Learning Geometry: the Development of Geometrical Concepts and the Role of Cognitive Processes

Mammarella, Irene C.; Giofrè, David; Caviola, Sara

doi:10.1016/b978-0-12-805086-6.00010-2

Cited by 13 publications

(24 citation statements)

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“…Children in primary schools are required to learn names and properties of a wide range of two-and three-dimensional shapes and figures (Fisher et al, 2013;Mammarella, Todeschini, Englaro, Lucangeli, & Cornoldi, 2012;van Hiele, 1986) and an adequate knowledge of the basic concepts and terms is therefore needed in the acquisition of complex geometrical concepts (Bizzaro et al, 2018;Swindal, 2000). Furthermore, as geometry is strictly connected to data manipulation and measurement, a second set of domain-specific abilities is represented by calculation skills (Mammarella, Giofr e, & Caviola, 2017), required, for example, to calculate perimeters and area of geometric figures. Finally, spatial geometrical abilities (Battista, 1990;Bizzaro et al, 2018;Clements, & Battista, 1992;Weckbacher & Okamoto, 2014), and geometrical mental imagery, that is the ability to mentally manipulate two-or three-dimensional figures, seems to be crucially involved.…”

Section: Cognitive Underpinnings Of Geometrymentioning

confidence: 99%

“…In the domain of geometry, WM seems to play an important role as solving geometric problems requires to maintain and manipulate visual and verbal materials (geometric figures, specific vocabulary, data, etc. ; Mammarella et al, 2017). According to the tripartite model proposed by Baddeley and Hitch (1974), WM is articulated in two independent domain-specific components (see also Baddeley, 1986;Engle, Kane, & Tuholski, 1999), respectively, processing verbal and visuospatial information, coordinated by a domain-general component, the central executive.…”

Section: Cognitive Underpinnings Of Geometrymentioning

confidence: 99%

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Learning a new geometric concept: The role of working memory and of domain‐specific abilities

Rivella

Cornoldi

Caviola

et al. 2021

Brit J of Edu Psychol

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It has been suggested that not only domain-specific factors but also working memory (WM) may play a crucial role in mathematical learning included Geometry, but the issue has not been deeply explored. In the present study, we examined the role of domain-specific factors and of verbal versus visuospatial WM on geometric learning of a new geometrical figure (trapezoid), never presented previously by the teachers participating to the study, after a lecture also involving manipulatives. Results on 105 children in their Year 4 indicated that not only some domain-specific components (geometric declarative knowledge and calculation) but also visuospatial working memory had a significant specific impact on the ability of solving geometric problems requiring to calculate the perimeter and the area of the new figure. On the contrary, verbal WM and geometrical mental imagery did not offer a specific contribution. These findings could have important educational implications, stressing the importance of taking into account the main different aspects supporting the acquisition of geometry.Geometry enables individuals to make sense of the world by understanding geometric shapes, principles, and relationships (National Council for Teachers of Mathematics, 2000). Geometrical knowledge is indeed considered one of the most important areas of mathematics (Arcavi, 2003;Zhang, Ding, Stegall, & Mo, 2012). Therefore, understanding how children learn to master geometrical concepts, in order to be able to solve concrete and progressively more abstract problems, is of a vital importance in the education domain (Clements & Sarama, 2011). In the present study, we examined the issue by considering the acquisition of a geometrical concept that was completely new to the students, analysing what cognitive underpinnings come to play in a traditional instruction setting where manipulatives had also been introduced.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Cognitive Underpinnings Of Geometrymentioning

confidence: 99%

Section: Cognitive Underpinnings Of Geometrymentioning

confidence: 99%

Learning a new geometric concept: The role of working memory and of domain‐specific abilities

Rivella

Cornoldi

Caviola

et al. 2021

Brit J of Edu Psychol

Self Cite

View full text Add to dashboard Cite

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“…These outcomes revealed that there is no significant difference in the scores in four categories. Nevertheless, some countries do not put geometry as a compulsory domain of mathematics while in fact, it scored the lowest compared to other math domains (Mammarella, Giofrè, & Caviola, 2017).…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the intended learning must be in accordance with the level that has been achieved by students, so that they can experience improvement to reach the next level. Therefore, the teacher needs to be able to understand a student reaching a certain level in geometric thinking (Mammarella et al, 2017). On the contrary, fewer geometry learning experiences lead to an inadequate experience of spatial ability (Armah et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Measuring Spatial Ability and Geometric Thinking Level of Prospective Elementary School Teachers Using the Rasch Model

2021

ilkonline

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The objectives: (1) measuring spatial ability and geometric thinking level of Prospective Elementary School Teachers (PGSD students), (2) analyzing difficulties faced on a certain spatial ability. The study used a mixed-method quantitative and qualitative. Researchers developed test items to measure the spatial ability and geometric thinking of 139 Prospective Elementary School Teachers (PGSD students), Universitas Negeri Semarang. The sampling method employed was cluster random sampling, while three students selected for the interview were based on the 'poor' and 'very poor' category. Data analysis with the Rasch Model showed that the item reliability, item validity, item separation, and unidimensionality were classified as 'good'. The results revealed that spatial ability and geometric thinking of Prospective Elementary School Teachers were classified as 'fair' (62.5%) and 'good' (31.7%). The difficulties in completing tasks of spatial ability primarily on the perception and relation, which happened due to their lacking of imagination.

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“…Gal & Linchevski, 2010. Σύμφωνα με τους Mammarella et al (2017), η αποτελεσματική λειτουργία αυτών των διεργασιών εξαρτάται από ποικίλες γνωστικές ικανότητες (π.χ. οπτικοχωρική και φωνολογική αντίληψη και μνήμη) και εκτελεστικές λειτουργίες (π.χ.…”

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Διερεύνηση Γεωμετρικών Γνώσεων Μαθητών Με Ήπιες Εκπαιδευτικές Ανάγκες

Παπαδάμ

Αγαλιώτης

2021

Psychology

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Geometry is a structural component of mathematics, with increased spatial and design requirements that cannot be easily met by students with mild disabilities. Systematic investigation of the difficulties encountered by students with mild disabilities in their effort to learn Geometry is a prerequisite for the implementation of effective intervention programs. However, research on this issue is relatively scarce. The aim of the present study was to assess the geometric knowledge of 54 students with mild disabilities (learning disabilities or ADHD) who attended the two last classes of elementary school. Participants were asked to recognize, describe and categorize geometric shapes and solid bodies that were presented in tactile mode and through pictorial representations. Semi-structured clinical interviews were used for gathering the data in the context of Curriculum Based Assessment and the Van Hiele’s model of geometrical thinking. Participants of both categories of mild disabilities presented difficulties in distinguishing shapes and bodies, properly using the terminology, and formatting inductive geometrical reasoning. Participants with learning disabilities had higher achievement when dealing with haptic relative to pictorial representations of geometric shapes and bodies. Sixth graders performed better than fifth graders. Results are discussed in terms of the differences between the two categories of mild disabilities as well as with regard to the implementation of intervention programs.

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Learning Geometry: the Development of Geometrical Concepts and the Role of Cognitive Processes

Cited by 13 publications

References 64 publications

Learning a new geometric concept: The role of working memory and of domain‐specific abilities

Learning a new geometric concept: The role of working memory and of domain‐specific abilities

Measuring Spatial Ability and Geometric Thinking Level of Prospective Elementary School Teachers Using the Rasch Model

Διερεύνηση Γεωμετρικών Γνώσεων Μαθητών Με Ήπιες Εκπαιδευτικές Ανάγκες

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