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Heavenly mathematics
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught.Heavenly Mathematicstraces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.
Heavenly Mathematicsis illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
eBook
The feasibility of an Android-based pocketbook as mathematics learning media in senior high school
Learning media is a tool to deliver the materials to students during teaching and learning process and used as a source of learning like textbooks. However, textbooks are sometimes considered less practical and boring. The innovation that follows the technology advancement is undeniably needed. Nowadays, students are very creative using smartphones. The students' creativity should be supported for better learning. One of the efforts is making use of a smartphone or mobile technology as a learning media. This study aims to develop an Android-based learning media called Trigonometry app and evaluate the validity and practicality of the learning media. This learning media is expected to help students learn mathematics. This study used the ADDIE development model. The learning media was validated by six experts and tested by 95 respondents. The results show that the learning media met the valid criteria with kappa value ranged from 0.562 to 0.843. The learning media was also considered practical based on the responses from the users. 86.32% of the users stated that the learning media was excellent and best imaginable. Therefore, the learning media is declared valid and practical to use in the classroom. It is necessary to conduct further research to investigate the use of the media in the classroom and its impact on students' learning and teaching practices.
Journal Article
The Analysis of Student Error in Solve the Problem of Spherical Trigonometry Application
Students tend to memorize the concept of trigonometry given by lecturers or written in textbooks without understanding the purpose and content in solving the problem trigonometry, so that students often experience errors in solving the problem trigonometry. Error student in doing trigonometry problem is one of the clues to detect student difficulties. The failure is a form of deviation from the right, the prescribed procedure, or the deviation from the expected. This research type is descriptive qualitative, which aims to get information about mistakes of students of mathematics education semester 2 of trigonometry of Academic Year 2017/2018 Universitas Al Asyariah Mandar, in solving the problem of spherical trigonometric applications consisting of 2 questions, (1) determining the direction qibla; and (2) distance between 2 countries. The types of errors in solving the problems referred to in the study grouped according to the classification of Newman's faults namely, (1) the failure of process skills; (2) carelessness/inaccuracies; (3) misunderstanding of problems; (4) errors in the use of notation; and (5) misconceptions of concepts. The instrument used to reveal the type of error is a diagnostic test that contains two questions concerning the application of spherical trigonometry and interviews. After triangulation, the most common mistake made by the student is the misconception of the concept. Student made a mistake because of lack of understanding the correct concept in this case that is the analogy of Napier in solving the matter of calculating the distance between two countries and the spherical triangle formula to solve the problem calculate the direction of qibla.
Journal Article
New Formulae for Combined Spherical Triangles
Spherical trigonometry formulae are widely adopted to solve various navigation problems. However, these formulae only express the relationships between the sides and angles of a single spherical triangle. In fact, many problems may involve different types of spherical shapes. If we can develop the different formulae for specific spherical shapes, it will help us solve these problems directly. Thus, we propose two types of formulae for combined spherical triangles. The first set are the formulae of the divided spherical triangle, and the second set are the formulae of the spherical quadrilateral. By applying the formulae of the divided spherical triangle, waypoints on a great circle track can be obtained directly without finding the initial great circle course angle in advance. By applying the formulae of the spherical quadrilateral, the astronomical vessel position can be yielded directly from two celestial bodies, and the calculation process concept is easier to comprehend. The formulae we propose can not only be directly used to solve corresponding problems, but also expand the spherical trigonometry research field.
Journal Article
BLAST FROM THE PAST! THE RISE AND FALL OF HAND-HELD CALCULATORS IN MATH EDUCATION
Irvine considers how technology has changed over the years. By 1980, scientific calculators were widely used. Over the next 15 years, scientific calculators enabled teachers to ignore trigonometry tables and interest rate tables in textbooks; render calculations with logarithms obsolete; feature real-world problems with \"messy\" data in their teaching; and positively affect students who previously feared or hated extensive arithmetical computations. In 1998, as part of the revised math curriculum, the Ontario Ministry of Education placed a strong emphasis on investigations and real-world problems. To support this stance, the Ministry provided $100 million for learning materials (textbooks and technology). Many math departments used this money to purchase graphing calculators and related technologies. Graphing calculators became regular fixtures in math classrooms and saw extensive use by students in analyzing data. Students learned about correlation and regression analysis, and investigated problems that were of interest to them, while learning the math behind real-world issues.
Journal Article
Teachers' Trigonometric Meaning
In this paper, we present the analysis of an experience with high school teachers in Mexico, who worked in a problem-situation related to inaccessible distance calculation in the context of a teacher's training program. After we identified a linear meaning in the relationship between the angle and distance, we set as our goal to understand why this fact is presented. Under the framework of a conceptual framework that articulates cognitive, educational, and social construction of knowledge trigonometric elements, we analyzed the reports submitted by each teacher after the resolution of the problem-situation and some textbooks. We identified that this linear meaning emerges from the activities regulated by the school trigonometric discourse, and is immersed in a phenomenon we call arithmetization of trigonometry.
Journal Article
EXECUTIVE DIRECTORS' REFLECTIONS ON PRACTICE
Lynda and Fred Ferneyhough reflect on the practice of teaching mathematics. Teaching mathematics has always been a challenge. Over time, formats, curriculum and school environment change. The classroom is a vastly different world now than it was in 1976, and it seems that the demands on teachers have increased substantially. They also convey the events that made them believe about the unforeseen days ahead in teaching mathematics including the election of a government that has indicated its goal to do away with discovery math.
Journal Article
Tuning Out the World with Noise-Canceling Headphones
Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In this article the authors present a GeoGebra-based trigonometric function modeling task along with examples of student thinking from implementation with second year algebra students. The goal is to draw attention to the importance of context throughout the modeling process.
Journal Article