Critical thinking is believed to have significant contributions to learners’ academic context in the era progression of technology and information. Critical thinking skills are needed to solve problems, especially in solving algebraic problems. This critical thinking process is influenced by several factors including cognitive style and gender. The purpose of this study was to understand the process of critical thinking from the perspective of cognitive style and gender on solving algebraic problems students in the mathematics department at Walisongo State Islamic University. The kind of research qualitative descriptive, a test MFFT used to analyze cognitive style students into groups impulsive or reflective cognitive style. Tests to analyze skills critical thinking based on Ennis consisting of Focus, Reason, Inference, Situation, Clarity, and Overview. The research indicated that style cognitive and gender significantly affected the way and the ability to think critically students. This study provides information that on the subjects of reflective cognitive style, male are better than female in terms of critical thinking skills and there are differences in the process. Male subjects on reflective cognitive style are better than female subjects, but for the cognitive style exclusive female subjects are better than men.

Indonesia Open University (UT: Universitas Terbuka) is a large, open university delivering distance education to students throughout Indonesia. An important aspect of its mission is to provide opportunities for Indonesian teachers to improve their education in-service. This includes two courses on classroom action research. In order to assess the effectiveness of these courses and, if necessary, improve them, a team of lecturers from UT conducted an investigation of the challenges teachers were facing in learning to conduct classroom action research through the UT modules. The team found that the modules did not adequately reflect an understanding of the actual characteristics of the teachers they were serving and were thus less effective than they might be in teaching teachers to conduct classroom action research. Changes in both the content and scheduling of the modules are recommended in order to more effectively promote classroom action research in Indonesian schools. AbstrakUniversitas Terbuka atau UT merupakan universitas besar yang menyelenggarakan pendidikan jarak jauh untuk mahasiswa di berbagai penjuru Indonesia. Aspek terpenting dari misi UT adalah menyediakan kesempatan kepada para guru Indonesia untuk meningkatkan kualitas pengabdian mereka di dunia pendidikan. Materi yang ditawarkan UT termasuk dua mata kuliah tentang penelitian tindakan kelas. Dalam rangka mengevaluasi efektifitas kelas ini, dan memperbaikinya jika perlu, tim dosen dari UT meneliti kendala yang dihadapi para guru dalam belajar melakukan penelitian tindakan kelas melalui modul UT. Tim menyimpulkan, modul kelas ini tidak merefleksikan pemahaman yang cukup tentang karakterisktik riil para guru yang diajar, dan karena itu, kurang efektif untuk dijadikan acuan mengajar penelitian tindakan kelas. Tim menyarankan beberapa perubahan pada isi dan penjadwalan modul, guna lebih mengefektifkan kampanye penelitian tindakan kelas di sekolah-sekolah di Indonesia.

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Mathematics proof plays an important role in learning the abstract algebra included group theory. The aim of this study was to describe the mental structures that might take place when FI students were learning the concept of group theory through APOS-based learning. This study was a descriptive qualitative. The participants of this study were eight (8) undergraduate students who were taking Introduction to Algebraic Structure 1, included group theory, at Universitas Negeri Semarang. Each of low and medium level of initial proof ability consisted of 3 participants, while high level of initial proof ability consisted of 2 participants. There were two instruments used to gather data: written examination in the course and a set of interview. The participants with low level of initial proof ability tended to construct the mental structure of Object for a set, did not construct the mental stucture of Object for the binary operation and the axioms of group. The participants with medium level of initial proof ability constructed the mental structure of object for a set, tended to construct Object for the binary operation, the axioms of group, and tended to construct the scheme of group. The participants with high level of initial proof ability constructed mental structure of Object for a set, has not fully constructed the mental structure of Object for the binary operation and for the axioms of group yet, as well as has not fully constructed the scheme of group.

The purposes of this study are 1) to describe the level of students’ critical thinking ability in learning Complex Analysis based on the results of diagnostic assessments, 2) to identify errors experienced by students in solving problems that measure mathematical critical thinking ability in learning Complex Analysis based on the results of diagnostic assessment, and 3) to determine instructional therapy for students who experience errors in solving problems that measure mathematical critical thinking ability in learning Complex Analysis based on results diagnostic assessment. The research design uses a combination of quantitative and qualitative research, with simultaneous models not balanced. The population of the research was Mathematics Department students of FMIPA UNNES in 2017/2018 who had participated in complex analysis studies consisting of two classes with a population size of 68. The samples were randomly selected from two classes with a sample size of 33. The four subjects were selected from two levels. Criticaland normal of each of the two students. Data were analysed quantitatively and qualitatively. The results of the study show that student learning outcomes on achieving critical mathematical thinking ability in complex analysis learning are complete. There are two levels of students’ critical thinking ability, namely critical and normal levels. The results of the analysis of students’ mathematical critical thinking ability, subject to a critical level, there are four indicators of questions that have not been reached. These indicators include aspects of assumptions, deductions, interpretations, and judging arguments. Subjects are of normal level, there are eleven indicators of questions that have not been reached. These indicators include all aspects of mathematical critical thinking ability namely, inferential, assumptions, deductions, interpretations, and judging arguments. The diagnosis of errors found that subjects with normal levels experienced errors of all types, namely errors of understanding, process, conclusion, transformation, and carelessness, as well as lack of material mastery. Subjects with critical levels experience misunderstanding and conclusions.