Khan Academy: Estrategia metodológica para el aprendizaje de las gráficas de funciones trigonométricas (original) (raw)
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Trigonometric Concepts: Pre-Service Teachers' Perceptions and Knowledge
Journal on Mathematics Education, 2018
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. Abstrak Penelitian ini mengeksplorasi persepsi dan pemahaman calon guru terhadap konsep trigonometri. Teknik convenience samping digunakan untuk memilih sampel sebanyak 119 calon guru sains/matematika tahun kedua (25 perempuan, 94 laki-laki) dari dua Sekolah Tinggi Pendidikan di Wilayah Utara Ghana. Trigonometry Perception Questionnaire (TPQ) dan Trigonometry Assessment Test (TAT) digunakan untuk mengumpulkan data tentang persepsi dan pengetahuan konseptual calon guru tentang trigonometri. Data dikodekan dan dimasukkan ke dalam Statistical Package for Service Solutions (SPSS versi 20) dan dianalisis menggunakan statistik deskriptif. Hasilnya menunjukkan bahwa calon guru menganggap trigonometri itu abstrak, sulit, dan membosankan untuk dipelajari; serta memiliki pengetahuan konseptual yang terbatas tentang konsep trigonometri dasar. Akibatnya, lebih dari 50% dari mereka tidak dapat membangun dan merekonstruksi struktur mental yang tepat untuk pemahaman yang bermakna sehingga memungkinkan mereka memberikan respon terhadap tugas trigonometri dasar yang penting. Untuk mencapai pendidikan matematika yang berkualitas, guru/pendidik harus mengubah kegiatan pembelajaran dan mengajar mereka agar mudah dipahami. Karena pemahaman adalah kunci untuk kegiatan pembelajaran, proses, dan pengetahuan guru, peneliti menyarankan untuk mengajar trigonometri dengan pemahaman konsep yang kuat selama program persiapan calon guru berlangsung.
Learners’ Graphical Efficacy When Solving Trigonometric Problems
MEJ (Mathematics Education Journal), 2023
This study explored grade 12 learners' graphical efficacy when solving problems involving trigonometric graphs. A structured test consisting of five trigonometric problems, with variations in context and structure, was administered to a purposefully selected group of 25 Grade 12 learners from the Sekhukhune District in South Africa. Insights into learners' graphing efficacy were obtained through task-based interviews. Data were analysed using direct interpretation which involved deductive thematic analysis of the task-based interviews and content analysis of the test scripts to match learners' responses to the themes drawn from the Meta-Representational Competence (MRC) framework. The results showed that most learners lack invention and functioning, critiquing and reflection efficacies and hence this affected their drawing and interpretation of the graphs and consequently lead to incorrect solutions. Furthermore, the results show most learners have critiquing efficacy. This indicates that learners lack graphical efficacy for solving trigonometric problems involving trigonometric functions. This finding has pedagogic implications: the apparent lack of graphical efficacy in graphical solutions may suggest inadequate mastery of the concept. Therefore, this study recommends that the teaching and learning of trigonometric graphs should consider the development of invention, functioning, critiquing and reflection efficacies.
Polya's Problem Solving Strategy in Trigonometry: An Analysis of Students
Mathematics and Statistics, 2021
This study is focused on investigating errors made by students and the various causal factors in working on trigonometry problems by applying sine and cosine rules. Samples were taken randomly from high school students. Data were collected in two ways, namely a written test that was referred to Polya's strategy and interviews with students who made mistakes. Students' errors were analyzed with the Newman concept. The results show that all types of errors occurred with a distribution of 3.83, 19.15, 24.74, 24.89 and 27.39% for reading errors (RE), comprehension error (CE), transformation errors (TE), process skill errors (PSE), and encoding errors (EE), respectively. The RE, CE, TE, PSE, and EE are marked by errors in reading symbols or important information, misunderstanding information and not understanding what is known and questioned, cannot change problems into mathematical models and also incorrectly use signs in arithmetic operations, student inaccuracies in the process of answering and also their lack of understanding in fraction operations, and the inability to deduce answers, respectively. An anomaly occurs because it turns out students who have medium trigonometry achievements make more mistakes than students who have low achievement.
LOS GRANDES INTERROGANTES DE LA EVALUACIÓN EN EDUCACIÓN FÍSICA
La evaluación no es una tarea fácil y mucho menos en nuestra área curricular de Educación Física. Por ello, ante la gran dificultad que puede plantear llevarla a cabo, hemos realizado el siguiente artículo con el fin de profundizar sobre los grandes interrogantes que giran en torno a su concepción. Para empezar, hemos querido partir del desconcierto terminológico que existe en torno a ella en la literatura bibliográfica, surgiéndonos preguntas como: ¿Qué entendemos por evaluar?, ¿Para qué y por qué evaluar?; interrogantes de carácter pedagógico, y ¿Qué, cómo, cuándo y a quién evaluar?; interrogantes de carácter técnico.
Mosharafa: Jurnal Pendidikan Matematika
AbstrakTujuan penelitian ini untuk mengetahui kesalahan yang dilakukan siswa yang memiliki gaya kognitif field dependent dan field Independent dalam menyelesaikan soal trigonometri berdasarkan prosedur Newman. Pendekatan yang digunakan adalah pendekatan kualitatif dengan jenis penelitian deskriptif. Pengumpulan data menggunakan tes GEFT (group embedded figure test), tes trigonometri, dan wawancara. Subjek penelitian ditentukan dengan purposive sampling dan dipertimbangkan berdasarkan beberapa kriteria, yaitu; (1) siswa berada pada kategori gaya kognitif field dependent atau field Independent , (2) siswa memiliki kemampuan komunikasi yang baik (berdasarkan informasi dari guru dan pengamatan dilapangan). Teknik analisis data dilakukan dengan tiga tahapan yaitu reduksi data, penyajian data, dan pembuktian serta penarikan kesimpulan. Hasil penelitian menunjukkan bahwa kesalahan siswa tertinggi pada kesalahan penarikan kesimpulan untuk siswa dengan jenis gaya kognitif yang berbeda. B...
Analysis of Students Mathematical Connection Errors in Trigonometric Identity Problem Solving
Periódico Tchê Química, 2020
A identidade trigonométrica é importante no aprendizado de matemática, porque exige que os alunos pensem crítica, lógica, sistematicamente e completamente. A resolução de problemas de identidade trigonométrica exige que os alunos relacionem conhecimento conceitual ou conhecimento processual, que depois é usado em perguntas. Este estudo envolveu alunos da série X do ensino médio, que foram examinados para descobrir os tipos de erros de conexão matemática e as causas dos erros. Antes das entrevistas baseadas em tarefas, 36 estudantes foram inicialmente submetidos a um teste. Com base em várias considerações, sete estudantes (três homens e quatro mulheres) foram selecionados para serem submetidos a uma entrevista baseada em tarefas. Esta pesquisa empregou um método qualitativo de pesquisa com desenho de estudo de caso. Os resultados da pesquisa indicam que os erros na conexão com o conhecimento conceitual são mais comumente o erro de conectar o conceito algébrico. Por outro lado, 86,11% dos estudantes experimentaram erros na conexão com o conhecimento processual. Esse erro ocorreu quando os alunos trabalharam em problemas com identidades trigonométricas que raramente encontravam em exercícios. Erros nas conexões matemáticas da identidade trigonométrica são causados pela falta de compreensão da operação aritmética algébrica, ênfase no conceito e conhecimento estratégico. Isso mostra que os alunos precisam de uma variedade de problemas para poderem dominar várias formas de identidades trigonométricas. O resultado desta pesquisa também reforça o importante papel dos conceitos algébricos como conhecimento prévio no estudo da identidade trigonométrica.
Phet Assisted Trigonometric Worksheet for Students’ Trigonometric Adaptive Thinking
Mosharafa: Jurnal Pendidikan Matematika
Fakta menunjukkan kesulitan dalam belajar geometri di universitas yaitu kesulitan menentukan fungsi Trigonometri untuk sudut negatif atau lebih besar dari 90 derajat, dan kesulitan menerjemahkan beberapa representasi fungsi Trigonometri. Masalah yang melibatkan kemampuan berpikir Trigonometri dapat diselesaikan dengan menampilkan perekayasaan informasi gambar, diagram atau animasi. Salah satu media dengan yang dapat menstimulasi berpikir Trigonometri adalah PhET Simulation. Media digital dapat menunjukkan performa yang lebih baik jika didukung lembar kerja untuk memandu proses pengikatan ilmu pengetahuan. Tujuan penelitian ini adalah bagaimana proses perancangan worksheet yang mengintegrasikan pemanfaatan media interaktif Phet Simulation. Penelitian pengembangan dijadikan sebagai pendekatan penelitian yang meliputi tiga bagian yakni problem and design solution analysis, product specification and development, serta prototype evaluation and limited test. Pengujian validator ahli memil...
Analysis of Students’ Difficulties in Solving Trigonometry Problems
Proceedings of the Proceedings of the 4th Progressive and Fun Education International Conference, Profunedu 2019, 6-8 August 2019, Makassar, Indonesia
This study aimed to describe the difficulties of students in solving math problems, especially in solving trigonometry questions.. The subjects of this study were freshmen majoring math program who had already taken trigonometry courses. The research type was qualitative descriptive research. Data collection tools were essay trigonometry tests, deep interviews and documentation. Data analysis techniques were carried out using document analysis techniques. The results show that the students have difficulty in understanding the information given to solve the problems. They do many errors in applying trigonometric concepts to answer the questions, because they do not calculate correctly the results of angle comparison. Besides, they incorrectly determine the angle of comparison between the angles obtained. Furthermore, the students were not familiar with the trigonometry questions because they were confused.This problem has hindered them from accomplishing the task in a given time.
Journal of Mathematics and Statistics Studies (JMSS), 2020
Shaped with Vygotsky’s Principle on Scaffolding, this study aimed to develop and validate learning materials known as Strategic Intervention Materials (SIMs) of the selected topics in Trigonometry in the STEM strand. This developmental study undertook three phases, namely: planning, development, and validation and guided by the ADDIE Model in the data analysis. In the planning stage, the least-mastered competencies (LMC) were selected based on the results of their final examination in Pre-Calculus in the field of Trigonometry. The researcher made two SIMs based on the identified (LMC). The second stage is the development of the materials that were presented and critiqued by the thesis adviser, students, colleagues, and SIM experts. In the last stage, the content and student validators validated the developed learning materials. The validators were purposively chosen. The adapted instrument was used in validating the materials. The developed SIMs were rated “excellent” by the content-validators and “more than adequate” by the student-validators. This implied that the content-validators considered the SIMs as teacher support materials that can be used to master the competencies in Pre-Calculus and learner enhancers to improve their competence as evaluated by the student-validators. The validation results of the two SIMs paved the way for the construction of the new learning material to confirm the findings and undergone validation were rated “excellent” and “more than adequate” by content and student validators respectively. It is recommended that teachers should develop more SIMs for other disciplines to address students’ difficulties in learning Trigonometry.
Article, 2023
The problem about learning in mathematics lies in the lack of application of teaching strategies for the resolution of the calculation in mathematical problems, problems of movement, mathematical regularity, equivalence, and uncertainty; in populations with difficulties to learn collaboratively. Here the application of mirror classes in populations with interactive problems is demonstrated, thus contributing to strengthening their knowledge from cooperative information management, the use of analysis skills based on co-evaluation. In this sense, the purpose of the study was to evaluate the mirror class, as a pedagogical strategy, in order to optimize the competence of solution of quantity problems in basic school students of two educational institutions in Lima, Peru. The study was conducted under the action research approach where the diagnostic and exit test, question guide and field diary were the instruments used for data collection. It was concluded that the mirror class as a pedagogical strategy favors the optimization of competition and solves quantity problems in basic education students. So, they also developed concrete knowledge, to assign them in cognition more enduringly as a form of social learning [El problema del aprendizaje en matemáticas radica en la falta de aplicación de estrategias de enseñanza para la resolución del cálculo en problemas matemáticos, problemas de movimiento, regularidad matemática, equivalencia e incertidumbre; en poblaciones con dificultades para aprender colaborativamente. Aquí se demuestra la aplicación de clases espejo en poblaciones con problemas interactivos, contribuyendo así a fortalecer sus conocimientos desde el manejo cooperativo de la información, el uso de habilidades de análisis basadas en la coevaluación. En este sentido, el propósito del estudio fue evaluar la clase espejo, como estrategia pedagógica, con el fin de optimizar la competencia de solución de problemas cuantitativos en estudiantes de educación básica de dos instituciones educativas de Lima, Perú. El estudio se realizó bajo el enfoque de investigación acción donde la prueba diagnóstica y de salida, la guía de preguntas y el diario de campo fueron los instrumentos utilizados para la recolección de datos. Se concluyó que la clase espejo como estrategia pedagógica favorece la optimización de la competencia y resuelve problemas de cantidad en estudiantes de educación básica. Así, también desarrollaron conocimientos concretos, para asignarlos en la cognición de forma más duradera como forma de aprendizaje social].