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1
Zhmud, Leonid. "What is Pythagorean in the Pseudo-Pythagorean Literature?" Philologus 163, no. 1 (May 29, 2019): 72–94. http://dx.doi.org/10.1515/phil-2018-0003.
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AbstractThis paper discusses continuity between ancient Pythagoreanism and the pseudo-Pythagorean writings, which began to appear after the end of the Pythagorean school ca. 350 BC. Relying on a combination of temporal, formal and substantial criteria, I divide Pseudopythagorica into three categories: 1) early Hellenistic writings (late fourth – late second centuries BC) ascribed to Pythagoras and his family members; 2) philosophical treatises written mostly, yet not exclusively, in pseudo-Doric from the turn of the first century BC under the names of real or fictional Pythagoreans; 3) writings attributed to Pythagoras and his relatives that continued to appear in the late Hellenistic and Imperial periods. I will argue that all three categories of pseudepigrapha contain astonishingly little that is authentically Pythagorean.
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Nurafni, Nurafni, Asih Miatun, and Hikmatul Khusna. "PROFIL PEMAHAMAN KONSEP TEOREMA PYTHAGORAS SISWA BERDASARKAN PERBEDAAN GAYA KOGNITIF FIELD INDEPENDENT DAN FIELD." KALAMATIKA Jurnal Pendidikan Matematika 3, no. 2 (October 31, 2018): 175–92. http://dx.doi.org/10.22236/kalamatika.vol3no2.2018pp175-192.
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This research is a descriptive qualitative approach which aims to describe profile of understanding of pythagoras theorem concept of students based on the difference of field independent and dependent cognitive style. The subjects of this study are 9th grade students of junior secondary school. Subject determination is done using GEFT instrument and mathematics teacher’s consultation, then continued by giving concept comprehension test on Pythagorean theorem material and interview. Checking the validity of data is done by time’s triangulation. The results showed that student: 1) states the meaning of Pythagoras's theorem given in his own language by noting Pythagorean theorem’s definition; 2) when using the concepts of Pythagoras theorem, students use triangle images as representations to facilitate an interpretation of given sides position. Then the students find the unknown values and use Pythagoras theorem to solve the problem; 3) using the necessary condition or sufficient condition of a concept to determine the area of a triangle using Pythagorean theorem by finding a side. While, the results for field independent cognitive style are student: 1) expresses the meaning of Pythagoras theorem by using their own language and mentioning the symbols; 2) using the concepts of Pythagorean theorem to solve the problem given by using multiplication operations to determine one of unknown sides. Then, student use pythagoras theorem to find the answer of the given problem; 3) using the necessary conditions or sufficient terms a concept of Pythagoras theorem by stating that it must be known two sides or not.
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Duarte, Carlos Lisboa, Hegildo Holanda Gonçalves, and Nádia Pinheiro Nobrega. "Tudo é número: uma análise conceitual da ideia de número em Pitágoras." Revista Principia - Divulgação Científica e Tecnológica do IFPB 1, no. 33 (May 16, 2017): 99. http://dx.doi.org/10.18265/1517-03062015v1n33p99-107.
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<p>This work is an analysis of the number concept based on the thoughts of Pythagoras, well as to seek an approximation of the historical reflections of the Pythagorean School in the Greek context of Classical Antiquity. The guiding objective of the study is to analyze the theory of the integers in the Pythagorean philosophy as ultimate cause of man and matter. From Methodological procedures point of view, the research was the bibliographical type, developed from already published material constituted, primarily, of books and journal articles through which we sought a dialogue with the developed studies concerning the subject in question. Through research it was reached the following findings: First, Pythagoras considered the number as the forming principle of the universe. However, he believed that the number constitutes the agreement between an indeterminate or unlimited element and another determinant or limiting and from there had been origin all things; Second, to the Pythagoreans the structure of numbers started from the assumption that in even numbers in even numbers predominates the indeterminate element and in the odd numbers the limiting element, for this reason they had the odd numbers as perfects, because in their distribution the odd numbers always had a limiting element. In sum, both Pythagoras as the Pythagoreans had in the cult of the number the basis of both his philosophy and his way of life.</p>
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Turenko, Vitalii. "VISION OF WOMEN IN CONTEXT APPEARANCES AND FUNCTIONING OF THE PYPHAGORIAN SCHOOL." Sophia. Human and Religious Studies Bulletin 16, no. 2 (2020): 54–57. http://dx.doi.org/10.17721/sophia.2020.16.11.
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The article, based on classical ancient sources and the most modern fundamental scientific works, explores and reveals the specifics of the existence of women in the early Greek philosophical school, founded by Pythagoras. There are three key reasons that led to the full existence of women along with men in the Pythagorean tradition: socio-political, doctrinal and vital. Accordingly, such a high status of women for the Pythagoreans is due not only to certain socio-political conditions of Greater Greece, or rather even the city of Croton, but also to the fact that the founder of this school, Pythagoras, unlike other early Greek thinkers, received philosophical knowledge from a woman, the Delphic Pythia Themistoclea. The doctrinal reason has been shown to be that Pythagoras himself preached the equality of women. If he had preached the opposite of the socio-political role of women in a given geographical region, he would not only not have been accepted, but even expelled. It is substantiated that the presence of women in this philosophical tradition is not a late Hellenistic fiction, but a real fact, based on the available sources of Aristotle's disciples – Dicaearchus and Aristoxenus, which testify to a rather ramified system of attracting women to the functioning of Pythagoreanism The proposed author's dichotomy of the representatives of this philosophical school known to us: pseudo-epigraphic and agraphic. Accordingly, the agraphic ones are known to us only by mentioning in certain ancient sources, while we know about the pseudo-epigraphic ones not only the names, but also preserved works and letters that are attributed to the Pythagorean thinkers.
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Farman, Farman, and Chairuddin Chairuddin. "PENGEMBANGAN MEDIA E-LEARNING BERBASIS EDMODO PADA MATERI TEOREMA PYTHAGORAS." AKSIOMA: Jurnal Program Studi Pendidikan Matematika 9, no. 4 (December 31, 2020): 872. http://dx.doi.org/10.24127/ajpm.v9i4.3114.
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Penelitian ini bertujuan untuk menyusun dan memperoleh media e-learning berbasis edmodo pada materi pythagoras yang valid, praktis dan efektif bagi peserta didik kelas VIII SMP-TQ Muadz Bin Jabal Kendari. Pembelajaran matematika berbasis e-learning menggunakan edmodo dipilih sebagai media alternatif dalam meningkatkan minat dan hasil belajar pada materi pythagoras. Pengembangan e-learning ini dikembangkan dengan model ADDIE yang terdiri atas beberapa langkah, yaitu: (1) analysis (2) design (3) development, (4) implementation dan (5) evaluation. Subyek uji coba dalam penelitian pengembangan ini adalah peserta didik Kelas VIII SMP Mu’adz Bin Jabal Kendari pada Tahun Ajaran 2019/2020 yang berjumlah 31 peserta didik.Uji kevalidan media pembelajaran digunakan lembar validasi dan untuk menguji keefektifan media pembelajaran digunakan angket respon peserta didik. Sedangkan uji keefektifan media pembelajaran digunakan tes hasil belajar materi teorema pythagoras. Berdasarkan penilaian oleh ahli dan pelaksanaan uji coba, diperoleh hasil bahwa media e-learning berbasis edmodo materi teorema Pythagoras memenuhi kriteria valid, praktis dan efektif. E-learning berbasis edmodo dapat dimanfaatkan untuk meningkatkan minat dan memfasilitasi pembelajaran interaktif yang mendukung pemahaman peserta didik SMP Kelas VIII pada materi Pythagoras. Abstract This study aims to compile and obtain edmodo-based e-learning media on pythagorean material which is valid, practical, and effective for grade VIII students of SMP-TQ Muadz Bin Jabal Kendari. E-learning based mathematics learning using edmodo was chosen as an alternative media in increasing interest and learning outcomes of Pythagorean material. This e-learning development is developed with the ADDIE model, which consists of several steps, namely: (1) analysis, (2) design, (3) development, (4) implementation, and (5) evaluation. The subjects in this development research were 31 students of grade VIII SMP Mu'adz Bin Jabal Kendari in the 2019/2020 academic year. The learning media's validity test used a validation sheet, and to test the effectiveness used student response questionnaire. At the same time, the test of the learning media's effectiveness used the learning outcomes test of the Pythagorean theorem. The experts' assessment and the implementation of trials found that the mathematics learning media of the Edmodo-based Pythagorean theorem met the valid, practical, and effective criteria. Edmodo-based e-learning can be used to increase interest and facilitate interactive learning that supports the understanding of grade VIII junior high school students on the pythagorean theorem material.
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Wares, Arsalan. "Pythagoras Meets Paper Folding." Mathematics Teacher 111, no. 5 (March 2018): 400. http://dx.doi.org/10.5951/mathteacher.111.5.0400.
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One of the most well-known theorems in mathematics, the Pythagorean theorem and its proof are a standard part of the school mathematics curriculum. The theorem is named for Pythagoras, a Greek mathematician and philosopher, born around 570 BCE. More than 400 proofs of the theorem exist, and this number continues to grow (Maor 2007). A future American president, James Garfield, generated an original proof five years before being elected; another proof is credited to twelve-year-old Einstein.
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Arifn, Muhammad Syamsul. "Misconceptions of student junior high school in Solving Pythagorean Theorem." MATHEdunesa 9, no. 2 (September 17, 2020): 461–67. http://dx.doi.org/10.26740/mathedunesa.v9n2.p461-467.
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The learning process in the classroom is said to be successful, if most students understand the concepts conveyed by the teacher. But, in the learning process, teacher found stundents has misconception. Misconceptions gotten by students, will affect students in the use of a concept between concepts in the mathematic. Identification misconception is one way to learning process get successful.
The purpose of this research was for describe the misconception and the solution of student’s misconception of class IX Junior High School 2 Sedati Sidoarjo at the solve the problem of Pythagorean Theorem. The qualitative research was used as form of this research, with the type of case study research. The data collection technique which was used were 1) Test methods, 2) interview method. The technique of data validation uses triangulation of method, by comparing test result data and interview. The results of this research can be showed as there were three types of misconceptions experienced by students that was classificational misconceptions, Correlational misconception, and Teoritical misconception; (1) students take types correlational misconception. The indicator is writing units incorrectly. Before learning about concept Pythagoras Theorem, students master about unit concept.; (2) students take types classification misconception. The indicator is students missing determine side figure two and three dimentional to Pythagoras Theorem. In this misconception, students difficult illustration skew right triangle.; (3) students take types teoritic misconceptioan. The indicator is students missing giving the reason of problem. In this misconception is about triple Pythagoras concept. Student determine triple Pythagoras with calculate not with concept giving as multiples or formulas. By knowing the description of misconceptions that occur in students, teachers take the steps of the learning process accurately so student do not misconceptions
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Lenz, Markus Alexander. "A Prophet of Divine Wisdom?—Giambattista Vico and the Construction of the Pythagorean Myth." Philological Encounters 5, no. 1 (March 9, 2020): 50–75. http://dx.doi.org/10.1163/24519197-12340069.
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Abstract In the nineteenth century, the reception of Giambattista Vico’s writings came along with nationalist interpretations of his Scienza Nuova as an ‘Italian Science’. This tendency was based upon an increased examination of the role that the philosopher Pythagoras and his Italian school of Croton played in Vico’s hierarchical conception of the ancient Greek and Italian civilizations. Writers, archaeologists and historians used the New Science as a metonymic reference work for their own nationalist concepts by updating the Pythagorean myth in accordance with relevant narratives of exclusive genealogies concerning an ancient Italian wisdom. These narratives follow tendencies in Vico’s own writings that were quoted strategically and mixed with further interpretations of the Scienza Nuova as reliable testimonial for a glorious Italian history. A theological poet characterized by deeper insight into the secrets of nature and some parts of the divine providence, Pythagoras gains his special position in Vico’s general conception of knowledge.
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Santacroce, Luigi, Ioannis Alexandros Charitos, Skender Topi, and Lucrezia Bottalico. "The Alcmaeon’s School of Croton: Philosophy and Science." Open Access Macedonian Journal of Medical Sciences 7, no. 3 (January 30, 2019): 500–503. http://dx.doi.org/10.3889/oamjms.2019.072.
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Among the first physicians and physiologists at the pre-Hippocratic medicine with contradictions and oscillating doctrines was Alcmaeon from Croton in the 6th century BC. For many, he shared as the father of scientific medicine. Unfortunately, we have only eighteen texts written for him and only five fragments of texts written by him. This saved extracts and testimonies they refer mostly to physiology, epistemology and psychology. Was born in the city of Croton (Κρότων) in Magna Graecia (southern Italy) was a reference point for the activity of physicians and philosophers over the years. Furthermore, Herodotus tells us about the excellent practice quality of the physicians, “compared to all the others known in that period”, among which Alcmaeon. But Croton is also famous as the centre of thought and activity of the philosopher Pythagoras of Samos (Πυθαγόρας ὁ Σάμιος, 580-500 BC) through his Pythagorean school around 530 BC.
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Ericksen, Donna, John Stasiuk, and Martha Frank. "Sharing Teaching Ideas: Bringing Pythagoras to Life." Mathematics Teacher 88, no. 9 (December 1995): 744–47. http://dx.doi.org/10.5951/mt.88.9.0744.
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The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) states that “[o]ne of the most important properties in geometry, the Pythagorean theorem, is introduced in the middle grades” (p. 113). Although the Standards document assigns much prominence to the Pythagorean theorem, our experience teaching at the university level has revealed that students know the theorem by name and can recite a2 + b2 = c2 but that they often cannot handle even simple computations using the formula. Students' experience with the Pythagorean theorem in high school needs to be broadened by their continually using the standard formula as well as applying the formula to geometric figures and special right triangles-in particular, the 30°-60°-90° and the 45°-45°-90° right triangles. The following game was developed to afford high school students more opportunity for practicing the formula in an engaging way. This game was created by the second author of the article, a high school classroom teacher, while he was a student in a class taught by another of the authors.
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Watson, Elaine K. "Pythagoras, Measurement, and the Geoboard." Teaching Children Mathematics 13, no. 7 (March 2007): 369–75. http://dx.doi.org/10.5951/tcm.13.7.0369.
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An elementary school principal, a former high school mathematics teacher, uses the geoboard in her work with a group of fifth–grade students. As the investigation of polygons progresses from symmetry to area to perimeter, hands–on applications of advanced mathematics topics such as the Pythagorean theorem and square roots emerge.
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Usyeldi, Usyeldi. "PENINGKATAN HASIL BELAJAR PESERTA DIDIK DENGAN MENGGUNAKAN MODEL PYTHAGORAS PADA MATA PELAJARAN MATEMATIKA DI KELAS VIII.1 SMP NEGERI 4 BASO." JURNAL EKSAKTA PENDIDIKAN (JEP) 1, no. 1 (September 11, 2017): 100. http://dx.doi.org/10.24036/jep/vol1-iss1/41.
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Mathematics instructional in Junior High School (SMPN) 4 Baso, Agam conducted through lecture method. The student-centered learning has not been performed at instructional. Most of students (60%) have not been mastered of mathematics. One of the efforts to improve learning outcomes is to use the Pythagorean model as a learning media. This research aims to improve the learning outcomes of students used the Pythagorean model of the Pythagorean Theorem. The research used classroom action research design. The research subjects were VIII.1 grade students of SMPN 4 Baso, Agam in the 2015/2016 academic year of 20 students. Data collection instrument were tests and observation sheet. The test was used to know the learning outcomes of students in each cycle. Observation sheet was used to determine the instructional process at each cycle. Data were analyzed with descriptive statistics. The results showed that: The average score of the students learning outcome in the first cycle of 66.5, the second cycle of 75.5 so that was increasing in the average score of the first cycle to the second cycle. Percentage of mastery learning of students in the first cycle of 60%, in the second cycle of 95%. Thus there was an improved of mastery learning of students from the first cycle to the second cycle. It can be concluded that the mathematics instructional by using Pythagoras models can improve to learning outcomes of students.
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Rusakov, Sergei Sergeevich. "Model of subjectivation in the philosophy of Pythagoreans." Философия и культура, no. 10 (October 2020): 50–57. http://dx.doi.org/10.7256/2454-0757.2020.10.33263.
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This article presents the analysis of the philosophy of Pythagoreans, dedicated to the search and conceptualization of the ideas of subjectivation. The goal of this research is to provide general characteristics to Pythagorean model of subjectivation, which was only partially described by M. Foucault in the writings on Ancient Greek “care of self’. The work employs the translated sources, in form of separate fragments of the compositions written by Pythagoreans, as well as a number of analytical works of Russian and foreign scholars. Considering the narrowness of available materials, the author does not intent to provide a comprehensive overview of the ideas of Pythagorean School, but emphasizes their special stance on subjectivity and personal becoming through a combination of spiritual practices. The scientific novelty consists in the attempt to describe the general ideas of Pythagoreans in the field of ethics, as well as formulate the Pythagorean model of subjectivation to fill the existing gams in M, Foucault’s works of later period. The following conclusions are formulated: it was established that not only ethical, but also political saturation of the history of Pythagoreanism is on par with the Socratian-Platonic model, characterized by Foucault as politically oriented (for example, thanks to analysis of “Alcibiades”); the four key techniques of self-care were derived and systematized; it was demonstrated that unlike Stoicism, Neo-Pythagoreanism did not adapt its doctrine in the field of ethics, and thus, did not receive due reflection in Hellenistic period of development of the “culture of self”.
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Guerrero, Carlos Rondero, Marcos Campos Nava, Agustín Alfredo Torres Rodríguez, and Juan Alberto Acosta Hernández. "Un Acercamiento A La Relación Pitagórica A Través Del Cálculo De Ternas." European Scientific Journal, ESJ 14, no. 6 (February 28, 2018): 58. http://dx.doi.org/10.19044/esj.2018.v14n6p58.
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The Pythagorean Theorem and more formally the Pythagorean Relationship (PR), is one of the most well-known and used results in the context of school mathematics, given that it is an axis of conceptual articulation between different areas of Mathematics. However, in the school context it is common for a Didactic Reductionism to be presented, only enunciating it and presenting the algebraic expression that relates the squares of the sides of a right triangle, leaving aside its great historical and epistemological significance. In view of this problem, this documentary research aims to design an alternative proposal to broaden the understanding of the Pythagorean Relationship, which is based on the calculation of Pythagorean Ternas. Three different methods are proposed to generate positive integers, that satisfy the Pythagorean Theorem and suggest questions that can guide learning activities to promote the understanding of some important elements within Mathematics, particularly in reference to the identification of numerical patterns.
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Beamer, James E. "Using Puzzles to Teach the Pythagorean Theorem." Mathematics Teacher 82, no. 5 (May 1989): 336–39. http://dx.doi.org/10.5951/mt.82.5.0336.
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One of the aims of a mathematics prog- gram is to familiarize the students with the Pythagorean theorem. The result, stated algebraically, is c2 = a2 + b2. Stated geometrically, the Pythagorean theorem refers to squares drawn on the three sides of a right triangle. The theorem states that the square drawn on the longest side has exactly the same area as that of the other two squares combined. Is it possible systematically to dissect the two smaller squares into pieces that will cover the larger square? The answer to this question is the focus of this article, which offers sugges-tions about how the Pythagorean theorem can be introduced to students in the middle school years. Enrichment challenges in the form of proofs suitable for high school geometry students are also included. Finally, three proofs of the Pythagorean theorem based on careful analysis of the puzzles are discussed. Senior high school students can be asked to prove that the pieces actually fit and to use this tessellation as a starting point to provide an alternative proof of the theorem.
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Divis, Danielle R., and Tyler Johnson. "Pythagoras, PVC Pipes, and Pianos." Mathematics Teacher: Learning and Teaching PK-12 114, no. 1 (January 2021): 47–54. http://dx.doi.org/10.5951/mtlt.2019.0385.
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This practitioner article describes a lesson carried out in a high school classroom at the conclusion of a unit on exponential growth. Two teachers use a series of music-related activities to engage students in using and connecting multiple representations of exponential growth while exploring musical frequencies on a piano.
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Wulandari, Lila, and Marchasan Lexbin Elvi Judah Riajanto. "Analisis Kesulitan Siswa SMP dalam Menyelesaikan Soal Materi Teorema Pythagoras." Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM) 3, no. 2 (April 30, 2020): 61. http://dx.doi.org/10.26740/jrpipm.v3n2.p61-67.
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Difficulties experienced by students in learning greatly affect the achievement of student learning outcomes. This study aims to describe the results of the identification of the types of difficulties and the causes of student difficulties when solving problems based on Polya stages. This type of research is descriptive qualitative with the instrument used in written tests. The subjects of the research were 36 students of class IX at SMP Negeri 9 Cimahi. Based on the analysis that has been done, it can be concluded that the difficulties experienced by junior high school students when completing the Pythagorean theorem questions in the school are 1) difficulty understanding the problem 100%, 2) difficulty planning the completion of 40%, 3) difficulty implementing the plan 54.4%, and 4) difficulty in re-checking 76.7%. The causes of difficulties include 1) students are not accustomed to writing things that are known and asked of a problem 2) students are not accustomed to drawing conclusions from a mathematical problem 3) Concept errors because students do not understand the concept of the material. So, it is necessary to improve the learning process that prioritizes learning concepts rather than memorizing. Students must be accustomed to solving the application problems of a material. So, students will be able to solve contextual problems related to the material.
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Yun, Jeong Oak, and Alfinio Flores. "The Pythagorean Theorem with Jelly Beans." Mathematics Teaching in the Middle School 14, no. 4 (November 2008): 202–7. http://dx.doi.org/10.5951/mtms.14.4.0202.
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principles and standards for school mathematics advocates an experimentation approach to middle-grades geometry study (nctm 2000). Students are asked to explore and examine a variety of geometric shapes and discover their characteristics and properties using hands-on materials. They also create inductive arguments about the pythagorean relationship. This empirical approach to the pythagorean theorem, for example, will lay the foundation for analytical proofs.
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Kerins, Bowen. "Delving Deeper: Gauss, Pythagoras, and Heron." Mathematics Teacher 96, no. 5 (May 2003): 350–57. http://dx.doi.org/10.5951/mt.96.5.0350.
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The Park City Mathematics Institute (PCMI) IS a three-week-long intensive mathematics experience for mathematicians of all levels. Each summer, it brings together high school and university mathematics educators, as well as researchers, undergraduates, and graduate students. In addition to a series of cross-program activities, each group has a specific program.
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Christensen, Evelyn B. "Pythagorean Triples Served for Supper." Mathematics Teaching in the Middle School 3, no. 1 (September 1997): 60–62. http://dx.doi.org/10.5951/mtms.3.1.0060.
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After an enjoyable, but exhausting, week of teaching, my family-myself, my husband, Ralph; and our children, Martin and Susan- sits down to Friday supper with that “let go” sense of relief that the weekend has finally arrived. As the meal begins, our eighth grader casually, with almost studied indifference, remarks, “I figured out a new math idea at school today.” Martin is an inquisitive, motivated student, but he is definitely very reserved.
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Egorochkin, Mikhail V. "Xenophanes and the Pythagoreans (D.L. IX, 20 = 21 A 1 DK)." ΣΧΟΛΗ. Ancient Philosophy and the Classical Tradition 15, no. 2 (2021): 643–67. http://dx.doi.org/10.25205/1995-4328-2021-15-2-643-667.
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According to Diogenes Laertius’ Lives of Eminent Philosophers, Xenophanes of Colophon, poet and philosopher of the 6th–5th centuries BC, was sold into slavery by the Pythagoreans Parmeniscus and Orestades (D.L. IX, 20 = 21 A 1 DK). This testimony has long been a source of concern to Hellenists, taking into account the high reputation that Pythagoras and his school gained in the history of European culture and philosophy. The paper provides a critical review of all the proposed corrections to the fragment in question. In the first part it considers conjectures and emendations made by the editors and translators Diogenes Laertius’ text since the Renaissance. Particular attention is paid to Ambrogio Traversari (1386–1439), the first translator of the Vitae philosophorum, whose translation already reveals a reluctance to follow the literal meaning of the testimony. The second part of the paper examines the restoration of the text proposed by Hermann Diels, which is still the most influential. The third part discusses the position of some modern scholars who, while refusing to correct the text of Diogenes Laertius, continue to suspect him to be mistaken. As a result, the paper shows that all corrections of Diogenes’ testimony, according to which Xenophanes was sold into slavery by the Pythagoreans, are vulnerable to criticism, and that consequently its literal reading may be correct.
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Ulandari, Nelpita, Rahmi Putri, Febria Ningsih, and Aan Putra. "Efektivitas Model Pembelajaran Inquiry terhadap Kemampuan Berpikir Kreatif Siswa pada Materi Teorema Pythagoras." Jurnal Cendekia : Jurnal Pendidikan Matematika 3, no. 2 (August 10, 2019): 227–37. http://dx.doi.org/10.31004/cendekia.v3i2.99.
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By the theory, the inquiry learning model can improve the students' mathematical creative thinking skills due to the students learn by themselves intensively, involved in the learning process directly and they can find and investigate any problems logically and systematically. This study aims to find out the inquiry learning process in the Pythagorean Theorem topic and its effectiveness to increase the sudents’ mathematical creative thinking skills. This research used the mixed method with sequential exploratory model. The population of this research is the VIII students of the state islamic junior high school (MTsN) 6 Kerinci. The VIII C and the VIII A of MTsN 6 Kerinci were selected as the experimental and the control group through random sampling technique. The data of learning process was obtained through observation and the data of students' mathematical creative thinking skills was obtained through the tests of mathematical creative thinking skills. The results of data analysis concluded that the inquiry learning model was effective to improve the students’ mathematical creative thinking skills.
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Booze, David A. "Delving Deeper: Visualizing Pythagorean Triples and Beyond." Mathematics Teacher 104, no. 5 (December 2010): 393–98. http://dx.doi.org/10.5951/mt.104.5.0393.
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Exploring the algebraic properties that form the framework for analytical generation of Pythagorean triples and quadruples is a challenging topic for high school algebra students. I have had considerable success in motivating my students to explore these properties by using a visual method. Students can use this visual method to find Pythagorean triples and quadruples easily and can capably and colorfully supply as many integer solutions as they desire to these well-known equations. Here I will present a visual method for producing integer solutions to the equations a2 + b2 = c2 and a2 + b2 + c2 = d2 and then develop an algebraic representation of this method.
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Booze, David A. "Delving Deeper: Visualizing Pythagorean Triples and Beyond." Mathematics Teacher 104, no. 5 (December 2010): 393–98. http://dx.doi.org/10.5951/mt.104.5.0393.
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Exploring the algebraic properties that form the framework for analytical generation of Pythagorean triples and quadruples is a challenging topic for high school algebra students. I have had considerable success in motivating my students to explore these properties by using a visual method. Students can use this visual method to find Pythagorean triples and quadruples easily and can capably and colorfully supply as many integer solutions as they desire to these well-known equations. Here I will present a visual method for producing integer solutions to the equations a2 + b2 = c2 and a2 + b2 + c2 = d2 and then develop an algebraic representation of this method.
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Rosmaiyadi, Rosmaiyadi, and Nurul Husna. "Ability of mathematical problem solving on junior high school students with field dependent cognitive learning style." Math Didactic: Jurnal Pendidikan Matematika 6, no. 2 (September 4, 2020): 198–211. http://dx.doi.org/10.33654/math.v6i2.917.
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Tujuan penelitian untuk mendeskripsikan kemampuan pemecahan masalah siswa dengan gaya kognitif field dependent, dan faktor yang mempengaruhi kemampuan belajar siswa pada materi Pythagoras. Jenis penelitian ini adalah penelitian deskriptif kualitatif. Instrumen utama dalam penelitian ini adalah peneliti sendiri dan didukung oleh instrumen tes, instrumen tes gaya kognitif dan pedoman wawancara. Subjek dalam penelitian ini adalah siswa yang berkemampuan matematika tinggi, sedang dan rendah yang masing-masing berjumlah dua orang. Data yang diperoleh dari penelitian dianalisis dengan menggunakan langkah reduksi data, penyajian data serta penarikan kesimpulan. Kesimpulan dari penelitian ini adalah: kemampuan pemecahan masalah siswa bergaya kognitif field dependent kelompok tinggi berkategori baik, siswa bergaya kognitif field dependent kelompok sedang dan kelompok rendah berkategori kurang baik pada tahap-tahap indikator kemampuan pemecahan masalah, faktor internal yang mempengaruhi kemampuan belajar siswa meliputi ketidakmampuan menemukan konsep, strategi yang tidak tepat, tidak mampu melakukan proses perhitungan dan menyelesaikan masalah, tidak memahami materi dengan baik, kurang paham terhadap konsep pythagoras, malas, serta tidak teliti, sedangkan faktor eksternal meliputi, alokasi waktu, kondisi kelas yang ribut, tidak sungguh-sungguh, bermain-main, dan mengobrol, sehingga hasil yang diperoleh kurang maksimal.
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Croton, Feano of, Mia of Croton, Melissa philosopher, Fintis of Spartan, Esara of Lucan, and Ptolemais of Cyrene. "Woman philosopher of the Pythagorean school about human nature and upbringing." Filosofiya osvity. Philosophy of Education 27, no. 1 (August 11, 2021): 239–60. http://dx.doi.org/10.31874/2309-1606-2021-27-1-14.
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The article offers academic translation into Ukrainian of a number of works by Pythagorean woman philosophers, which reveal the problems of human nature and personality education. The focus is on such pseudo-epigraphs of ancient woman thinkers as two letters by Theano of Crotone, letters of Miya of Crotone and Melissa, as well as treatises by Fintys of Sparta "On a woman prudence", Aesara of Lucania "On human nature" and excerpts from Porphyry’s "Pythagorean music" which contain fragments of the works of Ptolemais of Cyrene. The main themes of the above works and letters are the education of the individual in general, and women in particular. Accordingly, the basis of education should be an element of restraint and prudence in everything. If the child is brought up on this basis, he will be able to be strong and resilient during certain life situations. In the treatises of the Pythagorean women-philosophers it is noted that through the study of our own human nature (namely, the human soul) we can understand the philosophical foundations of natural law and morality. Therefore, a woman should use in her life not fleeting emotions and reactions to a particular event, situation, but also be moderate and prudent. These texts are significant in the context of understanding gender issues in the Hellenistic era. Based on the translated works, we can say that, according to thinkers, a number of virtues are common to both sexes (courage, justice and wisdom), moderation or abstinence are more common in women. At the same time, the limitation of the social role of women reflects an understanding of the nature of the female soul. Accordingly, the normative principle of harmony must be implemented in the context of the specific social roles allowed to women. At the same time, the availability of these texts indicates that philosophy is possible for both men and women, thus emphasizing the importance of involving the latter in knowledge and scientific knowledge.
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Tsai, Loh Seng. "Insightful Solution of a Geometry Problem with Instructional Cues: I. Group Experiments." Perceptual and Motor Skills 67, no. 3 (December 1988): 699–705. http://dx.doi.org/10.2466/pms.1988.67.3.699.
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The purpose was (1) to determine empirically the extent of insight exhibited by 429 high school and college students in solving a geometry problem directly solvable by insight without mathematical computations and (2) to study the effects of instructional cues and educational status. Educational status ranged from high school through college freshmen to upper-division students. Insightful solutions were achieved by about 4% of the participants under Condition I with no cues as a control, about 3% under Condition II where an unsolvable Pythagorean equation with two unknown sides was given, about 13% under Condition III giving a solvable Pythagorean equation with two sides of known lengths, and about 16% under Condition IV with an instructional cue that diagonals of a rectangle are equal. The last condition and the combined results suggest insightful solution increases with educational status. Two types of noninsightful responses were noted: empty or no answer and wrong response or incorrect approach through computations. The first type tends to increase, while the second to decrease from high school to college status probably due to a growing cautious deliberation with maturity and higher education. A training program on “the formation of insight sets” is proposed.
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Nurkhaeriyyah, Tsiyaab Sundus, Euis Eti Rohaeti, and Anik Yuliani. "ANALISIS KEMAMPUAN PENALARAN MATEMATIS SISWA MTS DI KABUPATEN CIANJUR PADA MATERI TEOREMA PYTHAGORAS." JPMI (Jurnal Pembelajaran Matematika Inovatif) 1, no. 5 (September 14, 2018): 827. http://dx.doi.org/10.22460/jpmi.v1i5.p827-836.
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This article is an analysis of the results of the test mathematical reasoning of grade IX students of Junior High School. The analysis focused to identify and recognize the qualities of difficulties experienced by students and to autheticate the mathematical reasoning level at the nineth grade students of junior high school in Kabupaten Cianjur. Qualitative descriptive is used as the research method. The samples brought for this research are 19 students of class IX in one of junior high school in Kabupaten Cianjur. Instrument test of reasoning ability of mathematic given as many as 6 items. The output of the analysis obtained based on written tests conducted is the degree of ability mathematical reasoning at students of junior high school in Kabupaten Cianjur is still classified low.
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Woodward, Ernest. "Soundoff: High School Geometry Should Be a Laboratory Course." Mathematics Teacher 83, no. 1 (January 1990): 4–5. http://dx.doi.org/10.5951/mt.83.1.0004.
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Present day instruction in geometry is ineffective. Results of the fourth mathematics assessment of the National Assessment of Educational Progress (NAEP) (Brown et al. 1988) indicate that fewer than half the eleventh-grade students who had taken geometry could apply the Pythagorean theorem in a routine problem and that fewer than a third of these students could find the perimeter of a rhombus drawn on grid paper. Eleventh-grade students who had taken geometry performed only slightly better on spatialvisualization tasks than eleventh-grade students who had not taken geometry.
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Peterson, Blake E. "The Back Page: Teaching the Pythagorean Theorem for Understanding." Mathematics Teacher 103, no. 2 (September 2009): 160. http://dx.doi.org/10.5951/mt.103.2.0160.
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One of my favorite lessons was developed not by me but by a group of student teachers. While conducting research on student teaching in mathematics classes at a Japanese junior high school, I observed a group of seven Japanese student teachers participate in a lesson study to develop a lesson on the Pythagorean theorem. The goal of the lesson was for the students to understand the meaning of the theorem. The student teachers looked in many textbooks, studied the different proofs of the theorem, and consulted their cooperating teachers.
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Peterson, Blake E. "The Back Page: Teaching the Pythagorean Theorem for Understanding." Mathematics Teacher 103, no. 2 (September 2009): 160. http://dx.doi.org/10.5951/mt.103.2.0160.
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One of my favorite lessons was developed not by me but by a group of student teachers. While conducting research on student teaching in mathematics classes at a Japanese junior high school, I observed a group of seven Japanese student teachers participate in a lesson study to develop a lesson on the Pythagorean theorem. The goal of the lesson was for the students to understand the meaning of the theorem. The student teachers looked in many textbooks, studied the different proofs of the theorem, and consulted their cooperating teachers.
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Leivas, José Carlos Pinto, and Anne Desconsi Hasselmann Bettin. "TEOREMA DE PITÁGORAS E O FRACTAL ÁRVORE PITAGÓRICA: UM EXPERIMENTO NO ENSINO FUNDAMENTAL." Cadernos de Educação Tecnologia e Sociedade 11, no. 3 (November 1, 2018): 444. http://dx.doi.org/10.14571/brajets.v11.n3.444-457.
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This article approaches a qualitative research that had as objective to use some notions of euclidean geometry of students of a nineth year of Elementary School to realize the need to know some aspects of fractal geometry to understand the world in which they live. As a teaching methodology was used Van Hiele Theory for the development of reasoning in geometry with the software Geogebra in the construction of the fractal Pythagorean Tree. The students realized activities of classification of geometric figures and elements of nature, that allowed them to group them in properties or characteristics in two geometries and, with exploration of the photography resource, it was possible, for example, to identify the self-similarity characteristic of the fractal objects. The results of the research showed the efficiency of the Van Hiele Theory and Geogebra in the understanding of properties of the two geometries, in particular, on the Pythagorean theorem.
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Reis, Jakson Ney da Costa. "FRACTAIS NO ENSINO MÉDIO: EXPLORANDO A ÁRVORE DE PITÁGORAS." Ciência e Natura 37 (August 7, 2015): 411. http://dx.doi.org/10.5902/2179460x14636.
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http://dx.doi.org/10.5902/2179460X14636Mathematics has its aesthetic beauty as one of the main attractions. There are times geometric patterns arouse the curiosity of many mathematicians. Is this universe Geometry that a subject is gaining more space, it is of Fractals. Working these fantastic structures in high school redeems the importance of showing this beauty in mathematics, in addition, the content is virtually forgotten by schools and almost always overlooked in the development of curricula. In this paper, we propose a brief analysis of the fractal known as Tree of Pythagoras, showing how you can work topics like Arithmetic and Geometric Progressions in order to arouse the curiosity of the student.
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Rachmawati, Ninda Sintyah, Junarti Junarti, and Anita Dewi Utami. "PELEVELAN MODEL MENTAL SISWA DALAM MEMAHAMI KONSEP TEOREMA PHYTAGORAS PADA SISWA SMP." Journal of Mathematics Education and Science 2, no. 2 (October 31, 2019): 97–106. http://dx.doi.org/10.32665/james.v2i2.102.
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A domain of learning, understanding is an absolute prerequisite for improving cognitive abilities. Leveling the mental model of students is one way in which a teacher can review the extent to which students understand based on their respective levels. The purpose of this study was to describe the six degrees of student's mental models in understanding the concept of using the Pythagoras theorem in junior high school students. The method used in this study is a qualitative research method. The subjects in this study amounted to 61 students who were a combination of 30 students of class VIII A and 31 students of class VIII B. The two classes of subjects were taken so that the six levels of the mental model were founded. The sixty-one items test questions were given. Each of the representatives of mental models who found the criteria was selected, namely two students to be interviewed so that 12 students were interview respondents. To ensure the validity of the data, researchers analyzed the data in two ways, namely data source triangulation and method triangulation. The results of the study showed a description of each level of the student's mental model in understanding the concept of using the Pythagoras theorem.
Suatudomain belajar, pemahaman merupakan prasyaratan mutlak untuk meningkatkankemampuankognitif. Pelevelan model mental siswa merupakan salah satu cara dimana seorang pengajar dapat meninjau sejauh manakah pemahaman siswa berdasarkan tingkatan masing – masing. Tujuan penelitian ini adalah untuk mendeskripsikan enam level model mental siswa dalam memahami konsep penggunaan teorema pythagoras pada siswa SMP. Metode yang digunakan dalam penelitian ini adalah metode penelitian kualitatif. Subjek dalam penelitian ini berjumlah 61 siswa yang merupakan gabungan dari 30 siswa kelas VIII A dan 31 siswa kelas VIII B. Dua kelas subjek tersebut diambil agar terpenuhi keenam level model mental. Keenam puluh satu subjek tersebut diberikan soal tes, kemudian dipilih masing – masing dari perwakilan model mental yang telah memenuhi kriteria yaitu 2 siswa untuk diwawancarai. Sehingga terdapat 12 siswa yang menjadi respondenwawancara. Untuk memastikan kevalidan data, peneliti menganalisis data dengan dua cara yaitu triangulasi sumber data dan triangulasi metode. Hasil penelitian menunjukkan deskripsi masing - masinglevel model mental siswa dalam memahami konsep penggunaan teorema pythagoras.
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Turenko, Vitalii. "Upbringing and education of children in context letters of Pythagorean woman philosophers." Filosofiya osvity. Philosophy of Education 27, no. 1 (August 11, 2021): 228–38. http://dx.doi.org/10.31874/2309-1606-2021-27-1-13.
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The article reveals in detail the understanding of raising children in the context of two pseudo-epigraphic letters of Pythagorean wonan thinkers – Theano and Myia of Crotone. Based on these letters, it was found that pedagogical issues were important in general for the whole Pythagorean tradition. In fact, we can say that this early Greek philosophical school was the first to systematically and comprehensively approach the problem of upbringing and education in ancient society. It is hypothesized that this topic is not accidentally in the center of attention of these philosophers, because their authority was the greatest among all other representatives of this philosophical school. The author’s position is proved that Theano of Crotone letter to Eubule focuses on moderation in education, which is aimed at avoiding luxury, fulfilling all children’s whims, comfort. This is the purpose of hardening in difficult circumstances in order to withstand with dignity all the potential difficulties of adult life. Accordingly, if you do not raise a child in certain restrictions, then, according to Theano, it may well be unprepared for certain trials that may occur. The thesis is substantiated that the key task of upbringing and education, according to Myia of Crotone letter, is moderation, prudence and balance, which is based on both archaic elements and Hellenistic plots, which testifies to the skill of writing this letter. It is revealed that the Pythagorean principles of education, according to both philosophers, have no gender difference. This is because both girls and boys, if they grow up in luxury, comfort and do not know the limitations, can potentially become dangerous both for themselves and for society as a whole. It is emphasized that according to the style of writing, these letters are not so much moral and ethical as paraenetic epistolary genre, ie they act as advice on the upbringing and education of the younger generation. Because of this, these letters are such sources of ancient culture, which are one of the few that are devoted to the philosophical understanding of upbringing and education.
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Andriawan, Angga, Asti Sari Setiawati, Indah Puspita Sari, and Siti Chotimah. "ANALISIS KEMAMPUAN BERPIKIR KRITIS MATEMATIS SISWA SMP PADA MATERI PYTHAGORAS." JPMI (Jurnal Pembelajaran Matematika Inovatif) 1, no. 4 (July 10, 2018): 559. http://dx.doi.org/10.22460/jpmi.v1i4.p559-568.
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This study aims to analyze the critical thinking skills of junior high school students on Pythagoras material. Subjects in this study are students of class VIII-F in SMP Negeri 1 Ngamprah with the number of students 37 people. The method used in this research is qualitative descriptive. This type is chosen because it aims to describe the skills of students in solving problems of mathematical critical thinking independently. The research phase is divided into three, namely planning, implementation, and reporting. The technique of collecting data in the form of test. Data analysis techniques based on indicators of mathematical critical thinking skills that has been determined by researchers include: (1) identifying the concepts used in problem solving, (2) formulating an action (strategy, tactics, or approach) in solving problems, (3) providing arguments or reasons for answering and solving problems, and (4) evaluating evidence or decisions taken in solving the problem. The results obtained quantitatively show that the level of mathematical critical thinking skills of students in SMP Negeri 1 Ngamprah in solving the problems on Pythagoras material still falls into the low category. The evidence from the percentage of each indicator with the highest rate of only 61%. Some factors influence the level of students critical thinking skills, including the preparation of incomplete and appropriate strategies, provide arguments without showing the truth, and the students' accuracy in working on the questions.
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Wijayanti, P., and A. N. Hidayanti. "Proving the Pythagorean Theorem to Junior High School students through the Asian method." Journal of Physics: Conference Series 1417 (December 2019): 012060. http://dx.doi.org/10.1088/1742-6596/1417/1/012060.
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Prevost, Fernand J. "Activities: The Conic Sections in Taxicab Geometry: Some Investigations for High School Students." Mathematics Teacher 91, no. 4 (April 1998): 304–41. http://dx.doi.org/10.5951/mt.91.4.0304.
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The urban world in which many of us live does not lend itself to the metric of Euclidean geometry. Assuming that the avenues are perpendicular to the streets in a city, the distance from “fifth and fifty-first” to “seventh and thirty-fourth” is not the familiar Euclidean distance found by applying the Pythagorean theorem. The distance must instead be measured in blocks from fifth to seventh avenues and then from fifty-first to thirty-fourth streets. This taxicab metric, one of several me tries used in mathematics (Eisenberg and Khabbaz 1992), is practical for many applications and helps students pursue interesting investigations while deepening their understanding of familiar topics.
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Hutapea, Maya L., Didi Suryadi, and Elah Nurlaelah. "ANALYSIS OF STUDENTS’ EPISTEMOLOGICAL OBSTACLES ON THE SUBJECT OF PYTHAGOREAN THEOREM." Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam 20, no. 1 (February 16, 2015): 1. http://dx.doi.org/10.18269/jpmipa.v20i1.555.
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This article explains mistakes made by junior high school students in solving Pythagorean Theorem problems as well as analysis of students’ difficulties in applying mathematical concepts (epistemological obstacles), in which these were reflected in their test answers. This research used descriptive exploratory method to describe symptom and phenomena, which occurs within the students’ mind while solving the problem. Data were obtained from a test of Pythagorean Theorem problems given to 99 students from three different schools clusters. Results suggested that students tends to use a quick way to solve the problems without adequate understanding of the concept, remember the term alone without a profound understanding of the concept, fail in solving the problems with implicit information and the problem that requires visual representation in the process of solving the problem. Students also did not like the word problems or a problem with long questions. Teachers play a pivotal role in helping the students to overcome epistemological obstacles such as by giving the students more exercises as well as using different tools and technique in teaching the concept.Keywords: learning obstacles, epistemological obstacles, pythagorean theoremABSTRAKArtikel ini menyajikan kesalahan yang dilakukan oleh siswa sekolah menengah pertama dalam menyelesaikan soal-soal terkait teorema phytagoras dan juga analisis mengenai kesulitan siswa dalam mengaplikasikan konsep matematik (epistemological obstacle). Kesalahan-kesalahan ini dapat dilihat dari jawaban yang diberikan siswa pada tes yang diberikan. Penelitian ini menggunakan pendekatan deskriptif untuk menjelaskan fenomena yang terjadi pada siswa dalam menyelesaikan soal-soal terkait teorema Phytagoras. Data yang diperoleh pada penelitian ini berasal dari hasil tes soal-soal Teorema phytagoras yang diberikan pada 99 siswa dari tiga cluster sekolah yang berbeda. Hasil analisis menunjukkan bahwa siswa cenderung menggunakan cara cepat untuk menyelesaikan persoalan tanpa memahami konsep, mengingat rumus secara utuh tanpa pemahaman yang mendalam terkait konsep phytagoras, gagal menyelesaikan soal yang memuat informasi yang implisit dan soal yang memuat informasi yang disajikan secara visual. Hasil wawancara menunjukkan bahwa siswa tidak suka soal cerita dan soal yang disajikan secara panjang lebar. Guru memainkan peran yang sangat penting dalam membantu siswa untuk mengatasi epistemological obstacle seperti dengan memberikan siswa latihan soal serta menggunakan berbagai media dan teknik pengajaran dalam mengajarkan konsep.Kata kunci: kesulitan belajar, kesulitan epistemologis, teorema phytagoras
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McDaniel, Michael. "Sharing Teaching Ideas: Not Just Another Theorem: A Cultural and Historical Event." Mathematics Teacher 96, no. 4 (April 2003): 282–84. http://dx.doi.org/10.5951/mt.96.4.0282.
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The typical student rarely gets a chance to hold an old, powerful piece of history. In mathematics, teachers have the opportunity to present just such museum pieces; and furthermore, the class can verify their truth. Too often, however, students cringe in the face of proof and thus miss their chance to appreciate the treasure. Mathematics teachers can impress these future doctors, lawyers, politicians, and journalists with some jewels of mathematics; and teachers do mathematics a disservice if they skimp on the presentation. Since students and teachers have the time, the intelligence, and the materials to demonstrate the validity of a theorem, they should take advantage of this opportunity and privilege. Significant results in the history of thought that students can understand should be occasions for great drama. The high school mathematics sequence includes proofs of the quadratic formula, the Pythagorean theorem, the fundamental theorem of integral calculus, and other results. In this article, I suggest rolling out the red carpet for the proof of an important theorem. I focus on the Pythagorean theorem; the interested reader can easily adapt the treatment to any theorem that is worthy of unusual notice.
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McDaniel, Michael. "Sharing Teaching Ideas: Not Just Another Theorem: A Cultural and Historical Event." Mathematics Teacher 96, no. 4 (April 2003): 282–84. http://dx.doi.org/10.5951/mt.96.4.0282.
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The typical student rarely gets a chance to hold an old, powerful piece of history. In mathematics, teachers have the opportunity to present just such museum pieces; and furthermore, the class can verify their truth. Too often, however, students cringe in the face of proof and thus miss their chance to appreciate the treasure. Mathematics teachers can impress these future doctors, lawyers, politicians, and journalists with some jewels of mathematics; and teachers do mathematics a disservice if they skimp on the presentation. Since students and teachers have the time, the intelligence, and the materials to demonstrate the validity of a theorem, they should take advantage of this opportunity and privilege. Significant results in the history of thought that students can understand should be occasions for great drama. The high school mathematics sequence includes proofs of the quadratic formula, the Pythagorean theorem, the fundamental theorem of integral calculus, and other results. In this article, I suggest rolling out the red carpet for the proof of an important theorem. I focus on the Pythagorean theorem; the interested reader can easily adapt the treatment to any theorem that is worthy of unusual notice.
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Rezende, Veridiana, Mariana Moran, Thais Michele Mártires, and Fabricia Carvalho Paixão. "O Fractal Árvore Pitagórica e Diferentes Representações: uma Investigação com Alunos do Ensino Médio." Jornal Internacional de Estudos em Educação Matemática 11, no. 2 (September 11, 2018): 160. http://dx.doi.org/10.17921/2176-5634.2018v11n2p160-171.
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A Geometria dos Fractais em sala de aula propicia diversas possibilidades de estudos de conceitos matemáticos, incentiva o uso de recursos tecnológicos, proporciona surpresas pela beleza e complexidade dos fractais. Apresentamos neste texto uma investigação acerca das possibilidades do uso de diferentes registros de representação semiótica aliado à Geometria dos Fractais, no que concerne ao ensino de matemática. E, para exemplificar estas possibilidades em sala de aula, relatamos uma situação de ensino, que foi implementada com quinze (15) alunos do 3º ano do Ensino Médio de uma escola pública do interior do Paraná, relacionada à construção do fractal Árvore Pitagórica. Como procedimentos metodológicos elaboramos cinco tarefas associadas ao fractal Árvore Pitagórica que tiveram por finalidade explorar diversos conceitos matemáticos emergidos no processo de construção deste fractal, nas quais foram contempladas as representações figural, numérica, algébrica e linguagem natural. As análises dos registros mostram que a implementação das tarefas possibilitou aos alunos: o estudo de diversos elementos matemáticos tais como: áreas e perímetros de quadrados e triângulos, teorema de Pitágoras, ângulos, congruência de triângulos, frações, potências, números decimais entre outros; as construções figurais da Árvore Pitagórica por meio de diferentes representações e a visualização das principais características de um fractal, bem como a compreensão de seu processo de construção.Palavras-chave: Ensino de Matemática. Representação Semiótica. Geometria dos Fractais.AbstractThe geometry of the fractures in the classroom provides several possibilities for studying mathematical concepts, encourages the use of technological resources, provides surprises for the beauty and complexity of the fractals. We present in this text an investigation about the possibilities of the use of different registers of semiotic representation allied to the Geometry of the Fractais, in what concerns the teaching of mathematics. And, to exemplify these possibilities in the classroom, we report a teaching situation, which was implemented with fifteen (15) students of the 3rd year of High School in a public school in the interior of Paraná, related to the construction of the Pythagorean Tree fractal. As methodological procedures we elaborated five tasks associated to the fractal Pythagorean Tree that had as purpose to explore several mathematical concepts emerged in the process of construction of this fractal, in which figural, numerical, algebraic and natural language representations were contemplated. The analysis of the registers shows that the implementation of the tasks enabled the students to study several mathematical elements such as: areas and perimeters of squares and triangles, Pythagorean theorem, angles, congruence of triangles, fractions, powers, decimals, among others; the figurative constructions of the Pythagorean Tree by means of different representations and the visualization of the main characteristics of a fractal, as well as the understanding of its process of construction.Keywords: Mathematics Teaching. Semiotic Representation. Geometry of Fractions.
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Alkholy, Inas. "The Presence of Secular Books: In Raphael’s Fresco: The School of Athens." Comparative Islamic Studies 2, no. 1 (March 18, 2008): 51–65. http://dx.doi.org/10.1558/cis.v2i1.51.
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This paper studies the presence of the secular book in visual art during the Italian Renaissance. It is the age of humanism, in which the image of the book was changed to be a symbol of secular knowledge. For more than twelve centuries, the book was present in art to represent the Holy Bible. It was utilized in Early Christian, Byzantine and Medieval art to show the sacred principles and the power of the church in people’s lives.
Although the Arabs began translating the classical works of Plato, Aristotle and others as early as the eighth century, their role in European Renaissance is rarely mentioned in art history sources.
The paper discusses Raphael’s fresco The School of Athens that shows a great concern on humanism and education from multi-cultured sources. Raphael represents Plato, Aristotle, Socrates, Euclid, Pythagoras and Ibn Rushd, the Muslim philosopher and physician. This fresco is an official and historical gratitude to all minds, which enlightened Europe and affected civilizations.
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Kneller, Shmuel. "My way of teaching mathematics in a social context (in junior high school)." Gifted Education International 28, no. 2 (April 18, 2012): 171–75. http://dx.doi.org/10.1177/0261429411434989.
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This article is not comprehensive. It aims at encouraging all teachers of mathematics ‘to look behind the subject matter’ and to probe what educational values it contains. More examples can easily be found. Suffice it to say that when Pythagoras proved his famous theorem, mankind ‘discovered’ that the square root of 2 is an irrational number. The fact that you cannot write its exact value as a decimal fraction gave people at that time the feeling that they had ‘lost control of their fate’. ‘Friendly’ and ‘perfect’ numbers were created at that time to ward off the doom. Similar feelings of despair followed the recognition that the Earth is not the center of the universe and the use of the atom bomb. All three events in the history of science even led to mass suicides. The examples given above call upon all educators to use the subject matter to enrich social understanding and to help youngsters to build a healthier society.
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Ali, Ibnu. "Dua Mazhab Emanasi dalam Filsafat Islam Klasik dan Implikasi Teologisnya." Maraji: Jurnal Ilmu Keislaman 3, no. 1 (September 1, 2016): 55–79. http://dx.doi.org/10.36835/maraji.v3i1.62.
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Islamic philosophy, which has been an accumulation of relation between pure logic and religious texts (naql), has a uniquely different features from the philosophy of Aristotle. This is because the Islamic philosophy has met not only with the pre-Islamic sciences but it also has thoroughly interacted with various branches of the Islamic knowledge such as theology, taṣawwuf, uṣûl al-fiqh, and târîkh al-tashrîʻ. The interaction has resulted in numerous different thoughts within the Islamic philosophy itself as can be identified among the peripatetic Islamic philosophers. The article is intended to describe that in discussing cosmological matter, the majority of these philosophers put emphasis on Plotinus’s concept of emanation. However, the concept has led to distinctively diverse schools of philosophy in Islam. The study finds that the philoso-phers with strong background of scientific disciplines produced considerably different thought of emanation from those with strong background of Islamic knowledge. The first school consists of scientists-philosophers affiliated to the thought of Pythagoras, Plato, and Aristotle though with new concepts they proposed. The second school comprises Sufi-philosophers whose concepts have been strongly influenced by intuition though there have been conceptual differences based on their spiritual experiences.
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Rocha, Mariana, and Pierpaolo Dondio. "Effects of a videogame in math performance and anxiety in primary school." International Journal of Serious Games 8, no. 3 (September 17, 2021): 45–70. http://dx.doi.org/10.17083/ijsg.v8i3.434.
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The present paper describes the design and evaluation of a videogame developed to support math education and overcome math anxiety (MA) at the primary school level. The game narrative is based on the history of math. The player travels back on time and meets on-player characters such as Pythagoras of Samos and Ada Lovelace, learning about how math was used during their times. The player is invited to play a minigame where the concepts shared by the characters are used as a strategy to win. The game’s evaluation consisted of a pre and post-testing study that measured students’ math performance and MA levels. The experiment also included a group interview to collect students’ perceptions about the game. The experiment lasted five weeks, and 88 students from three primary schools played the game on weekly sessions 45-60 minutes long. Statistical analysis suggested the game significantly improves students’ math performance. However, the results indicated that female students from one of the classrooms had higher MA levels after playing the game. In addition, qualitative data shows students had a high level of engagement with the gameplay.
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Et.al, Mohd Faizal Nizam Lee Abdullah. "Improving Student’s Higher-Order Thinking Skills in Solving Pythagoras Theorem Problems through Digital Learning Module." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (April 11, 2021): 653–57. http://dx.doi.org/10.17762/turcomat.v12i3.770.
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The aim of this study is to improve student’s higher-order thinking skills (HOTS) in solving Pythagoras theorem problems through digital learning module. The digital learning module involved in this study is the i-Think module (Mi-T1). This study employed the quasi experimental design with pre and post-test applied to both, control and experimental groups. The control and experimental groups consisted of the same number of Form One (aged between 12 and 13 years old) student that about 30 students each, with the control group had 14 females and 16 males, whereas the experimental group had 15 males and 15 females. Learning activities were carried out according to the teacher’s time-table and were completed in 5 weeks, approximately 10 hours per group, whereby the control group used the official text book (provided by the Ministry of Education for all students to be used in school) and the experimental group utilized Mi-T1. In addition, a survey was administered to the experimental group to measure the participants’ perceived usefulness of digital learning module. The analysis of independent sample t-test showed that the experimental group had significantly improved in their higher-order thinking skills compared to the control group. The survey data also indicated that the participants in the experimental group perceived the usefulness of the digital learning module to be equally high. Premised on these findings, the digital learning module, Mi-T1 can be used to improve students’ higher-order thinking skills in solving Pythagoras Theoremproblems.
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Hernández Castro, David. "Empedocles without Horseshoes." Symposion 6, no. 2 (2019): 129–46. http://dx.doi.org/10.5840/symposion20196210.
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Scholars have generally analysed Empedocles’ criticism of sacrifices through a Pythagorean interpretation context. However, Empedocles’ doctrinal affiliation with this school is problematic and also not needed to explain his rejection of the ‘unspeakable slaughter of bulls.’ His position is consistent with the wisdom tradition that emanated from the Sanctuary of Apollo in Delphi, an institution that underwent significant political and religious changes at the end of the 6th Century B.C., the impact of which was felt all over Magna Graecia. The ritual practice of sacrifice played an important role in Delphi, but the sanctuary also gave birth to a school of wisdom that was highly critical of the arrogance (hybris) of large sacrifices. Asocio-cultural analysis of the Akragas of the first half of the 5th Century B.C. provides new arguments that support this interpretation. The work of Empedocles contains more evidence of being influenced by the Delphi school of wisdom than by Orphism or Pythagoreanism.
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Grossi, Vittorino. "Para leer la espiritualidad de san Agustín. Elementos culturales." Augustinus 65, no. 1 (2020): 23–51. http://dx.doi.org/10.5840/augustinus202065256/25712.
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The article offers an outline of the context of the classical culture in which Christianity developed in the first three centuries, highlighting the humanistic culture of Seneca, the neo-Pythagorean school of the Sextii and the popular preaching of the Cynical Philosophers. On the other hand, the context of classical culture in Christianity of the 4th and 5th centuries is addressed, to highlight the problems that arose when trying to combine “culture” and Christianity. As an example of this problem, the case of Basil the Great and his Discourse to the young is offered. Subsequently, the article presents a series of open questions about the future of spirituality in relationship with «culture / cultures». The article ends with a discussion about Roman Paideia and the Christian Paideia.
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Ashrafian, Hutan. "Differential diagnosis of the finger swelling on Pythagoras in the “School of Athens” (1509–1511) by Raphael (1483–1520)." Rheumatology International 37, no. 12 (October 7, 2017): 2123–24. http://dx.doi.org/10.1007/s00296-017-3838-7.
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