AbstrakGeometry has a special place in the math curricula at schools. This is because the contents of geometry considered usefel in the daily life. Based on the fact, many students faced difficulties to understand the geometry theory. For this purpose, this article offered van Hielle teory as one of alternative to solve the students' problem.
Etnomatematika menjadi kajian tren penelitian saat ini. Etnomatematika memberikan pengaruh positif dalam pembelajaran matematika dengan melibatkan potensi budaya. Matematika perlu dikomunikasikan dengan menyisipkan budaya sehingga siswa mudah memahami materi. Oleh karena itu, etnomatematika perlu diintegrasikan dengan suatu model pembelajaran. Dengan demikian, tujuan penelitian ini adalah untuk mengembangkan perangkat pembelajaran model probing-prompting berbasis etnomatematika yang dapat melatih komunikasi matematis siswa. Penelitian ini menggunakan model pengembangan Instructional Development Institute (IDI) dengan tiga tahapan, yaitu menentukan, mengembangkan, dan mengevaluasi. Subjek penelitian adalah 30 siswa kelas 8 MTs Negeri Sidorejo Banyuwangi. Pengumpulan data dilakukan melalui angket, observasi, lembar validasi, dan tes. Perangkat pembelajaran yang dikembangkan berupa kisi-kisi soal, soal tes, LKS, dan RPP. Hasil penelitian menunjukkan bahwa perangkat pembelajaran memenuhi kriteria valid, praktis, dan efektif. Perangkat pembelajaran ini dapat digunakan guru untuk mengembangkan kemampuan komunikasi matematis siswa.
Study about spectra of graph has became interesting work as well as study about commuting and non commuting graph of a group or a ring. In this paper, we investigate adjacency spectrum, Laplacian spectrum, signless Laplacian spectrum, and detour spectrum of commuting and non commuting graph of dihedral group D2n.Keywords: graph, spectrum, commuting graph, non commuting graph, dihedral group. INTRODUCTIONLet G be a graph of order n (n ≥ 1) and let its vertex set is V(G) = {v1, v2, …, vn}.
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