TEORIA DOS CAMPOS CONCEITUAIS: INTEGRANDO ARITMÉTICA, GEOMETRIA E ÁLGEBRA NO ENSINO DAS FRAÇÕES / CONCEPTUAL FIELDS THEORY: INTEGRATING ARITHMETIC, GEOMETRY AND ALGEBRA IN THE FRACTIONS TEACHING

Jonatan Ismael Eisermann; Julhane Alice Thomas Schulz; Mariele Josiane Fuchs

doi:10.7867/1982-4866.2021v27n1p42-58

TEORIA DOS CAMPOS CONCEITUAIS: INTEGRANDO ARITMÉTICA, GEOMETRIA E ÁLGEBRA NO ENSINO DAS FRAÇÕES / CONCEPTUAL FIELDS THEORY: INTEGRATING ARITHMETIC, GEOMETRY AND ALGEBRA IN THE FRACTIONS TEACHING

Revista Dynamis ◽

10.7867/1982-4866.2021v27n1p42-58 ◽

2021 ◽

Vol 27 (1) ◽

pp. 42

Author(s):

Jonatan Ismael Eisermann ◽

Julhane Alice Thomas Schulz ◽

Mariele Josiane Fuchs

Keyword(s):

Arithmetic Geometry ◽

And Algebra

A presente pesquisa visa analisar as potencialidades de uma aprendizagem pautada na Teoria dos Campos Conceituais, elaborada por Gérard Vergnaud, e desenvolvida através de uma sequência didática, envolvendo o conteúdo de Frações, a uma turma de 6º ano do Ensino Fundamental do Ensino Regular. Trata-se de uma pesquisa qualitativa ancorada na própria prática, por meio do desenvolvimento de um estudo de caso, e na bibliografia de renomados educadores matemáticos e pesquisadores da área. Nesse contexto, o pesquisador atuava como professor de matemática na turma em questão, focando-se na constante análise acerca da construção do conhecimento discente a partir de um ensino previamente planejado com vistas às diferentes representações e estruturas de frações. Os resultados evidenciaram uma aprendizagem significativa, na qual a relação dos conceitos construídos encaminhou a assimilação de novos saberes, oportunizando o desenvolvimento de diferentes habilidades.

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THE HISTORICAL ARGUMENT FOR TEACHING ARITHMETIC, GEOMETRY AND ALGEBRA TOGETHER IN THE FIRST YEAR OF THE HIGH SCHOOL

School Science and Mathematics ◽

10.1111/j.1949-8594.1905.tb17517.x ◽

1905 ◽

Vol 5 (9) ◽

pp. 712-716

Author(s):

Willard S. Bass

Keyword(s):

High School ◽

Arithmetic Geometry ◽

First Year ◽

Historical Argument ◽

And Algebra

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TEORI ALJABAR AL-KHAWARIZMI

JURISDICTIE ◽

10.18860/j.v0i0.2170 ◽

2012 ◽

Author(s):

Riana Afliha Eka Kurnia

Keyword(s):

Arithmetic Geometry ◽

Islamic History ◽

Scientific World ◽

And Algebra

Islam generates leaders and scientists who influence and contribute greatly to the development of science. One of them is Al-Khwarizmi who is known as a scientist in the field of mathematics. He also produced many other works in the scientific world. Field of education has demonstrated that al-Khwarizmi was a prominent Islamic scientist. His knowledge and expertise not only in the field of Shari’ah but also in the fields of philosophy, logic, arithmetic,geometry, music, arithmetic, Islamic history and chemistry. His work is very fonumental and it’s very well known, namely calculation and algebra. His prominent role in arithmatics of which he gave the cornerstone in mathematics combining arithmatichs and algebra forms and he introduced hindu’s numerical system to Europe. For his work, he is well known in moslem and westen works of knowledge. He is named as the Father of Algebra. Islam banyak melahirkan tokoh-tokoh dan ilmuwan yang memberi pengaruh dan kontribusi besar bagi perkembangan ilmu pengetahuan. Salah satunya adalah Al-Khawarizmi dikenal sebagai ilmuwan di bidang matematika. Beliau juga banyak menghasilkan karya-karya lain dalam dunia ilmu penge- tahuan. Dalam pendidikan telah dibuktikan bahwa al-Khawarizmi adalah seorang tokoh Islam yang berpengetahuan luas. Pengetahuan dan keahliannya bukan hanya dalam bidang syari’at tapi di dalam bidang Falsafah, Logika, Aritmatika, Geometri, Musik, Ilmu Hitung, Sejarah Islam dan Kimia. Karyanya yang sangat fonumental dan sangat terkenal,di bidang matematika, yaitu mengenai perhitungan dan Aljabar. Kiprah Al-Khawarizmi yang paling menonjol memang dalam bidang Aritmatika, yaitu memberi dasar dan tonggak dalam matematika, menggabungkan bentuk-bentuk Aritmatika dan Aljabar, serta me- ngenalkan bilangan-bilangan Hindu ke benua Eropa. Atas jasanya itu beliau hingga sekarang sangat dikenal, baik di dunia ilmu pengetahuan Islam dan Barat. Atas karyanya di bidang Matematika tersebut beliau akhirnya di beri gelar Bapak Aljabar.

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The Latin Mathematics of Medieval Europe

Sourcebook in the Mathematics of Medieval Europe and North Africa ◽

10.23943/princeton/9780691156859.003.0002 ◽

2016 ◽

Author(s):

Menso Folkerts ◽

Barnabas Hughes ◽

Immo Warntjes ◽

Menso Folkerts ◽

Barnabas Hughes ◽

...

Keyword(s):

Foreign Exchange ◽

Arithmetic Geometry ◽

The Third ◽

Medieval Europe ◽

And Algebra ◽

Second Period

This chapter is about the mathematics that developed in Latin Catholic Europe, circa 800–1480. During this time, the quadrivium, a term which referred to the four subjects—arithmetic, geometry, music, and astronomy—provided the template for the curricula of the first period of Latin mathematics. The second period, covered in the years 1140–1480, witnessed the birth of universities and the wealth of studies gathered and translated in Spain and Italy that would become much of the curricula for these institutions. Finally, the third period, which overlaps about half of the second, lasted 1300–1480. During this time, students learned abacus and algorism, as well as foreign exchange, geometry, and algebra. This type of education would flourish and spread throughout Italy and into the rest of Europe, thus setting the stage for the explosion of mathematics in the Renaissance.

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Η ΜΑΘΗΜΑΤΙΚΗ ΠΑΙΔΕΙΑ ΚΑΙ Η ΟΡΟΛΟΠΑ ΤΗΣ ΣΤΟ ΒΥΖΑΝΤΙΟ ΚΑΤΑ ΤΟΝ ΒΙΕΝΝΑΙΟ ΕΛΛ. ΦΙΛ. ΚΩΔ. 65 (φ. llr-126r)

Eoa kai Esperia ◽

10.12681/eoaesperia.61 ◽

2003 ◽

Vol 5 ◽

pp. 51

Author(s):

ΜΑΡΙΑ ΧΑΛΚΟΥ

Keyword(s):

The Other ◽

Arithmetic Geometry ◽

Human Needs ◽

Metal Workers ◽

Modern Greek ◽

15Th Century ◽

The Subject ◽

Mathematical Terminology ◽

And Algebra

In this article we present some few results of our study on the mathematicalcontent of the unpublished part (f. 11 r-126r) of Cod. Vind. Phil. gr. 65 (the other parthas been published by H. Hunger and K. Vogel), which is the subject of our Dr. thesis(to be submitted). This 15th century Byzantine MS includes the solution of problemsof practical arithmetic, geometry and algebra, the roots of which can be traced back toantiquity. Most of them are related to practical human needs and therefore they couldbe used not only by practical men like merchants, metal workers, builders and otherpeople but also by state employers to calculate taxes. The mathematical terminologyused in this MS has been strongly influenced by latin works; nevertheless itscomparison with modern Greek mathematical terminology reveals -apart from somedifferences- many identities and similarities showing the continuity of Greek mathematicaltradition through the centuries.

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MENINGKATKAN KETERAMPILAN MENGGUNAKAN SOFTWARE R SEBAGAI SOLUSI UNTUK MENINGKATKAN INOVASI PEMBELAJARAN BAGI GURU-GURU MATEMATIKA SMA DAN SMK DI JAKARTA TIMUR

Sarwahita ◽

10.21009/sarwahita.122.10 ◽

2015 ◽

Vol 12 (2) ◽

pp. 134-140

Author(s):

Widyanti Rahayu ◽

Siti Rohmah Rohimah

Keyword(s):

High School ◽

Mathematics Teachers ◽

Arithmetic Geometry ◽

Main Task ◽

Vocational High School ◽

R Software ◽

Software Training ◽

National Education ◽

Learning Mathematics ◽

And Algebra

ABSTRAKKondisi yang dialami oleh banyak guru matematika antara lain yaitu kurangnya inovasi dalam pembelajaran matematika. Guru wajib memiliki kualifikasi akademik, kompetensi, sertifikat pendidik, sehat jasmani, dan rohani, serta memiliki kemampuan untuk mewujudkan tujuan pendidikan nasional.untuk menjamin keterlaksanaan tugasnya secara professional. Untuk meningkatkan kompetensi guru-guru khususnya guru-guru di Sekolah Menengah Atas dan Sekolah Menengah Kejuruan perlu diberikan pelatihan-pelatihan software yang menunjang tugas utamanya sebagai pendidik. Salah satu software yang berguna untuk pembelajaran matematika diantaranya Software R. Software R dapat digunakan untuk menjelaskan banyak topik dalam matematika antara lain: masalah aritmatika, geometri, maupun aljabar. Sofware R juga dapat digunakan guru untuk membantu evaluasi pembelajaran maupun untuk mengolah data penelitian. Melalui pelatihan software R bertujuan agar guru mampu berinovasi untuk meningkatkan kemampuan dan kreativitas mengajar matematika guru- guru di Sekolah Menengah Atas dan Sekolah Menengah Kejuruan di Jakarta Timur. Feedback dari kegiatan pelatihan yang diselenggarakan, peserta memberikan respon positif terhadap pelatihan tentang Software R. ABSTRACTConditions experienced by many teachers of mathematics, among others, the lack of innovation in learning mathematics. Teachers are required to have academic qualifications, competencies, certificates of educators, physically and mentally, and have the ability to realize the goals of national education. To ensure professional execution of their duties. To improve the competence of teachers, especially teachers in Senior High School and Vocational High School need to be given software training that support the main task as educator. One of the software that is useful for learning mathematics such as Software R. Software R can be used to explain many topics in mathematics, among others: the problem of arithmetic, geometry, and algebra. Software R also can be used by teacher to assist evaluation of learning and also to process research data. Through software training R aims to enable teachers to innovate to improve the skills and creativity of teaching mathematics teachers in High School and Vocational High School in East Jakarta. Feedback from the training activities held, the participants gave a positive response to the training on Software R.

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