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All Journal Union: Jurnal Ilmiah Pendidikan Matematika Mosharafa: Jurnal Pendidikan Matematika Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Hilbert Journal of Mathematical Analysis
Ali, Amrizal Marwan
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Chemistry Computer Science & IT Control & Systems Engineering Education Engineering Mathematics Physics Other

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Eksplorasi Masalah Isoperimetrik pada Bangun Ruang Ali, Amrizal Marwan; Hakim, Denny Ivanal
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 12 Issue 1 June 2024
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v12i1.24918

Abstract

In two-dimensional figures, the isoperimetric problem is defined as finding two-dimensional figures that will produce the largest area among several two-dimensional figures with the same perimeter. In this research, the isoperimetric problem is extended to find the shape with the largest volume among the shapes that have the same surface area. The aim of this research is to solve isoperimetric problems in three-dimensional shapes obtained by comparing various shapes of three-dimensional shapes. The discussion in this research is limited to three-dimensional shapes in the form of prisms with regular n-sided bases, pyramids with regular n-sided bases, cylinders, cones, and spheres. This research method uses concepts from calculus, trigonometry and algebra to prove the isoperimetric theorem with a simple and elementary approach. The result of this research is that the order of the maximum volume of three-dimensional shapes if the surface area is the same from smallest to largest is a pyramid with an equilateral triangular base, a pyramid with a square base, a prism with an equilateral triangular base, a pyramid with a regular n-sided base (n≥5), cone, prism with square base, prism with regular n-sided base (n≥5), cylinder, and sphere.
Isoperimetric problems on n-sided prisms Ali, Amrizal Marwan; Hakim, Denny Ivanal
Hilbert Journal of Mathematical Analysis Vol. 3 No. 1 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i1.36

Abstract

In two-dimensional figure, the isoperimetric problem refers to finding two-dimensional figure that will produce the largest area among several shapes with equal perimeter. This research extends the isoperimetric problem to finding three-dimensional shapes with maximum volume among those having equal surface area. Our main goal is to solve the isoperimetric problem for prisms with regular n-sided base, prisms with irregular n-sided base and cylinder. In this research, the discussion is limited to prisms with regular and irregular bases. Our problem is equivalent with the problem of finding the smallest surface area of a given three-dimensional figure with the same volume. We will use a geometric approachin our proof. we will see the relationship between isoperimetric problems in two dimensional figures and isoperimetric problems in three-dimensional figure. We obtain the results of the isoperimetric problem from two prisms with regular n-sided bases and a prism with regular m-sided bases with n≤m, two prisms with regular n-sided bases and a prism with circular bases (cylinder), and two prisms with regular n-sided bases and a prism with irregular n-sided bases.
The Implications of Providing Ill-Structured Problems on Students’ Learning Outcomes in the Topic of Polynomial Sukardi; Afifi, Fakhrunnisa Cahya; Ali, Amrizal Marwan
Mosharafa: Jurnal Pendidikan Matematika Vol. 12 No. 4 (2023): October
Publisher : Department of Mathematics Education Program IPI Garut

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31980/mosharafa.v12i4.1198

Abstract

Dalam matematika, masalah tidak terstruktur sering kali memberikan tantangan tersendiri bagi siswa karena keterbatasan informasi yang diberikan untuk menyelesaikan masalah tersebut. Tujuan penelitian ini adalah untuk mengetahui implikasi pemberian masalah tidak terstruktur terhadap hasil belajar siswa, khususnya pada materi suku banyak sesuai dengan silabus Kurikulum 2013. Penelitian ini merupakan penelitian eksperimen semu yang melibatkan subjek sebanyak 64 orang siswa kelas XI tahun ajaran 2022/2023 di SMA Santo Paulus Pontianak yang terbagi ke dalam dua kelompok, yaitu kelompok kontrol dan kelompok perlakuan, masing-masing sebanyak 32 orang siswa. Baik siswa di kelompok kontrol maupun kelompok perlakuan sama-sama menerima metode pembelajaran yang sama. Namun, siswa di kelompok perlakuan disodorkan sejumlah masalah tidak terstruktur secara berkelanjutan. Tes kemudian diberikan pada akhir pembelajaran. Nilai tes, baik siswa pada kelompok kontrol maupun kelompok perlakuan, dianalisis normalitasnya dengan menggunakan uji Kolmogorov-Smirnov, kemudian diuji signifikansinya dari segi rata-rata dengan menggunakan uji- tidak berpasangan. Penelitian ini menghasilkan fakta bahwa pemberian masalah tidak terstruktur membuahkan dampak positif terhadap hasil belajar siswa. Dengan kata lain, penggunaan masalah tidak terstruktur pada materi suku banyak dapat menjadi alternatif untuk meningkatkan hasil belajar siswa, khususnya siswa SMA Santo Paulus Pontianak. The aim of this study is to determine the implications of providing ill-structured problems on students’ learning outcomes, specifically in the topic of polynomial according to the 2013 Curriculum syllabus. The subjects of this study were 65 students in grade XI of the 2022/2023 academic year at SMA Santo Paulus Pontianak, which was divided into two groups: the control group and the treatment group, with 32 students in each group. Both the control group and the treatment group received the same teaching method. However, the treatment group was consistently given a series of ill-structured problems. The implications of ill-structured problems on students’ learning outcomes were assessed through the analysis of daily evaluation scores conducted during the final session. This study found that the provision of ill-structured problems had a positive impact on students’ learning outcomes. This conclusion was drawn from statistical calculations using the independent -test on the daily evaluation scores of the two groups, resulting in -value of -2.2504 (equivalent to -value of 0.01415) at a significance level of 5%. The study concludes that providing of ill-structured problems in the topic of polynomial can be an alternative to improve students’ learning outcomes, particularly at SMA Santo Paulus Pontianak.
Ethnomathematical studies on the Gedong Songo temple Ali, Amrizal Marwan; Prasetia, Yasin
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 11 No 2 (2023)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v11i2.14428

Abstract

The lack of information about designing buildings, measuring, patterning and calculating from ancient people, makes the concept of mathematics applied by people in the past remains unknown. It is necessary to study mathematics from a cultural point of view of society. This study is carried out through a cultural approach, or what is commonly referred to as ethnomathematics. Mathematics that is used by recognized cultural groups, such as national communities, ethnic groups, labor organizations, children of particular age groups, and professional classes, is known as ethnomathematics. Finding the mathematical principles used to construct the Gedong Songo Temple in Candi Village, Bandungan, Semarang Regency, Central Java, is the goal of this study. The object of research in this case is the Gedong Songo Temple. The approach taken is a qualitative one. In this study, an ethnographic technique was used. Data collection is done by literature study and observation. This research is structured descriptively, starting from reviewing problems related to ethnomathematics, formulating problems, collecting theories, analyzing, discussing data, and making conclusions. The findings demonstrated that geometry, symmetry, periodic patterns, and ratios are among the mathematical concepts used in the construction of the Gedong Songo Temple. The findings of this study can be used to improve mathematics instruction in cultural contexts. In addition, further studies on ethnomathematics can be carried out to see more comprehensively the mathematical concepts applied to the structure of the temple building.
Co-Authors Afifi, Fakhrunnisa Cahya Hakim, Denny Ivanal Prasetia, Yasin Raden Mohamad Herdian Bhakti