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The mathematical abilities of students with reasoning are closely interrelated. The HOTS-type problem is an effort to improve reasoning ability. The ability of students to solve HOTS questions is still relatively low. Through a differentiated learning model, it is expected to help students in the learning process that suits their needs. The purpose of this study is to describe the application of differentiated learning models and describe the mathematical reasoning ability of students who have low, medium, and high abilities. This type of research is qualitatively descriptive with instruments in the form of observation sheets, questionnaires, test questions and interviews. Data analysis techniques include data reduction, data presentation, and conclusions. Test the validity of data using triangulation techniques. The results of this study show that differentiated learning can improve students' ability to reason. Four indicators of mathematical reasoning are, students' ability to present mathematical problems in the form of written statements, students' ability to make conjectures, students' ability to manipulate mathematics, and students' ability to draw conclusions from problems. Subjects with a high level of reasoning meet two indicators. Whereas subjects with moderate levels of reasoning met only three indicators and subjects with low levels of reasoning met only two indicators. Mathematics teachers should provide learning that is in accordance with the learning style of students and students should also do HOTS type questions more often. [ABSTRACT FROM AUTHOR]

This study aims to describe the characteristics of critical thinking of female OSN participants in solving math problems. This research is a case study qualitative approach. The research subjects were female participants of OSN SMP Mathematics Tulungagung Regency. The subject selection technique was snowball sampling. Research instruments were test questions and interview guidelines. Data collection techniques include written tests, interviews, documentation. Data validity checking triangulation techniques and reference adequacy. Data analysis includes data reduction, data presentation, conclusion drawing. Based on the research results, the subject fulfills 11 indicators, namely (1) reading carefully, repeatedly, writing mathematical sentences without explaining, focusing the question, (2) explaining the plan by understanding the problem, choosing the formula, writing the formula, (3) working coherently, structured, according to the formula, (4) explaining the information obtained by remembering the material and formulas used, (5) explained the steps to solve the problem clearly, coherently, thorough workmanship, and confidently, (6) argued according to his knowledge, relevant, and accurate but not logical, (7) used one solution and detected other possible plans by trying first, (8) explained other possible steps by paying attention to each stage, (9) tried to solve based on the plan made, (10) found the value of the element subsumed in the formula, the answer was correct and (11) was sure the answer was correct, checking by checking the calculation of the substitution of numbers in the formula from the beginning. [ABSTRACT FROM AUTHOR]