The semiotic and conceptual genesis of angle

Tanguay, Denis; Venant, Fabienne

doi:10.1007/s11858-016-0789-5

Cited by 14 publications

(12 citation statements)

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“…Interestingly, the studies situated in Duval's theory of figural apprehension have focused on the construction of concepts of 2D shapes, in spite of acknowledging that the objects used are 3D in nature (e.g., Gómez-Chacón & Kuzniak, 2015;Tanguay & Venant, 2016;Vendeira & Coutat, 2017). Additionally, these studies fail to provide an account on the role of language in mediating the meanings of shapes and their representation, while being situated in the multilingual context (e.g., Arıcı & Aslan-Tutak, 2015;Duroisin & Demeuse, 2015).…”

Section: Duval's Theory Of Figural Apprehension (1995)mentioning

confidence: 99%

Use of theories and models in geometry education research: A critical review

Sharma

2019

WJE

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The aim of this article is to provide a critical review of the theories and the model used in the field of geometry education research. The article critically discusses van Hiele’s theory, Fischbein’s theory of figural concepts, Duval’ s theory of figural apprehension, the Spatial Operational Capacity (SOC) model by Wessels and van Niekerk, and the Sfard’s commognition theory. The van Hiele’s theory proposed a sequential order of development through which the learners construct their understanding of geometry concepts. Fischbein’ s theory of figural concepts suggested that a geometric figure is always comprised of a visible representation and a concept. Duval’s theory of figural apprehension underscored the heuristic value of a geometry figure for solving geometry problems. The SOC model by Wessels and van Niekerk emphasised the importance of instructional design incorporating a variety of physical and mental objects to work with to develop geometry concepts. Finally, the article discusses Sfard’s commognition theory that emphasises the communicative function of language in developing geometry concepts. There are two major concerns highlighted with respect to these theories and the model. Firstly, these theories and model emphasise the development of the two-dimensional geometry concepts, neglecting the development of the concepts of three-dimensional geometry. Secondly, these theories and the model fail to acknowledge the multilingual context of geometry class. The article aims to highlight the dearth of studies that explore the multilingual context of geometry class and calls for future studies in this direction.

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Section: Duval's Theory Of Figural Apprehension (1995)mentioning

confidence: 99%

Use of theories and models in geometry education research: A critical review

Sharma

2019

WJE

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“…Existing research has focused on documenting the ways students and teachers conceptualize angles, angle measure, and radian angle measure. Other studies have investigated elementary textbooks' treatment of the representations of angle and angle measure (Tanguay & Venant, ; Vinner & Hershkowitz, ). In this report, I extend the investigation to high‐school textbooks' representations of angle measure, specifically radian angle measure, since the Common Core State Standards for Mathematics [CCSSM] suggest introducing radian angle measure in high school (National Governors Association Center for Best Practices [NGA] & Council of Chief State School Officers [CCSSO], ).…”

Section: Introductionmentioning

confidence: 99%

“…In this report, I extend the investigation to high‐school textbooks' representations of angle measure, specifically radian angle measure, since the Common Core State Standards for Mathematics [CCSSM] suggest introducing radian angle measure in high school (National Governors Association Center for Best Practices [NGA] & Council of Chief State School Officers [CCSSO], ). I will focus on textbook representations of radian angle measure, while drawing from empirical studies of angle (Filippaki & Papamichael, ; Keiser, ; Mitchelmore & White, ; Tanguay & Venant, ), angle measure (Tallman & Frank, ; Thompson, ), and radian angle measure (Akkoc, ; Moore, ; Topcu, Kertil, Akkoc, Yilmaz, & Onder, ). This study aims to investigate textbook representations of radian angle measure to gain insight into the concept of radian angle measure from a curricular perspective.…”

Section: Introductionmentioning

confidence: 99%

“…Some studies of angle conceptions have drawn a distinction between the qualitative and the quantitative views of angle (Matos, , ; Tanguay & Venant, ). The distinction between the qualitative and the quantitative views of angle stems from the general difference between conceptualizing a geometric object as a quality and conceptualizing its quantity.…”

Section: Introductionmentioning

confidence: 99%

“…Angle measure, however, should be quantitative, where the quantitative view of angle supports the learner in identifying the “measurable attributes of openness” (Moore, , p. 228). The quantitative view of angle could also be problematic, as some studies (e.g., Keiser, ; Moore, ; Tanguay & Venant, ) have reported struggles with angle measure that relate to students' quantitative views of angle. For example, students who attended to the length of the rays believed that an angle would have a different measure when the length of the rays and the bounded area between them are different (Keiser, ).…”

Section: Introductionmentioning

confidence: 99%

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Textbook representations of radian angle measure: The need to build on the quantitative view of angle

Alyami

2020

School Sci & Mathematics

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Empirical studies of angle, angle measure, and radian angle measure have primarily focused on documenting students' and teachers' conceptions. Representations of angle measure have the potential to inform and build on these conceptions. To gain insight into the concept of radian angle measure from a curricular perspective, I investigated the representations of radian angle measure in eight widely used U.S. high school mathematics textbooks. The data for this study are the 20 figures and the 8 definitions of radian angle measure in the textbooks. Inductive content analysis was used to identify the frequency of observable characteristics in the representations. Textbook figures of radian angle measure most frequently focus on a one‐radian angle. Textbook figures also demonstrated radian angle measures in terms of π, in standard position, even when the Cartesian‐coordinate plane was not in the figure. The frequently used characteristics of radian representations could inadvertently reinforce a qualitative concept of angle, instead of fostering the quantitative attributes of radian angle measure. Moving forward, analyzing conceptions that are evoked by the frequently used representations of radian angle measure could build a link between evidence from this study and studies of learning.

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