Development Guided Reinvention Principle In PMRI Approach In Use The Teacher Guide In Elementary School

Since 2001, four teacher education institutes (LPTK) are developing a localized, Indonesian version of realistic mathematics education. It is known as PMRI, Pendidikan Matematika Realistik Indonesia. PMRI is an adaptation of Realistic Mathematics Education (RME) as it has been developed by the Freudenthal Insitute in Netherlands. Since 1968, Dutch researchers, developers and educational designers have been working on the ongoing development of RME. Considering the number of schools in the country, the scale of the pilot project is small. For a large scale implementation of PMRI, the PMRI movement goes into a new phase while maintaining the basic principles. The pilot model uses close cooperation between teacher educators and teachers and a bottom-up approach, meaning teachers, principals, and to some extent parents, are involved in the various stages of development. However, in large scale dissemination, sustainable top-down support is required. The challenge then is to find a dissemination strategy that keeps the principles of the movement. The partners agreed upon two strong pillars under the dissemination strategy,i.e a. Establishment of an expanding network of local PMRI resource centers at each participating LPTK (later, called P4MRI) as starting points for further dissemination. b. Developing teaching materials based on classroom experience and classroom research. As far as I know, PMRI team does not do a research about teacher guide. So, as a writer for the PMRI book (the student and teacher book), I have two questions for teacher that can the teacher book help teachers to teach mathematics with PMRI approach? and can the teacher book help teachers to develop the PMRI characteristics? I want to know how students in grade 1 to solve problems about addition, subtraction, and mixed between addition and subtraction. Because of that reason, I made a student sheet. The content of the student sheet are problems about how many passenger in a train which moves from one station to another. I used the PMRI approach to develop the student sheet. I develop a teacher guide which help the teacher to use the student sheet and to do the teaching learning process with the PMRI approach. The content of the teacher guide are teaching learning goals, mathematics concepts, tools and materials, time, and student and teacher activities. At 8 October 2010, I get an opportunity to try out the student sheet and the teacher guide on class II C, Kanisus. Based on my observation, there are two strategies which are used by students to solve the problems in the student sheet, that is 1. Stacked to bottom (almost every students used this strategy); 2. “Menghitung ke samping” (only one student used this strategy). One of indicators from the guided reinvention principle in PMRI approach is that students can find a new concept or strategy from a teaching learning process which is followed by the students. Base on my observation in the classroom, the indicator from the guided reinvention principle in PMRI approach does not appear on the lesson of that day. So, I can say that in the teaching learning process on that day the guided reinvention principle in PMRI approach does not appear. From my explanation, there are some problems which are solved by the research, i.e. 1. How is a teacher’s understanding about the guided reinvention principle in PMRI approach on a primary school which is used PMRI approach? 2. How the guided reinvention principle in PMRI approach can be appeared by a teacher on a primary school which is used PMRI approach? 3. What are indicators that a teacher can appear the guided reinvention principle in PMRI approach on a primary school which is used PMRI approach? 4. How is a teacher understanding about the mathematics concepts which are found by students in the teaching learning process which uses PMRI approach? 5. How is the process to design a teacher guide which helps teachers to appear the guided reinvention principle in PMRI approach on a primary school which is used PMRI approach? If I will answer those research questions, then I will do a qualitative and design research. I will develop a valid, practice, and effective teacher guide which helps teachers to appear the guided reinvention principle in PMRI approach on a primary school which is used PMRI approach when I do a design research. Key words: student book, teacher book, PMRI,and a guided reinvention principle

Fast magnetohydrodynamic oscillation of longitudinally inhomogeneous prominence threads: an analogue with quantum harmonic oscillator

Previous works indicate that the frequency ratio of second and first harmonics of kink oscillations has tendency towards 3 in the case of prominence threads. We aim to study the magnetohydrodynamic oscillations of longitudinally inhomogeneous prominence threads and to shed light on the problem of frequency ratio. Classical Sturm--Liouville problem is used for the threads with longitudinally inhomogeneous plasma density. We show that the spatial variation of total pressure perturbations along the thread is governed by the stationary Schr\"{o}dinger equation, where the longitudinal inhomogeneity of plasma density stands for the potential energy. Consequently, the equation has bounded solutions in terms of Hermite polynomials. Boundary conditions at the thread surface lead to transcendental dispersion equation with Bessel functions. Thin flux tube approximation of the dispersion equation shows that the frequency of kink waves is proportional to the expression \alpha(2n+1), where \alpha is the density inhomogeneity parameter and n is the longitudinal mode number. Consequently, the ratio of the frequencies of second and first harmonics tends to 3 in prominence threads. Numerical solution of the dispersion equation shows that the ratio only slightly decreases for thicker tubes in the case of smaller longitudinal inhomogeneity of external density, therefore the thin flux tube limit is a good approximation for prominence oscillations. However, stronger longitudinal inhomogeneity of external density may lead to the significant shift of frequency ratio for wider tubes and therefore the thin tube approximation may fail. The tendency of frequency ratio of second and first harmonics towards 3 in prominence threads is explained by the analogy of the oscillations with quantum harmonic oscillator, where the density inhomogeneity of the threads plays a role of potential energy.Comment: 8 pages, 7 figures (accepted in A&A

Spatio-temporal wavelet regularization for parallel MRI reconstruction: application to functional MRI

Parallel MRI is a fast imaging technique that enables the acquisition of highly resolved images in space or/and in time. The performance of parallel imaging strongly depends on the reconstruction algorithm, which can proceed either in the original k-space (GRAPPA, SMASH) or in the image domain (SENSE-like methods). To improve the performance of the widely used SENSE algorithm, 2D- or slice-specific regularization in the wavelet domain has been deeply investigated. In this paper, we extend this approach using 3D-wavelet representations in order to handle all slices together and address reconstruction artifacts which propagate across adjacent slices. The gain induced by such extension (3D-Unconstrained Wavelet Regularized -SENSE: 3D-UWR-SENSE) is validated on anatomical image reconstruction where no temporal acquisition is considered. Another important extension accounts for temporal correlations that exist between successive scans in functional MRI (fMRI). In addition to the case of 2D+t acquisition schemes addressed by some other methods like kt-FOCUSS, our approach allows us to deal with 3D+t acquisition schemes which are widely used in neuroimaging. The resulting 3D-UWR-SENSE and 4D-UWR-SENSE reconstruction schemes are fully unsupervised in the sense that all regularization parameters are estimated in the maximum likelihood sense on a reference scan. The gain induced by such extensions is illustrated on both anatomical and functional image reconstruction, and also measured in terms of statistical sensitivity for the 4D-UWR-SENSE approach during a fast event-related fMRI protocol. Our 4D-UWR-SENSE algorithm outperforms the SENSE reconstruction at the subject and group levels (15 subjects) for different contrasts of interest (eg, motor or computation tasks) and using different parallel acceleration factors (R=2 and R=4) on 2x2x3mm3 EPI images.Comment: arXiv admin note: substantial text overlap with arXiv:1103.353

Inti Dasar – Dasar Pendidikan Matematika Realistik Indonesia

Tujuan ditulisnya dasar-dasar PMRI adalah sebagai standar informal dalam USAha mencari karakteristik PMRI sebagai tambahan atau pembeda dari RME. Dalam “inti dasar-dasar PMRI” ini tidak atau belum disajikan contoh realitas pembelajaran dengan PMRI didalam kelas. Dalam tulisan ini masih diutamakan “dasar filosofis”, “dasar teoretik” dan “dasar aplikatif” dengan sedikit contoh pengarahan didaktik

PMRI and Metacognitive Scaffolding

PMRI (Pendidikan Matematika Realistik Indonesia) has been implemented in some Primary Schools in Indonesia since 2001. Sanata Dharma University (USD) in Yogyakarta is one of the four universities which founded the PMRI Movement. Sanata Dharma University tries to keep its commitment to apply and develop PMRI as one alternative to improve the quality of mathematics education in Indonesia. In the process of development, P4MRI in USD also pays attention to the results of research in various disciplines, e.g. cognitive psychology, cognitive science and neuro science. One of the weakness of mathematics teaching and learning in Indonesia is the teacher centre approach. It is used in practice by most of teachers in the classroom. Their paradigm is related to teaching paradigm. In PMRI we use the learning paradigm in practicing the idea of Freudenthal that mathematics is human activities and pupils learn mathematics based on their experiences. We ask teachers to help students improving their understanding of mathematics by familiarizing them to pose questions to themselves: what, how and why. In solving a problem, the teacher lets them freely to find out their strategy and discuss it in their small group. The teacher helps them by giving some comments on their planning of solution or some suggestions, e.g. “ do some exploration, make a table or a figure, or specialize!” Key words: PMRI, Metacognition, Metacognitive Scaffoldin

Credit Constraints and the Persistence of Unemployment

In this paper, we argue that credit market imperfections impact not only the level of unemployment, but also its persistence. For this purpose, we first develop a theoretical model based on the equilibrium matching framework of Mortensen and Pissarides (1999) and Pissarides (2000) where we introduce credit constraints. We show these credit constraints not only increase steady-state unemployment, but also slow down the transitional dynamics. We then provide an empirical illustration based on a country panel dataset of 19 OECD countries. Our results suggest that credit market imperfections would significantly increase the persistence of unemployment.Credit markets, labor markets, unemployment, credit constraints, search frictions.

Compressed Sensing and Parallel Acquisition

Parallel acquisition systems arise in various applications in order to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating such problems by providing more overall measurements. In this work we consider the combination of compressed sensing with parallel acquisition. We establish the theoretical improvements of such systems by providing recovery guarantees for which, subject to appropriate conditions, the number of measurements required per sensor decreases linearly with the total number of sensors. Throughout, we consider two different sampling scenarios -- distinct (corresponding to independent sampling in each sensor) and identical (corresponding to dependent sampling between sensors) -- and a general mathematical framework that allows for a wide range of sensing matrices (e.g., subgaussian random matrices, subsampled isometries, random convolutions and random Toeplitz matrices). We also consider not just the standard sparse signal model, but also the so-called sparse in levels signal model. This model includes both sparse and distributed signals and clustered sparse signals. As our results show, optimal recovery guarantees for both distinct and identical sampling are possible under much broader conditions on the so-called sensor profile matrices (which characterize environmental conditions between a source and the sensors) for the sparse in levels model than for the sparse model. To verify our recovery guarantees we provide numerical results showing phase transitions for a number of different multi-sensor environments.Comment: 43 pages, 4 figure