Constructing Abstract Mathematical Knowledge in Context

Dreyfus, Tommy

doi:10.1007/978-3-319-17187-6_7

Cited by 13 publications

(22 citation statements)

References 17 publications

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“…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). Thus, the RBC+C model is important because it enables one to examine the abstraction process over cognitive ones (Dreyfus, 2007;Dreyfus, Hershkowitz, & Schwarz, 2001a, 2001bHerskhowitz et al, 2001).…”

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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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 purpose of our research project is to support them to cope with the quantity and quality of mathematical contents they have to master in a given time. From appraisal of the literature on learning mathematics, it seems well-advised to design a learning environment that enables students to involve themselves with the subject matter in context (Dreyfus, 2012) and to discuss their approaches with peers and teachers (von Glasersfeld, 1991), as well as to address selected affective aspects, namely beliefs, attitudes, and approaches to learning, see section 2.1. 2.10 (pages 33 to 38).…”

Section: The Design Research Approachmentioning

confidence: 99%

“…The course was housed in moodle, one of the university's elearning platforms. Some effort was taken in order to assemble tests with automatic evaluation to make sure the students had enough practise material, in compliance with the demand to present the subject matter in context (Dreyfus, 2012) and treat the students as independent learners (see Chapter 3). The lecture script was uploaded, as well as information on the organisation of the project, e.g.…”

Section: E-learning Coursementioning

confidence: 99%

Learning Strategies in Engineering Mathematics

Griese

2017

Studien Zur Hochschuldidaktik Und Zum Lehren Und Lernen Mit Digitalen Medien in Der Mathematik Und in Der Statistik

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“…The above cited theory [21] emphasises``constructing as the central epistemic action of mathematical abstraction''. This paper's main point is, that``constructing'' is most appropriately supported by a system, that guides students through stepwise problem solving, that suggests a next step if the student gets stuck.…”

Section: Interactive Operation Fostering Abstractionmentioning

confidence: 99%

“…[26,21], is most appropriately supported by self-contained systems, by``systems that explains themselves''.…”

Section: Interactive Operation Fostering Abstractionmentioning

confidence: 99%

Formal Abstraction in Engineering Education - Challenges and Technology Support

Neuper¹

2017

ADN

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Abstract. This is a position paper in the the field of Engineering Education, which is at the very beginning in Europe. It relates challenges in the new field to the emerging technology of (Computer) Theorem Proving (TP).Experience shows, that teaching abstract models, for instance the wave equation in mechanical engineering and in electrical engineering, is difficult. This paper suggests novel technology to support learning in a novel way such that abstract models are better understood eventually.Such support acknowledges learning and mastering abstraction as a long-term process, which requires revisiting physical and mathematical concepts again and again, which in turn continuously raises the level of abstraction at an individual pace and fosters students' familiarity with formal descriptions capturing essential properties of models and respective elements.The paper discusses the potential of TP to support students' process of abstraction and expected impact on teaching mathematics at engineering faculties.

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Constructing Abstract Mathematical Knowledge in Context

Cited by 13 publications

References 17 publications

The Abstraction Process of Limit Knowledge

The Abstraction Process of Limit Knowledge

Learning Strategies in Engineering Mathematics

Formal Abstraction in Engineering Education - Challenges and Technology Support

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