Artefacts teach-math. the meaning construction of trigonometric functions (original) (raw)
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2013
This thesis is concerned with how a group of student teachers make sense of trigonometry. There are three main ideas in this study. This first idea is about the theoretical framework which focusses on the growth of mathematical thinking based on human perception, operation and reason. This framework evolves from the work of Piaget, Bruner, Skemp, Dienes, Van Hiele and others. Although the study focusses on trigonometry, the theory constructed is applicable to a wide range of mathematics topics. The second idea is about three distinct contexts of trigonometry namely triangle trigonometry, circle trigonometry and analytic trigonometry. Triangle trigonometry is based on right angled triangles with positive sides and angles bigger than 0 [degrees] and less than 90 [degrees]. Circle trigonometry involves dynamic angles of any size and sign with trigonometric ratios involving signed numbers and the properties of trigonometric functions represented as graphs. Analytic trigonometry involves...
The High School Students’ View of Trigonometry Problems to Develop Their Mathematics Reasoning
2017
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...
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.
Teaching and learning trigonometry with technology
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.
Teaching mathematics through history: Some trigonometric concepts
2007
On the one hand, the History of Science can be used as an implicit resource in the design of a syllabus, to choose context, mathematical problems and auxiliary sources. In addition, History can be used to program the sequence of the learning of a mathematical concept or idea. However, students do not have to accurately follow the historical sequence of the evolution of an idea, it should be remembered that the historical process of the constitution of knowledge was collective and depended on several social factors. In the past, most of the mathematicians had the aim of solving specific mathematical problems and they spent a lot of years working on them. In contrast, students are learning these concepts for the first time and sometimes they do not have enough motivation. Nevertheless, the knowledge of the historical evolution of a mathematical concept will provide teachers with tools to help the students to understand these concepts. At the same time it may also indicate the way to t...
Painless trigonometry: a toolcomplementary school mathematics project
EuroLogo, 2007
Since 2001-02, we have been working in our mathematics classrooms with the materials and digital tools provided by a government-sponsored national programme: the Teaching Mathematics with Technology programme (EMAT). The main computer tools of the EMAT programme are Spreadsheets (Excel), Dynamic Geometry (Cabri-Géomètre), and Logo (MSWLogo). At the beginning we used these tools independently, but in more recent years we have tried to develop long-term projects that incorporate all the tools, and that also serve as means to introduce students to topics of mathematics that are normally considered too advanced for them (such as trigonometry). In this paper we report the design and results of one of those projects, a trigonometry project, that we first implemented in the academic year 2005-06 with 6 groups of the first two grades of two junior secondary schools in Mexico. Approximately 250 students of 12-14 yrs of age participated, in total, in the project in that year. We believe in the importance of using, in an integrated and complementary way, a variety of tools for learning since we consider that each tool brings with it a different type of knowledge and constitutes a different epistemological domain (Balacheff & Sutherland, 1994). We also believe in the importance of constructionist (Harel & Papert, 1991) or programming activities for meaningful learning. With those fundamental theoretical premises, we developed the long-term trigonometry project for introducing young students to the Pythagorean theorem, basic trigonometry concepts, and their applications using explorations and constructive activities with Cabri-Géomètre, Excel and Logo (Figure 1). Students thoroughly enjoyed the activities and gained interest in mathematics. They also developed problem-solving and collaborative skills. Furthermore, in written tests after the project, the students showed an understanding of the "advanced" trigonometry concepts, as well as of other algebraic ideas.
Elementary School Teachers' Mathematical Connections in Solving Trigonometry Problem
Research in Social Sciences and Technology, 2018
This study aims to reveal mathematical connections of elementary school teachers in solving trigonometric problem. The subjects of this study were 22 elementary school teachers as the prospective participants of Professional Teacher Education and Training (PTET). They came from several districts of South Sulawesi Province. The teachers were given trigonometry problem. Trigonometryproblemscould encourage teachers to connect geometrical and algebraic concept, graphical representation and algebraic representation, as well as daily life context. The result shows that most of the subject teachers of this study solved the problem according to procedures they know without considering everyday life context. On the other hand, there were some subjects who connected problem with everyday life context using graphical, verbal, or numerical representation. Thus, subjects who were able to connect problem information with appropriate concepts and procedures are categorized as substantive connections. While the subjects who were ableto connect problem information with mathematical concepts but less precise in using the procedure are categorized as classification connections.
Difficult Topics in Junior Secondary School Mathematics: Practical Aspect of Teaching and Learning Trigonometry, 2013
Abstract: This paper presented practical aspect of teaching and learning Trigonometry to serve as a guide to both teachers and students of Mathematics. It is aimed at reducing the level of difficulties teachers and students of mathematics are facing in terms of delivery and comprehension. The paper identifies Trigonometry as difficult topic alongside simultaneous linear equation, word problems and change of subject of formula that causes challenges to both Mathematics teachers and educators. Problems of teaching and learning as well as the strategies that could be employed in teaching and learning of Sine, Cosine and Tangent of a triangle were explicitly explained and discussed. The paper recommends that Mathematics teachers should endeavor to teach difficult topics concretely and explicitly.
Exploring Grade 11 Learners’ Mathematical Connections when Solving Trigonometric Equations
Symmetry, 2023
In this paper, we explored the intra-mathematical connections that grade 11 learners make when solving trigonometric equations. The study was guided by Mowat's theory of mathematical connections in which nodes and links are used to connect mathematical concepts and topics. We used a qualitative case study design within an interpretive paradigm to explore the intra-mathematical connections learners make as they solved trigonometric equations. The study was conducted in a high school in Mankweng Circuit, Limpopo Province, South Africa. Convenience sampling was used to select 30 learners who participated in the study. Data was collected using documents and task-based interviews. Data were analysed using inductive thematic analysis. The findings showed that learners made were able to make algebraic connections when solving trigonometric equations. They, however, were unable to make connections within trigonometry itself. This study, therefore, recommends that teachers stress the importance of connections when teaching trigonometry so that learners will not learn trigonometric concepts in isolation. In addition, it is recommended that further research be conducted on teaching strategies to improve learners' mathematical connection skills when solving trigonometric equations.
Students understanding of trigonometric functions
In this article students' understanding of trigonometric functions in the context of two college trigonometry courses is investigated. The first course was taught by a professor unaffiliated with the study in a lecture-based course, while the second was taught using an experimental instruction paradigm based on Gray and Tall's (1994) notion of procept and current process-object theories of learning. Via interviews and a paper-and-pencil test, I examined students' understanding of trigonometric functions for both classes. The results indicate that the students who were taught in the lecture-based course developed a very limited understanding of these functions. Students who received the experimental instruction developed a deep understanding of trigonometric functions. * Responses to question 1a (approximate sin 340˚) were judged to be "correct" if they were between 0 and -0.5.