Purpose: This research emphasizes the need to map villages' conditions and identify village potentials, evaluate the effectiveness of development capability, and address the rural-urban development gap with clustering algorithms. The study employs the village development index (IPD) indicators obtained from the village potential dataset, with various numerical and categorical indicators, to capture both tangible and intangible aspects of village potential. Challenges such as missing data and outliers in IPD data collection can be found. The study aims to evaluate the effectiveness of clustering algorithms, with integrated and separated imputation processes, in handling these data issues and to track the development of villages in the Bogor Regency, West Java, Indonesia, based on the village’s potential (PODES) dataset.
Methods: Three clustering algorithms, such as k-prototype, simple k-medoids, and Clustering of Mixed Numerical and Categorical Data with Missing Values (k-CMM) are compared. The pre-processing data, which is the imputation process for the first two algorithms, is conducted separately, while the k-CMM has an integrated imputation process. Both imputation stages are tree-based algorithms. Cluster evaluation is based on internal criteria and external criteria. Clusters resulting from the k-prototype and simple k-medoids are selected by internal validity indices and compared to k-CMM using external validity indices for several numbers of clusters (k = 3,4,5).
Result: According to data exploration, the IPD of Bogor Regency, West Java, Indonesia dataset contains ± 5% of outliers and six missing values in some chosen variables. Tree-based imputation methods are applied separately in k-prototype and simple k-medoids, jointly in k-CMM. Based on the elbow and gap statistics methods, this research aims to determine the optimum number of clusters k = 3. The internal validity indices performed on k-prototype and simple k-medoids resulting in three clusters (k = 3) are optimum. Trials on several clusters (k = 3,4,5) for three algorithms show that the k-prototype with k = 3 performs the best and is most stable among the two other algorithms with IPD datasets containing many outliers; external validity indices evaluate cluster results.
Novelty: This research addresses issues commonly found in mixed datasets, including outliers and missing values, and how to treat problems before and during cluster analysis. An improvement of Gower distance is applied in the medoid-based clustering algorithm, and the k-CMM algorithm is the first algorithm to integrate the imputation process and clustering analysis, which is interesting to explore this algorithm’s performance in clustering analysis.

Learning outcomes are a series of skills, knowledge, attitudes and values ??obtained by students in their thinking process during learning activities. This research aims to improve the learning outcomes of class X-4 students on opportunity material by applying the problem based learning model assisted by wordwall media. To see an increase in learning outcomes, classroom action research was carried out for two cycles using the method of observation and analysis of test results with research instruments in the form of pretest posttest questions in the 2023/2024 academic year. The subjects of this classroom action research were 34 students from class X-4 at SMA Negeri 9 Surabaya. The research results showed a consistent increase in learning outcomes over two cycles in the opportunity material. Before the action was taken there were 18 students who had not reached the KKM and only 16 students had completed it so the percentage of completion was 47.05% with an average learning outcome of 67.76. In the first cycle, the number of students who completed their learning outcomes reaching the KKM increased to 28 with a completion percentage of 82.35% and an average learning outcome of 78.23. In cycle II, the number of students whose learning outcomes achieved the KKM consistently increased so that there were 31 with a completion percentage of 91.17% and an average learning outcome of 89.54.

The success of the learning process is highly desired in school education. One of the key factors in achieving success is the teacher's selection of appropriate methods for delivering the lesson material in class, which contributes to students' learning outcomes. In mathematics instruction, particularly on the topic of Statistics in class X-7 at SMA Negeri 9 Surabaya, the results have been unsatisfactory, with an average score of 59 for the 2023/2024 academic year. Therefore, improvement is needed through the implementation of the Team Assisted Individualization (TAI) cooperative learning model. The subjects of this study are students of class X-7 at SMA Negeri 9 Surabaya for the 2023/2024 academic year, consisting of 36 students. This study involves a mathematics teacher and an observer. The data collection tools used include formative tests, observation sheets for the teacher, students, and group discussion activities, as well as reflection questionnaires on the learning process. Based on the research findings, it can be concluded that the application of the TAI cooperative learning model can improve the learning outcomes of class X-7 students at SMA Negeri 9 Surabaya on the topic of Statistics. This study is expected to encourage teachers to implement the TAI cooperative learning model in Statistics to enhance students' learning outcomes in Mathematics.

This study began with the problem of low Mathematics learning outcomes of class X-5 students of SMA Negeri 9 Surabaya, which were below the Minimum Completion Criteria (KKM) of 75. This study aims to improve the Mathematics learning outcomes of class X-5 students of SMA Negeri 9 Surabaya. This study is a classroom action research (PTK) conducted in two cycles in the 2023/2024 academic year with 37 students. The data collection method in this study used observation techniques. The instruments used were pretest and posttest questions. The results of the analysis showed that the application of the problem based learning (PBL) learning model succeeded in improving students' Mathematics learning outcomes in statistics material. Student learning outcomes increased from the pre-cycle to cycle I and to cycle II. Before the action, only 10 students achieved KKM with a classical completion percentage of 27.02%. In cycle I, the number of students achieving KKM increased to 26 with a classical completion percentage of 70.27%. In cycle II, the number of students achieving KKM increased again to 31 with a classical completion percentage of 88.57%.
 

This study was conducted by looking at the low learning outcomes of class X-2 students at SMA Negeri 9 Surabaya in the previous material, namely SPLTV. This study was conducted with the aim of improving students' mathematics learning outcomes in the quadratic equation material by implementing a cooperative learning model of the team games tournament (TGT) type using the help of wordwall. This study is included in classroom action research which is carried out in two cycles. The subjects of the study used were 36 class X-2 students at SMA Negeri 9 Surabaya. The research data were obtained through pretest, observation, and posttest. The analysis data from the pretest and posttest results were in the form of quantitative data which would be used to determine the increase in student learning outcomes. While the analysis data from the observation results in the form of qualitative data were used as a guideline to improve and perfect learning activities from cycle I to cycle II. Based on the results of the study that has been carried out, it shows that implementing a cooperative learning model of the team games tournament (TGT) type using the help of wordwall on the quadratic equation material can improve the learning outcomes of class X-2 students at SMA Negeri 9 Surabaya. The classical completeness of the pretest cycle I was 44.4%. After the implementation of the TGT type cooperative learning model, there was an increase to 77.8% in the posttest of cycle I. In cycle II, it increased again to 94.6% with a classical completion target of 85%.