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The lack of understanding and skills in solving mathematical problems is now a significant concern in many countries. Other factors, such as learning interests, influence students' understanding of these concepts. Therefore, it is necessary to explore students' understanding of arithmetic (profit and loss) based on Bruner's theory regarding learning interest. The study was conducted at a Vocational School in East Java, Indonesia, with 26 students participating as research subjects. The research methodology used was qualitative, with data collected through questionnaires on learning interests, profit and loss concept tests, and interviews. Data were analyzed using a process of reduction, presentation, and conclusions. The findings revealed that subjects with high and medium learning interest categories can meet the stages of Bruner's theory (enactive, iconic, and symbolic). However, subjects with medium learning interests do not need help understanding what happens in the problem—the subject with low learning interest can only reach iconic and symbolic stages in Bruner's theory. Thus, teachers should design appropriate learning strategies and media for students with medium and low learning interests so that they have a good conceptual understanding.

Peserta didik jenjang SMP berada pada capaian terendah yang hampir mendekati kategori kurang (

Literasi dan numerasi adalah dua kemampuan esensial yang sangat berguna bagi peserta didik yang harus diajarkan sejak di sekolah dasar yang juga sebagai generasi penerus bangsa. Namun, hasil dari survei PISA menunjukkan bahwa skor kemampuan literasi dan numerasi terutama peserta didik sekolah dasar (SD) di Indonesia masih rendah yaitu berada jauh di bawah rata-rata. Oleh karena itu, perlu adanya pendampingan guru SD untuk mengembangkan literasi dan numerasi melalui kegiatan kolaboratif. Pendampingan ini dilakukan oleh Dosen Universitas PGRI Madiun dan Mahapeserta didik dari program Kampus Mengajar. Mitra pengabdian kepada masyarakat ini adalah SDN Kebon 1 Kabupaten Ngawi, Jawa Timur, Indonesia. Kegiatan pengabdian ini dilaksanakan menjadi 3 tahap yaitu perencanaan, pelaksanaan dan evaluasi. Tahap persiapan dimulai dengan melakukan pengamatan dan wawancara dan dilanjutkan dengan pelaksanaan kegiatan melalui Forum komunikasi dan koordinasi pendampingan dengan kepala sekolah dan guru. Selanjutnya, implementasi berbagai kegiatan kolaboratif untuk mengembangkan kemampuan literasi dan numerasi baik di dalam maupun luar kelas. Tahap evaluasi dengan melakukan refleksi dan pelaporan secara berkala sehingga kegiatan pendampingan ini dapat mengembangkan kemampuan literasi dan numerasi pada peserta didik SDN Kebon 1.

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking activity arrangement adapted to students' thinking when solving problems. The problem used in this research is a mathematical problem that triggers students to produce answers quickly with confidence that the answers are correct at a high level. Another problem is about probability because the mode of occurrence of students' learning difficulties at the secondary school level occurs when learning the concept of probability. This is qualitative research with a case study approach. The research subjects were students of Mathematics Education in semester 1. The results showed that thinking activity one could condition the occurrence of type 1 default-interventionist interaction. Thinking activity two could condition the occurrence of type 2 default-interventionist interaction. Thinking activity three could condition the occurrence of type 3 default-interventionist interaction. This research concluded that the default-interventionist interaction occurred because the content and arrangement of the thinking activity conditioned the subjects to pay attention to information gradually and change the subjects’ beliefs. Lecturers were recommended to produce, develop, and research thinking activities on topics other than probability at various levels of education. The default-interventionist interaction was essential to be conditioned when system one dominated students' thinking, causing difficulties.

Comprehending and formulating strategies for geometry problems that require higher-order thinking skills (HOTS) is crucial in enhancing mathematics education. This study implements a qualitative case study approach to comprehend how prospective mathematics teachers with varying Adversity Quotients (AQ) solve geometry Higher-Order Thinking Skill (HOTS) problems. We selected 3 participants from 167 Indonesian prospective mathematics teachers to solve the three- and two-dimensional HOTS problems and were invited to an interview session. The three participants represent three types of participants: a climber student (high AQ), a camper student (medium AQ), and a quitter student (low AQ). Our findings show that each student had different responses to deal with the obstacles they faced while solving the problem. The climber student is more adept at solving problems than the camper and quitter students. In addition to identifying specific implications, this study offers a comprehensive understanding of AQ's significant role in solving mathematical problems. This knowledge serves as a concrete foundation for guiding the future advancement of curricula, assessment methods, and instructional approaches in mathematics education, particularly in the field of geometry. This research contributes to enhancing educational practices and policies on a broader scale.

Education for all is an important issue of concern in the world of education, including higher education. To accommodate this, higher education certainly needs to pay attention if there are students who experience special needs, especially regarding the absorption of lecture material. The aim of this research is to help students achieve the expected competencies in the English for Early Childhood course, especially for students who have special needs who are slow learners. The method used to develop learning media refers to Design Based Research from Technology Perspective. The research results show that through the Direct Instruction learning model based on digital books, it is easier for students to learn and practice how to provide English language stimulation to young children.

Learning mathematics that emphasizes understanding concepts and solving problems requires learning media. The use of learning media is still low, so learning outcomes are far from the minimum completeness criteria (the student's lowest score), apart from learning media. Besides the media, learning models are essential to discover fun and not dull mathematics. This study aimed to improve learning achievement in data-building material through tangram media with the PjBL model for class IV at SD Negeri Gerih 7, East Java, Indonesia. The research method used was Collaborative Classroom Action Research. The subjects of this study were 23 students in grade IV at SD Negeri Gerih 7, East Java, Indonesia, in the 2022/2023 academic year. The test results obtained were in the form of pre-cycle class average values of 59.13, 64.78 in the results of the first cycle, and 77.82 in the results of the second cycle. It can be concluded that the PjBL learning model and the tangram media effectively improve the achievement results of fourth-grade students at SD Negeri Gerih 7, East Java, Indonesia.

Literasi dan Numerasi merupakan kompetensi yang perlu dikuasai dan diajarkan di sekolah. Namun, guru belum pernah mempelajari bagaimana cara mengajarkannya. Penelitian ini bertujuan untuk mendeskripsikan kesiapan guru matematika sekolah menengah dalam mengajarkan literasi dan numerasi. Data diperoleh melalui metode survei dengan desain cross-sectional pada awal implementasi kurikulum merdeka di Indonesia. Responden adalah 47 guru matematika yang merespon survei, yaitu 52,2% guru di sekolah menengah atas atau sederajat dan 47,8% guru di tingkat sekolah menengah pertama atau sederajat. Hasil penelitian menunjukkan bahwa: 1) sebanyak 51,1% responden dikategorikan siap untuk mengajarkan literasi dan numerasi, 2) sebanyak 19,2% guru menyatakan siap dan telah mengajarkan literasi numerasi tetapi memilih metode pengajaran yang kurang tepat, 3) sebanyak 6,3% guru menyatakan siap mengajarkan literasi numerasi namun belum mempunyai pengalaman dalam mengajarkan literasi numerasi ataupun pemecahan masalah, 4) sebanyak 23,4% guru mempunyai pengalaman mengajar literasi numerasi melalui pemecahan masalah tetapi menyatakan tidak siap mengajarkan literasi numerasi. Temuan penelitian ini adalah hampir separuh jumlah guru masih belum siap mengajarkan literasi dan numerasi karena kurangnya keyakinan untuk mengajarkannya ataupun kurangnya pemahaman terhadap literasi dan numerasi. Oleh karena itu, peneliti merekomendasikan dilaksanakannya sosialisasi atau pelatihan pengajaran literasi dan numerasi melalui media online sebagai sumber informasi yang paling diminati responden Â

Facing the current digital era, correct and accurate decisions are needed to deal with the problems. This research aimed to explore the decision-making abilities of prospective mathematics teacher students in solving geometric proof problems. This research was a qualitative descriptive study with research subjects 3 out of 32 students of the 2nd semester Mathematics Education study program. The research instrument is the researcher himself, who is assisted with geometric proof problem tests and interview guidelines. Data analysis was including reduction, presentation, and conclusion. The validity of the research data was tested using methods triangulation. The research results show that subjects with a proof ability of K2 can build and clarify geometric concepts/principles and can assess the reasonableness of ideas even though the subject feels unsure about their choice. Subjects with a proof ability of K3 can build and clarify geometric concept/principle ideas but cannot assess the reasonableness of proof ideas. Subjects with a proof ability of K4 can build ideas of geometric concepts/principles, can clarify even though they are incomplete, and cannot assess the reasonableness of proof ideas. Students need to be equipped with decision-making skills in solving proof problems as preparation to become mathematics teachers in the future.

An open-ended problem in learning mathematics is a problem with more than one answer or method of solving. In solving open-ended problems in learning mathematics, one of the abilities students must use is decision-making ability. Each student has a variety of capacities, so this study aims to determine students' decision-making abilities in solving open-ended problems in learning mathematics. The type of research used is descriptive qualitative research. The subjects of this study were four students with different numbers of correct answers in working on open-ended problems. Data collection was carried out using tests and interviews. The results showed that (1) the decision-making ability of the subject who answers correctly for both problems is complete because they fulfill all indicators, the subject can identify goals, make decisions, evaluate the results of determination, and present and remember between problems with things known to the problem and related to decisions that have been taken correctly; (2) decision-making ability for subjects with wrong answers on one number or two numbers is incomplete because they only fulfilled two indicators, the subject can identify goals, make decisions, is less able to evaluate decision results and present and remember between problems with things known to the problem, and related to decisions that have been taken with correct. Mathematics teachers should often reinforce students to practice operating integers because it is a prerequisite for learning mathematics at the middle and high school levels.

Adult mathematical literacy of high school students rarely gets attention, even though they need this skill to face various life challenges and situations. This research aims to describe the adult mathematical literacy based on activities of mathematical literacy’s processes domain when solving problems. Therefore, three high school students with equivalent mathematical abilities in specialization mathematics and compulsory mathematics are selected as research subjects. Data collection are through tests and interviews. The Data reduced, triangulated using the triangulation method, presented, and used in concluding. The results indicate that high school students with high mathematical abilities can use the ability to formulate situations mathematically, using concept facts, procedures, and mathematical reasoning; and interpret mathematical solutions. However, in formulating the situation, they tend only to identify aspects or components whose value is known by using familiar symbols. They also tend to make mistakes in making mathematical reasoning, especially if the problem involves reasoning with many criteria and conditions, as well as errors in interpreting solutions that contain limitations or constraints. The results suggested to familiarize students with everyday problems that involve reasoning to help students recognize problem situations as mathematical situations and generate creativity in using mathematical knowledge

This study aims to reveal the profile of open-start problem-solving with ethnomathematics regarding student learning styles. This research is a qualitative research study on 3 out of 31 students of Junior High School of 3 Magetan taken by purposive sampling. The three students carried out four stages: understanding the problem, planning problem-solving strategies, implementing problem-solving strategies, and reviewing again. The results of the research show that students with a visual learning style solve problems by understanding problems through writing known and being asked and drawing illustrations, planning problem-solving strategies by making examples, carrying out solving strategies by working on the calculation process; students with an auditory learning style solve problems by understanding problems through writing known and being asked, planning strategies by making problems and formulating formulas used, implementing solutions by doing calculations and reviewing; students with a kinesthetic learning style solve problems by understanding issues through writing known and being asked, making examples and writing the formulas used, carrying out solving strategies by applying the calculation process and reviewing the results obtained. However, of the three styles, the results of the accepted work were not correct because they did not write down the conclusions and were not thorough enough.

Students’ lack of mathematical literacy skills is also accompanied by the lack of mathematical literacy skills of most pre-service teachers. The purpose of this study is to investigate the decision-making process conducted by pre-service teachers in solving mathematical literacy problems. This qualitative descriptive study involved two subjects taken from 42 pre-service mathematics teacher students. Each subject was identified based on their pattern in solving mathematical literacy problems correctly and inappropriately. Data were collected through tests of mathematical literacy problems and test-based interviews. The results showed that there were differences in the decision-making process done by the students with correct and incorrect problem solving, namely: (1) building ideas, having three vs. two solution ideas, formulating and employing correctly vs. formulating correctly and employing inappropriately; (2) clarifying ideas, giving reasons for each idea vs. having wrong reasons due to calculation errors, interpreting correctly vs. interpreting incorrectly; and (3) assessing the reasonableness of an idea, providing logical reasons with one choice vs. logical reasons with one choice but less sure. Based on the findings, it can be concluded that the creativity of prospective teacher students in building ideas is still low and reasoning in expressing and choosing ideas is still weak, causing immature decision making. The finding of this study provides suggestions for educators to provide structured assignments and for other researchers to find factors influencing pre-service teachers’ decision-making in mathematics problem-solving to improve pre-service teachers’ decision-making skills.

Pada masa pandemi covid 19 pembelajaran dilaksanakan secara online dengan memanfaatkan e-learning. Multimodal model merupakan komponen pokok dalam pembelajaran online, yang meliputi konten, sosial emosional, tanya jawab, refleksi dan evaluasi. Penelitian ini bertujuan untuk mendeskripsikan efektifitas penerapan multimodal model melalui e-learning pada pembelajaran geometri bidang. Jenis penelitian ini adalah deskriptif. Subjek penelitian adalah mahasiswa semester 1 program studi pendidikan matematika sebanyak 63 mahasiswa. Pengumpulan data menggunakan teknik dokumentasi, observasi dan tes. Hasil penelitian menunjukkan bahwa penerapan multimodal model efektif dalam pembelajaran geometri bidang. Komponen multimodal model meliputi konten, tanya jawab, sosial emosional, evaluasi dan refleksi dapat terlaksana dengan baik melalui e-learning. Penerapan multimodal model melalui e-learning membutuhkan aplikasi pendukung agar dapat optimal dalam pelaksanaannya, terutama pada komponen sosial emosional dan tanya jawab. selain itu, penerapan multimodal model dapat menumbuhkan kreatifitas dosen dalam menciptakan media yang mendukung pembelajaran online, seperti video berbasis powerpoint dan audio. Kata Kunci: E-learning; geometri bidang; multimodal model; pandemi covid 19. Abstract During the Covid 19 pandemic, learning was carried out online by utilizing e-learning. The multimodal model is a key component in online learning, which includes content, social emotional, question and answer, reflection and evaluation. This study aims to describe the effectiveness of the application of the multimodal model through e-learning in field geometry learning. This type of research is descriptive. The research subjects were the first semester students of the mathematics education study program, totaling 63 students. Collecting data using documentation techniques, observation and tests. The results showed that the application of the multimodal model was effective in learning field geometry. The multimodal components of the model including content, question and answer, social emotional, evaluation and reflection can be carried out well through e-learning. The application of the multimodal model through e-learning requires supporting applications so that it can be optimal in its implementation, especially in the social emotional component and question and answer. In addition, the application of the multimodal model can foster the creativity of lecturers in creating media that supports online learning, such as powerpoint-based videos and audio. Keywords: Covid-19 pandemic; e-learning; field geometry; multimodal.

As part of 21st-century skills, communication is an essential skill for students. Students 'mathematical communication tends to below, one of which is influenced by students' self-confidence. For this reason, the purpose of this study is to describe the mathematical communication skills in solving circle problems based on students' self-confidence. Determining the subject using purposive sampling technique, namely from 36 students of class VIII SMP in Madiun, East Java, Indonesia, obtained two subjects with high self-confidence (SCT) and one subject with low self-confidence (SCR). A qualitative descriptive approach was used in this study. Tests and interviews were used as data collection techniques. Data were analyzed through reduction, presentation, and concluding. The results of this study include: SCT is capable while SCR is less able to meet the indicators of mathematical communication skills both in writing and orally at the stages of understanding problems, implementing plans, and checking back; and SCT can meet mathematical communication indicators both written and oral, while SCR is less able to meet written mathematical communication indicators but can verbally at the stage of planning completion. The level of self-confidence of students differentiates their mathematical communication skills in solving problems. Thus, a teacher needs to design an appropriate question to train students' mathematical communication skills with low self-confidence.

This case study aims to explore how male and female Indonesian mathematics teachers enact decision-making processes in teaching High-Order Thinking Skills (HOTS). Non-random purposive sampling technique was used to select the participants. The participants involved in this study were two Indonesian mathematics teachers who teach HOTS in their classrooms. The participants were chosen from 87 Indonesian mathematics teachers in 23 secondary schools in East Java, Indonesia, who were invited to our survey and confirmed that they taught HOTS and underwent classroom observation. Data were collected from classroom teaching and interview sessions. The data of classroom teaching consisted of a video-audio recording of two meetings and field notes of observation. In the interview session, we recorded the teachers’ responses during semi-structured interviews. We coded and explained our interpretation for each code. We also conducted investigator triangulation by comparing coding and interpretation made by two researchers and discussing them to find the best representation of the meaning of the data. Our findings indicate that both male and female teachers performed four steps of decision making, consisting of giving problems, asking students to solve, checking, and obtaining new ideas. The difference of male and female teachers’ decision-making process is observed in the process of giving problem (non-contextual vs contextual), how they ask students to solve and check the solution (individual vs group), and the criteria of the new idea of problem-solving (correct vs the best solution). The study findings can be a catalyst for enacting decision-making steps in teaching HOTS. Also, these can be a reflective practice for mathematics teachers to improve their teaching quality.

Penelitian ini bertujuan untuk menganalisis kemampuan metakognitif siswa SMP dalam menyelesaikan permasalahan pada materi pola bilangan ditinjau dari brain dominance. Penentuan subjek berdasarkan brain dominance siswa kelas VIIIC SMP Negeri 13 Madiun. Berdasarkan angket brain dominance yang dibagikan diperoleh 4 subjek yang terdiri dari 2 subjek left brain dominance dan 2 subjek right brain dominance. Jenis penelitian yang digunakan adalah penelitian kualitatif. Teknik pengumpulan data dalam penelitian ini berdasarkan hasil angket, tes, dan wawancara. Teknik keabsahan data dilakukan dengan triangulasi teknik. Analisis data dilakukan dengan reduksi data, penyajian data, dan verifikasi data serta penarikan kesimpulan. Kesimpulan dari hasil penelitian ini adalah (1) subjek left brain dominance memenuhi tiga aspek memenuhi tiga aspek kemampuan metakognitif yaitu mengembangkan perencanaan, memonitor pelaksanaan dan mengevaluasi tindakan dan dari ketiga aspek yang termunculkan siswa dengan left brain dominance memiliki tingkat kemampuan metakognitif reflective use. (2) subjek rightt brain dominance memenuhi tiga aspek memenuhi tiga aspek kemampuan metakognitif yaitu mengembangkan perencanaan, memonitor pelaksanaan dan mengevaluasi tindakan dan dari ketiga aspek yang termunculkan siswa dengan right brain dominance memiliki tingkat kemampuan metakognitif aware use dan strategic use Abstract This study aims to analyze the metacognitive abilities of junior high school students in solving problems in the number pattern material in terms of brain dominance. In determining subjects based on brain dominance of VIIIC grade students of SMP Negeri 13 Madiun. Based on the brain dominance questionnaire distributed obtained 4 subjects consisting of 2 subjects left brain dominance and 2 subjects right brain dominance. The type of research used is qualitative research. Data collection techniques in this study are based on the results of questionnaires, tests, and interviews. The data validity technique is done by triangulation techniques. Data analysis was performed by data reduction, data presentation, and data verification and conclusion drawing. The conclusions from the results of this study are (1) the left brain dominance subject fulfills three aspects of fulfilling three aspects of metacognitive abilities namely developing planning, monitoring implementation and evaluating actions and of the three aspects that arise students with left brain dominance have a level of reflective use metacognitive ability. (2) the rightt brain dominance subject fulfills three aspects of meeting three aspects of metacognitive abilities, namely developing planning, monitoring implementation and evaluating actions and of the three aspects that arise students with right brain dominance have a level of metacognitive abilities aware of use and strategic use

Self-Assessment of Digital Argumentation (SADA) is considerable instrument to assess students’ digital argumentation (DA) in e-learning model. The research objectives were: (1) to investigate how SADA can be used as an instrument for assessing students’ DA; and (2) to access students’ DA through SADA in e-Biology class. The study population was 132 students of Biology Education Department of UNIPMA in which the 64 students as the samples were taken purposively. The instrument used was the SADA questionnaire. The data were analyzed using Rasch model. The statistical summary showed that the interaction between respondents and items was very good (Cronbach alpha was 0.95 > 0.8). Meanwhile, the person reliability (0.92) and item reliability (0.75) were categorized as were categorized as "good". This study also revealed that there were 26.69% of students classified as having high DA, 40.63% have a moderate DA, and 29.69% have a low DA. This research proves that SADA can be used to measure students' self-assessment in doing their DA during e-learning. SADA also helps students evaluate their own learning process.

Reasoning that is constructed from remembering is imitative reasoning, while the opposite is creative reasoning. This study aims to explore creative mathematical reasoning in solving geometric problems. Mathematical creative reasoning is reasoning that contains elements of novelty, plausibility, and mathematical foundation. This type of research is descriptive qualitative, which is explorative. The research subjects were the first-semester student in the mathematics education study program with 32 students. The results showed that from 32 students, there was only one student identified as having creative mathematical reasoning in solving geometry problems. Creative mathematical reasoning can be identified when the subject is able to reason algorithmically but is aware of problems so they cannot be resolved algorithmically so that they must form new reasoning, which consists of novelty, plausibility, and mathematical foundation. Creative mathematical reasoning arises after students make an algorithmic reasoning process, but find no solution. Novelty is the weakest indicator of creative mathematical reasoning, so it requires scaffolding to bring it up.

Discovery learning is a learning model that enhancescreative thinking skill including develops students' creative mathematical reasoning. Creative mathematical reasoning process includes novelty, plausibility, and mathematical foundation. This research aims to describe students’ creative mathematical reasoning of the mathematics education department on Geometry. The data was collected based on the observation and individual evaluation of students.The results showed that Discovery Learning can (1) grow as much as 35.48% of students have complete creative mathematical reasoning (novelty, plausibility, and mathematical foundation), (2) grow as much as 64.52% of students have incomplete creative mathematical reasoning, and (3) grow novelty by 77.42%.

This study aimed to improve creative thinking ability of students through REACT learning strategy approach in probability topics. REACT learning strategy approach has 5 stages, consist of Relating, Experiencing, Applying, Cooperating, and Transferring. The type of research is Classroom Action Research. The study population was twelfth grade students of SMAN 1 Nglames, and the sample used was one class of XII MIA 2 consist of 32 students. The data collection technique uses (1) test scores of students' creative thinking skills which include the initial and final tests, (2) the results of observations during the learning process, (3) the results of interviews with the subject of the interview. Data were analyzed through descriptive analytic techniques. Based on the data analysis, it was found that each component of creative thinking had the following percentage increase in fluency (5.22%), flexibility (8.81%), originality (21.57%), and elaboration (29.29%). The results showed that REACT learning through three stages, namely the initial stage, the core (Relating, Experiencing, Applying, Cooperating, and Transferring), and the closure can improve students' creative thinking skills, especially in the probability topics.

This research aimed to describe pedagogical content knowledge of mathematics pre-service teacher through the lesson study application in microteaching. This descriptive qualitative research was conducted in Universitas PGRI Madiun with Mathematics pre-service teachers as subjects. The data were collected through observation, unstructured interviews, and documentation. Data from learning practice and pedagogical content knowledge were analyzed based on a scoring criteria framework that refers to microteaching assessment guidelines. The results showed that there was an increase in mathematics pre-service teacher learning practice (lesson planning increased from average to good, pre-learning activities increased from average to good, while learning activities increased from average to good, and closing activities increased from average to good). There was an increase in mathematics pre-service teacher content knowledge (increased in concept mastery from average to good and increased in material understanding from average to good). There was also an increase in mathematics pre-service teacher pedagogical knowledge (increased in clarity of learning scenarios from average to excellent, increase in the ability to use learning media from average to good, increase in the appropriateness of assessment techniques with learning objectives from average to good).

This study aims to describe the types of explanations made by pre-service teachers in mathematics learning. In this research, the types of explanations are used to describe the explanatory trends used by pre-service teachers in mathematics teaching. The descriptive qualitative research was chosen in this research. The research subjects are pre-service teacher as the students of Mathematics Education of PGRI Madiun University and Madura University who are studying Field Experience Practice. Of the 105 mathematics student, five students with a cumulative grade achievement of more than 3.50 were observed during the teaching practice at the school for approximately five meetings. The research data was obtained from observation, video recording, and interview. Data analysis was done through data condensation, data presentation, and conclusion/verification focused on pre-service teacher explanation on mathematics learning activity. The research findings indicate that the explanation used by the pre-service teacher in the mathematics learning starting from the most frequently used is the descriptive explanation (51,7%), giving of reason (36,2%) and interpretative (12,1%). Descriptive explanations are used to describe mathematical procedures. The type of reason-giving explanation is used to explain reasons based on mathematical principles. Furthermore, the interpretative explanation is used to explain the concepts and facts of mathematics.

Pemecahan masalah sangat diperlukan baik dalam proses pembelajaran maupun dalam kehidupan. Pemecahan masalah membutuhkan suatu kemampuan berpikir tingkat tinggi. Khususnya dalam geometri pemecahan masalah yang sering dihadapkan adalah masalah pembuktian. Melalui pembuktian selain mengetahui kebenaran suatu teorema juga dapat mengasah kemampuan berpikir logis mahasiswa. Tujuan dari penelitian ini adalah untuk mengetahui kemampuan pemecahan masalah pembuktian geometri oleh mahasiswa calon guru matematika Universitas PGRI Madiun. Jenis penelitian ini adalah penelitian deskriptif dengan pendekatan kualitatif dengan subjek penelitian sebanyak 2 mahasiswa berkemampuan akademik tinggi dan rendah yang melakukan pembuktian teorema geometri berdasarkan langkah-langkah pemecahan masalah Polya. Hasil penelitian disimpulkan bahwa kemampuan pemecahan masalah pembuktian geometri mahasiswa berkemampuan tinggi dalam setiap tahap pemecahan masalah adalah mahasiswa mampu menentukan hipotesis dan kesimpulan dengan bahasa matematis sendiri, mengaitkan dan menggunakan definisi, postulat dan teorema yang telah dibuktikan sebelumnya untuk menyusun pembuktian yang logis disertai visualisasi. Mahasiswa berkemampuan tinggi mampu menyusun metode pembuktian yang berbeda dari yang telah dilakukan. Mahasiswa dengan kemampuan rendah belum mampu merumuskan kesimpulan dengan bahasa matematika sendiri dan belum mampu membuat hubungan antar definisi, postulat dan teorema sehingga belum mampu menyusun pembuktian yang logis. Mahasiswa dengan kemampuan rendah belum mampu menyusun pembuktian yang berbeda dari yang telah dilakukan. Berkaitan dengan kemampuan pemecahan masalah ditemukan factor yang sangat mempengaruhi kemampuan pemecahan masalah mahasiswa yaitu kemandirian belajar (self regulated learning).

Problem Posing approach is necessary for teacher training students. Problem Posing can train students to create questions/problems and their solutions. Make problem then solve it is part of student’s creative thinking ability. Differential equations problem is one of the materials that learned in mathematics education courses. Every teacher training student of mathematics has diverse skills. This diversity certainly brings various creative thinking skills as well. The purpose of this study is to determine the ability of student’s creative thinking in mathematical education courses, differential equation problem posing. This study uses a qualitative approach with descriptive methods. Sources of data in this study are the students of mathematics education consist of one student of each with high, medium, and low begining math ability. The data collection was conducted by using observation, testing, and interviews. Technique authenticity of data using a triangulation method. Data analysis technique done in stages, data reduction, data presentation, drawing conclusions, and verification. The result of this study were (1) Students with high initial capability not have fluency and flexibility of thought, but it shows the novelty think that qualifies as a Creative Thinking Ability Level (CTAL) 2 is creative enough, (2) Students with prior knowledge currently have the fluency of thought, but do not have the flexibility and novelty think that qualifies as a Level capabilities creative thinking (CTAL) 1 is less creative, (3) Students with prior knowledge low yet has grace, eloquence, and the novelty of thought that goes into the criteria of creative thinking ability Level (CTAL) 0 is not creative.

Possessing and developing metacognitive abilities are an essential part of the learning process. This study is a class action research on the use of critical analysis to identify its influence on students’ metacognitive abilities and critical thinking skills as well as to discover the relationship between metacognitive abilities and critical thinking skills. The sample of this study is 76 students from 217 students taking cell biology and non-vascular plants subject during the fall semester. It is a descriptive quantitative study with critical analysis assignments. Critical analysis rubric is used to collect the data of students’ critical analysis and the essay test to measure students’ critical thinking and metacognitive ability. The data of metacognitive ability and critical thinking were analyzed using regression test. The result showed there was a positive influence of the use of critical analysis to the student metacognitive abilities and critical thinking skills. The results of a simple correlation analysis of metacognitive abilities and critical thinking skills show the means value (r) of 0.904, which means that there is a strong positive relationship between the two components. The higher the student’ metacognitive skills, the higher their critical thinking skill will be.

Matematika merupakan salah satu mata pelajaran yang wajib ditempuh mulai dari tingkat dasar hingga ke jenjang yang lebih tinggi. Kesulitan siswa dalam pembelajaran matematika adalah terletak pada penalaran dalam menyelesaikan masalah bentuk soal cerita termasuk didalamnya pada materi persamaan kuadrat. Berdasarkan hal tersebut penelitian ini bertujuan untuk mengetahui profil penalaran siswa kelas X SMA dalam menyelesaikan masalah persamaan kuadrat ditinjau dari kemampuan awal siswa. Penelitian ini menggunakan pendekatan kualitatif dengan jenis penelitian deskriptif kualitatif. Sumber data yang digunakan pada penelitian ini adalah siswa. Teknik pengumpulan data melalui tes tulis dan wawancara. Analisis data dalam penelitian ini dilakukan dengan tahapan reduksi data, penyajian data, dan penarikan simpulan. Berdasarkan hasil penelitian diperoleh kesimpulan bahwa (1) Siswa dengan kategori kemampuan awal tinggi memiliki kecenderungan menggunakan unsur-unsur penalaran induktif dan deduktif dengan baik. Siswa dapat memecahkan masalah persamaan kuadrat dalam bentuk soal cerita dengan baik sesuai dengan langkah-langkah penyelesaian masalah. (2) Siswa dengan kategori kemampuan awal sedang memiliki kecenderungan menggunakan unsur-unsur penalaran induktif dan deduktif dengan cukup baik. Siswa dapat memecahkan masalah persamaan kuadrat dengan baik tetapi kurang mampu dalam menentukan cara lain untuk mencari jawaban. (3) Siswa dengan kategori kemampuan awal rendah memiliki kecenderungan menggunakan unsur-unsur penalaran induktif dan deduktif dengan kurang baik. Siswa kurang mampu dalam memecahkan masalah persamaan kuadrat sesuai langkah-langkah pemecahan masalah dan tidak mampu dalam menentukan cara lain untuk mencari jawaban.

Tujuan penelitian ini adalah: (1) Untuk mengetahui manakah model pembelajaran yang lebih efektif Numbered Heads Together (NHT) dengan alat peraga Geoboard atau model pembelajaran konvensional terhadap prestasi belajar matematika siswa. (2) Untuk mengetahui apakah terdapat perbedaan pengaruh motivasi tinggi, sedang, dan rendah pada siswa terhadap prestasi belajar matematika. (3) Untuk mengetahui apakah terdapat interaksi antara penerapan model pembelajaran Numbered Heads Together (NHT) dengan alat peraga Geoboard dan model pembelajaran konvensional terhadap prestasi belajar matematika siswa yang mempunyai motivasi tinggi, sedang maupun rendah. Populasi pada penelitian ini adalah siswa kelas VII MTs Al Istiqomah tahun ajaran 2014/2015. Teknik pengambilan sampelnya dengan cluster random sampling dan sampelnya yaitu kelas VII B sebagai kelas eksperimen yang diajar dengan model pembelajaran Numbered Heads Together (NHT) dengan alat peraga Geoboard, dan kelas VII D sebagai kelas kontrol yang diajar dengan model pembelajaran konvensional. Teknik pengumpulan data untuk data prestasi belajar menggunakan metode tes dan data motivasi belajar siswa menggunakan metode angket. Uji hipotesis penelitian menggunakan anava dua jalan dengan sel tak sama. Kesimpulan dari hasil penelitian ini adalah (1) Model pembelajaran Numbered Heads Together (NHT) dengan alat peraga Geoboard lebih efektif daripada model pembelajaran konvensional terhadap prestasi belajar matematika siswa. (2) Motivasi belajar siswa tinggi, sedang, dan rendah pada siswa tidak berpengaruh terhadap prestasi belajar matematika siswa. (3) Tidak terdapat interaksi antara penerapan model pembelajaran Numbered Heads Together (NHT) dengan alat peraga Geoboard dan model pembelajaran konvensional terhadap prestasi belajar matematika siswa yang mempunyai motivasi tinggi, sedang maupun rendah.

Penelitian ini bertujuan untuk mengembangkan perangkat pembelajaran matematika pada materi segitiga dan segiempat dengan pendekatan RME (Realistic Mathematics Education) yang berkualitas baik (memenuhi kriteria kevalidan, kepraktisan, keefektifan). Pengembangan perangkat pembelajaran menggunakan model pengembangan perangkat pembelajaran 4-D yang dimodifikasi menjadi 3-D. untuk mengetahui kriteria kevalidan, keprakisan, dan keefektifan dilakukan pengumpulan data dengan cara penilaian validasi, penilaian observasi, pengisian angket, dan melakukan tes hasil belajar. Setelah itu dilakukan analisis data menggunakan metode statistik deskriptif. Hasil menunjukan, bahwa perangkat pembelajaran dikatakan valid oleh ketiga validator sehingga kriteria dipenuhi. Selain itu kepraktisan perangkat pembelajaran juga memenuhi kriteria penilaian dengan ditunjukannya nilai kemampuan aktivitas guru dalam mengelola pembelajaran di kelas pada ujicoba terbatas 0,99 dan ujicoba lapangan 0,90. Sedangkan aktifitas siswa dapat ditunjukan dengan nilai pada ujicoba terbatas 3,28 dan ujicoba lapangan 3,30, yang menunjukan kriteria kepraktisan perangkat pembelajaran terpenuhi. Sedangkan untuk kriteria keefektifan perangkat pembelajaran dapat ditunjukan dengan hasil respon positif siswa adalah diatas 80% seluruhnya pada semua komponen penilaian pada ujicoba terbatas maupun ujicoba lapangan. Untuk tes hasil belajar dapat ditunjukan dengan melihat ketuntasan klasikal siswa pada tahap ujicoba terbatas maupun lapangan secara berturut-turut 100% dan 76,7%, sehingga kriteria keefektifan juga terpenuhi. Dari hasil penelitian pengembangan perangkat pembelajaran matematika diatas maka dapat disimpulkan bahwa perangkat pembelajaran mempunyai kualitas baik karena telah memenuhi kriteria kevalidan, kepraktisan dan keefektifan.

Untuk mengajarkan komunikasi matematika yang baik kepada siswa maka seorang guru harus memiliki kemampuan komunikasi matematika yang baik terlebih dahulu terutama dalam menyelesaikan masalah. Tujuan dari penelitian ini adalah untuk mengetahui kemampuan komunikasi matematika mahasiswa calon guru matematika laki-laki dan perempuan dalam menyelesaikan masalah persamaan diferensial. Penelitian ini merupakan penelitian dengan pendekatan kualitatif jenis deskriptif eksploratif. Subjek penelitian adalah satu mahasiswa calon guru matematika laki-laki dan satu mahasiswa calon guru matematika perempuan. Teknik pengumpulan data dilakukan melalui tes tertulis, penyampaian tes secara lisan, dan wawancara mendalam. Teknik keabsahan data menggunakan triangulasi waktu. Teknik analisis data meliputi reduksi data, penyajian data, dan verifikasi serta penarikan kesimpulan. Hasil penelitian menunjukkan bahwa kemampuan komunikasi matematika mahasiswa perempuan baik secara tertulis maupun lisan dalam menyelesaikan masalah persamaan diferensial lebih baik jika dibandingkan dengan mahasiswa laki-laki. Kata Kunci: Kemampuan Komunikasi Matematika, Menyelesaikan Masalah, Persamaan Diferensial, Gender