The purpose of this study is to determine differences in student's learning achievement consisting of learning outcomes and science process skills. This research was conducted in a special school for girls and used two experimental classes, namely experimental class-1 and experimental-2 class. The experimental class-1 is the class applied by PjBL with a brain-based STEAM approach, while the experimental class-2 is a class that uses PjBL with the STEAM approach without brain-based. This research is a quasi-experimental study with a nonequivalent pretest-posttest control group design. The data analysis technique used is the T-test. The brain-based learning activities applied in this study are listening to music, drinking water, doing a brain gym, working on crossword puzzles, and group determination based on the dominance of students' brains. The results showed that the average value of the N-Gain score of student learning outcomes in the experimental class-1 was 80,72. Student learning outcomes experimental class-2 is 73,12. In science process skills, the experimental class-1 students had an average N-Gain score of 72,50, while the experimental-2 class was 60,88. The conclusion is the experimental class 1 students have higher learning achievement than students in the experimental class 2.

Research in education often involves a latent variable. Statistical analysis technique that has the ability to analyze the pattern of relationship among latent variables as well as between latent variables and their indicators is Structural Equation Modeling (SEM). SEM partial least square (PLS) was developed as an alternative if these conditions are met: the theory that underlying the design of the model is weak, does not assume a certain scale measurement, the sample size should not be large and the data does not have the multivariate normal distribution. The purpose of this paper is to compare the results of modeling of the educational quality in high school level (SMA/MA) in Sumenep Regency with structural equation modeling approach partial least square with three schemes estimation of score factors.This paper is a result of explanatory research using secondary data from Sumenep Education Department and Badan Pusat Statistik (BPS) Sumenep which was data of Sumenep in the Figures and the District of Sumenep in the Figures for the year 2015. The unit of observation in this study were districts in Sumenep that consists of 18 districts on the mainland and 9 districts in the islands. There were two endogenous variables and one exogenous variable. Endogenous variables are the quality of education level of SMA/MA (Y1) and school infrastructure (Y2), whereas exogenous variable is socioeconomic condition (X1). In this study, There is one improved model which represented by model from path scheme because this model is a consistent , all of its indicators are valid and its the value of Rsquare increased which is: Y 1 =0.651Y 2. In this model, the quality of education influenced only by the school infrastructure (0.651). The socioeconomic condition did not affect neither the school infrastructure nor the quality of education. If the school infrastructure increased 1 point, then the quality of education increased 0.651 point. The quality of education had an R 2 of 0.418, which indicates that 41.8 percent of variance in the quality of education is explained by the school infrastructure, the remaining 58.2% is explained by the other factors which were not investigated in this work.

The principle of education for sustainable development (ESD) is that no child is left behind. Hence, the fourth sustainable development goal (SDG) of the United Nations (UN) emphasizes inclusion and equity in education by focusing on eliminating disparities among regions. This study explores factors related to education quality through modeling in rural areas of Sumenep Regency, in East Java, Indonesia. Currently, only a few kinds of research studies involve spatial data, latent variables and, at the same time, tests of their spillover effects. The modeling herein is the spatial autoregressive model with latent variables (SAR-LVs). The latent variables were estimated using the weighted least square (WLS) method, while the Lagrange multiplier (LM) test was used for spatial dependence testing. The parameters of the SAR-LVs were estimated using two-stage least square (2SLS). The results show that the quality of education is directly influenced by the infrastructure of the schools but not by the socioeconomic conditions of the local communities. The autoregressive spatial coefficient has a significant but negative effect, which shows a negative spillover from districts with a lower quality of education to the ones with a high quality of education. This is due to the students competition to get registered for a favorite or good quality school in a particular district, which stimulates the migration of students from its neighboring districts. This reveals the inequality of school quality, since not all students can get access to schools with good quality. Through this study, some recommendations are given as a contribution to achieving the fourth SDG in Indonesia.

In Science, students tend to use the ability, which is dominantly controlled by their left-hemisphere brain. This study explores how science process skills (SPS) affect cognitive learning achievement (CLA) of dominantly right-brained and left-brained students. By applying project-based learning on the topic that integrates STEAM elements, this research examines the differences of the effects among those groups. The respondents were 32 8th-grade students from two randomly selected intact classes. This study employed a test to measure exogenous (SPS) and endogenous (CLA) latent variables. The partial least square - structural equation modeling (PLS-SEM) and multi-group PLS-SEM were employed to analyze the results. The evaluation of the outer model shows that both latent variables were valid and reliable. The factor loading value for all indicators of each latent variable was over 0.7. The cross-loading value indicates a higher correlation between the latent variable and its indicators compared to the other variables' indicators. The composite reliability and Cronbach's alpha values were over 0.7. The significance test shows that all indicators of each latent variable were valid. The evaluation of the inner model through the significance test (α=5%) suggests that the science process skill influenced CLA with a coefficient of 0.907. Meanwhile, the 0.822 R-square value demonstrates the variability of the SPS can explain the variability of CLA of 82.2%. The multi-group-SEM test reveals a difference in the effect of SPS toward CLA among dominantly right-brained and left-brained students. While the path coefficient for the former was 0.94, the latter was 0.881.

The focus of this research is to develop a Lagrange multiplier (LM) test of spatial dependence for the spatial autoregressive model (SAR) with latent variables (LVs). It was arranged by the standard SAR, where the independent variables were replaced by factor scores of the exogenous latent variables from a measurement model (in structural equation modeling) as well as their dependent variables. As a result, an error distribution of the SAR-LVs should have a different distribution from the standard SAR. Therefore, this LM test for the SAR-LVs is based on the new distribution. The estimation of the latent variables used a weighted least squares (WLS) method. The estimation of the SAR-LVs parameter used a two-stage least squares (2SLS) method. The SAR-LVs model was applied to the model with a positive and negative spatial autoregressive coefficient to illustrate how it was interpreted.