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181	Mathematics	ABS-260
SIMULATION STUDY TO RELIABILITY TEST IN STRUCTURAL EQUATION MODELING Ferra Yanuar, Aidinil Zetra, Susi Marisa Andalas University Abstract Structural Equation Modeling (SEM) is a statistical technique that is able to analyze relationships between latent variable and its measured variables and amongs latent variables. The purposes of this present study are to construct political participation model in Padang, West Sumatera using SEM approach then implement the reliability tests to the proposed model. The political participation model in this study uses a multidimensional construct, such as Political awareness, political knowledge and political participation. Meanwhile each construct is measured by two and more measured variables. The multidimensional construct reliability in this study was estimated by using Coefficient of Reliability (CR), Coefficient of Reliability Composite Score McDonald’s ω, and Coefficient of Reliability Construct Weighted Ω_ω. Simulation study is done for several size samples and this study yield that all three indicator of reliability tests resulted similar values. This resulted informs that any constructs in proposed model of political participation is reliable and the coresponding proposed model could be accepted. Keywords: Multidimensional construct, political participation, reliability tests, Structural Equation Modeling (SEM) PermaLink | Plain Format | Corresponding Author (Ferra Yanuar)

182	Mathematics	ABS-266
The Application of Empirical Bayes to Model Dengue Fever in Padang, Indonesia Ferra Yanuar, Hazmira Yozza, Siti Juriah, Rahmatika Fajriyati Department of Mathematics, Faculty of Mathematics and Natural Science, Andalas University, Kampus Limau Manis, 25163, Padang – Indonesia Abstract The Dengue Fever is an infectious disease which has always been one of the main health problems in Indonesian society. Dengue Fever is transmitted by Aedes Aegypti mosquito bites. The purposes of this study is to estimate the relative risk of spreading the dengue fever disease in Padang. Estimation is done using the Small Area Estimation method with the Empirical Bayes approach. Small area estimation is useful for estimating parameters in small subpopulations (areas) which have limited number of samples thus acceptable parameter values are hard to be obtained. In this study the construction of the model is based on Poisson-Gamma model and secondary data from Dinas Kesehatan Padang 2017 is used. This study resulted that for each district in Padang, the average relative risk of the spreading of dengue fever is almost the same, which are at medium and low level. Keywords: Dengue Fever, Empirical Bayes, Small Area Estimation, Poisson-Gamma model PermaLink | Plain Format | Corresponding Author (Ferra Yanuar)

183	Mathematics	ABS-285
SEIRS model and simulation for Hepatitis B Syafruddin Side 1 , Muhammad Abdy 1 , and Wahidah Sanus 1 1Department of Mathematics, Faculty of Mathematics and Natural Sciences,Universitas Negeri Makassar Abstract This study discusses the process of the SEIRS model on the spread for Hepatitis B. The mathematical model of the SEIRS for Hapatitis B is a model by dividing the population class into four variables namely Susceptible-Exposed-Infected-Recovered-Suspected (SEIRS) which is a four dimensional nonlinear differential equation system. The model obtained analyzed and simulated using data assuming the initial values ​​of variables and parameters and processed using Maple Software. The simulation results provide predictions of the number of Hepatitis B sufferers who can be a preventative solution. If R0>1 , the hepatitis B disease becomes endemic and if R0>=1, the hepatitis B disease will disappear by itself. Keywords: Hepatitis B, SEIRS Model, Endemic and free disease PermaLink | Plain Format | Corresponding Author (Syafruddin Side)

184	Mathematics	ABS-286
A note on generalized Holder’s inequality in p-summable sequence spaces Al Azhary Masta1, Eka Rahma Kurniasi2, Rajab Vebrian2, and Iis Juniati Lathifah2 1Department of Mathematics Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi 229, Bandung 40154, INDONESIA 2Department of Mathematics Education, STKIP Muhammadiyah, Jl. KH. Ahmad Dahlan 51, Kabupaten Bangka Tengah, Bangka Belitung, 33684, INDONESIA Abstract In this paper we present sufficient and necessary conditions for generalized Ho ̈lder’s inequality in p summable sequence spaces which complete the Masta, et al. result in 2018. One of the keys to prove our results is to use the norm of the characteristic sequence of the balls in Z^n. Keywords: Holders inequality, sufficient and necessary conditions, p-summable sequence spaces PermaLink | Plain Format | Corresponding Author (Al Azhary Masta)

185	Mathematics	ABS-287
A sufficient condition for generalized Ho ̈lder’s inequality in Orlicz sequence spaces Siti Fatimah1, Al Azhary Masta1, Ifronika2, Risnina Wafiqoh3, and Putri Cahyani Agustine3 1Department of Mathematics Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi 229, Bandung 40154, INDONESIA 2Analysis and Geometry Research Group, Bandung Institute of Technology, Bandung, INDONESIA 3Department of Mathematics Education, STKIP Muhammadiyah, Jl. KH. Ahmad Dahlan 51, Kabupaten Bangka Tengah, Bangka Belitung, 33684, INDONESIA Abstract In this paper we present a sufficient condition for generalized Ho ̈lder’s inequality in Orlicz sequence spaces. One of the keys to prove our results is to use the norm of the characteristic sequence of the balls in R^n. Keywords: Ho ̈lders inequality, sufficient and necessary conditions, p-summable sequence spaces PermaLink | Plain Format | Corresponding Author (Al Azhary Masta)

186	Mathematics	ABS-295
Holder’s inequality in Discrete Morrey spaces Al Azhary Masta1, Indra Rukmana2 , Siti Fatimah3, and Muhamamd Taqiyuddin3 1,3 Department of Mathematics Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi 229, Bandung 40154, INDONESIA 2 Raudhatul Jannah Sunior High School, Residence Grand Cilegon, Banten 42426, INDONESIA 4 Department of Mathematics Education, University of Georgia, Athens, United State of America Abstract Morrey spaces is a generalization of Lebesgues spaces. There are two type of Morrey spaces, i.e continous Morrey spaces and discrete Morrey spaces. In this paper we present sufficient and necessary conditions for Ho ̈lder’s inequality in discrete Morrey spaces. One of the keys to prove our results is to use the norm of the characteristic sequence of the balls in Z^n. Keywords: Ho ̈lders inequality, sufficient and necessary conditions, discrete Morrey spaces PermaLink | Plain Format | Corresponding Author (Al Azhary Masta)

187	Mathematics	ABS-299
k-means and GIS for Mapping Natural Disaster Prone Areas in Indonesia Suwardi Annas (a*), Zulkifli Rais (a) a) Department of Statistics, Universitas Negeri Makassar Jalan Mallengkeri, Makassar 90224, Indonesia *suwardi_annas[at]unm.ac.id Abstract The number of natural disasters in Indonesia is very high occurrences. However, the data collected based on natural disasters has a complexity data structure. One of the efforts to make prevention by grouping the areas of natural disaster. The proposed methods to analyze the data are k-means and Geographical Information System (GIS). The k-means method has mapped the areas of natural disaster based on districts into 3, 4, 5, 6 and 7 of clusters. This result showed that the best cluster resulted by 7 of clusters with the smallest root mean square standard deviation (RMSD) than other clusters. Although k-means has obtained the best cluster, however, it was difficult to present the clustering of natural disaster districts in the map. Therefore, a GIS method was used to improve the cluster visualization of k-means. The main purpose of GIS is to develop a visual map of the natural disaster districts according to a given cluster of the k-means. GIS method can be a useful tool to improve the visualization information of k-means clustering and enables interpretation of the disparities of natural disaster by districts in Indonesia. Keywords: GIS; k-means; Natural disaster; RMSD PermaLink | Plain Format | Corresponding Author (Suwardi Annas)

188	Mathematics	ABS-312
Joint modeling of wet condition characteristics of Makassar city Wahidah Sanusi(a*), Sahlan Sidjara(a), Sudarmin(b), Muhammad Abdy(a) a) Department of Mathematics, Universitas Negeri Makassar, Parangtambung, Makassar, 90224, Indonesia *wahidah.sanusi[at]unm.ac.id b) Department of Statistics, Universitas Negeri Makassar, Parangtambung, Makassar, 90224, Indonesia Abstract A multivariate analysis on rainfall variables is needed to understand relationships among characteristics of rainfall variables. The monthly rainfall amount records from three stations during the period of 1985-2014 in Makassar are used. The Standardized Precipitation Index is employed to classify data into wet category. The aim of this study is to investigate the most appropriate joint probability distribution function of wet duration and wet severity based on bivariate Archimedean copulas. The copulas are Gumbel-Hourgaard, Frank, Joe, and Clayton. Parameter of copulas are estimated by Kendall’s tau correlation coefficient. The study result show that the Frank copula was identified as the best copula in joint modelling between wet duration and wet severity at MMP and BRP stations, meanwhile the Gumbel-Hougaard copula at BBMKG station. This results could be useful information for determining return periods of wet condition characteristics. Keywords: Bivariate distributions; copula; wet duration; wet severity PermaLink | Plain Format | Corresponding Author (Wahidah Sanusi)

189	Mathematics	ABS-60
Numerical Algorithm for Space-Fractional Diffusion Equations via PAOR Andang Sunarto and Jumat Sulaiman 1.IAIN Bengkulu, Indonesia. 2.Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Malaysia. Abstract In this study, we examines the effectiveness of the Preconditioned Accelerated Over-Relaxation (PAOR) iterative method together with an unconditionally implicit finite difference approximation equation to solve space-fractional diffusion equations (SFDE’s) by using the Caputo’s space-fractional derivative. For this, the implicit approximation equation and preconditioned matrix are used to construct the corresponding preconditioned linear system in which its coefficient matrix is large scale and sparse. Then, formulation and implementation the PAOR iterative method are also presented. Based on numerical algorithm results of the proposed iterative method, it can be concluded that the proposed iterative method (PAOR) is superior to the PSOR and PGS iterative methods. Keywords: PAOR, Space-fractional diffusion equations, Implicit finite difference, Caputo’s PermaLink | Plain Format | Corresponding Author (Andang Sunarto)

190	Mathematics	ABS-326
Generalized Estimating Equation (GEE) Method Approach to Determine The Best Longitudinal Regression Model on Human Development Index Data In West Java Hilda Nurmuslimah, Asep Solih Awalluddin, Rini Cahyandari Islamic State University of Sunan Gunung Djati Bandung Abstract Longitudinal regression is a statistical method used to analyze the relationship between one or more independent variables and dependent variables on longitudinal data. Longitudinal data is the result of observation of a study in several different periods. Collecting data periodically causes the correlation in each object observation so that longitudinal data could not be analyzed with the usual regression methods. One of method used for regression analysis of correlated data is Generalized Estimating Equation (GEE). GEE method provides many types of correlation structures that are independent, exchangeable, AR(1) and unstructured. This research has intention to determine the best longitudinal regression models on study case of Human Development Index (HDI) in 2010-2014 used GEE method and four different correlation structures. The best model of it will be determined by using Quasi-likelihood Information Criterion (QIC) test. The result of analysis by seeing the smallest value of QIC is AR (1). Keywords: Longitudinal Regression,Generalized Estimating Equation,Correlation,Human Development Index PermaLink | Plain Format | Corresponding Author (Hilda Nurmuslimah)

191	Mathematics	ABS-341
The Application of Graph Theory for Changing Active to Passive Sentence in Indonesian Language Susila Bahri, Nova Noliza Bakar, Des Welyyanti, Aulia Rahmayu Firdaus Andalas University Abstract In this study, the mathematical model for changing active sentence to passive sentence in Indonesian language is constructed. In the construction process, the ten types of words are expressed as vertices on directed graphs called sentence graphs. The edges of the graphs are weighted with positive integers in the order of words in the sentence. The graph is then expressed as an adjacency matrix. The matrices form vector spaces. Finally, a linear transformation is carried out to get a sentence graph. Keywords: changes active sentences to passive, sentence graph, adjacency matrix, linear transformation PermaLink | Plain Format | Corresponding Author (Susila Bahri)

192	Mathematics	ABS-346
Risk of Death for Low Birth Weight Babies Using Cox Regression Dewi Murni, Yenni Kurniawati, Rosi Ramayanti UNP Abstract Low Birth Wieght (LBW) is one of the factors triggering the occirence of infant mortality in the neonatal period. Factors affecting the risk of low birth weight is a factor of maternal death, fetal factors, infant birth weight factors and socio economic factors. That this study aims to look at the factors that affect the risk of death LBW base on the chance of death factors. One statistical analysis used in looking at the relationship of LBW risk of death is the Cox regression model. The results of this study indicate that the factors that influence the risk of LBW death are gestational age and infant birth weight. Opportunity risk of death for LBW who have gestational age <37 weeks is 8.424 times greater than the LBW who have ≥37 weeks gestation. Then chances LBW risk of death with birth weight <1499 gr was 8.547 times greater than the LBW with birth weight 1500-2499 gr. Keywords: LBW, neonatal, Cox Regression PermaLink | Plain Format | Corresponding Author (Dewi Murni)

193	Mathematics	ABS-108
Correlation between Coefficient of Thermal and Thermal stress fracture resistance on Ceramics filter exhaust Husty Serviana Husain Universitas Pendidikan Indonesia Abstract Data from 2017 to Dec. 14 2018 shows that there is a trend increase from the Coefficient of Thermal (CTE) from the Ceramics filter product from a company A and this makes a decrease in the meting point value of the Ceramic filter product which has approached the customer min spec (≥ 650 oC). A CTE value is needed that can be used as a standard to ensure the melting point value does not come out of the customer spec value. By using the correlation method a minimum CTE value will be used as a standard to guarantee the quality of the Ceramics filter from company A Keywords: CTE, Statistics, Correlation PermaLink | Plain Format | Corresponding Author (Husty Serviana Husain)

194	Mathematics	ABS-122
The metric dimensions of bridge graphs for some classes of graphs Amrullah, Turmuzi M, Syahrul A., Baidowi, Nani K. Universitas Mataram Abstract The metric dimension of a graph is one of the interesting problems in the research of dimensions of the graph. There are many open problems that have not been resolved until now, some of them are metrics dimension of the bridge graph and metrics dimension of the disconnected graph. This paper presents the metrics dimension of the bridge graph in several classes of graphs namely circle, complete, and star graphs. We know that the metric dimensions of the complete, circle or star graph have been obtained. The bridge graph B (G_1,G_2,e) is a graph which is obtained from the operation of adding edge e to graphs G_1 and G_2. To obtain the metric dimension of the bridge graph from the graphs G_1 and G_2 on edge e, pd(B (G_1,G_2,e)), we used the graph structure of G_1, G_2 and the properties of the bridge graph based on the endpoint on the edge e. The results, we have show the metric dimension of the bridge graph B(G_1,G_2,e) for the circle, complete, or star graphs. Keywords: metric dimension, bridge graph, circle graph, complete graph, star graph PermaLink | Plain Format | Corresponding Author (Amrullah Amrullah)

195	Mathematics	ABS-123
Analytical Study and Numerical Solutions of Bird Flu Epidemic Model with Vaccination Arrival Rince Putri (a*), Mahdhivan Syafwan (b) a,b) Department of Mathematics, Andalas University, Kampus Unand Limau Manis, Padang, 25163, Indonesia *arrivalputri[at]gmail.com Abstract Mathematical modeling is a tool used for the mechanism of strategy in controlling epidemics. In this paper, a basic model for bird flu epidemic is developed. Vaccination treatment of bird flu is a common method used to control disease. The bird flu model is reformulated by taking into account vaccination. Those models are system of ordinary differential equations. Stability of both the models are discussed and associated with the threshold number stating population is free of disease or infected. Numerical solutions are given on phase plane to confirm the analytical results. Keywords: Epidemic model; Vaccination; stability; Threshold number; Numerical solutions PermaLink | Plain Format | Corresponding Author (Arrival Rince Putri)

196	Mathematics	ABS-125
Study of Stability for Some Simple Epidemic Models Arrival Rince Putri1 (a*), Riri Lestari (b) a,b) Department of Mathematics, Andalas University, Kampus Unand Limau Manis, Padang, 25163, Indonesia *arrivalputri[at]gmail.com Abstract The Susceptible Infected and Removed (SIR) model is extended by considering three treatments, without vaccination, vaccination in susceptible individuals, and mutation in disease viruses. Equilibrium points of those models were determined. Stability of those models was analyzed and associated with threshold parameters. Analytical result was confirmed by numerical result showing plot solution and behaviour of the system in phase plane. The results of this study inform parameters that affect stability of the system so that the best policy to prevent endemic can be proposed. Keywords: Epidemic model; Vaccination; Mutation; Stability; Numerical PermaLink | Plain Format | Corresponding Author (Arrival Rince Putri)

197	Mathematics	ABS-131
A Modified Lax-Friedrichs Method for the Shallow Water Equations Kartika Yulianti, Rini Marwati, Suci Permata Hati Universitas Pendidikan Indonesia Abstract In this paper, we present a simple modified Lax-Friedrich method for the numerical solution of shallow water equations. In the proposed method, we approximate the next-step value by applying the Lax–Friedrichs method at the half grid of space. The method were applied to simulate the wave propagation at a rest pool for non-flat topography. Based on the simulation, the proposed method is more accurate in terms of fulfill the conservation law than the classical Lax-Friedrichs method and it shows good agreement with steady analytical solution. Keywords: Shallow water equations, Lax-Friedrichs method, Modification PermaLink | Plain Format | Corresponding Author (kartika yulianti)

198	Mathematics	ABS-140
Staggered numerical modelling for investigating effectiveness of seawall and vegetation on the reduction of wave run-up Iryanto1*, Muhamad Mustamiin1, Munengsih Sari Bunga1, Ikha Magdalena2 , and Novry Erwina2 1 Informatics Department, Politeknik Negeri Indramayu, Indonesia. 2 Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia. Abstract In this research, we develop mathematical model to investigate the effectiveness of embankment and vegetation on the reduction of wave run-up. We solve the model numerically using a staggered finite volume method. Wave run-up test on a sloping beach is conducted to show the accuracy of our numerical scheme. In this case, we compare our numerical results with results of laboratory experiment of Synolakis in 1987. Further, sensitivity analysis is presented to see the effect of the characteristic of the structures. Keywords: Wave run up, staggered finite volume, overtopping, wave mitigation PermaLink | Plain Format | Corresponding Author (Iryanto Iryanto)

199	Mathematics	ABS-147
Toeplitz Algebras of Cyclically Ordered Groups Isnie Yusnitha, Rizky Rosjanuardi, Sumanang Muhtar Gozali Department of Mathematics Education, Universitas Pendidikan Indonesia Abstract Suppose G is a cyclically ordered group. In general, a positive cone P(G) is not necessarily a semigroup. Nevertheless, for particular class of cyclically ordered group G, namely linear cyclically ordered group, P(G) is a semigroup. Furthermore, one can verify that the semigroup P(G) admits a representation on a Hilbert space. We develop the classical Toeplitz algebra theory to more general setting of ordered group, that is, to each cyclically ordered group G such that the positive cone P(G) is a semigroup, we define a Toeplitz algebra Τ (G). Keywords: cyclically ordered group, linear, semigroup, Toeplitz algebras PermaLink | Plain Format | Corresponding Author (Isnie Yusnitha)

200	Mathematics	ABS-150
Several Properties of Discrete Orlicz Spaces Pradipta Swiantana Prayoga, Siti Fatimah, and Al Azhary Masta Universitas Pendidikan Indonesia Abstract Introduced by Z. W. Birnbaum and W. Orlicz in 1931, Orlicz spaces are generalization of the Lebesgue spaces. There are two kinds version of Orlicz spaces which are continuous Orlicz spaces denoted by \(L_Φ\) and discrete Orlicz spaces denoted by \(l_Φ\). The properties of \(L_Φ\) spaces are already known. The aim of this study is to discuss the properties of discrete Orlicz spaces. We will see that the properties of continuous Orlicz spaces are also valid on discrete Orlicz spaces. Methods in this research are by using the properties of Young function and Luxemburg Norm. The result of this research is to show that several properties of continuous Orlicz space are also valid on discrete Orlicz space. Keywords: Lebesque spaces, continue Orlicz spaces, discrete Orlicz spaces PermaLink | Plain Format | Corresponding Author (Pradipta Swiantana Prayoga)

201	Mathematics	ABS-157
COMPARISON BETWEEN CONVEX AND QUASICONVEX FUNCTIONS ON R WITH DEVELOPMENT Encum Sumiaty, Endang Dedy Department of Mathematics Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudhi no. 229, Bandung 40154, Indonesia Abstract According to study about convex function, A. W. Roberts and D. E. Varberg[17] have studied further. In this paper, we will introduce some basic properties about convex function and quasiconvex fucnction on R. Some comparison between properties of convex function and quasiconvex function will be presented also. Our results are quasiconvex function can be represented as monotone function either or at most as two combination of monotone functions, as consequences it is discontinuous mostly at countable points, and it is not differentiable at zero measure set only. However the results are still fundamental, but we will learn as clear as we can. Keywords: Convex Function, Quasiconvex Function, Convex Function Space, Quasiconvex Function Space PermaLink | Plain Format | Corresponding Author (Encum Sumiaty)

202	Mathematics	ABS-158
Two Dimesional Interpolation Using Tensor Product of Two Chebyshev Systems that Minimizing Integral Energy order N Lukita Ambarwati, Devi Eka Wardhani Universitas Negeri Jakarta Abstract In this paper we will solve the interpolation problem on two dimension, that is given k points (xi,yi,ci), i=1,2,...,k, we will found continuous function U(x,y) such that U(xi,yi)=ci, i=1,2,...,k and U minimizing integral energy order N. The support points (xi,yi) did not have rectangular grid form. We will use tensor product of two Chebychev systems as a base of interpolation function space. Keywords: Interpolation, Non rectangular grid form, Tensor product, Chebyshev Systems, Minimizing energy PermaLink | Plain Format | Corresponding Author (Lukita Ambarwati)

203	Mathematics	ABS-221
On cyclically ordered groups and theirs direct product Sumanang Gozali, Rizky Rosjanuardi, Isnie Yusnitha UPI Abstract In this paper we review the main properties of cyclically ordered groups . Moreover, for two cyclically ordered groups A and B, we construct a cyclic order on the direct product A×B. Keywords: cyclic order, cylic ordered group, direct product PermaLink | Plain Format | Corresponding Author (Sumanang Muhtar Gozali)

204	Mathematics	ABS-223
Poisson Autoregressive Spatial Model to Detect Factors that Influence the Number of HIV AIDS Patients in East Jakarta Siti Rohmah Rohimah UNJ Abstract The AIDS Commission (KPA) recorded the highest number of sufferers of Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) in East Jakarta in DKI Jakarta. This study aims to determine the factors that influence spatially and non-spatially on the number of people with HIV / AIDS in East Jakarta. The results of this study are expected to be useful in eradicating HIV / AIDS, especially in East Jakarta and generally for other regions that have the same characteristics as East Jakarta. The parameter estimation method in this study used the maximum likelihood method. The results showed that spatial and non-spatial factors had a significant effect with alpha 5%. In addition, the addition of spatial factors gave smaller standard error value. Therefore, it can be concluded that the Poisson autoregressive spatial model provided better parameter estimation results than the Poisson regression model. Keywords: HIV / AIDS, Spatial Autoregressive Poisson, Poisson Regression, Maximum Likelihood PermaLink | Plain Format | Corresponding Author (Siti Rohmah Rohimah)

205	Mathematics Education	ABS-257
Teacher Knowledge to Overcome Student Errors in Pythagorean Theorem Proof: A Study Based on Didactic Mathematical Knowledge Framework Rudi (a), Didi Suryadi (b), Rizki Rozjanuardi (c) Universitas Pendidikan Indonesia Abstract Teachers’ ability in overcoming to student errors is significantly affected by teachers’ knowledge. Discussion and studies related to what knowledge teachers should possess have resulted in a theoretical framework. This article aims at describing teacher knowledge to responding to student errors in Pythagorean Theorem proof using a didactic mathematical knowledge approach. This research applies qualitative design. Five junior high school mathematics teachers in Indonesia participate in this study. Data were collected using written tests on teachers’ competence and structured interview. Research findings show that two participants cannot accurately answer the questions in the instrument which measures teachers’ mathematical knowledge needed to overcome student errors. Another finding indicates that those teachers who do not possess mathematical knowledge in dealing with student errors are also not completed with good didactic knowledge, especially on cognitive, epistemic, ecological, and interactional aspects. Based on the analysis of participants’ responses, it can be concluded that teacher knowledge to overcome student errors in Pythagorean Theorem proof is significantly affected by other knowledge components. Keywords: Didactic mathematical knowledge, Pythagorean Theorem proof, student errors, teacher knowledge PermaLink | Plain Format | Corresponding Author (Rudi Rudi)

206	Mathematics Education	ABS-270
Identification Of Student’ Critical Thinking Ability In Solving Open Ended Mathematics Problem Viewed From Cognitive Styles Masriyah, Khofidhotur Rofiah, Umi Hanifah Universitas Negeri Surabaya Institut Teknologi dan Sains Nahdlatul Ulama Pasuruan Abstract Mathematics has an important role in developing the human mind power, one of them is critical thinking. The critical thinking ability might be taught by using problem solving. The strategy that is used to solve the problem can be affected by student’cognitive style. The research purpose is to identify student’ critical thinking ability in problem solving based on their cognitive styles. The research subjects are two student who have reflective or impulsive cognitive style. The data were collected by giving cognitive style, mathematics ability, and problem solving tests, and interview. The research result showed that the reflective student has seven indicators of critical thinking ability, they are the ability to comprehend and express the meaning of information, distinguish relevant and irrelevant information, analyze the data, collect and organize information, find ways of completion, draw conclusions, and evaluate the completion. Based on the level of critical thinking, she is very critical. While impulsive student has four of the seven indicators of critical thinking ability, they are the ability to comprehend and express the meaning of information, distinguish relevant and irrelevant information, collect and organize information, and draw conclusions. Based on the level of critical thinking, she is critical enough. Keywords: Critical Thinking Abilities, Problem Solving, Cognitive Style PermaLink | Plain Format | Corresponding Author (Masriyah Masriyah)

207	Mathematics Education	ABS-15
Analysis of Mathematical Understanding of Prospective Mathematics Teachers in The Conic Concept with Rasch Model Eyus Sudihartinih; Tia Purniati; Ade Rohayati Universitas Pendidikan Indonesia Abstract This study aims to obtain a general description of the analysis of mathematical understanding of prospective mathematics teachers in the conic concept with Rasch models. This study was pre-experimental with a type of one-shot case study involving students of prospective mathematics teachers in the second semester consisting of 29 women and 10 men at one university in Indonesia. This study uses a test instrument in the form of an essay question consisting of three questions designed by a research team that is a lecturer in analytic geometry courses. The results of the analysis of mathematical understanding of prospective mathematics teachers in analytic geometry lectures with the Rasch model show that only a small proportion of students have high mathematical understanding. The results of the Rasch model measurement to examine the instruments show that the items used are not reliable and cannot be accepted to measure the mathematical understanding of prospective mathematics teachers in the conic concept. So that further research is needed on the instruments and mathematical understanding of prospective mathematics teachers in conic concept lectures with the Rasch model. Keywords: mathematical understanding, pre-experimental, analytic geometry lectures, Rasch models, Item-Response theory PermaLink | Plain Format | Corresponding Author (Eyus Sudihartinih)

208	Mathematics Education	ABS-271
Application of Problem Based Learning Approach with Probing-Prompting Techniques to Improve Students Adaptive Reasoning Capabilities Nia Gardenia(a),(b)*, Tatang Herman(a), Andri Rahadyan(b), Taufiqulloh Dahlan(c) a)Departemen Pendidikan Matematika, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi No. 229, Bandung 40154, Indonesia b)Departemen Pendidikan Matematika, Universitas Indraprasta PGRI, Jl. Nangka No. 58C (TB. Simatupang), Tanjung Barat, Jagakarsa, RT.5/RW.5, Jakarta Selatan, DKI Jakarta 12530, Indonesia c)Departemen Pendidikan Matematika, Universitas Pasundan, Jl. Tamansari No. 6-8, Tamansari, Bandung Wetan, Kota Bandung, Jawa Barat 40116, Indonesia Abstract This study aims to obtain an overview of the adaptive reasoning abilities of students who get mathematics learning through the Problem Based Learning approach with Probing-Prompting techniques compared to students who get conventional learning. The subjects in this study were eighth grade students of SMP Negeri 3 Lembang, West Bandung Regency. The problems underlying this research include the adaptive reasoning ability of students in Indonesia is still low so innovation is needed in learning that can develop students adaptive reasoning abilities. This research is a quasi-experimental research. Data obtained through research instruments in the form of tests and non-tests. Data analysis was carried out quantitatively. Quantitative analysis was performed by calculating the N-gaint using the normality test, and the Mann-Whitney U test. The results showed an increase in students adaptive reasoning abilities in both groups, an increase in the adaptive reasoning abilities of students who obtained mathematics learning through the Problem Based Learning approach with Probing- Prompting is better than students who get conventional learning. Keywords: problem based learning approach, probing-prompting technique, adaptive reasoning ability PermaLink | Plain Format | Corresponding Author (Nia Gardenia)

209	Mathematics Education	ABS-281
Future of Teachers Education: Preparation And Expert Validity Instruments of Class Culture Wardani Rahayu (1*). Erwin Sulaeman (2) (1*.2) State University of Jakarta, JL. Rawamangun Muka Jakarta Timur 13220 Indonesia Abstract The purpose of this study is to find out how the dimensions, aspects, and items of classroom culture instruments. This study was adopted from the interpretive-constructivist paradigm using the quality methodology. Research subjects were 9 experts who were randomly. Instrument modification from WIHIC is with dimensions of teacher support, involvement, investigation, authentic task orientation, cooperation, equity, access, interaction, transformation, and using technology. The results showed that the assessors provided advice and input in examining the appropriateness of the dimensions, items and aspects being assessed. Systematically the preparation of PPG class culture instruments produced 54 items that were declared valid based on expert agreement. Existing statement items met various measurement criteria that can be used to measure the class culture of PPG students in Indonesia. The dimension that needed to be corrected was the authentic task orientation indicator. Almost all experts provided improvement in aspects of language. Keywords: class culture, expert validity, WIHIC PermaLink | Plain Format | Corresponding Author (Wardani Rahayu)

210	Mathematics Education	ABS-26
Teaching Fraction with Multiple Representations S Widodo; T Ikhwanudin 1Universitas Pendidikan Indonesia, Jl. Dr. Setiabudhi 229, Bandung 40154, Indonesia 2PPPPTK TK dan PLB, Jl. Dr. Cipto No. 9, Bandung 40171, Indonesia Abstract This research aims to analyze students’ understanding when fraction is taught with multiple representations. The respondent 27 student of the 7th graders in the junior high school. The research approach was qualitative. The data were collected through paper and pencil measure, observation, and interview. The data were analyzed by grounded theory with coding and constant comparison. The results showed two types of students’ understanding, there are procedural understanding (syntax thinking) and conceptual understanding (semantic thinking). The findings are then elaborated using some related theories to justify the results Keywords: Fraction, Multiple representation PermaLink | Plain Format | Corresponding Author (Suprih Widodo)

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