Dinamik geometri ortamında öğrencilerin trigonometri öğrenmelerinin bilişsel analizi : bir öğretim deneyi (original) (raw)
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Artefacts teach-math. the meaning construction of trigonometric functions
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Trigonometry is an area of the high school mathematics curriculum strictly related to algebraic, geometric, and graphical reasoning. In spite of its importance to both high school and advanced mathematics, research has shown that trigonometry remains a difficult topic for both students and teachers. A new approach the teaching of trigonometry – calibrated for the 21 st century - opens the question of the place and nature of trigonometry in contemporary high school mathematics. In this prospective, the authors have carried out a study aimed at explaining connections between research and teaching practice of trigonometric functions emphasizing conceptual understanding, multiple representation and connections, mathematical modelling, and mathematical problem-solving. This paper shows a teaching approach for meaning construction of trigonometric functions with the aid of technological artefacts.
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Modern school classrooms have access to a range of potential technologies, ranging from calculators to computers to the Internet. This paper explores some of the potential for such technologies to affect the curriculum and teaching of trigonometry in the secondary school. We identify some of the ways in which the teaching of trigonometry might be supported by the availability of various forms of technology. We consider circular measures, graphs of functions, trigonometric identities, equations and statistical modeling and focus on activities that are not possible without the use of technology. Modern technology provides an excellent means of exploring many of the concepts associated with trigonometry, both trigonometric and circular functions. Many of these opportunities for learning were not available before technology development and access within schools we enjoy today. This paper suggests some of the avenues for exploration.
Pythagoras, 2014
Trigonometry is an important section in mathematics that links algebraic, geometric and graphical reasoning. Many secondary school learners are not familiar with these types of reasoning; thus, trigonometry presents a challenge for these learners. The traditional ‘chalk and talk’ method of teaching trigonometry is used by many teachers; however, this article is based on a case study that explores the innovative use of a dynamic online software program in the teaching and learning of Grade 10 trigonometric graphs. The participants in this study were 25 Grade 10 mathematics learners from one school in the south of Durban, KwaZulu-Natal, South Africa. Data were collected by using two trigonometry worksheets, semi-structured interviews with selected learners and lesson observations. The worksheets were constructed based on the following focus areas: behaviour of graphs, interpretation of graphs, modelling and overall performance of the learner. In all focus areas, the participants’ scor...
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Many people do not like learning Mathematics because it requires highly analytical skills to solve for only one problem. It also same in mastering the field of algebra, it’s already difficult, moreover to learn trigonometry which involves many calculations of formulas in the form of corners in the triangle. It’s really not easy because it allows the combination between algebra and geometry. Though, the universe of the world is full of models of trigonometry measurements, then by studying trigonometry means that we have applied much different knowledge. The student difficulties in understanding trigonometry material are seen when students are faced with trigonometry problems that require reasoning based from real life. Students have lack of opportunities to solve the problems with this type of reasoning is a factor that limits the opportunities and positive perceptions of students in learning mathematics. Based on research, by the development of trigonometry problems that are relevan...
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This study explored the activitiesusing a graphing calculator of 10th-grade high school students on the trigonometry topic. A total of 65 students were divided into two classes, the first class consisted of 32 students, and the second class consisted of 33 students. The main objective of this study is to present classroom activities enriched with graphing calculators and observe responses about teaching with this approach. This study is research on developing learning designs within the Didactical Design Research (DDR) framework presented in an exploratory narrative. Data were collected by using two trigonometry worksheets and lesson observations. The worksheets were constructed based on the following focus areas: behaviour of graphs, constructing related-angle formula, and overall performance of the learner. The result of this research is a learning design that has been tested on 65 high school students. The research results on how to analyze the results of the implementation of st...
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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). Technology is promoted and effective tool to teach and learn geometry. When technology is used appropriately, it can provide a rich environment in which students ’ geometric understanding and intuition can be developed (NCTM, 1989). Calculators and computers with appropriate software transform the mathematics classroom into a laboratory much like the environment in many science classes, where students use technology to investigate, conjecture, and verify their findings (NTCM, 1989)....
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Trigonometry consists of a multifaceted mathematical field whose fundamental concepts, sine and cosine, have many different representations, some of them approached throughout secondary education. Unfortunately, many of its aspects are taught individually, leading students to make isolated, unconnected meanings on them. This empirical study discusses an alternative view towards trigonometry, in an attempt to create connections among the different aspects, under the scope of one meaningful context; that of periodicity. The use of digital media enables the application of this unconventional proposal, through a set of specially designed activities. In this paper we present a brief description of the main study-in-progress, as well as the results gained by its first implementation to 9th- Grade students, in terms of their meaning making on trigonometric concepts.
Trigonometry, technology, and didactic objects
Students have difficulty constructing coherent understandings of trigonometry and trigonometric functions (Brown, 2005;. This study conjectured that their weak understandings of angle measure and compartmentalized knowledge of right triangle and unit circle trigonometry are sources of the problem. The response was to devise an instructional sequence to promote these foundational understandings and connections. A critical part of this instruction was the use of dynamic applets. These applets were intended as didactic objects to facilitate meaningful conversations supporting student learning. This report discusses the design and implementation of these applets and their role in promoting discourse that facilitated knowledge construction.
Difficult Topics in Junior Secondary School Mathematics: Practical Aspect of Teaching and Learning Trigonometry, 2013
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