Embodied Semiotic Activities and Their Role in the Construction of Mathematical Meaning of Motion Graphs

Botzer, Galit; Yerushalmy, Michal

doi:10.1007/s10758-008-9133-7

Cited by 27 publications

(30 citation statements)

References 20 publications

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“…An understanding of graphing, however, involves not only interpretation and translation but also construction. Although technological advances such as graphing calculators and computer programs promote exploration and understanding of functions (e.g., Ainley, Nardi, & Pratt, 2000; Botzer & Yerushalmy, 2008; Hennessy, Fung, & Scanlon, 2001; Kieran, 2001; Levert, 2003; Nicolaou, Nicolaidou, & Zacharia, 2007; Noble, Nemirovsky, Dimattia, & Wright, 2004; Schwartz & Hershkowitz, 1999), they do not always help students gain a full understanding of function (Schoenfeld, Smith, & Arcavi, 1993).…”

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confidence: 99%

Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y‐intercept

Hattikudur

Prather

Asquith

et al. 2012

School Sci & Mathematics

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Middle-school students are expected to understand key components of graphs, such as slope and y-intercept. However, constructing graphs is a skill that has received relatively little research attention. This study examined students' construction of graphs of linear functions, focusing specifically on the relative difficulties of graphing slope and y-intercept. Sixth-graders' responses prior to formal instruction in graphing reveal their intuitions about slope and y-intercept, and seventh-and eighth-graders' performance indicates how instruction shapes understanding. Students' performance in graphing slope and y-intercept from verbally presented linear functions was assessed both for graphs with quantitative features and graphs with qualitative features. Students had more difficulty graphing y-intercept than slope, particularly in graphs with qualitative features. Errors also differed between contexts. The findings suggest that it would be valuable for additional instructional time to be devoted to y-intercept and to qualitative contexts.

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confidence: 99%

Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y‐intercept

Hattikudur

Prather

Asquith

et al. 2012

School Sci & Mathematics

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“…The cognitive development occurring in such symbolic-reconstructive learning is considered to be a sophisticated way of knowing (Arzarello, Robutti, & Bazzini, 2005). Related to this theoretical framework and in conjunction with development of interactive technology tools, studies in mathematics education emphasize that sensual cognition is essential in the learning process of mathematical concepts (to mention only a few works that are related to the learning of calculus: Arzarello et al, 2005;Bartolini Bussi & Mariotti, 2008;Botzer & Yerushalmy, 2008;Tall, 2009). The case study that we discuss in the present article occurred in settings that support perceptual-motor engagement of students mediated by a computerized artifact and a task designed to lead to the appropriation of particular mathematics content.…”

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confidence: 99%

Signifying the accumulation graph in a dynamic and multi-representation environment

Yerushalmy

Swidan

2011

Educ Stud Math

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The present study focuses on the accumulation process involved in the integration of a single-variable function. Observing the work of two high-school calculus students who had not yet learned any other integral-related ideas, we analyze the emergence of the semiotic relationship between personal and mathematical meanings, as expressed through the understanding of mathematical signs in integration tasks. Adopting Radford's educational perspective whereby learning is defined as a process of objectification, we identify a three-stage evolution of the double semiotic meaning of the lower boundary and of its role in the definition of the accumulation graph: (1) objectifying a zero accumulation in relation to the lower limit, (2) objectifying zero as marking the zero sum of accumulated areas, and (3) objectifying the accumulation graph as dependent on the lower-limit value. This evolution is marked by semiotic changes related to the pivotal role of the "zeros" in the accumulation graph.

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“…For example, Celine made use of iconic representational gestures (Roth 2001). Botzer and Yerushalmy (2008) argue how such gestures imply that Celine mentally stretched the graph in order to compare it with the original one, thus revealing her perceptual-motor and analytical thinking (see, e.g. Robutti 2006).…”

Section: The Role Of Perceptual-motor Experiences In Developing Graphmentioning

confidence: 99%

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

Duijzer

Heuvel–Panhuizen

Veldhuis

et al. 2019

ZDM Mathematics Education

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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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Embodied Semiotic Activities and Their Role in the Construction of Mathematical Meaning of Motion Graphs

Cited by 27 publications

References 20 publications

Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y‐intercept

Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y‐intercept

Signifying the accumulation graph in a dynamic and multi-representation environment

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

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