۔۔ ۔کے پروفائل پر بلّی دیکھ کر
پالی میں نے بھی اک بلّی
دیکھی تیرے گھر جب بلّی
تیرے گھر میں جو بلّی ہے
بھولی بھالی سی دِکھتی ہے
خوب شرارت پر کرتی ہے
تیرے بستر پر بیٹھی ہے
مجھ کو کیسے گھور رہی ہے
تجھ سے ملنے جب آتا ہوں
اِس کے بسکٹ بھی لاتا ہوں
یہ کتنے نخرے کرتی ہے
بس تیرے جیسی لگتی ہے
کیک بیکری کے کھاتی ہے
اور پھر بھی گھورے جاتی ہے
یہ سب کچھ دیکھا میں نے تو
پالی میں نے بھی اک بلّی
ایسی نہیں پر میری بلّی
تیری بلّی ، تیری بلّی
ایسی نہیں پر میری بلّی
Abstract This research motivated by the findings of learning obstacles experienced students in material around square. This is known based on the results of test questions conducted during preliminary study to fourth grade elementary school students. To overcome learning obstacles experienced by students, researchers will design a didactic design. The purpose of this study is to describe the didactic design on the material around square and describe the students' responses the implementation of didactic design. The didactic design can be interpreted learning design that emphasizes the didactic aspect, namely the teacher's teaching method. This study uses method with a Didactical Design Research (DDR) research design consisting of three research stages, namely a prospective analysis of the didactic situation before learning (prospective analysis) in the form of a Hypothetical Didactic Design including ADP (Pedagogical Didactic Analysis), metapedadidactive analysis, and retrospective analysis (retrospective analysis), with data collection techniques used in the form of interviews, observations, and attitude scales. The research subjects were 26 students in grades IV and VI and 1 teacher for grade IV at SDN 1 Sindangrasa. Based on results of study, through application of the didactic design carried out in stages I and II, can help overcome learning obstacles experienced by students in the material around a square. This is shown from the students' responses on the attitude scale, results of the LAS (Student Activity Sheet) work and interviews with teachers. In addition, didactic design is able to create a fun and meaningful learning atmosphere for students. Keywords: learning obstacle, didactical design research, square, meaningful learning, LAS Abstrak Penelitian ini dilatarbelakangi oleh adanya temuan learning obstacle yang dialami siswa pada materi keliling persegi. Hal ini diketahui berdasarkan hasil soal tes yang dilakukan pada saat studi pendahuluan kepada siswa kelas IV Sekolah Dasar. Untuk mengatasi learning obstacle yang dialami siswa, peneliti akan merancang sebuah desain didaktis. Tujuan dari penelitian ini adalah untuk mendeskripsikan desain didaktis pada materi keliling persegi serta memaparkan respon siswa dan guru terhadap implementasi desain didaktis tersebut. Desain didaktis dapat diartikan sebagai desain pembelajaran yang lebih menekankan pada aspek didaktik yakni cara pengajaran guru. Penelitian ini menggunakan metode Didactical Design Research (DDR) yang terdiri dari tiga tahap penelitian, yakni analisis situasi didaktis sebelum pembelajaran (prospective analysis) berupa Desain Didaktis Hipotesis termasuk ADP (Analisis Didaktis Pedagogis), analisis metapedadidaktif, dan analisis retrospektif (retrospective analysis), dengan teknik pengumpulan data yang digunakan berupa wawancara, observasi, dan skala sikap. Subjek penelitian yaitu 26 siswa kelas IV dan VI serta 1 guru kelas IV SDN 1 Sindangrasa. Berdasarkan hasil penelitian, melalui penerapan desain didaktis yang dilakukan pada tahap I dan II dapat membantu mengatasi learning obstacle yang dialami siswa pada materi keliling persegi. Hal ini ditunjukkan dari respon siswa pada skala sikap, hasil pengerjaan LAS (Lembar Aktivitas Siswa) serta wawancara terhadap guru. Selain itu, desain didaktis mampu menciptakan suasana pembelajaran yang menyenangkan dan bermakna bagi siswa. Kata kunci : hambatan belajar, desain didaktis, persegi, pembelajaran bermakna, LAS
MR Image Reconstruction Using PMRI and Compressed Sensing Magnetic Resonance Imaging (MRI) is a safe and non-ionizing medical imaging modality that provides excellent soft tissue contrast. The main limitation in MRI is its long data acquisition time. Parallel MRI (pMRI) and Compressed Sensing (CS) provide a framework to lessen the MRI data acquisition time. Both pMRI and CS acquire less data in k-space and then minimize the aliasing artifacts by using dedicated reconstruction algorithms. PMRI was introduced in late 1990’s and some of its reconstruction algorithms are commercially available in the latest MRI scanners. CS was introduced in 2007 and it is mostly used in research. Recently, Graphical Processing Units (GPU) have been used to reduce the computation time in the parallel algorithms. GPU can also be used in MRI reconstruction algorithms to reduce the computation time of reconstruction algorithm (one of the main limitation in MRI). The objective of this thesis is to explore and develop new methods to improve the performance of pMRI and CS. There are four main contributions in this regard. (i) A Graphical Processing Unit (GPU) based design is developed in Compute Unified Device Architecture (CUDA) for fast implementation of Sensitivity Encoding (SENSE), a pMRI reconstruction algorithm. The results show that the proposed GPU implementation of SENSE significantly reduces its computation time while maintaining the reconstructed image quality as compared to the conventional SENSE implementation. (ii) Receiver coil sensitivity information plays an important role in SENSE reconstruction. Eigen-value method is used for sensitivity estimation in the proposed work for SENSE reconstruction on GPU and the results are compared with the conventional Pre-scan method. The results show that Eigen-value method considerably improves the SNR of the reconstructed images as compared to the results obtained using Pre-scan method. (iii) Conjugate Gradient SENSE (CG-SENSE), proposed by Pruessmann uses both the Non-Cartesian (NC) and Cartesian k-space for image reconstruction. NC trajectories are increasingly used in recent MR imaging because they are fast and provide efficient coverage of k-space. NC trajectories are computationally extensive and require special operations including gridding and de-gridding. A GPU based implementation of the gridding and de-gridding operations is proposed in this thesis that significantly reduces the computation time of CG-SENSE while maintaining the reconstructed image quality. (iv) A combined application of CG-SENSE (a pMRI reconstruction xi algorithm) and Projections onto Convex Sets (POCS) (a CS reconstruction algorithm) is proposed for reconstructing fully-sampled MR images from the under-sampled data. The results of the proposed method are compared with CG-SENSE and POCS reconstruction separately. The results show that the proposed method allows higher acceleration factors in MRI data acquisition and notably improves the reconstructed image quality.