Trigonometric Concepts Research Articles

The Influence of Family Dynamics and Environment on Academic Performance and Understanding of Trigonometry

This article is the result of a research that was carried out to obtain the degree of Master's Degree in Education in the postgraduate program of the Faculty of Education of the Popular University of Cesar and monographic work of the degrees in Mathematics and Computer Science and Mathematics and Physics of the same university. The main objective of this study was to analyze the influence of the family environment on the learning and academic performance of students in tenth grade trigonometry from a public educational institution in the city of Valledupar. Applying a mixed method, the research employed a simultaneous integrated design, where quantitative and qualitative data were collected and analyzed at the same time. This approach allowed for a complete and nuanced understanding of the research questions, providing a holistic view by exploring family dynamics and environment and how these impact performance and understanding of trigonometry. As for the implications for educational practice, it is evident that there is a need to implement strategies that involve families in the teaching-learning process of trigonometry, since the data collected revealed a clear correlation between the level of parental participation in education and students' understanding of trigonometric concepts. In addition, the study found that a positive and supportive family environment contributed significantly to higher academic achievement in trigonometry.

PENERAPAN MODEL TEAM ASSISTED INDIVIDUALIZATION (TAI) UNTUK MENINGKATKAN HASIL BELAJAR MATEMATIKA

This study aims to improve the mathematics learning outcomes of tenth-grade students at SMA Negeri 6 Denpasar through the implementation of the Team Assisted Individualization (TAI) model in trigonometry. The research methodology utilized is classroom action research, involving collaboration between teachers and students. The steps of Team Assisted Individualization (TAI) are integrated into the teaching process, where students work in small teams to assist each other in understanding trigonometric concepts. Classroom action research is conducted in two cycles, with each cycle consisting of planning, implementation, observation, and reflection. Student learning outcomes data are obtained through formative tests and observations during the learning process. The research results are expected to provide insights into the effectiveness of the Team Assisted Individualization (TAI) model in enhancing the understanding and academic achievement of tenth-grade students at SMA Negeri 6 Denpasar in trigonometry. The implications of this research are anticipated to contribute positively to the development of innovative and student-oriented mathematics teaching methods.

Pre-Service Teachers Perceptions and Knowledge in Padangsidimpuan City : Concepts of Trigonometric

AbstractThis paper explored pre-service teachers’ perceptions and knowledge of trigonometric concepts. Convenience sampling technique was used to select a sample of 200 (50 females, 150 males) second year science/mathematics pre-service teachers from two Colleges of Education in the Padangsidimpuan City. Trigonometry Perception Questionnaire (TPQ) and Trigonometry Assessment Test (TAT) were used to collect data on pre-service teachers’ perceptions and conceptual knowledge of trigonometry. Data were coded and keyed into Statistical Package for Service Solutions (SPSS version 20) and analysed using descriptive statistics. The results suggested that pre-service teachers perceived trigonometry as abstract, difficult and boring to learn; and had limited conceptual knowledge of basic trigonometric concepts. Consequently, more that 65 % of them were unable to construct and reconstruct the appropriate mental structures for meaningful understanding to enable them respond to important basic trigonometry tasks. To achieve quality mathematics education, teacher educators must change their instructional practice and teach for understanding. Since understanding is the key to teacher’s instructional actions, processes and knowledge, we recommend teaching trigonometry for understanding during teacher preparation.

A Study of The Effects of Classroom Structure and Instructional Methods on Students Learning of Trigonometric Concepts in Mathematics

To think in a methodical and logical way, mathematics is an essential skill. On top of that, it may be used to learn new things in many other subjects. Recently, there has been a need to find better ways to teach mathematics, especially trigonometry, at senior high schools (SHSs), in order to increase students' understanding of the subject. Thus, numerous studies on what makes a good teaching style that helps students understand the material are necessary. Research has shown that students in higher education, particularly those at the secondary school level, suffer when teachers are unable to relate to the elements of a meaningful-based teaching approach. This study sheds insight on the ways in which a student's learning environment and instructional approaches affect his or her capacity to learn trigonometry, an area where academic policy-makers and educators are now developing transformational initiatives.The study objectives of this article are founded on the premise that environmental motivating characteristics are necessary to excite students' attention and intellect when learning trigonometry, a real-life method that depends on the size and distance of an object. As a result, this program aims to improve and make better use of two features—the classroom environment and instructional method —in elementary and secondary school settings.

ANALYZING COMMON TRIGONOMETRIC ERRORS AMONG FIRST-YEAR PRIMARY SCHOOL STUDENT TEACHERS AT THE UNIVERSITY OF BOTSWANA

Trigonometry is a fundamental mathematical concept taught at all levels of education, including primary schools. A strong understanding of trigonometry is essential for prospective teachers, especially those pursuing a career in primary school education. However, research suggests that students frequently encounter challenges and make common errors when learning trigonometric concepts. These errors have a significant impact on their overall performance and their ability to effectively teach these concepts. This study investigates the prevalent trigonometric errors made by first-year primary school student teachers at the University of Botswana. The research explores the root causes of these errors and aims to provide insights to enhance teaching methodologies within teacher training programs. By addressing these errors, the study aims to improve the quality of mathematics education in Botswana's primary schools, empowering future teachers to teach trigonometry effectively. The study includes a comprehensive analysis of common errors and recommendations for instructional interventions, drawing on responses from student answer scripts. It highlights the importance of developing a solid foundation in trigonometric concepts and the need for effective strategies to address these errors.<p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/soc/0075/a.php" alt="Hit counter" /></p>

Hypothetical Approach to the Teaching of Trigonometric Concepts Using Cooperative Learning

In this paper, we propose a teaching strategy to enhance the teaching and learning of trigonometry, called cooperative teaching and learning (CTL). The proposed method stems from the need of developing a pedagogical approach that promotes understanding and interest in the learning of trigonometry based on the cooperative learning (CL). This study therefore sought to explore the features of CTL that promote students’ learning of the concepts of trigonometry. The study employed systematic review as the research approach for the collection of the data. The review analysis covered 40 research studies on a meaningful-based pedagogies that allow students to make meaning of the subject matter. The study revealed that: positive interdependence, individual accountability, promotive face-to-face interaction, social skill, and group processing characterize the features of CTL suitable for the teaching of the concept of trigonometry. The study suggests that the teaching and learning of trigonometry through the use of the features of the CTL provide students with the opportunity to actively create ideas and work through high-order trigonometric tasks. The study contends that in order to implement CTL effectively in the mathematics classroom context, the features of CTL must be conceptualized in a way that is consistent with the desired objectives of a given mathematical topic.

Pengaruh Model Pembelajaran Needham terhadap Pemahaman Konsep Trigonometri

Abstract: The purpose of this study was to determine whether the Needham learning model had a positive effect on students' understanding of trigonometric concepts. The research methods used are experimental and the study design used is quasi-experimental involving only post-tests. The study population consisted exclusively of students in Class X of Madrasah Aliya Al-Mubarok for the 2021/2022 school year. The samples in this study were classes X IPA 1 and X IPA 2 drawn using a cluster random sampling technique. Correct t-test statistics were used for data analysis. Based on the results of data analysis obtained 3.617 and 1,678. Based on these results, obtained , it can be concluded that there is a positive effect of the application of the Needhaam learning model on students' understanding of concepts. Keywords: Needham Learning Model; Concept Understanding; Trigonometry

Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment

In this paper, we explored the type of mathematical connections Grade 11 learners make when solving two-dimensional (2D) trigonometric problems in an Activity-Based Learning (ABL) environment. We followed a qualitative case study design within an interpretive paradigm. Convenience sampling was used to select a whole class of 45 Grade 11 learners from one of the public non-fee-paying secondary schools in Capricorn District, Limpopo Province of South Africa. Group work presentations and classroom interactions were used to collect data. Data were analyzed using deductive thematic analysis guided by the mathematical connections’ framework. The findings indicated that learners managed to make procedural, meaning, reversibility, different representations, feature, and inclusion part whole as well as integrated connections as they worked on 2D trigonometric problems in an ABL environment. We established that learners did not make generalization part-whole connections. In addition, we found that some learners lacked mathematical connections skills and failed to solve the problems. Engaging learners in an ABL environment provided a fine-grained approach that allowed them to make mathematical connections. We, therefore, recommend that teachers should create an ABL environment to enable learners to make different types of mathematics connections during the teaching and learning of trigonometric concepts.

Interconnection of Mathematics and Dhuha Time

The interconnection of mathematics and religion can be done by looking at the interconnectedness of mathematics and the sunnah dhuha. The uniqueness of the sunnah dhuha, provides a challenge to see how mathematics is present in the initial determination of the dhuha time, to make it easier for humans to do. In this study, the library research method was used as a research method to see the mathematical interconnection with dhuha time. There are four steps carried out in the research, the first is data collection, the second is data reduction, third is display data, and fourt data analysis and interpretation. From the research that has been done, the mathematical concepts that exist in determining the timing of the dhuha prayer are the basic concepts of mathematical arithmetic operations (addition, subtraction, multiplication, and division), trigonometric concepts, basic concepts of geometry (acute angles), and the concept of calculating time. . In the initial calculation of the implementation of dhuha prayer, the concept of trigonometry (sin, cos, tan), the basic concepts of arithmetic operations, and the concept of calculating the amount of time used. The basic concept of geometry (an acute angle) is connected with the angle formed at the height of the sun at the beginning of the time of the dhuha prayer seen from the observer.

Implicit Misconceptions in Prospective Mathematics Teachers’ Reasoning About Trigonometric Concepts

The likelihood of misunderstanding and misrepresenting trigonometric ideas motivated an investigation of implicit misconceptions in prospective mathematics teachers’ reasoning about particular trigonometric concepts. To access the participants’ implicit misconceptions, a qualitative approach and case study design in particular were employed. Three prospective teachers chosen purposefully composed the sample. The student teachers majored in mathematics and were in the final year of training. Four diagnostic questions based on trigonometry were administered followed by semi-structured interviews. Qualitative analyses of calculations and interview transcripts revealed implicit misconceptions in participants’ reasoning. The prospective teachers reasoned that trigonometric equations can be resolved in the same way as conventional algebraic equations. Likewise, they demonstrated an erroneous notion that inverse trigonometric functions are evaluated just like indices. Besides, the participants incorrectly considered elements of domains of trigonometric functions to be synonymous with such functions’ extreme values. Overall, prospective teachers’ reasoning demonstrated didactical obstacles. It is therefore proposed that mathematics teacher education should include opportunities for prospective teachers to reason about mathematics concepts in a manner that prevents didactical obstacles. Furthermore, mathematics educators should engage in instructional practices which facilitate prospective teachers’ acquisition of in-depth understanding of mathematics conceptual relationships and differences.

Analysis of Senior High School Student’s Difficulty in Resolving Trigonometry Conceptual Problems

Trigonometry is one of the topics in mathematics in senior high school that must be studied and has an important effect in the development of students’ creative thinking skills, but in reality there are some difficulties experienced by students. This research focuses on analysis difficulty in resolving trigonometry conceptual problems among senior high school students in every creative thinking skills level. This research used a descriptive method aimed to identify the difficulties and cause of the difficulties experienced by five students. The difficulties are associated with concept of trigonometry and related problems. Data collection was done based on students’ work through test, interview, and observations. The results revealed that students’ difficulties in understanding the concept of trigonometry can be found at almost every level of creative thinking skills. The difficulty is identifying the application of trigonometric concepts in daily life and seeing the interrelationships between the problems given.

Trigonometric Concept of Fluoroscopy-Guided Percutaneous Renal Access.

Percutaneous nephrolithotomy is the standard surgical management of large renal calculi. Percutaneous renal access using the triangulation method has been an enigma for the endourologist to master and teach. This surgical conundrum is due to the uncertainty in the angle and depth required to puncture the target calyx. We describe a novel trigonometric method of renal access where both the angle and the depth of puncture are easily determined before the puncture.

A Lightweight Cryptographic Algorithm using Pseudo Stream Cipher and Trigonometric Technique with Dynamic Key

IoT (Internet of things) equipments is used heavily, but they are poor in security issue and security can be pierced. Also the message that the IoT device transmit is the main cause for their security lapse. that the IoT devices send may lead to the breach of users’ privacy. To make the communication secure between IoT nodes and servers, a lightweight cryptographic algorithm using pseudo stream and trigonometric function with dynamic key is proposed. This algorithm works in different phases, the first is mutual authentication followed by key synchronization and then a trigonometry function for encryption and decryption, with updation of key after specific time period. The algorithm assures that the IoT node will not be overloaded and the security is enhanced by reducing the chance of cryptanalysis. The mutual authentication, session key synchronization and updation of session key are completed through several encrypted communication. Here, the key length and update cycle are variable to prevent attack. We compare the security and performance for mutual authentication, with some light weight authentication scheme and performance of encryption algorithm are compared to other algorithm like Hill Cipher, RC4, RSA. According to analysis the proposed mutual authentication and secret key for session synchronization can provide more security features with low over head of communication which is suitable for protect communication security of IoT with limited resource and power. The encryption decryption algorithm provides better performance. Trigonometric concept is used in the design of encryption decryption algorithm.

Sinusoidal: An Exploration of Mathematics and Movement

Mathematic theory often takes place in two-dimensional forms. Whether hand-drawn graphs, or three-dimensional models on a screen, the presentation of the subject often lacks the length, breadth, and depth it deserves. Through four phases of research, I explored how one can model mathematic concepts through movement and music, both demonstrably and abstractly. I began my research by basing small dance/movement phrases in simple trigonometric concepts and giving my dancers tasks exploring related subjects. I then examined how other choreographers, both past and present, employed mathematic approaches in their work. To accompany my choreographic work and complete my project, I created a musical score using only single-tone sine wave frequencies. Finally, I interviewed my dancers, as well as other dancers and engineers, to understand how the piece was perceived as both a work of art and an informative display. Through my research, I hope to further the embodied and aesthetic understanding of applied simple and complex mathematic concepts.

The improvement of trigonometry ability through connected mathematics learning models and scientific approaches

The objectives of the study was to determine the effect of the connected math learning model with a scientific approach to the ability to understand the concept of trigonometry. This study is a quasi-experiment with a sample of 80 students of Class X Senior High School Bengkulu. This research instrument is a test of comprehension ability of trigonometric concepts. The analysis of data with Ancova. The result of the research were the ability to understand the concept of trigonometry of students taught by the learning model of connected mathematics is higher than students who are taught conventionally for students who learn through the scientific approach. The ability to understand the concept of trigonometry students taught by the connected mathematics learning model was lower than students who are taught conventionally for students who study without a scientific approach. The ability to understand the concept of trigonometry students who learn through a scientific approach was higher than students who learn without a scientific approach for students who are taught connected mathematics learning models. The ability to understand trigonometric concepts of students who learn through a scientific approach was lower than students who learn without a scientific approach for students taught with conventional learning.

Analysis of student’s error in resolving the Pythagoras problems

This study aims to describe the error made by students in solving Pythagoras questions, to analyse the factors that cause the students to make those errors, and to identify whether students are able to associate trigonometric concepts with Pythagoras. The subject of this study was the eleventh grade students of SMP Negeri 1 Yogyakarta Academic Year 2018/2019. There were 31 samples of students taken as the object of the research. The data collection used was a test. The classification of students’ errors type was done based on Newman process skill errors, inaccuracy, errors in understanding the questions’ intention and errors in the use of notation or misconception. The data analysis technique of the research was conducted through data reduction, data presentation and conclusion. The results showed that the errors percentage in the process was 38%. The less accurate percentage was 25%. The percentage of errors in understanding the intent of the problem was 10%. The percentage of errors in the use of notation was 15%. The percentage in misconception was 12%. The type of errors made by the students were: (1) students not know the meaning of symbols. (2) students not know the purpose of the question. (3) students not know the formula used in problem solving. (4) students cannot solve problems in the algorithm. (5) students cannot solve the problem according to the questions and some students are not able to associate the concept of pythagoras with trigonometry.

Analysis of Translation Understanding from Verbal to Visual on Trigonometry Concept

Constructing representations in the form of visualization can help students connect with problem situations and facilitate students' ability to communicate their understanding of the problem. This implies the ability to translate mathematical concepts. This research is a descriptive study that aims to describe the ability to translate trigonometric ideas from verbal forms to visual forms of students. This research was conducted at mathematics education of STKIP Santu Paulus Ruteng which involved 75 first-level students as a sample. The results of this study indicate that the students’ at the mathematics education department of STKIP Santu Paulus Ruteng, especially in the new semester, were mostly still capable of teaching the translation of trigonometric concepts from verbal to visual forms, some of which were at the PU level with a percentage of 35.2%. In the second level, 30.6% is in the PUSM, SU category, 17.6%, NU is 13.8% and SM is 2.8%. The results of this research can be used as references for high school teachers to find out their graduation profile in terms of translational skills and also input for lecturers to be able to adjust the lecture process based on the characteristics that have been produced

Meaning and Understanding of School Mathematical Concepts by Secondary Students: The Study of Sine and Cosine

Meaning and understanding are didactic notions appropriate to work on concept comprehension, curricular design, and knowledge assessment. This document aims to delve into the meaning of school mathematical concepts through their semantic analysis. This analysis is used to identify and establish the basic meaning of a mathematical concept and to value its understanding. To illustrate the study, we have chosen the trigonometric notions of sine and cosine of an angle. The work exemplifies some findings of an exploratory study carried out with high school students between 16 and 17 years of age; it collects the variety of emergent notions and elements related to the trigonometric concepts involved when answering on the categories of meaning which have been asked for. We gather the study data through a semantic questionnaire and analyze the responses using an established framework. The subjects provide a diversity of meanings, interpreted and structured by semantic categories. These meanings underline different understandings of the sine and cosine, according to the inferred themes, such as length, ratio, angle and the calculation of a magnitude.

TRIGONOMETRIC CONCEPTS: PRE-SERVICE TEACHERS’ PERCEPTIONS AND KNOWLEDGE

This paper explored pre-service teachers’ perceptions and knowledge of trigonometric concepts. Convenience sampling technique was used to select a sample of 119 (25 females, 94 males) second year science/mathematics pre-service teachers from two Colleges of Education in the Northern Region of Ghana. Trigonometry Perception Questionnaire (TPQ) and Trigonometry Assessment Test (TAT) were used to collect data on pre-service teachers’ perceptions and conceptual knowledge of trigonometry. Data were coded and keyed into Statistical Package for Service Solutions (SPSS version 20) and analysed using descriptive statistics. The results suggested that pre-service teachers perceived trigonometry as abstract, difficult and boring to learn; and had limited conceptual knowledge of basic trigonometric concepts. Consequently, more that 50% of them were unable to construct and reconstruct the appropriate mental structures for meaningful understanding to enable them respond to important basic trigonometry tasks. To achieve quality mathematics education, teacher educators must change their instructional practice and teach for understanding. Since understanding is the key to teacher’s instructional actions, processes and knowledge, we recommend teaching trigonometry for understanding during teacher preparation.

On problematic aspects in learning trigonometry

ABSTRACTIn this paper, research on some problematic aspects high school students have in learning trigonometry is presented. It is based on making sense of mathematics through perception, operation and reason in the case of trigonometry. We analyzed students' understanding of trigonometric concepts in the frame of triangle and circle trigonometry contexts, as well as the transition between these two contexts. In the conclusion, we present some new problematic aspects we noticed.The research was carried out with two groups of high school students, one of them at the beginning of their trigonometry learning (17 years old) and the other at the end of their high school education (19 years old). The students were given a questionnaire similar to that of Chin and Tall, and we analyzed the students' response. In our research, we noticed that students have difficulties with properties of periodicity and the fact that trigonometric functions are not one-to-one. In addition, there is poor understanding of radian measure and a lack of its connection to the unit circle.