Comparing infinite sets — a process of abstraction

Tsamir, Pessia; Dreyfus, Tommy

doi:10.1016/s0732-3123(02)00100-1

Cited by 45 publications

(49 citation statements)

References 11 publications

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“…Reorgnizing, building with and construction activities do not always have a linear shape, but they can occur at the same time.They have been validated and useful for describing and analysing the processes of abstraction of other contents, in other social settings and other learning environments. They have been established by a considerable number of research studies incuding ours (BiknerAhsbahs, 2004;Dreyfus and Kidron, 2006;Ozmantar and Roper, 2004;Ron et al, 2006;Stehlíková, 2003;Tabach and Hershkowitz, 2002;Tabach et al, 2001Tabach et al, , 2006Tsamir and Dreyfus, 2002;Williams, 2002Williams, , 2003Williams, , 2004Williams, , 2005Wood and McNeal, 2003;Wood et al, 2006).…”

Section: Terminologymentioning

confidence: 87%

“…The subject of the research is Prakasita, a grade 9, Junior high school of Hang Tuah 1 Surabaya, Indonesia. The data of the research were collected by using a task-based interviews (Tsamir and Dreyfus, 2002).…”

Section: Methodsmentioning

confidence: 99%

“…The results of this construction are more complex than the initial concepts for students. Guler and Arslan (2015), Hershkowitz et al (2001) and Tsamir and Dreyfus (2002) divided abstraction into three epistemic actions: recognizing, building with and constructing. Recognizing is identifying a mathematic structure in a previous knowledge construct.…”

Section: Introductionmentioning

confidence: 99%

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Students abstraction in re-cognizing, building with and constructing a quadrilateral

Budiarto¹,

Rahajuand²,

Hartono³

2017

Educ. Res. Rev.

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This study aims to implement empirically students' abstraction with socio-cultural background of Indonesia. Abstraction is an activity that involves a vertical reorganization of previously constructed mathematics into a new mathematical structure. The principal components of the model are three dynamic nested epistemic actions: recognizing, building-with, and constructing. This study identified the abstraction profile of a junior high school student in constructing quadrilateral relationship. The student was asked a question related to quadrilateral. The interview was developed based on her answers by using keywords, "what, how, or why". The result of the student's abstraction and attributes were used to recognize the differences and similarities of quadrilateral shapes, building-with attributes by linking the characteristics of every two quadrilaterals, and constructing a network of relationships among quadrilaterals by drawing a figure of such networks.

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Section: Terminologymentioning

confidence: 87%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Students abstraction in re-cognizing, building with and constructing a quadrilateral

Budiarto¹,

Rahajuand²,

Hartono³

2017

Educ. Res. Rev.

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show abstract

“…While forming a piece of knowledge, an individual makes associations with previous subject matter in the recognizing stage, uses it for problem-solving in the building-with stage, sets up a new knowledge structure in the construction stage, and reinforces the formed knowledge in the consolidation stage. Abstraction emerges by requiring further construction and also covers strengthening (Tsamir & Dreyfus, 2002). The act of construction forms as a result of the materialization of recognizing and building-with, which are nested in one another (Dreyfus, 2007;Dreyfus, Hershkowitz, & Schwarz, 2001b).…”

Section: Abstraction the Abstraction Process And The Rbc+c Abstractmentioning

confidence: 99%

“…In addition, functions (Hershkowitz et al 2001), absolute value (Özmantar, 2004, 2005), linear equations (Sezgin-Memnun & Altun, 2012), infinity (Tsamir & Dreyfus, 2002), and triangles along with its variations (Yeşildere & Türnüklü, 2008a, 2008b have been explored in particular.…”

Section: Abstraction the Abstraction Process And The Rbc+c Abstractmentioning

confidence: 99%

The Abstraction Process of Limit Knowledge

2017

EDUC SCI-THEOR PRACT

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The RBC+C abstraction model is an effective model in mathematics education because it gives the opportunity to analyze research data through cognitive actions. For this reason, we aim to examine the abstraction process of the limit knowledge of two volunteer participant students using the RBC+C abstraction model. With this aim, the students' abstraction processes were examined over recognition, building-with, construction, and consolidation. In the process, three problems that enable students to use their pre-knowledge were designed by the researchers to reveal the students' mathematical thinking levels, abstraction processes, and finally to improve a new structure. These problems were used in the application, and students' dialogues were videorecorded. The semi-constructed interview and observation data-collection methods were used in this process, and one of the researchers participated in the study as a participant observer. The data was analyzed and interpreted by transcribing the video recordings into written text and grouping them into the cognitive actions of the RBC+C model. In conclusion, these students were indicated to have managed recognizing and buildingwith their pre-knowledge on sequence, function, and infinity, and thus constructing knowledge on limits.

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Constructing Abstract Mathematical Knowledge in Context

Dreyfus

2015

Selected Regular Lectures From the 12th International Congress on Mathematical Education

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Comparing infinite sets — a process of abstraction

Cited by 45 publications

References 11 publications

Students abstraction in re-cognizing, building with and constructing a quadrilateral

Students abstraction in re-cognizing, building with and constructing a quadrilateral

The Abstraction Process of Limit Knowledge

Constructing Abstract Mathematical Knowledge in Context

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