This study research was aimed at finding the validity, practicality and effectiveness of Problem based learning model assisted by Geogebra and describing the improvement of students' mathematical critical thinking skills. The learning devices developed are the Lesson Implementation Plan, teacher's book, student's book, Student Worksheet and student's mathematical critical thinking ability test instrument. This research is a Research and Development, using the Thiagarajan, Semmel and Semmel development models, the 4-D model. Learning devices had fulfilled the valid criteria's according to experts, and tested in class XI at MAN Labuhanbatu. The results of research had shown that the learning device of problem based learning model assisted by Geogebra had fulfilled the practical criteria's and effective and could improve students' mathematical critical thinking skills.

Open ended approach is a learning approach that presents a problem that has more than one answer or settlement method. Open ended approach encourages students to develop creative ideas and mathematical mindset by remembering previous mathematical concepts, so that with the open-ended approach, students are expected to have a much better mathematical creative thinking ability. The purpose of this research is to analyze the improvement of students creative thinking ability by using learning materials developed through autograph assisted open-ended approach. This research is a development research using Thiagarajan 4D model with define stage, design, develop, an dessiminate. The subject of this research is Junior High School Swasta Imelda Medan. The teaching materials that will be developed in this study are learning tools that include Learning Implementation Plan (RPP), teacher book (BPG), Student book (BS) and, student worksheet (LAS) and creative thinking ability test. From results of trial I and II by using learning materials developed through autograph assisted open-ended approach effectively used in learning mathematics so that there is an increase in creative thinking ability of students.

This study to: (1) To analyze the effect of KAM on mathematical communication skills and students independence between the PBL and STAD models with the help of geogebra-( 2) To analyze the difference between the improvement of mathematical communication skills and student independence between PBL and STAD models assisted by geogebra (3) to analyze the interaction between learning models and early mathematical abilities on students^ mathematical communication skills and independence. This research is categorized into the type of quasi-experimental research (quasi-experimental). The population of this study were all students of class VIII SMP Muhammadiyah 16 Lubuk Pakam and the samples were class VIII-1 (Experiment 1) and VIII-2 (Experiment 2). The results of the study are: (1) obtained Fcount is greater than Ftable (79.968 > 4.042) and with a probability value (sig) of learning factor of 0.000 so that there is an effect of KAM on students mathematical communication and Ftable (21.007 > 4.042) and with a probability value (sig) of learning factor of 0.000 so that there is an effect of KAM on independence-(2) Fcount is greater than Ftable (43.451 > 4.042) and with a probability value (sig) of 0.000 so that there is a difference in the increase in mathematical communication skills

Tuberculosis (TB) is an infectious disease that is very dangerous and can cause death and Tuberculosis (TB) is an infectious disease that causes the most deaths or is called the world’s biggest killer among infectious diseases, claiming more than 4000 lives every day. The unprecedented Corona Virus pandemic has a serious impact on people with pre-existing health conditions such as Tuberculosis. Tuberculosis is not caused by heredity and Tuberculosis is curable. Treatment of TB disease is time-consuming and costly. Therefore the term prevention is better than cure very precisely for Tuberculosis. One of the efforts made by the government is to provide vaccines. This study uses the SIR (susceptible, infected, and recovered) model by considering the effect of vaccines. Also, this study adopts the application of the Optimum Control theory which aims to provide control over the parameters that affect the spread of Tuberculosis. The purpose of this study is not only to show the dynamics of the spread of tuberculosis but also to see to what extent the effect of vaccines reduces the spread of tuberculosis. And how does the optimal control theory influence the spread of tuberculosis?This research is proposed to estimate the basic reproduction number (R0) from the dynamics of the Tuberculosis epidemic. The basic reproductive number ((R0) is often used as a threshold parameter to determine the boundary betweenextinction and endemic. If R0<1 indicates the dengue virus will become extinct and if R0> 1 shows the Tuberculosis is endemic. By considering vaccines identified a slowing of the spread of tuberculosis.

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