Making sense of shape: An analysis of children's written responses

Walcott, Crystal; Mohr, Doris; Kastberg, Signe E.

doi:10.1016/j.jmathb.2009.04.001

Cited by 38 publications

(24 citation statements)

References 11 publications

(12 reference statements)

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“…A more detailed study is required to put forth why they go out of formal definitions. In addition, the results obtained in this study putting forth that the teachers find it more effective to have the students make the definition instead of the teacher expressing the definition directly is in accordance with literature data (De Villiers, 1998;Walcott et al, 2009).…”

Section: Discussion Conclusion and Implicationssupporting

confidence: 89%

Middle school mathematics teachers pedagogical content knowledge regarding teaching strategies on quadrilaterals

AkkaÅŸ¹,

TÃ1⁄4rnÃ1⁄4klÃ1⁄4²

2014

Educ. Res. Rev.

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Pedagogical content knowledge is consisted of two components: student knowledge and teaching strategies. Teaching strategies was defined under two sub-headings as strategies for specific topics and specific strategies for any topic. The purpose of this study was to examine the method with which quadrilaterals were taught by mathematics teachers with regard to the teaching strategies component of pedagogical content knowledge. 30 middle school mathematics teachers working at 12 different schools in Turkey participated in this study. Interview method was used for data acquisition. The interview was intended to put forth the strategies that the teachers used for defining, classification and visualization which were included in the strategies of the framework used for the study. Content analysis was used to analyze the data acquired in this study. Study results showed that the definition strategy was used together with the visualization strategy. It was also determined that informal definitions were used in addition to formal definitions and that in general a personal definition was given by listing the various properties of quadrilaterals. The teachers who participated in this study generally used the partial classification of quadrilaterals and the transformation classification of quadrilaterals.Key words: Pedagogical content knowledge, teaching strategies, quadrilaterals. INTRODUCTIONTeacher education research has been suggested as a new field of study by Shulman (1986) and has created a framework to determine what teachers need and develop effective teaching according to some factors. In this framework, Shulman (1987) has examined pedagogical content knowledge as consisting of two components: student knowledge and teaching strategies. When components of the knowledge to understand students in various different pedagogical content knowledge models are examined (Grossman, 1990;Fennema and Franke, 1992;Schoenfeld, 1998;Magnusson et al., 1999;An et al., 2004;Ball et al., 2008;Park and Oliver, 2008;Kovarik, 2008) it is observed that student knowledge is examined in six different sub-components such as revealing the current knowledge of students, associating preliminary knowledge with new knowledge, valuing *Corresponding author. E-mail: elifnurakdogan@hotmail.com student questions and thoughts, taking into consideration the individual differences, predicting student thought and determining-knowing the misconceptions of students. It is also observed that the teaching strategies component in these models is examined under six different sub-components such as strategies for specific topics, specific strategies for any topics, demonstrations, (examples, real world problems, problems), analogies, illustrations, samplings, explanations.Various researches have carried out on the pedagogical content knowledge components which was put forth by Shulman (Park and Oliver 2008, different components have been listed in detail by different researchers). In this examination, Park and Oliver (2008) have determined that many of these ...

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Section: Discussion Conclusion and Implicationssupporting

confidence: 89%

Middle school mathematics teachers pedagogical content knowledge regarding teaching strategies on quadrilaterals

AkkaÅŸ¹,

TÃ1⁄4rnÃ1⁄4klÃ1⁄4²

2014

Educ. Res. Rev.

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“…Esta complementariedad vinculada a los diferentes atributos que podemos considerar en las figuras, apoyan la existencia de un nivel "sincrético" entre lo perceptual y lo analítico en una clasificación por niveles más generales Fujita, 2012;Hershkowitz et al, 1990;Yesil-Dagli y Halat, 2016). Nuestros resultados indican que conforme avanzan los cursos, mayor es la capacidad para analizar las figuras geométricas y menor la influencian de la perspectiva perceptual (aprehensión perceptual); sin embargo, esta progresión no es uniforme para los diferentes atributos de una figura (Walcott, Mohr y Kastberg, 2009). …”

Section: Discusión Y Conclusionesunclassified

Investigación en educación matemática : [actas del XXI Simposio de la Sociedad Española de Investigación en Educación Matemática : Zaragoza, 6-9 de septiembre de 2017]

Catalán¹,

Moreno²,

López³

2017

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“…One of the reasons for having students operate with prototypical figures is their static understanding in the typical position: considering quadrilaterals to be static figures with certain properties (e.g., a trapezium is a figure with one pair of parallel sides, one of which is parallel to the bottom edge of the paper). This has been considered to be the main reason for students not being able to conceptualize the interrelationships among different quadrilaterals (Walcott et al 2009). …”

Section: Understanding Of Two-dimensional (2-d) Figures By Childrenmentioning

confidence: 99%

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

Swoboda

Vighi

2016

ICME-13 Topical Surveys

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This survey confirms that one of the research trends in early geometrical reasoning has been a focus on creating a theoretical basis for research in this area. The main reason for the work on the theoretical foundations has been the fact that building geometrical concepts proceeds according to other regularities more than it takes place while building arithmetic knowledge. In this way, a broad research area was outlined. The first theory was created by Dina and Pierre Van Hiele (the Netherlands), but many on-going studies are related to this issue and many have focused on analysing and further expanding this theory.In parallel, new conceptual approaches that capture the question of the theoretical basis in a different way have been created. They should be considered complementarily, as they repeatedly point to the other aspects of the geometrical knowledge. The examples discussed in this paper come from the circles of scholars gathered around Alain Kuzniak (France) and Milan Hejný (Czech Republic). A networking between Van Hiele's theory and the description of geometrical paradigms created by Kuzniak examine ways that children work at the lowest levels. This allows analysis of how they gain experience, which is the basis for the transition in the area of further paradigms. This is therefore a departure from the theories that have a linear structure and focus only on a successive development.Milan Hejný indicates new aspects for descriptions of understanding of geometrical concepts, but first and foremost, he connects his proposals with the concept of schema-oriented education, where creating skills and procedures should be seen from a long perspective. In his theoretical background, a relatively new trend concerning the development of geometric reasoning is a pro-ceptual approach to the concepts. The formation of geometrical concepts is related to the empirical

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Making sense of shape: An analysis of children's written responses

Cited by 38 publications

References 11 publications

Middle school mathematics teachers pedagogical content knowledge regarding teaching strategies on quadrilaterals

Middle school mathematics teachers pedagogical content knowledge regarding teaching strategies on quadrilaterals

Investigación en educación matemática : [actas del XXI Simposio de la Sociedad Española de Investigación en Educación Matemática : Zaragoza, 6-9 de septiembre de 2017]

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

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