Mathematics Commons^™

Relations Between Distorted And Original Angles In Str, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Using the Oblique-Length Contraction Factor, which is a generalization of Lorentz Contraction Factor, one shows several trigonometric relations between distorted and original angles of a moving object lengths in the Special Theory of Relativity.

Differential Graded Contact Geometry And Jacobi Structures, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We study contact structures on nonnegatively graded manifolds equipped with homological contact vector fields. In the degree 1 case, we show that there is a one-to-one correspondence between such structures (with fixed contact form) and Jacobi manifolds. This correspondence allows us to reinterpret the Poissonization procedure, taking Jacobi manifolds to Poisson manifolds, as a supergeometric version of symplectization.

Nsf's Math-Science Partnership Projects- Measuring The Trickle-Down Effect Of American Tax Dollars, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Teacher Learning In Lesson Study, Jennifer M. Lewis, Davida Fischman, Iris Riggs, Kelli Wasserman

The Mathematics Enthusiast

This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students’ autonomous problem‐solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among the teams’ composition, leadership, and content foci.

Supporting Middle School Mathematics Specialists’ Work: A Case For Learning And Changing Teachers’ Perspectives, Joy W. Whitenack, Aimee J. Ellington

The Mathematics Enthusiast

In this paper, we highlight one whole‐class discussion that took place in a middle school mathematics Rational Number and Proportional Reasoning course, one of the six mathematics courses teachers take to complete our state‐wide middle school mathematics specialist program. Statistical measures indicate that teachers made gains in their understanding of concepts and substantial gains in their views of teaching and preparedness. We provide a microanalysis of one of the lessons, to explain, in part, how they might have made this progress. To develop our argument, we coordinate a social analysis with an analysis of the types of specialized mathematical knowledge …

Feedback To Support Learning In The Leadership Institute For Teachers, Cathy Kinzer, Janice Bradley, Patrick Morandi

The Mathematics Enthusiast

Feedback is a type of formative assessment used to inform instruction and advance learning. Feedback serves as a mechanism to connect teaching and learning at the student level. Learners receive feedback, formally or informally, as they engage in learning experiences. Within the Leadership Institute for Teachers, a National Science Foundation funded research project, we are exploring feedback as a research‐informed process to support learning and improvement for individuals, teams, and university courses. There is an explicit focus on creating a culture of critical thinking and reasoning, taking ownership for learning both individually and collectively, and understanding how to improve teaching …

A Partnership's Effort To Improve The Teaching Of K-12 Mathematics In Rapid City, South Dakota, Ben Sayler, June Apaza, Vicki Kapust, Susan Roth, Becky Carroll, Pam Tambe, Mark St. John

The Mathematics Enthusiast

Over the span of ten years, a National Science Foundation‐funded partnership effort has collected and analyzed multiple forms of evidence, both direct and indirect, about improved teaching of mathematics within Rapid City Area Schools. This article describes the project's impact on K‐12 teaching and factors contributing to that impact. The authors argue that improvements in teaching are attributable largely to a robust infrastructure established to support teacher growth. Direct evidence includes classroom observations conducted by the project's external evaluation team. Indirect evidence exists in the form of data on student outcomes: achievement on the state's multiple‐choice accountability measure and achievement …

Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii

Doctoral Dissertations

The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …

Decoupling The Stationary Navier-Stokes-Darcy System With The Beavers-Joseph-Saffman Interface Condition, Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

Topics In Electromagnetic, Acoustic, And Potential Scattering Theory, Umaporn Nuntaplook

Mathematics & Statistics Theses & Dissertations

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves — is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering …

Bimodules Over Cartan Masas In Von Neumann Algebras, Norming Algebras, And Mercer's Theorem, Jan Cameron, David R. Pitts, Vrej Zarikian

Department of Mathematics: Faculty Publications

In a 1991 paper, R. Mercer asserted that a Cartan bimod- ule isomorphism between Cartan bimodule algebras A1 and A2 extends uniquely to a normal -isomorphism of the von Neumann algebras gener- ated by A1 and A2 (Corollary 4.3 of Mercer, 1991). Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel, 1988 (Theorem 2.5, there). Unfortunately, the arguments in the literature supporting their Theorem 2.5 contain gaps, and hence Mercer's proof is incomplete.

In this paper, we use the outline in Pitts, 2008, Remark 2.17, to give a proof of Mercer's Theorem under the additional …

Optimal Control Modeling And Simulation, With Application To Cholera Dynamics, Chairat Modnak

Mathematics & Statistics Theses & Dissertations

The theory of optimal control, a modern extension of the calculus of variations. has found many applications in a wide range of scientific fields, particularly in epidemiology with respect to disease prevention and intervention. In this dissertation. we conduct optimal control modeling, simulation and analysis to cholera dynamics. Cholera is a severe intestinal infectious disease that remains a serious public health threat in developing countries. Transmission of cholera involves complex interactions between the human host, the pathogen, and the environment. The worldwide cholera outbreaks and their increasing severity, frequency and duration in recent years underscore the gap between the complex …

Penggunaan Pita Melalui Pembelajaran Missouri Mathematics Project Untuk Memahamkan Siswa Tentang Luas Permukaan Bola, Pentri Arfia Dewi

Jurnal Pendidikan Sains

Penelitian ini akan mendeskripsikan penggunaan pita melalui pembelajaran Missouri Mathematics Project untuk memahamkan siswa tentang luas permukaan bola. Pembelajaran yang dilaksanakan berdasarkan pada tahapan pembelajaran Missouri Mathematics Project yang dipadukan dengan bahan manipulatif. Penelitian ini merupakan penelitian tindakan kelas. Setiap siklus terdiri dari tiga kali pertemuan. Dalam penelitian ini juga dilakukan kajian dari jawaban siswa. Hasil penelitian ini menunjukkan bahwa penerapan pembelajaran menggunakan bahan manipulatif bola dan pita dapat memahamkan siswa tentang luas permukaan bola.

Pembelajaran Berbantuan Multimedia Berdasarkan Teori Beban Kognitif Untuk Meningkatkan Kemampuan Menyelesaikan Masalah Program Linear Siswa X Tkr 1 Smkn 1 Doko, Fifi Damayanti

Jurnal Pendidikan Sains

Berdasarkan teori beban kognitif, pembelajaran efektif terjadi apabila beban intrinsic dikelola dengan baik, beban germane ditingkatkan, dan beban extraneous dikurangi. Penerapan multimedia merupakan salah satu upaya untuk mencapai pembelajaran yang efektif. Penelitian ini mengkaji penerapan pembelajaran matematika berbantuan multimedia dalam meningkatkan kemampuan siswa menyelesaikan masalah program linear. Penelitian ini menggunakan pendekatan penelitian tindakan kelas yang dilaksanakan dalam dua siklus. Hasil penelitian menunjukkan bahwa penggunaan multimedia dapat mengelola beban intrinsic, meningkatkan beban germane, dan mengurangi beban extraneous, sehingga kemampuan siswa dalam menyelesaikan masalah program linear meningkat.

Kajian Morfologi, Anatomi, Dan Agronomi Antara Kedelai Sehat Dengan Kedelai Terserang Cowpea Mild Mottle Virus Serta Pemanfaatannya Sebagai Bahan Ajar Di Sekolah Menengah Kejuruan, As’Ad Syamsul Arifin

Jurnal Pendidikan Sains

Salah satu penyebab rendahnya produktivitas kedelai di Indonesia adalah serangan virus belang samar kacang tunggak, Cowpea mild mottle virus (CPMMV). Penelitian ini merupakan penelitian survei yang bertujuan untuk menggambarkan dan mengumpulkan informasi mengenai kajian morfologi, anatomi, dan agronomi terhadap infeksi CPMMV pada varietas yang terinfeksi dan yang tidak terinfeksi. Data dianalisis secara deskriptif dan inferensial menggunakan ANAVA melalui program SPSS for Windows versi 16. Hasil penelitian menunjukkan bahwa varietas Gumitir sehat, Anjosmoro sehat, Mahameru sehat, MLGG 0021, dan MLGG 0268 memiliki ukuran daun, panjang petiol, serta nisbah daun (L/W dan L/PL) lebih besar dibandingkan varietas yang sakit. Varietas Argopuro sakit …

Pengaruh Model Siklus Belajar Berbantuan Mind Map Terhadap Prestasi Belajar Fisika Ditinjau Dari Kinerja Laboratorium Siswa Kelas Viii Smpn 1 Rejoso Kabupaten Pasuruan, Ary Analisa Rahma

Jurnal Pendidikan Sains

Penelitian ini bertujuan untuk menguji pengaruh model siklus belajar berbantuan mind map terhadap prestasi belajar fisika ditinjau dari kinerja laboratorium siswa kelas VIII pada materi cahaya di SMP Negeri 1 Rejoso, Kabupaten Pasuruan. Penelitian ini merupakan penelitian eksperimen semu dengan rancangan faktorial 2 × 2. Subjek penelitian berjumlah 204 siswa. Instrumen penelitian terdiri atas instrumen perlakuan yang meliputi silabus, RPP, dan LKS, serta instrumen pengukuran berupa instrumen kinerja laboratorium dan tes prestasi belajar fisika. Hasil penelitian menunjukkan bahwa prestasi belajar fisika siswa yang belajar menggunakan model siklus belajar berbantuan mind map lebih tinggi dibandingkan dengan siswa yang belajar melalui pembelajaran …

Pengembangan Profesionalitas Berkelanjutan/Continuing Professional Development (Cpd) Guru Bersertifikat Pendidik Di Smk Rumpun Teknologi Se-Malang Raya, Sujianto Sujianto

Jurnal Pendidikan Sains

Penelitian ini bertujuan untuk mendeskripsikan pengembangan profesionalitas berkelanjutan guru bersertifikat pendidik melalui investasi pengembangan diri, publikasi ilmiah, dan karya inovatif, baik secara mandiri, berkelompok, maupun melembaga. Penelitian menggunakan rancangan deskriptif kuantitatif dengan subjek guru kejuruan bersertifikat pendidik di wilayah Malang Raya. Instrumen penelitian meliputi kuesioner (angket) dan pedoman wawancara. Hasil penelitian menunjukkan bahwa pemberlakuan Undang-Undang Guru dan Dosen (UU Nomor 14 Tahun 2005) yang disertai pemberian tunjangan profesi sejatinya memberikan harapan besar dalam mendorong minat guru untuk terus mengembangkan profesionalitasnya. Namun, temuan penelitian menunjukkan kondisi yang berbeda. Tingkat pengembangan profesionalitas berkelanjutan guru bersertifikat pendidik di SMK rumpun teknologi se-Malang Raya …

Analisis Variasi Genetik Varian Jati Arboretum Dengan Penanda Mikrosatelit, Imas Cintamulya

Jurnal Pendidikan Sains

Seleksi tanaman jati untuk memperoleh sifat unggul tidak cukup hanya melalui penanda morfologi, tetapi juga perlu menggunakan penanda molekuler berdasarkan polimorfisme DNA. Oleh karena itu, perlu dilakukan kajian tanaman jati dari segi genetik pada level DNA untuk melihat variasi genetik. Informasi tentang variasi genetik jati diperlukan dalam pengadaan bibit untuk pembangunan hutan tanaman industri, dengan tujuan mencegah inbreeding dan mendukung upaya konservasi. Penelitian ini bertujuan untuk menganalisis variasi genetik varian jati arboretum menggunakan penanda molekuler mikrosatelit serta menyusun buku pengayaan kajian dasar-dasar molekuler tumbuhan, khususnya penanda mikrosatelit, dalam menganalisis variasi genetik varian jati arboretum yang berkualitas. Langkah-langkah penelitian meliputi isolasi …

Pembelajaran Kooperatif Tai Dan Game Puzzle Dalam Meningkatkan Motivasi Belajar Dan Pemahaman Konsep Matematika, Any Herawati

Jurnal Pendidikan Sains

Penelitian ini mendeskripsikan rancangan dan pelaksanaan pembelajaran kooperatif Team Assisted Individualized (TAI) dan game puzzle dalam meningkatkan motivasi belajar serta pemahaman konsep fungsi komposisi dan fungsi invers di SMA Negeri 3 Malang. Penelitian ini merupakan penelitian tindakan kelas dengan pendekatan mix research, yang dilaksanakan dalam tiga siklus. Subjek penelitian adalah siswa kelas XI IPA 1 semester genap tahun pelajaran 2011/2012 sebanyak 33 siswa, terdiri atas 13 siswa laki-laki dan 20 siswa perempuan. Data yang dikumpulkan meliputi motivasi belajar dan pemahaman konsep matematika siswa. Hasil penelitian menunjukkan bahwa pembelajaran kooperatif TAI dan game puzzle mampu meningkatkan motivasi belajar dan pemahaman konsep. …

Persepsi Pengelola Terhadap Peran Sistem Informasi Manajemen (Sim) Berbasis Teknologi Informasi (Ti) Dalam Pengelolaan Administrasi Sekolah Menengah Kejuruan Kota Mojokerto, Tri Wahjoedi Hidajat

Jurnal Pendidikan Sains

Peran sistem informasi manajemen (SIM) berbasis teknologi informasi sangat penting dalam pengelolaan sekolah untuk meningkatkan kualitas pelayanan, proses, dan prestasi belajar siswa. Oleh karena itu, penelitian ini bertujuan untuk mengungkap dan mendeskripsikan persepsi pengelola terhadap peran SIM berbasis TI dalam pengelolaan administrasi SMK di Kota Mojokerto. Penelitian ini menggunakan rancangan deskriptif kuantitatif dan dilaksanakan pada sembilan SMK di Kota Mojokerto dengan 45 pengelola administrasi akademik sebagai populasi. Teknik pengambilan sampel yang digunakan adalah sampel jenuh, yaitu seluruh populasi dijadikan sampel. Hasil penelitian menunjukkan bahwa: (1) secara umum, persepsi pengelola terhadap peran SIM berbasis TI dalam pengelolaan administrasi SMK tergolong penting, …