerofsky 2015).…”

Section: Introductionmentioning

confidence: 99%

Invited Lectures from the 13th International Congress on Mathematical Education

et al. 2018

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How Multimodality Works in Mathematical Activity: Young Children Graphing Motion

Cited by 13 publications

References 19 publications

Touchscreen Tablets: Coordinating Action and Perception for Mathematical Cognition

Touchscreen Tablets: Coordinating Action and Perception for Mathematical Cognition

Embodied Learning Environments for Graphing Motion: a Systematic Literature Review

Invited Lectures from the 13th International Congress on Mathematical Education

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