Academic literature on the topic 'Trigonometry textbooks'

http://dx.doi.org/10.5902/2179460X16491This work aims to present new activities for teaching trigonometry in Elementary Education. The idea is to show how to teach the main trigonometric relations through exercises that guide students, gradually, to conclusions of these trigonometry relations. The suggested activities make use of “GeoGebra ”software, a feature that enables the construction of trigonometric circles that facilitate the understanding by students. This paper presents not only the sine relations, cosine and tangent for acute angles, as it is usually proposed by textbooks 9th year of elementary school, but also relationships with secant, cosecant and cotangent, and it is not limited to acute angles and the study of right triangles, this leaving, the student more prepared for the challenges of high school and to their professional life.

How trigonometry is used and portrayed differently in mathematics and physics textbooks highlights potential sources for student struggle, constraints on our trigonometry curriculum, and lessons learned when looking across STEM disciplines.

Objectives In this study, the triangulation task actually used in the middle school class is analyzed from the perspective of the mathematical modelling tasks. Methods Various triangulation tasks were collected from middle school trigonometry textbooks and activity sheets produced and used by teachers, and classified based on whether connectivity and openness, which are the core characteristics of mathematical modelling tasks, were met, and cognitive activities required. Then, mathematical modelling tasks is selected from among the teacher-designed tasks, and the activities of the tasks and the interviews of the teachers in each mathematical modelling tasks are interpreted according to the mathematical modelling cycle. Results Teacher-designed tasks were found to have higher connectivity and openness than textbook tasks, including familiar material, offering practical and specific data, or insufficient data to solve the task. On the other hand, all tasks selected as mathematical modelling tasks among teacher-designed tasks emphasized simplifying, mathematising, and working mathematically, but relatively put less emphasis on understanding, interpretation, and validation. In particular, the process after working mathematically turned out to be limited to the extent of attaching units to the mathematical results, rounding it, or reviewing whether the calculation of the result were correct. In addition, all tasks used only the concept of tangent and did not require other concepts of trigonometric ratio. Conclusions Several examples of triangulation tasks can be found in Korean and foreign mathematical modelling studies. As such, mathematical modelling teaching/learning method is useful to teach trigonometry due to its usefulness in real life. According to the results of this paper, teachers want to design assignments rich in connectivity and openness so that students can recognize the usefulness of the concept of trigonometric ratio. Furthermore, if the various cognitive activities in the mathematical modelling cycle are evenly included, and various trigonometry tasks including various models are designed, it would lead more meaningful teaching and learning of mathematical modelling as well as trigonometry and ultimately it would help students improve problem-solving skills.

Although high school textbooks from early in the 20th century show that spherical trigonometry was still widely taught then, today very few mathematicians have any familiarity with the subject. The first thing to understand is that all six parts of a spherical triangle are really angles — see Figure 1.This shows a spherical triangle ABC on a sphere centred at O. The typical side is a = BC is a great circle arc from to that lies in the plane OBC; its length is the angle subtended at O. Similarly, the typical angle between the two sides AB and AC is the angle between the planes OAB and OAC.

This study aims to describe the level of creativity of questions in class X high school/vocational high school mathematics textbooks, the subject matter of the trigonometry series, and comparisons based on the creativity indicators of questions. The type of research used is descriptive qualitative. To ensure the credibility of the data, the researcher uses a triangulation method. The subject of this study were Competency Test questions in Mathematics Textbooks K13 curriculum, written by Dicky Susanto, Theja Kurniawan, Savitri K. Sihombing, Eunice Salim, Marianna Magdalena Radjawane, Ummy Salmah, Ambarsari Kusuma Wardani, published by the Center for Curriculum and Books (2021). Chapter Series Sequences and Trigonometry Comparisons of 10 questions. In this study, the level of creativity in these questions will be analyzed in stages based on the creativity indicators used in solving them. The results of this study are that the percentage of questions for each level of creativity is: Very Creative 0%, Creative 80%, Quite Creative 20%, Less Creative 0%, Not Creative 0%. From these results, it was found that the Competency Test questions contained in Class X SMA/SMK Mathematics Textbooks were written by Dicky Susanto, Theja Kurniawan, Savitri K. Sihombing, Eunice Salim, Marianna Magdalena Radjawane, Ummy Salmah, Ambarsari Kusuma Wardani, published by the Central Curriculum and Bookkeeping (2021) is Creative. Keywords: [Question Creativity Level; Creative Problem Indicators; Textbook Analysis]

Most trigonometry textbooks teach the graphing of polar equations as a two-step process: (1) plot the points corresponding to values of θ such as π, π/2, π/3, π/4, π/6, and so on; and then (2) connect these points with a curve that follows the behavior of the trigonometric function in the Cartesian plane. Many students have difficulty using this method to graph general polar curves. The difficulty seems to stem from an inability to convert changes in the value of the trigonometric equation as a function of angle (abscissa vs. ordinate in Cartesian coordinates) to changes of the radius as a function of angle (r[θ] in polar coordinates). GeoGebra provides a tool to help students visualize this relationship, thus significantly improving students' ability

AbstrakPenelitian ini bertujuan untuk mengembangkan bahan ajar berupa buku ajar matematika berbasis multiple intelligences pada materi trigonometri untuk meningkatkan kemampuan berpikir kritis siswa kelas X SMAN 3 Wajo dan mengetahui tingkat kevalidan, kepraktisan, dan keefetifannya. Jenis penelitian yang digunakan adalah Research & Development dengan mengacu pada model 4D yang terdiri dari Define, Design, Development dan Dissseminate. Produk yang dikembangkan berupa buku ajar berbasis multiple intelligences pada materi trigonometri yang diantaranya terdiri dari beberapa aspek multiple intelligences yaitu logis-matematis, visual-spasial, linguistik-verbal, interpersonal dan intrapersonal. Berdasarkan hasil ujicoba terbatas yang dilakukan, diperoleh bahwa (1) Buku ajar berbasis multiple intelligences dikembangkan dengan menggunakan model pengembangan 4D (define, design, development, dan disseminate), (2) Bahan ajar valid berdasarkan rata-rata penilaian hasil validasi buku ajar beserta instrumen lainnya adalah 4,17 dengan kategori sangat valid, (3) Praktis karena persentase rerata untuk respons siswa adalah 81,25% pada kategori positif dan persentase rerata respons guru adalah 92,50% pada kategori sangat positif, (4) Efektif karena rerata kemampuan guru dalam mengelola pembelajaran ialah 4,28 berada pada kategori baik, persentase rata-rata aktivitas siswa adalah 64,53% berada pada kategori baik, dan persentase ketuntasan belajar siswa berada pada kategori tinggi yaitu 80,65%. Sehingga pengembangan bahan ajar berbasis multiple intelligences pada materi trigonometri di kelas X SMAN 3 Wajo sudah memenuhi kriteria kevalidan, kepraktisan, dan keefektifan. AbstractThe study aims to develop teaching material in the form of mathematics textbook based on multiple intelligences in trigonometry material to improve critical thinking ability of class X students of SMAN 3 Wajo and to determine the level of validity, practicality, and effectiveness. The type of research used is Research and Development with reference to the 4D model which consists of Define, Design, Development, and Disseminate. The product developed is a textbook based on multiple intelligences on trigonometric material which includes several aspects of multiple intelligences, namely logical mathematical, visual-spatial, linguistic-verbal, interpersonal and intrapersonal. Based on the result of limited trials conducted, it was found that (1) Multiple intelligences based textbook were developed using the 4D development model (define, design, development, and disseminate), (2) Valid based on the average assessment of the validation results of the textbooks and other instruments is 4.17 in the very valid category, (3) Practical because the average percentage of student responses is 81.25% in the positive category and the average percentage of teacher response is 92.50% in the very positive category, (4) Effective because the teacher’s average ability in managing learning is 4.28 in the good category, the average percentage of student activity is 64.43% in the good category, and percentage of student learning completeness is in the high category, namely 80.65%. So, the development of teaching material based on multiple intelligences on trigonometric material in class X SMAN 3 Wajo has met the criteria of validity, practicality, and effectiveness.

After de1iving the law of sines, which is found in most trigonometry textbooks, use a visual representation to demonstrate that the relationship holds for numerical values. I have used the TI-92 calculator to accomplish this teaching strategy through demonstrations. lfTI-92s are available for classroom use, constructing and evaluating the ratios are better activities. Teachers could also use The Geometer's Sketchpad or Geometric Supposer.

Learning media is a help assistant for students to understand mathematics concept. Sometimes textbooks are very boring and not interesting therefore an innovation using a technology based media is needed. This research aims to make a learning media to improve students’ ability on the topic of trigonometry. The learning process will use hawgent dynamic mathematic software as a mathematics learning media. The problems that we are going to find out through this research are 1) can developing a learning media such as hawgent dynamic mathematic software improve students’ mathematical ability? and 2) did the student show a positive response in the learning process when using hawgent dynamic mathematic software? This research will use the ADDIE method. The target of this research are 30 high school students. The instruments use for this research are the cognitive test, interview and observation. According to the research result, there is an improvement in the students’ mathematical ability for trigonometry when using hawgent dynamic mathematic software. This means that the implementation of hawgent dynamic mathematic software in the learning process is successful. Students are more active and enthusiastic in class. In conclusion, developing hawgent dynamic mathematic software can improve the students’ mathematical ability in trigonometry as students’ show positive response when the learning process is helped by hawgent.

This article examines high school students' engagement in a set of trigonometry problems. Students completed this task independently in an online environment with access to Internet search engines, online textbooks, and YouTube videos. The findings imply that students have the resourcefulness to solve procedure-based mathematics problems in an online environment without formal instruction. This article suggests that self-directed online learning could be more effective for solving procedure-based problems than multi-step problems. Moreover, to be successful in online learning environments, students may need training to improve keyword searching skill and their ability to utilize various online learning tools.

This work establishes itself as objective analysis of the process of elaboration of the definitions of the trigonometric functions, particularly the definition of the cosine function. Thus, it is given a guideline regarding the development of a curriculum in which students are not sparked off the concept of trigonometric function based only on the triangle and trigonometric cycle. Therefore, the biggest challenge is to develop arguments for teaching about and investigate further the concepts of trigonometry. Thus, although we like the first chapter a brief explanation about the history of trigonometry, the work focuses on the development of the definition cosine of some forms, namely: the one presented in textbooks as it observes that it is made with support Euler function, setting via power series, the setting based on the exponential function domain in complex and, finally, setting as a solution of an initial value problem, that is, a differential equation that satisfies a given initial condition. From there will be an analysis of these definitions by observing the viability of each to be presented to high school students.
Neste trabalho, se estabelece como objetivo a análise do processo de elaboração das definiçõoes das funçõoes trigonométricas, particularmente, a definição da funçãao cosseno. Desse modo, é dada uma diretriz no que toca a elaboração de um currículo em que os alunos não fiquem ateados ao conceito de função trigonométrica apenas com base no triângulo retângulo e no ciclo trigonométrico. Portanto, o maior desafio é desenvolver argumentos didáticos para tal, bem como investigar mais detalhadamente as concepções da trigonometria. Com isso, apesar de termos como primeiro capítulo uma breve explanação sobre a história da trigonometria, o trabalho tem como foco o desenvolvimento da definição cosseno de algumas formas, sendo elas: a apresentada nos livros didáticos em que se observa que a mesma é feita com suporte da função de Euler, a definição através de séries de potências, a definição com base na função exponencial com domínio nos complexos e, por fim, a definição como solução de um problema de valor inicial, isto é, uma equação diferencial que satisfaz uma determinada condição inicial. A partir daí será feita uma análise dessas definições observando-se a viabilidade de cada uma delas ser apresentada para os alunos do Ensino Médio.

The purpose of this study was to compare the effectiveness of utilizing microcomputers with traditional, textbook-based classroom instruction for teaching the graphing of trigonometric functions in grade 12 algebra. The study was conducted over six teaching days in two phases. In phase one, the Microcomputer First group was given a classroom demonstration using a Macintosh microcomputer and the software program "Master Grapher". The students in this group then completed exercises in a microcomputer laboratory utilizing the same software program, working either individually or In pairs. The Textbook First group was given a traditional lesson and an assignment from a textbook. A researcher-developed test to assess comprehension of graphing trigonometric functions was administered to both groups on the third day. In phase two of the study, the treatments were reversed. A second posttest was administered on the third day of phase two. This permitted the comparison of the effectiveness of the order of the treatments: microcomputer followed by textbook Instruction with textbook followed by microcomputer Instruction. Posttest 1 and 2 scores were analyzed using an analysis of covariance, with an achievement score comprised of Algebra 12 test scores received prior to the experiment as the covariate. As well, Posttest 2 scores were analyzed using two covariates, the Algebra 12 test scores and Posttest 1 results, to determine the effect of the treatments. On posttest 1, the adjusted mean score of students in the Textbook First group was significantly higher (p ≤ .05) than the adjusted mean score of the students in the Microcomputer First group. The analysis of covariance using two covariates on posttest 2 indicated no statistically significant difference between the adjusted mean score of students in the Textbook First group who had just completed the microcomputer treatment, and the adjusted mean score of students in the Microcomputer First group who had just completed the textbook treatment. On posttest 2, the analysis of covariance using one covariate showed that the difference between the adjusted mean scores of the two groups was not statistically significant indicating that the order of treatment was not related to achievement. However, effect sizes of .86 for posttest 1 and .22 for posttest 2 indicated that in both phases, students completing the textbook treatment scored higher on the achievement tests than students completing the microcomputer treatment. When the data for both posttests were arranged according to gender, time of the day the class was taken, and whether the course was being repeated, no statistically significant relationships were detected. In conclusion: (a) traditional, textbook-based classroom teaching produced higher achievement scores on a test of graphing trigonometric relations than teaching which used a microcomputer and the software program "Master Grapher"; (b) student achievement was not affected by the order in which they were given the two treatments; and (c) there was no relationship between the treatment and factors of gender, time of day, and repetition of the course.
Education, Faculty of
Curriculum and Pedagogy (EDCP), Department of
Graduate

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This study discusses the pedagogical potentialities of the History of Mathematics in the textbooks of High School in the content of Trigonometry. It is important to analyze the historical passages in the content of Trigonometry in the textbooks of High School, from the categories of meanings proposed by Alencar (2014) and of the pedagogical potentialities of the History of Mathematics, pointed out by Miguel (1993), and to verify which of the pedagogical potentialities of the History of Mathematics identified in textbooks have the potential to be more effective for the teaching of mathematics. It is characterized as a research of a qualitative nature in order to ascertain aspects regarding the nature of the content and the objective of the historical passages, describing the fundamental characteristics that made it possible to classify them according to the pedagogical potentialities of the History of Mathematics. The data were constructed from the analysis of the historical passages in the content of Trigonometry in the six textbooks of mathematics of the second year of High School, approved by PNLD 2015. Before the analysis, we observe that the History of Mathematics is used as an accessory to the mathematical content. Most of the historical passages extol the contribution or discovery of an important personality in the History of Mathematics, revealing as a pedagogical potential the history as a source of motivation and objectives for teaching-learning of mathematics, which seems to be the least interesting Understanding of mathematical concepts. The potentialities that treat the History of Mathematics as didactic strategy were identified in a reduced portion of historical passages. These potentialities should be further explored, since they contribute to a change of perception in relation to mathematics, they enable the demystification of mathematics as an isolated and finished science, as they show the motivations and applications of mathematical concepts in history. Another aspect revealed is that, in consonance with the literature, the potentiality "History as an instrument in the formalization of mathematical concepts" (MIGUEL, 1993), as having the potential to be more effective for teaching mathematics, plays The role of transforming the student into an active subject, leading him to an understanding of the content and the formalization of mathematical concepts. We observed a certain interest in using the History of Mathematics in the textbooks analyzed. However, we realize that this use should focus more on the pedagogical potentialities that deal with the importance of a mathematical concept throughout history that inserts the History of Mathematics within a sociocultural, political and economic context, contributing to the teaching- Learning and for a change of perception regarding Mathematics. We conclude that in the process of choosing the textbook, the teacher needs, besides the evaluation criteria of the PNLD, to find out which collections approach the History of Mathematics as a didactic resource. Which collections reveal the historical development of the content, evidencing its origin, evolution and the different formalizations of the same concept over time.
Este estudo discute as potencialidades pedagógicas da História da Matemática nos livros didáticos do Ensino Médio no conteúdo de Trigonometria. Com o objetivo de analisar as passagens históricas no conteúdo de Trigonometria nos livros didáticos do Ensino Médio, a partir das categorias de sentidos propostas por Alencar (2014) e das potencialidades pedagógicas da História da Matemática, apontadas por Miguel (1993); verificar quais das potencialidades pedagógicas da História da Matemática identificadas nos livros didáticos têm o potencial de ser mais efetiva para o ensino da matemática. Caracteriza-se como uma pesquisa de natureza qualitativa com o intuito de aferir aspectos quanto à natureza do conteúdo veiculado e quanto ao objetivo das passagens históricas, descrevendo as características fundamentais que possibilitaram classificá-las de acordo com as potencialidades pedagógicas da História da Matemática. Os dados foram construídos a partir da análise das passagens históricas no conteúdo de Trigonometria nos seis livros didáticos de matemática do segundo ano do Ensino Médio, aprovados pelo PNLD 2015. Diante das análises, observamos que a História da Matemática é utilizada como acessório ao conteúdo matemático. A maioria das passagens históricas enaltece a contribuição ou descoberta de uma personalidade importante na História da Matemática, revelando como potencialidade pedagógica a história como fonte de motivação e de objetivos para o ensino-aprendizagem da matemática, que parece ser a potencialidade menos interessante do ponto de vista da compreensão de conceitos matemáticos. As potencialidades que tratam a História da Matemática como estratégia didática foram identificadas em uma parcela reduzida de passagens históricas. Essas potencialidades deveriam ser mais exploradas, visto que contribuem para uma mudança de percepção em relação à matemática, possibilitam a desmistificação da mesma como uma ciência isolada e acabada, à medida que mostram as motivações e aplicações de conceitos matemáticos na história. Outro aspecto desvelado consiste que, em consonância com a literatura, a potencialidade ―A história como um veiculado fundamentais e quanto que ao objetivo possibilitaram das passagens históricas, classificá-las descrevendo acordo as as de com instrumento na formalização de conceitos matemáticos” (MIGUEL, 1993), como a que tem potencial de ser mais efetiva para o ensino da matemática, por desempenhar o papel de transformar o aluno em um sujeito ativo, levando-o à compreensão do conteúdo e à formalização de conceitos matemáticos. Observamos um certo interesse em utilizar a História da Matemática nos livros didáticos analisados. Porém, percebemos que essa utilização deve centrar-se mais nas potencialidades pedagógicas que tratam da importância de um conceito matemático ao longo da história, que insere a História da Matemática dentro de um contexto sociocultural, político e econômico, contribuindo para o processo de ensino-aprendizagem e para uma mudança de percepção em relação à Matemática. Concluímos que no processo de escolha do livro didático, o professor precisa, além dos critérios de avaliação do PNLD, averiguar quais coleções abordam a História da Matemática como um recurso didático, que revelam o desenvolvimento histórico do conteúdo, evidenciando sua origem, evolução e as diferentes formalizações de um mesmo conceito ao longo do tempo.

This article examines high school students' engagement in a set of trigonometry problems. Students completed this task independently in an online environment with access to Internet search engines, online textbooks, and YouTube videos. The findings imply that students have the resourcefulness to solve procedure-based mathematics problems in an online environment without formal instruction. This article suggests that self-directed online learning could be more effective for solving procedure-based problems than multi-step problems. Moreover, to be successful in online learning environments, students may need training to improve keyword searching skill and their ability to utilize various online learning tools.

Abstract James Thomson Snr (1786–1849) is perhaps best known as the father of one of the most significant natural philosophers of the nineteen century; Lord Kelvin. Thomson was, however, an important mathematician and mathematical educator in his own right. In Belfast he taught both school and college level mathematics at the Belfast Academical Institution and wrote a number of successful textbooks on arithmetic, calculus, trigonometry, and geography. This chapter focuses on Thomson’s life and work in Belfast over the period 1814–1832, surveying the texts he wrote while there, and giving examples of the standard of mathematical teaching and examining in Belfast at the time.

Abstract Early modern navigators were required to pass examinations prior to being promoted. These were an important element of nautical training programmes, not only shaping classroom curricula and practices, but teaching mathematical techniques to diverse maritime communities from the sixteenth century onwards. Far from being monolithic, there were five distinct types of examination, each focused on a different skill. The earliest type comprised a hands-on demonstration of physical tools, including instruments, maps, and even knots. The second capacious category relied on traditional dialogues to help memorize information—about piloting, cosmography, and geography. The last type to be introduced, by the Dutch East India Company (VOC), required candidates to calculate numerical answers for the ship’s position. Evidence of these extremely influential examinations appears in textbooks, student manuscripts, and fill-in-the-blank tests through the end of the eighteenth century. This chapter analyses the relationship between practice tests and published manuals to trace how these examinations facilitated the understanding of arithmetic and geometry, trigonometry and tables, making an indelible impact on the decks of ships and beyond.

Abstract This chapter provides a description of the technical development of the drawing of Sundials between the fourteenth and the twentieth centuries. It covers the various types of dials, including horizontal, vertical, declining/inclining, table dials, and portable (pocket) dials It discusses the change from geometric to trigonometric methods. It tracks this change through a close analysis of the main textbooks written by mathematicians during these centuries, and it then provides examples of surviving dials. Next it examines the social and pedagogic uses of dials. Lastly it explores the wide variety of ingenious solutions found for the construction of these dials.