Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Cognitive analysis of students’ learning of trigonometry in dynamic geometry environment : a teaching experiment
Download
index.pdf
Date
2015
Author
Şahin, Zülal
Metadata
Show full item record
Item Usage Stats
174
views
103
downloads
Cite This
Trigonometry is a part of mathematics in which algebra and geometry converge. Dealing with trigonometric functions at secondary level is known as a difficult task because it requires to work with right triangles, the unit circle, and graphs of trigonometric functions simultaneously. For most students, this means excessive amount of formulas unless they can establish connections among different representational systems. There is a consensus in the literature that appropriate use of technology can be effective in helping students make such connections. Dynamic geometry environments can be a useful tool in teaching trigonometry due to their opportunities that enable to construct mathematical objects within different representational systems in a dynamically-and-linked way. The overarching purpose of this study was to design an instruction in dynamic geometry environment in order to support secondary students’ concept images on core trigonometric functions, i.e., sine and cosine, in different representations (i.e., symbolic, circular, and graphic). The instructional sequence was designed initially through inspiring from research literature on trigonometry, historical development of trigonometry, our exploratory teaching experience, and initial interview results. And then, design of the instruction was continued through revising as a result of the on-going prospective and retrospective cognitive analysis of the data that were collected during the 17-week teaching experiment from two pairs of secondary students separately. Students were encouraged to reason about dynamically-linked transformations of the core trigonometric functions within and between representational registers, as well as reasoning about dynamically-changed visual components referring to the core trigonometric functions. When compared with their initial serious recognition and discrimination troubles, as the study progressed, significant improvements were observed in students’ recognition and discrimination abilities within and between different representational registers. The cognitive analysis of the data revealed the importance of students’ constructions of well-defined concept definition images on foundational trigonometric concepts (i.e., angle, angle measure, trigonometric value, trigonometric functions, and periodicity) in order to recognize the same trigonometric object within different representational registers. The importance of the basic visual features’ discrimination in comprehension of trigonometry was also revealed in this study. When the basic visual features referring to trigonometric functions (i.e., radius of the circle, position of the center, position of the reference point on the circle referring to trigonometric value) were systematically varied in the (unit) circle register, and their dynamic-and-linked oppositions in the graphical register were constructed, the students developed significant understandings that enabled them to discriminate the basic form of sine and cosine functions from their general forms. Finally, the findings of the study revealed that the discrimination ability required to be reasoning about the new situations emerging as a consequence of the changed-visual features through focusing on trigonometrically relevant objects (e.g., reference point(s), reference right triangle, radius, displacement amount and direction) rather than detailed processes (e.g., ordinate of a point, procedural definition of sine or cosine).
Subject Keywords
Mathematics
,
Trigonometry
,
Geometry
,
Mathematics teachers
,
Teaching
,
Teacher effectiveness.
,
Cognitive learning.
URI
http://etd.lib.metu.edu.tr/upload/12619521/index.pdf
https://hdl.handle.net/11511/25260
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
An Analysis of prospective middle school mathematics teachers‘ argumentation structures in technology and paper-pencil environments
Erkek, Özlem; Işıksal Bostan, Mine; Department of Elementary Education (2017)
The purpose of the current study was to investigate the nature of argumentation structures of prospective middle school mathematics teachers while solving geometry tasks within the GeoGebra and Paper-Pencil groups. The study employed qualitative case study design and the data of which were collected from 16 prospective middle school mathematics teachers during the fall semester of the 2013-2014 academic year. Data were based on the video recordings of the implementations, the focus group interviews and docu...
Development of a test for assessing teachers’ mathematical content knowledge for teaching geometric measurement at elementary grade level
Esen, Yasemin; Çakıroğlu, Erdinç; Çapa Aydın, Yeşim; Department of Elementary Education (2013)
The purpose of this research was to develop and provide evidence for the construct validity of an instrument designed to measure pre-service mathematics teachers' mathematical knowledge for teaching (MKT) measurement specifically on the concepts of length, area and volume.The test is referred as the Test of Mathematical Knowledge for Teaching Measurement (TMK-M).It was aimed to contribute to fill the gaps for lack of valid measures to be used for assessing elementary mathematics pre-service teachers’ MKT. T...
Exploring secondary mathematics teachers’ conceptions of mathematical literacy
Genç, Murat; Erbaş, Ayhan Kürşat; Department of Secondary Science and Mathematics Education (2017)
The purpose of this research study was to investigate secondary mathematics teachers’ conceptions of mathematical literacy. In doing so, the following three crucial interrelated issues were addressed: (i) teachers’ conceptions of what the notion of mathematical literacy means, (ii) teachers’ conceptions of how the development of mathematical literacy could be facilitated, and (iii) teachers’ conceptions of what a mathematics curriculum emphasizing mathematical literacy should look like. The data gathered fo...
Prospective middle school mathematics teachers’ developing understanding of geometric transformations
Avcu, Seher; Çetinkaya, Bülent; Department of Sociology (2017)
The purpose of this study was to explore prospective middle school mathematics teachers’ developing understanding of geometric transformations during the implementation of a seven-week instructional sequence designed to have them gain a mapping understanding of geometric transformations. This instructional sequence involved exploring geometric transformations in both static and dynamic geometry environments. Participants of the study were sixteen prospective middle school mathematics teachers. Design-based ...
Students’ development of geometrical concepts through a dynamic learning environment
Ubuz, Behiye (2004-07-11)
Geometry is one of the important areas of mathematics over the world. Geometry provides experiences that help students develop understanding of shapes and their properties. It enables students to solve relevant problems and to apply geometric properties to real-world situations. National Council of Supervisors of Mathematics endorsed that geometry was one of the ten proposed basis skill areas (NCSM, 1976) and is indeed a basic skill that should be taught to students of all ability levels (Sherard, 1981). Te...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
Z. Şahin, “Cognitive analysis of students’ learning of trigonometry in dynamic geometry environment : a teaching experiment,” Ph.D. - Doctoral Program, Middle East Technical University, 2015.