Delving Deeper: Fibonacci Identities, Matrices, and Graphs

2005 ◽  
Vol 98 (6) ◽  
pp. 400-403 ◽  
Author(s):  
Danrun Huang
Keyword(s):  
Mathematics Teacher ◽  
Fibonacci Numbers

In “Fibonacci and Related Sequences” published in the “Delving Deeper” department of the Mathematics Teacher February 2004, Richard Askey presents “general strategies used to help discover, prove, and generalize” identities for Fibonacci numbers. He also suggests some problems for further delving, including proving one key identity by using matrices. That proof is the focus of this article.

Pythagorean Triples from Harmonic Sequences

2001 ◽  
Vol 94 (3) ◽  
pp. 218-222
Author(s):  
Angelo S. DiDomenico ◽  
Randy J. Tanner
Keyword(s):  
Mathematics Teacher ◽  
Fibonacci Numbers ◽  
Whole Numbers ◽  
Multiplication Tables ◽  
Pythagorean Triples ◽  
Mathematical Experience ◽  
Ancient Times

Pythagorean triples have intrigued generations of mathematics explorers, including students, since ancient times. One of their most charming features is their connection with various other areas of mathematics. In the Mathematics Teacher, for example, authors have shown that Pythagorean triples can be generated from the Fibonacci numbers (Bertucci 1991), from geometric sequences (Carbeau 1993), and from both the addition and multiplication tables of whole numbers (DiDomenico 1993, 1995). These findings are indeed fascinating; when shared with students, they spark interest and curiosity and lead to a truly enriching mathematical experience. Students, in fact, independently found that Pythagorean triples could be generated from Fibonacci numbers and geometric sequences. This article reveals another surprising connection that shows how all primitive Pythagorean triples can be generated from harmonic sequences.

MATHEMATICS TEACHER EDUCATION AND THE FLEXIBLE USE OF TECHNOLOGIES IN DIGITAL AGE

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Hans-Georg Weigand
Keyword(s):  
Teacher Education ◽  
Mathematics Teacher ◽  
Industrial Revolution ◽  
Empirical Studies ◽  
Mathematics Teacher Education ◽  
Digital Technologies ◽  
Digital Age ◽  
Competence Model ◽  
Advantages And Disadvantages ◽  
Concept Representations

Advantages and disadvantages of the use of digital technologies (DT) in mathematics lessons are worldwidedissussed controversially. Many empirical studies show the benefitof the use of DT in classrooms. However, despite of inspiringresults, classroom suggestions, lesson plans and research reports,the use of DT has not succeeded, as many had expected during thelast decades. One reason is or might be that we have not been ableto convince teachers and lecturers at universities of the benefit ofDT in the classrooms in a sufficient way. However, to show thisbenefit has to be a crucial goal in teacher education because it willbe a condition for preparing teachers for industrial revolution 4.0.In the following we suggest a competence model, which classifies– for a special content (like function, equation or derivative) –the relation between levels of understanding (of the concept),representations of DT and different kind of classroom activities.The flesxible use of digital technologies will be seen in relationto this competence model, results of empirical investigations willbe intergrated and examples of the use of technologies in the upcoming digital age will be given.

THE SYSTEM OF INFORMATICS COMPETENCIES FOR THE MATHEMATICS TEACHER

2020 ◽  
pp. 57-72
Author(s):  
Nadiia Ponomareva
Keyword(s):  
Information Technology ◽  
Secondary Education ◽  
Mathematics Teachers ◽  
Mathematics Teacher ◽  
Systems Analysis ◽  
Web Technologies ◽  
Key Competencies ◽  
Teachers Training ◽  
Technology Specialists ◽  
Further Development

As a result of the analysis of domestic and foreign standards of key competencies, basic and complete secondary education, teachers’ training (in particular, mathematics teachers’ training) and information technology specialists training, the system of informatics competencies of a mathematics teacher, developed by Yu. S. Ramskyi, was updated in terms of the structure, content and indicators of competencies formation. It has been found out that the formation of the informatics competencies of a mathematics teacher begins with basic informatics competencies, the further development of which occurs primarily in the competencies in system administration, web technologies, programming and systems analysis.

Pengembangan E-modul Berbasis Smartphone Pada Materi Integral Tak Tentu Berorientasi Keterampilan Abad Ke-21

2020 ◽  
Vol 3 (2) ◽  
pp. 222-233
Author(s):  
Veronika Fany Monica Yuniarti ◽  
Nurul Anriani ◽  
Cecep Anwar H. F. Santosa
Keyword(s):  
Research And Development ◽  
21St Century ◽  
Mathematics Teacher ◽  
21St Century Skills ◽  
Research Method ◽  
Effective Medium ◽  
Developmental Research ◽  
High Category ◽  
Research Show

Abstrak: Penelitian ini bertujuan untuk menghasilkan aplikasi e-modul berbasis smartphone pada materi integral tak tentu berorientasi keterampilan abad ke-21 yang valid, praktis, dan efektif. Penelitian menggunakan metode Research and Development (R&D) dari Borg dan Gall yang dimodifikasi menjadi enam langkah. Hasil penelitian menyatakan bahwa hasil skor validasi ahli materi sebesar 4.2 termasuk kategori valid, ahli media diperoleh 3.8 termasuk kategori valid dan guru matematika diperoleh 3.7 termasuk kategori valid. Sedangkan hasil efektivitas diperoleh dari persentase ketuntasan 70% dengan kategori tinggi, dan n-gain sebesar 0,7682 termasuk kategori interpretasi tinggi. Lebih jauh, hasil praktis diperoleh 44.55 jumlah rata-rata skor pernyataan yang termasuk kategori sangat praktis dan 39.80 jumlah rata-rata skor pernyataan yang termasuk kategori praktis. Berdasarkan hasil tersebut maka dapat disimpulkan bahwa pengembangan aplikasi e-modul berbasis smartphone merupakan media yang valid, praktis, dan efektif. Abstract: The research aims to produce a valid, practical, and effective smartphone-based e-module applications 21st-century skills-oriented integral material. The Research method was developmental research (R&D) according to Borg and Gall which was modified into six steps. The results of the research show that the validity of material experts score is 4.2 (valid category), media experts obtained is 3.8 (valid category) and the mathematics teacher score is 3.7 (valid category). While the effectiveness results obtained from the percentage of completeness of 70% with a high category and n-gain of 0.7682 including the high interpretation category. As well as the practical results obtained 44.55 the average number of statements in the very practical category and 39.80 the average number of statements in the practical category. Based on these results it can be concluded that the development of smartphone-based e-module applications is a valid, practical, and effective medium.

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