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Reflective thinking is the ability of a person to select the knowledge he has to solve the problem at hand, starting from analyzing the problem, evaluating, to concluding. This study aims to describe the reflective thinking skills of students of class VIII C SMP N 1 Pundong in solving mathematical problems in the subject matter of relations and functions. This type of research is descriptive qualitative. The subjects of this study were 26 students taken using the purposive sampling method. The results of this study indicate that the percentage of achievement in the first indicator of reflective thinking describes a case based on mathematical concepts of 72.11%. The second indicator of reflective thinking to identify mathematical concepts or formulas involved in mathematical problems is 54.81%. The third indicator of reflective thinking draws an analogy from two similar cases of 24.04%. The fourth indicator of reflective thinking evaluates based on mathematical concepts was 38.46%. And the fifth indicator of reflective thinking makes conclusions using mathematical concepts by 42.31%. So that the average reflective thinking ability of students in class VIII C is 46.35% in the medium category.

Problems in the macroeconomy that are often faced by various countries are economic growth that is not on target yet. One indicator of economic growth is the value of Gross Regional Domestic Product (GRDP). The GRDP value can be predicted with a multivariate linear regression model. Multivariate linear regression will depend on the assumption of homogeneity and non-multicollinearity. In this research, a GRDP regression model was constructed based on expenditure data current prices in Indonesia and the factors that influence it. The results of the GRDP data exploration and the factors that influence are outliers data and multicollinearity occurs. So that not only a multivariate linear regression model is needed, but also a multivariate linear regression model that is robust to outliers is a robust principal component analysis (RPCA) method. This RPCA method will reduce the dimensions while overcoming the existence of outliers data. Thus, the purpose of this research is to determine the regression model with the RPCA method with robust estimation is the estimated minimum covariant determinant (MCD). The dependent variable used is the GDP of expenditure at current prices in Indonesia in 2018 and the independent variable is net export (X1), inventory change (X2), gross domestic fixed capital formation (X3), government consumption expenditure (X4), expenditure household non-profit consumption (X5), and consumption expenditure household (X6). The results show model which is constructed the GDP prediction is only affected by gross domestic fixed capital formation that is Ŷi = 0.657 + 3.068Wi1 with R2 = 85%

The mathematic literacy performance is the capability that is gotten by students applied on daily activities. The ability which uses logical thinking and knowledge that they got can solve the proses of learning till the subject can be used for life in 21 centuries. This research supposes to describe mathematic ability of student on grade XI IPA 1 SMA N 1 Karangdowo. This type of research is qualitatively descriptive. The research subject of 32 students which are taken using purposive sampling method. The result of research shows that mathematic literacy performance of student only reach on the third level, those are can present the resource information. The first indicator is 87,50% which the highest categorized. The second indicator is 75,78% which the higher categorized. The third indicator is 70,31% which the medium categorized. The fourth indicator is 39,06% which the low categorized. The fifth indicator is 1,56% which the lower categorized and on the sixth indicator is 0%, so that overall can be seen the average mathematic literacy performance for student grade XI IPA 1 is 45,70% with low categorized. The teacher should not push comprehension routine procedural but also variety in giving problem.

Written mathematical communication helps students in the learning process, helps teachers to assess students’ understanding, and becomes the link between the known and the written information with the understood information. The concept of understanding or procedures will be more meaningful if the students can communicate their ideas well. The study aims to describe and analyze students’ written mathematical communication abilities. This research is a qualitative descriptive study. The researchers employ tests and interviews in collecting data. The validity of the data uses the triangulation method. The results reveal that the students who have high communication ability can reach written communication indicators even though not all indicators are achieved correctly. The students who don’t have high communication ability face difficulty in expressing ideas in the form of mathematical symbols/notations so that they use meaningless notation. Meaningless notations are written based on the known information in the task and the results of students’ thinking when they experience difficulties. These students also have not been able to use algebraic expressio ns and draw conclusions correctly. They directly write the results of the answers without the procedure. They state that concluding is unnecessary. Overall, the students who have high, medium, and low ability can draw Venn diagrams even though the diagram is improper.

Tetanus is caused by Clostridium tetani bacteria that infect open wounds. Tetanus infection can cause death if not treated promply. SIR models are constructed to explain the spread of infectious diseases. Tetanus is not an infectious disease, but SIR models still can be used. Infected persons can not transmit the disease through contact. Tetanus infection is affected by the environment and first aid when injured. Lack of environment and awareness in first aid will increase the case of tetanus. Prevention efforts are done by vaccination in children, women of childbearing age, and pregnant women as protection for mother and baby (maternal antibody). The purposes of this research are to formulate SIR model with vaccination and maternal antibody (MSVIR) for tetanus disease and to apply the model in Indonesia. The MSVIR model is a first order linear differential equation system with five dependent variables, there are M, S, V, I, and R, and an independent variable t (time). The parameter’s values were estimated based on data in 2009-2014. The accuracy of this model was measured based on data in 2015-2016 years. The relative error rates on 2015-2016 were -0.0567 and 0.0825. The model is considered good enough. Based on the predictions during 2011-2030, the incidence of tetanus will increase 6.62% by 1.2% average increase per year.

Tuberculosis (TB) is a contagious disease prevented by the vaccination of Bacillus Calmette-Geurin (BCG). The sufferer is treated by giving the Directly Observed Treatment Shortcourse (DOTS). The patients sometimes do not take the medicine regularly so that the TB-bacteria do not completely vanish from their body. The bacteria only weaken so the patients can be re-infected (relapse). Mathematical modelling can be used to determine TB transmission based on changes in the number of TB patients. By concerning vaccination and relapse factors, a susceptible vaccinated infected recovered (SVIR) model with relapse in TB transmission need to be developed. Indonesia got the second rank in the new case of TB in the world. In the national program of TB prevention, Indonesia has three indicators i.e. prevalence, incidence, and mortality rate. In this article, we derive SVIR model with relapse in TB transmission, then apply the model in Indonesia and measure its accuracy. Furthermore, we also predict the three indicators of TB in Indonesia. The model is nonlinear first-order differential equations. The model is applied in Indonesia by estimating parameters based on 2004-2014 data. Model accuracy is measured based on relative errors in 2015 and 2016. Absolute values of relative error S, V, I, R, and TB incidence are less than 0.1. Thus, the model is said to be quite accurate and can be used to predict the prevalence, incidence, and mortality rates of TB in Indonesia. The prediction of these three indicators shows a decline year by year with an average decrease of 1.90% for prevalence and mortality rates and 1.68% for incidence rates.

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys' prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys' prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys' prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

Geometry is one branch of mathematics that an important role in learning mathematics in the schools. This research aims to find out about Discovery Learning with SAVI approach to achievement of learning geometry. This research was conducted at Junior High School in Surakarta city. Research data were obtained through test and questionnaire. Furthermore, the data was analyzed by using two-way Anova. The results showed that Discovery Learning with SAVI approach gives a positive influence on mathematics learning achievement. Discovery Learning with SAVI approach provides better mathematics learning outcomes than direct learning. In addition, students with high self-efficacy categories have better mathematics learning achievement than those with moderate and low self-efficacy categories, while student with moderate self-efficacy categories are better mathematics learning achievers than students with low self-efficacy categories. There is an interaction between Discovery Learning with SAVI approach and self-efficacy toward student's mathematics learning achievement. Therefore, Discovery Learning with SAVI approach can improve mathematics learning achievement.

The student with visual impairment, total blind category depends on the sense of touch and hearing in obtaining information. In fact, the two senses can receive information less than 20%. Thus, students with visual impairment of the total blind categories in the learning process must have difficulty, including learning mathematics. This study aims to describe the problem-solving process of the student with visual impairment, total blind category on mathematical literacy issues based on Polya phase. This research using test method similar problems mathematical literacy in PISA and in-depth interviews. The subject of this study was a student with visual impairment, total blind category. Based on the result of the research, problem-solving related to mathematical literacy based on Polya phase is quite good. In the phase of understanding the problem, the student read about twice by brushing the text and assisted with information through hearing three times. The student with visual impairment in problem-solving based on the Polya phase, devising a plan by summoning knowledge and experience gained previously. At the phase of carrying out the plan, students with visual impairment implement the plan in accordance with pre-made. In the looking back phase, students with visual impairment need to check the answers three times but have not been able to find a way.

Mathematics authentic assessment is a form of meaningful measurement of student learning outcomes for the sphere of attitude, skill and knowledge in mathematics. The construction of attitude, skill and knowledge achieved through the fulfilment of tasks which involve active and creative role of the students. One type of authentic assessment is student mini projects, started from planning, data collecting, organizing, processing, analysing and presenting the data. The purpose of this research is to learn the process of using authentic assessments on statistics learning which is conducted by teachers and to discuss specifically the use of mini projects to improving students' learning in the school of Surakarta. This research is an action research, where the data collected through the results of the assessments rubric of student mini projects. The result of data analysis shows that the average score of rubric of student mini projects result is 82 with 96% classical completeness. This study shows that the application of authentic assessment can improve students' mathematics learning outcomes. Findings showed that teachers and students participate actively during teaching and learning process, both inside and outside of the school. Student mini projects also provide opportunities to interact with other people in the real context while collecting information and giving presentation to the community. Additionally, students are able to exceed more on the process of statistics learning using authentic assessment.

Mathematics learning achievement is influenced by the internal and external factor of the students. One of the influencing external factors is social interaction with friends in learning activities. In modern learning, the learning is student-centered, so the student interaction is needed to learn about certain basic competence. Potential and motivation of students in learning are expected to develop with good social interaction in order to get maximum results. Social interaction is an important aspect of learning Mathematics because students get the opportunity to express their own thoughts in order to encourage a reflection on the knowledge they have. This research uses the correlational descriptive method involving 36 students for the tenth grade, eleventh grade, and twelfth grade of SMA Negeri 1 Wuryantoro and data collecting technique using questionnaire for social interaction and documentation for learning outcome. The result of this research shows that learning achievement and social interaction of students are not good. Based on the result of data analysis, it is shown that the social interaction and Mathematics learning achievement are still in the low level. This research concludes that students' social interaction influences student learning achievement in Mathematics subjects.

This research aims to determine the students' thinking level based on bloom taxonomy guidance and reviewed from students' Intrapersonal Intelligence. Taxonomy bloom is a taxonomy that classifies the students' thinking level into six, ie the remembering, understanding, applying, analyzing, creating, and evaluating levels. Students' Intrapersonal Intelligence is the intelligence associated with awareness and knowledge of oneself. The type of this research is descriptive research with qualitative approach. The research subject were taken by one student in each Intrapersonal Intelligence category (high, moderate, and low) which then given the problem solving test and the result was triangulated by interview. From this research, it is found that high Intrapersonal Intelligence students can achieve analyzing thinking level, subject with moderate Intrapersonal Intelligence being able to reach the level of applying thinking, and subject with low Intrapersonal Intelligence able to reach understanding level.

This study aims to determine the extent to which the students 'thinking level based on SOLO taxonomy in geometry learning viewed from students' self efficacy (SE). This research utilizes descriptive research with qualitative approach. The data was collected by giving SE questionnaires to 32 students of grade VIII Junior High School which were then categorized into three (high, medium, and low). The subjects of the study were taken by one student in each SE category (high, medium, and low) which then given the problem solving test and the result was triangulated by interview. From this research, it is found that students with high SE can achieve uniructural-relational thinking level, subject with medium SE can be reach the level of unistructural-multistructural thinking, and subject with low SE able to reach unistructural-pristructural level. By paying attention to SE in learning, especially in problem solving process, it is expected that the educator can prepare the learning as well as possible so as to obtain optimal learning achievement.

Comic is one of the frequently used media in our daily life. This media has been familiar for the community. Comic is mostly used as entertainment facilities. Along with the current development, comics are not only functioned as a means of entertainment, but also used in the field of education. There were some problems in a classroom which encouraged the researchers to use comics as a solution for those problems. This article aims at discussing on comics as an instructional media which is appropriate for students. This research uses research and development (R and D) method. The results obtained from this study are based on the students' responses of the questionnaires and validation to help them understanding the system of linear equations material. Results show that comics can be used to replace LKS (student worksheet). Feedbacks from students and validators also show that comic is an attractive medium. It is said so since comics link the concrete into abstract things so that it is easily understood by the students.

The demand of a product is linearly dependent on the retail price and quality of the product. We address a closed-loop supply chain where the manufacturer manufactures products according to the demand and sells them through a retailer in the market. A third party collects the used products from costumers and sends to the manufacturer to increase the quality. If the products can retrieve the original quality, thus the process is called remanufacturing. Not every products can retrieve the original quality, thus manufacturer refurbish this products with lower price. We construct four different scenarios – centralized and decentralized led by manufacturer, retailer, and third party. From the comparison of the result obtained in the numerical example, we conclude that the joint profit obtained under centralized, manufacturer-led, and retailer-led policies is higher than third party-led policy.

Ebola is a deadly infectious disease and has caused an epidemic on several countries in West Africa. Mathematical modeling to study the spread of Ebola disease has been developed, including through models susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR). Furthermore, susceptible exposed infected isolated recovered (SEIIhR) model has been derived. The aims of this research are to derive SEIIhR model for Ebola disease, to determine the patterns of its spread, to determine the equilibrium point and stability of the equilibrium point using phase plane analysis, and also to apply the SEIIhR model on Ebola epidemic in Sierra Leone in 2014. The SEIIhR model is a differential equation system. Pattern of ebola disease spread with SEIIhR model is solution of the differential equation system. The equilibrium point of SEIIhR model is unique and it is a disease-free equilibrium point that stable. Application of the model is based on the data Ebola epidemic in Sierra Leone. The free-disease equilibrium point (Se; Ee; Ie; Ihe; Re )=(5743865, 0, 0, 0, 0) is stable.

This research is aimed to find out the effect of learning model towards learning achievement in terms of students' logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students' achievements with NHT learning model by Concept Maps were better than students' achievements with TGT model by Concept Maps and Direct Learning model. The students' achievements with TGT model by Concept Maps were better than the students' achievements with Direct Learning model. 2) The students' achievements that exposed high logical mathematics intelligences were better than students' medium and low logical mathematics intelligences. The students' achievements that exposed medium logical mathematics intelligences were better than the students' low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

A regression model is the representation of relationship between independent variable and dependent variable. The dependent variable has categories used in the logistic regression model to calculate odds on. The logistic regression model for dependent variable has levels in the logistics regression model is ordinal. GWOLR model is an ordinal logistic regression model influenced the geographical location of the observation site. Parameters estimation in the model needed to determine the value of a population based on sample. The purpose of this research is to parameters estimation of GWOLR model using R software. Parameter estimation uses the data amount of dengue fever patients in Semarang City. Observation units used are 144 villages in Semarang City. The results of research get GWOLR model locally for each village and to know probability of number dengue fever patient categories.

In this study, we consider a stochastic integrated manufacturer-retailer inventory model with service level constraint. The model analyzed in this article considers the situation in which the vendor and the buyer establish a long-term contract and strategic partnership to jointly determine the best strategy. The lead time and setup cost are assumed can be controlled by an additional crashing cost and an investment, respectively. It is assumed that shortages are allowed and partially backlogged on the buyer's side, and that the protection interval (i.e., review period plus lead time) demand distribution is unknown but has given finite first and second moments. The objective is to apply the minmax distribution free approach to simultaneously optimize the review period, the lead time, the setup cost, the safety factor, and the number of deliveries in order to minimize the joint total expected annual cost. The service level constraint guarantees that the service level requirement can be satisfied at the worst case. By constructing Lagrange function, the analysis regarding the solution procedure is conducted, and a solution algorithm is then developed. Moreover, a numerical example and sensitivity analysis are given to illustrate the proposed model and to provide some observations and managerial implications.

GWOLR model combines geographically weighted regression (GWR) and (ordinal logistic reression) OLR models. Its parameter estimation employs maximum likelihood estimation. Such parameter estimation, however, yields difficult-to-solve system of nonlinear equations, and therefore numerical approximation approach is required. The iterative approximation approach, in general, uses Newton-Raphson (NR) method. The NR method has a disadvantage—its Hessian matrix is always the second derivatives of each iteration so it does not always produce converging results. With regard to this matter, NR model is modified by substituting its Hessian matrix into Fisher information matrix, which is termed Fisher scoring (FS). The present research seeks to determine GWOLR model parameter estimation using Fisher scoring method and apply the estimation on data of the level of vulnerability to Dengue Hemorrhagic Fever (DHF) in Semarang. The research concludes that health facilities give the greatest contribution to the probability of the number of DHF sufferers in both villages. Based on the number of the sufferers, IR category of DHF in both villages can be determined.

In this research, an integrated vendor-buyer inventory model with a random number of defective items under fuzzy random lead time demand is developed. The length of lead time affects the competitive abilities of a business directly and it can be controlled by adding a crashing cost. It is assumed that the lead time demand is normally distributed and the shortages are permitted, which are partially backlogged. In the model, lead time demand, annual demand rate, adjustable production rate, and backorder fraction are imprecise in nature and are represented by the triangular fuzzy numbers. Signed distance method is used to defuzzify the fuzzy total inventory cost. The objective is to determine simultaneously the optimal order quantity, the lead time, and the number of deliveries, which minimise the expected total average cost. An algorithm procedure of finding the optimal solution is developed. Furthermore, numerical example and sensitivity analysis are carried out to illustrate the proposed integrated model.