Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study

Date

2015-02-01

Author

Sahin, Zulal
Yenmez, Arzu Aydogan
Erbaş, Ayhan Kürşat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

221
views

0
downloads

The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up, model-eliciting, and model-exploration activities were used to stimulate participants to reflect and construct ideas about the concept of change. The data indicated that the participants' understanding of derivative was rather instrumental. Their explanations couldn't reveal the role of the big ideas regarding the concept of derivative with respect to what they mean, why and how they are related to the derivative and to each other. The results highlighted the fact that even if one of big ideas is ignored, the concept of derivative may not be fully understood relationally due to the compartmentalization of these big ideas in students' conceptual systems. If this happens to be the case, even though students can solve differentiation tasks/problems correctly, which implies procedural understanding, they may not be actually making sense of what the concept of derivative conceptually means.

Subject Keywords

Derivative, Mathematical modeling, Rate of change, Relational understanding

URI

https://hdl.handle.net/11511/53586

Journal

EURASIA JOURNAL OF MATHEMATICS SCIENCE AND TECHNOLOGY EDUCATION

Collections

Department of Mathematics and Science Education, Article

Suggestions

OpenMETU
Core

Context-Based Lessons with 5E Model to Promote Conceptual Understanding of Chemical Reactions and Energy Concepts Cigdemoglu, Ceyhan; Geban, Ömer (2015-01-01) This study explores whether the context-based approach with 5E model (CBA-5E) can lead to better understanding of chemical reactions and energy concepts when compared to conventional instruction (CI). Additionally, the study delves into the effect of treatment with regards to gender. Eleventh grade science-major classes with 175 students from two public high schools were enrolled. The experimental groups were treated with CBA-5E, the control groups as CI, the treatments were randomly assigned to the groups....
Material Processuality: Alternative Grounds for Design Research Tönük Kruıthof, Damla (Informa UK Limited, 2020-01-01) This article opens discussion on the positivist epistemology underlying the understandings of materials in design research that have been brought along as a result of theory and methods inherited from engineering and psychology. Examining the ambitions of work that seeks to operationalize knowledge created by these methods in the design process, we propose that attending to the processuality of material forms is a more adequate way for design research to capture the multiplicity of materials. We develop thi...
Normative and emotional responses in a peer conflict paradigm : a developmental study on 3- and 5- year old Turkish children Köksal, Özgün; Hohenberger, Annette Edeltraud; Department of Cognitive Sciences (2012) The purpose of the study is to investigate the development of normative understanding and its relation to emotional states. Two samples of late 3- and 5-year-old Turkish pre-school children were studied. We adopted a peer conflict paradigm in which we taught two children conflicting rules for playing a game and asked them to play the game together, later (incompatible condition). Since children had learned different rules we expected them to protest when their partners played the game with a different rule....
Scientific epistemological beliefs, perceptions of constructivist learning environment and attitude towards science as determinants of students approaches to learning Özkal, Kudret; Öztekin, Ceren; Department of Elementary Science and Mathematics Education (2007) The purpose of this study was to investigate scientific epistemological beliefs, perceptions of constructivist learning environment, attitude towards science, prior knowledge and gender as determinants of students’ approaches to learning. This study was carried out in 2005-2006 Spring Semester. One thousand, one hundred and fifty two eighth grade students from seven public schools in Çankaya, a district of Ankara participated in this study. Epistemological Beliefs Questionnaire, Constructivist Learning Envi...
Concurrent validity and test-retest reliability of the information processing styles Baloğlu, Mustafa; Zelhart, PF (2000-12-01) To investigate concurrent validity and test-retest reliability of thr Information Processing Styles, 62 students majoring in social sciences evaluated the accuracy of the checklist in describing their dominant types. Each student had a friend who read the descriptions of thy dominant types(s) of the student and rated their perceived accuracy of that categorization. Analyses indicated the inventory is reliable and valid.

Citation Formats

Z. Sahin, A. A. Yenmez, and A. K. Erbaş, “Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study,” EURASIA JOURNAL OF MATHEMATICS SCIENCE AND TECHNOLOGY EDUCATION, pp. 177–188, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53586.