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A significant amount of scholarly investigation has recently focused on metacognitive activity. However, the examination of metacognitive variations in solving math problems that are still limited in scope. This case study examines gender differences in activity variations of metacognitive activities, specifically awareness, regulation, and evaluation, in prospective teachers solving mathematical problems based on mathematical models. Participants were selected through purposive sampling. Twelve male and sixteen female participants were chosen from those who participated in the 'capita selecta' mathematics course at a public university in West Java, Indonesia. The data were collected through mathematical problem-solving tasks and interviews. The results show that the variations in metacognitive activities between male and female participants are different. Females tend to be more complex and structured in their evaluation activities, while males tend to be more complex and structured in their awareness activities. Based on the results, recommendations are made for future studies.

Many studies reported the importance of mathematical justification in collaborative problem-solving (CPS). However, not all tasks could stimulate mathematical justification in CPS. This study explores the potential of a decision-making task in facilitating mathematical justification in CPS of a derivative topic. Two groups of 12 graders in Bandung, Indonesia solved a task. The group works were observed, recorded, and the written works were collected. The findings showed that the task encouraged the groups to focus on justifying mathematical claims. Both groups successfully solved the task, yet different mathematical justifications were observed. We discussed the possible roles of the task difficulty and groups’ mathematics ability in promoting mathematical justifications. Checking the effectiveness of the task on a larger sample was recommended for further studies.

The aim of the study is to describe students’ visual thinking process in solving third dimensional problems. This research was descriptive study with qualitative approach. Two girls students with the higher rank in mathematics’ test and representing a student with field dependent cognitive style and a student with field independent cognitive style were selected as the research subject. The data were collected by giving third dimensional problems test based on Polya’s steps of problem solving and interviews. The student’s visual thinking is described based on looking, seeing, imagining, & showing process. The results shows that FI & FD student were looking & seeing in understanding the problems, seeing & imagining in devising a plan, in carying out the plan, FI student was showing relative short steps, but FD student was showing right solution in different steps. In looking back, both students was not showing a looking back process.

Developing the Indonesian Version of the Object-Spatial Imagery and Verbal Questionnaire (IDN-OSIVQ) aims to create a culturally adapted and validated instrument for assessing object-spatial imagery abilities in the Indonesian population. The research utilized a developmental method to test the instrument's reliability and validity through rigorous adaptation procedures, including translation, back-translation, expert review, and pilot testing. Data from 153 students were analyzed to establish the internal consistency, construct validity, and factor structure of the IDN-OSIVQ. Results showed that the IDN-OSIVQ scales had satisfactory internal reliability, with principal component analysis confirming distinct and coherent factors. Object imagery had the highest average score (3.6662), while spatial imagery had the lowest (3.1765). Criterion validity was established as participants' ratings correlated favorably with corresponding tasks. Gender differences were observed: men scored higher on spatial imagery and women on object imagery, yet these differences did not overshadow the strong associations between cognitive style ratings and objective measures. The cultural adaptation process ensured the questionnaire's relevance and comprehensibility, enhancing its applicability. The findings support the IDN-OSIVQ as a reliable and valid tool, suggesting future research should involve more diverse age groups.

The study aims to describe the creative thinking process of junior high school students with different Adversity Quotient (AQ) categories (quitter, camper, and climber) in solving numeracy problems. This qualitative research involves three subjects representing distinct AQ categories. Data collection includes the ARP questionnaire, numeracy problem-solving tests, and interviews, with analysis using the Pierce sign concept. Findings reveal camper and climber subjects effectively separate information in the ideation stage, while quitter and climber subjects associate knowledge concepts in generating idea. In preparing a plan for application, camper and climber subjects strategize based on information and knowledge, while in applying an idea, quitter subjects surrender, campers choose easier alternatives, and climbers persist with pre-planned strategies. Results suggest tailored motivation according to students' AQ categories can enhance teacher-student engagement.

Instruments are tool that used to collect research data. The instrument consists of two types, namely the main and supporting instruments. In this paper, we develop the supporting instruments which are used in qualitative research such as commognitive perspective. The instrument development aims to explore and reveal students' cognition in understanding derivative tasks that are valid and reliable. It means the instrument is needed in order to explore cognition and communication in an inseparable manner according to the theory used in this research. The two supporting instruments that developed in this study are the mathematical ability test (MAT) and the derivatives understanding task (TMT). Moreover, the developed MAT instrument is accompanied by source questions, grids and indicators. The MAT consists of 10 questions, and this was tested empirically in the category of valid and high reliability. Furthermore, TMT is developed as a reference for exploring student commognition. The TMT consists of 14 questions. The preparation and development of the instruments in this study are based on relevant theories and supported by empirical data. At the expert review step, validation is carried out in terms of content, construct and language by experts. Each step is tested for readability, then suggestions and comments are provided for improvement. The final results obtained show that the two supporting instruments (MAT and TMT) are feasible to use in exploring student commognition because these bring up keywords, visual mediators, endorsed narratives, and routines, as a commognition characterher.

Proof of geometry is a topic that involves mathematical reasoning abilities and relates to perseverance involving hard work, the spirit of achievement, and self-confidence. The current important problem that occurs at this time is that students who are future teachers of mathematics still experience difficulties in compiling proofs, especially those who are not challenged to work hard. This qualitative research explores mathematics teacher candidates' reasoning abilities and perseverance in proving geometric theorems. Therefore, the research design used a case study. There were three participants in this study, and they were student prospective mathematics teachers' s taking geometry courses. Data were collected through working documents, open questionnaires, and semi-structured interviews and were analyzed using iterative techniques consisting of data condensation, data exposure, and verification. The study's results showed that students' prospective teachers did not prioritize proof in solving geometry problems, even though they worked hard to solve the problems independently until they were finished. The students' perseverance also impacts their mathematical reasoning in proving geometric theorems. Students with more hard work values tend to have more reasoning values. The results of this study have implications that there needs to be an effort from the teacher to get used to giving proof questions to support students' perseverance and mathematical reasoning abilities.

This study is descriptive research that aims to describe students' collaborative problem solving (CPS) skills in solving mathematics problems. The subjects in this study were 6 students at grade XI consisting of 2 students with high mathematical abilities, 2 students with moderate mathematical abilities, and 2 students with low mathematical abilities. The six of them were divided into 3 groups consisting of 2 students with different mathematical abilities. The three groups were given mathematics problems to be solved collaboratively. The results of this study were analyzed using the semiotic Peirce model approach which uses a trichotomous relationship between representamen (Z), interpretant (I), and object (O) to show the CPS process that occurs. The results of the study show that students' CPS skills vary. The CPS process of high and moderate mathematical ability students is running quite well. Meanwhile, the CPS process of high and low mathematical ability students and moderate and low mathematical ability students was not as good as expected because of the little interaction or discussion between the members of the group in solving problems

This study aims to investigate mathematics teacher educators’ (MTE) knowledge in noticing preservice teachers’ pedagogical content knowledge (PCK) on the hierarchical classification of the quadrilateral. A multiple case study was conducted to analyze the responses of ten MTEs in an online moderated-forum group discussion (M-FGD) from their written work on the MTE-PCK test completed prior to the M-FGD. The PCK test consisted of two tasks: the task that examines MTEs’ knowledge to predict pre-service teachers’ reason in representing the hierarchical classification of quadrilateral in Venn diagrams, and the task that examines MTEs’ knowledge in making a flowchart as a recommendation to mathematics teacher to analyze the validity of quadrilateral classification. Results show that the MTEs indicate two considerations of noticing pre-service teachers’ PCK on the quadrilateral classification: by definition and properties of quadrilaterals and by the visual appearance of quadrilaterals. Despite this, 20% of them were indicated to perform a lack of understanding of the hierarchical classification of quadrilaterals, as indicated by invalid flowcharts of validating the hierarchical classification of the quadrilateral.

Metacognitive regulation is an important ability for undergraduate students to have in solving collaborative problems. However, before carrying out research on exploring metacognitive regulation in collaborative problem-solving, the development of suitable instruments must be carried out. The right instrument will produce the correct data. In this study, two instruments were developed, which are tasks containing mathematical problems and task-based interview guidelines. In addition, this study also identified appropriate problem criteria used to explore metacognitive regulation in collaborative problem-solving. The results showed that the problems that can trigger metacognitive regulation in collaborative problem-solving fulfil the following criteria: problems to prove, non-routine problems, open-ended problems, geometric problems, and without DGE. The use of semi-structured interview guidelines can also help deepen students' exploration of metacognitive regulation in collaborative problem-solving. The findings of this study are especially important for researchers who will develop instruments to examine metacognitive regulation, especially in collaborative problem-solving.

This study aims to describe the learning trajectories of male and female students in solving fraction problems. The research subjects consisted of a male student and a female student who had the same mathematical ability. Learning trajectory data for both subjects were taken through fractional problem solving tests and in-depth interviews. Observations focused on the four stages of problem solving strategies, namely understand the problem, divide a plan, carry out the plan, and look back. Data analysis begins with examining all data, reducing data, grouping data, categorizing, coding, and finally checking data through time triangulation. The results of the study show that in understanding the problem, boys identify goals and information to solve the problem to state its completeness, and girls identify information to solve the problem to state its completeness. In making plans, girls complete in detail and involve many concepts, while boys only have one concept, so girls' learning trajectories are longer. While carrying out the plan, the two solve problems according to the plan. Looking back, girls used more than one method alternative while boys only used one alternative.

Contextual problems are non-routine problems that are related to real or daily life in the form of story questions, so that students are able to apply various contextual problems in learning mathematics. In solving contextual problems, it will be different from one student to another, this is because the creative thinking of each student is not the same. Creative thinking is the process of coming up with many ideas/possible answers of a problem, which has aspects of fluency, originality, and flexibility to generate the ideas. While the stages of creative thinking are: 1) synthesizing ideas, 2) building ideas, 3) planning ideas, and 4) implementing ideas. This research is a descriptive study with a qualitative approach that aims to describe the creative thinking of high school students in solving contextual problems in class X based on the level of creative thinking (creative and creative enough). The subjects in this study were 2 (two) students based on the level of creative thinking. Data collection was done in written form (Creative Thinking Test) and interview. Based on the results of research on creative thinking of high school students in solving contextual problems, information was obtained that: a) students with a creative level of thinking (creative) carry out steps in determining concepts, ideas sourced from everyday experience, generating different ideas from each problem with various patterns, determine and develop strategies to implement ideas based on the information received, but there are a few obstacles in implementing the final problem, but already have a strong concept, even though it is not shown how big the prize is through the stages of synthesizing ideas, building ideas, planning ideas, and implement ideas. b) students with a level of creative thinking (sufficient) carry out steps to recall arithmetic sequence formulas, based on the information obtained in the problem, generate different ideas/patterns based on the knowledge received by students during learning, determine and organize the ideas used, but not thorough in answering the questions, but the ideas given are correct and appropriate and not answering the final problem through the stages of synthesizing ideas, building ideas, planning ideas, and implementing ideas. The implication of this research in mathematics education and learning is to find out the steps for students' creative thinking, knowledge and strategies in solving contextual problems

Self-efficacy, problem solving, and gender differences are aspects that many researchers concern to today. Therefore, the purpose of this study was to describe the profile of students’ self-efficacy in solving problems based on gender. We used a qualitative approach with exploratory research to answer the research objectives. We used the Mathematical Ability Test (TKM) instrument, Mathematical Problem-Solving Tasks (TPMM), and interview guidelines to consider the selected subjects. Next, two students were selected (14 years old, of different gender, and had good math skills) to participate in the study. Data from transcripts and student work were used to perform data analysis. The results revealed that there were fundamental differences between the two subjects based on three dimensions of self-efficacy (magnitude, strength, and generality). This is discussed further in this article. Finally, we suggest to explore the influence of regional culture on students’ self-efficacy in the classroom.

Pengajuan dan pemecahan masalah merupakan pemicu keterampilan berpikir kritis maupun berpikir kreatif yang sesuai dengan tujuan kurikulum saat ini. Kedua konsep tersebut perlu diimplementasikan dalam pembelajaran, sehingga para guru perlu dibekali keterampilan merancang pembelajaran tersebut sekaligus memahami konsep masalah, pemecahan dan pengajuan masalah. Untuk mencapai tujuan tersebut, diperlukan program pelatihan guru untuk memantapkan pemahaman guru tentang pemahaman konten dan desain pembelajaran berbasis pengajuan dan pemecahan masalah matematika. Guru yang terlibat adalah 22 guru SMP yang ditugaskan oleh Dinas Pendidikan Kabupaten Magetan. Metode pelaksanaan terdiri dari tahap persiapan dengan melakukan koordinasi dengan mitra dan tim pelatih untuk merancang instrumen dan materi pelatihan. Tahap pelaksanaan terdiri dari kegiatan tatap muka dan kegiatan mandiri dengan diawali pemberian angket untuk analisis awal (pra-tes), pemberian materi pelatihan, praktik penyusunan soal, presentasi, dan kegiatan mandiri merancang perangkat pembelajaran. Tahap selanjutnya evaluasi dan tindak lanjut dilakukan dengan pemberian angket akhir pelatihan (pasca-tes) dan angket refleksi kegiatan. Hasil pelatihan menunjukkan 81,8% guru mampu memahami konsep dan mendesain pembelajaran berbasis pengajuan dan pemecahan masalah. Hasil evaluasi kegiatan guru menunjukkan 95,45% guru cenderung mengatakan baik dan menyarankan kegiatan perlu ditindaklanjuti.

Penelitian ini bertujuan menghasilkan sebuah produk baru yaitu bahan ajar untuk mata kuliah statistika secara umum yang terintegrasi literasi statistis berbasis EPUB dengan kategori valid, praktis, dan efektif. Prosedur pengembangan bahan ajar menggunakan 5 tahapan ADDIE. Subjek uji coba dan implementasi melibatkan 2 universitas di Kalimantan Tengah yaitu 53 mahasiswa semester V Universitas Palangkaraya yang memprogram mata kuliah Analisis Data di Program Studi Pendidikan Matematika dan 41 mahasiswa V Universitas Muhammadiyah Palangkaraya yang memprogram mata kuliah Statistika Pendidikan di Program Studi PGSD. Analisis data dilakukan dengan mengkonversi total skor data secara kuantitatif. Berdasarkan hasil validasi dan uji coba serta implementasi bahan ajar memenuhi kriteria sangat valid dan praktis dengan rata-rata ahli media dan ahli materi yaitu 89,42%. Tahap implementasi menunjukan hasil penilaian dosen terhadap bahan ajar yang dikembangkan termasuk pada kategori sangat praktis dengan skor 82,9% dimana rata-rata hasil tes literasi statistis mahasiswa di Universitas Palangkaraya yang menggunakan EPUB mengalami kenaikan sebesar 31,2% sedangkan hasil implementasi di Universitas Muhammadiyah Palangkaraya mengalami kenaikan sebesar 13,8%.

Learning during the COVID-19 period is a concern in the world of education. This is because the learning system has changed from the previous one and it has not been used by both students and teachers. In response to this, it is necessary to conduct action research using the Kemmis and McTaggart models on online-onsite mathematics learning, namely boldly through online platforms and the request of students. The subjects of this study were seventh-grade junior high school students who found 27 people. In contrast, the object of this research is to increase students’ creative problem-solving skills and increase teacher activity and student behaviour. Through the instruments used in online-onsite based learning, the results show that there is an increase in the percentage of classical learning completeness in creative problem-solving abilities of students who pass the minimum KKM in the 1st cycle from the percentage of initial ability results but have not shown achievement. While the results of observations of student behaviour and teacher activities meet the criteria achieved. Therefore, it is continued to cycle II by correcting the weakness in cycle I. The implementation of cycle II shows that all performance indicators have been achieved. Through these results, of course, it is a consideration that in improving problem-solving skills, it is recommended to do online-onsite based learning, especially in mathematics.

A whole attention in didactic situations that might occur/ influence is the strength of didactic engineering as a research design for the development of mathematics learning media. The results of the epistimological obstacle and didactic obstacle analysis of students' creative thinking abilities in geometric material showed a gap between expectations and reality. Based on the results of the a priori analysis, flipbook media is appropriate to be used as one of the media development innovations to improve elementary students' creative thinking skills. Armed with completeness and a clear structure, this media got implementation results that show valid, practical as learning media and and not yet effective because students need time to adapt a new media but it can be seen that there was an increase from the value of presentation student who pass the minimum learning completeness criteria from 0% up to 46%. Based on the results of the a posteriori analysis which is validated by the results of the a priori analysis, it showed that this media can be used to improve students' creative thinking skills in terms of learning outcomes and other didactic phenomena during and after using the media

The purpose of this quantitative research with correlational design is to determine whether there is independent learning with learning motivation in online-based mathematics learning. So, it can support the success of learning process. This study was conducted in the odd semester of the 2021/2022 Academic Year. All seventh-grade students of SMP Santo Yoseph Medan were used as the research population. While the samples of this study were all students of class VII-A who collected 30 people and all students of class VII-B who collected 31 people. In mathematics learning, all students are taught online through the Zoom cloud meeting platform, WhatsApp, and Google Classroom. Sampling was done by purposive sampling technique. The study instruments is a learning independence questionnaire and student learning motivation questionnaire. The results of the questionnaire were analyzed based on product moment correlation data. Data analysis of the research results showed sig. (2-tailed) < 0.05 so that there is a significant relationship between learning independence and students' learning motivation in online-based mathematics learning with a value of 0.433 including the category of moderate correlation.

Pembelajaran matematika di kelas masih banyak yang menekankan pemahaman siswa tanpa melibatkan kemampuan berpikir kreatif. maka pembinaan soal soal olimpiade perlu dilakukan oleh lembaga non formal. Salah satunya adalah Klinik Pendidikan MIPA (KPM) yang mengembangkan kelas khusus dan disebut siswa berbakat yang menitik beratkan pembelajaran matematika berupa soal-soal olimpiade yang menuntut siswa untuk berlatih mempergunakan nalarnya untuk berpikir kreatif. Subyek penelitian ini terdiri dari 38 siswa laki-laki dan siswi perempuan kelas 5 berbakat di KPM Cabang Surabaya. Adapun indikator berpikir kreatif yang digunakan adalah indikator kefasihan, indikator fleksibilitas, indikator kebaruan. Instrumen yang dipakai pada penelitian yakni : Tes evaluasi dan wawancara. Untuk mengetahui perbedaan kemampuan berpikir kreatif siswa laki-laki dan perempuan pada penelitian ini menggunakan Uji Mann Whitney, mendapatkan hasil bahwa Z hit= 6,375 > Z tabel= 1,96. Sehingga dapat disimpulkan bahwa Ho ditolak atau Terima H1. Kesimpulannya kemampuan berpikir kreatif siswa laki-laki berbeda dengan kemampuan berpikir kreatif siswi perempuan. Kemampuan berpikir kreatif siswa laki-laki dan perempuan dalam menyelesaikan masalah matematika terkait soal matematika olimpiade memperlihatkan bahwasannya siswa laki laki lebih banyak yang menyelesaikan dengan cara penyelesaian sama dengan yang dibuat pertama. Kemampuan berpikir kreatif siswa perempuan dalam menyelesaikan soal olimpiade rata rata sudah mampu menyelesaikan penyelesaian lebih dari satu cara. Untuk indikator kebaruan siswi perempuan sudah mampu menjawab jawaban lebih dari satu dan beragam. Tingkat kemampuan berpikir kreatif siswa perempuan lebih tinggi hal ini terlihat dari persentase 53,85% siswa perempuan pada tingkat berpikir kreatif. Sedangkan siswa laki-laki sebesar 16,67 % tingkat berpikir kreatif. Berdasarkan hasil wawancara, bahwasnnya memperlihatkan baik siswa perempuan maupun siswa laki-laki sama-sama menunjukkan bahwa sudah memiliki tingkat kemampuan berpikir kreatif yaitu sangat kreatif , kreatif dan kurang kreatif.

This study aims to describe the creative thinking abilities of students based on their level of creative thinking in solving math problems in the context of Covid-19. Data collection was carried out by providing a test for solving mathematics problems in the context of Covid-19. Data analysis techniques were data reduction, data presentation, and conclusion drawing. Data analysis is to see how the student is solving problems with what ideas can be given. The research subjects were four students with different levels of creative thinking, then interviewed how the students completed these problems. The results showed that the subject at level 0 (not creative) only gave one answer and one way of solving the problem. Subjects with creative thinking level 1 (less creative), able to produce two different answers, and able to present data in two ways of presenting data, but only one is correct. Then the subject with level 2 (creative enough), can give one answer correctly and two ways of presenting the data correctly. While the subject with level 3 (creative) thinking can produce two different answers correctly and two ways of presenting data correctly.

This research aims to describe secondary-level students' thinking processes in terms of their attitude toward mathematics in constructing proof by mathematical induction. This qualitative research involved two students who were selected from 30 students of second grade of senior high school that categorized into two groups, namely the students who have a positive and negative attitude toward mathematics by using Attitude Toward Mathematics Inventory (ATMI) questionnaire. One student from each category was selected to be given a proving test and interviewed. Students’ process of proving test and interview recording were collected and analyzed to identify their thinking process. This research points out that both students who have positive and negative attitudes towards mathematics can recall the information in their memory regarding the characteristics and steps to prove using mathematical induction. However, the student who has negative attitudes towards mathematics tends to experience some difficulties in processing information, especially in the induction step, caused by panic, depression, and insecurity. The student who has a positive attitude towards mathematics also experiences some difficulties in the proving process, namely understanding what to prove and compiling the induction steps. However, she keeps trying and believes that she would be able to solve it. Hence, she can solve the proof completely.

This research deals with the challenge of helping student who has difficulty in constructing trigonometry proof. This qualitative research that describing scaffolding process using questions involves 20 students in second grade of senior high school, then selects a student from the 11 students who cannot solve the proof completely. Student’s work on proving test and interview recording are collected and analysed data to identify student’s difficulty, type of scaffolding to help, and development produced. This research points out the difficulty student faces are: difficulty in devising strategy, stuck in the process, unable to find the next step, and unable to find relation between two terms. Scaffoldings given are: asking the characteristic of what to be proven, asking a concept that may be used, directive question, facilitative utterance, trans active prompt and bridging analogy. Furthermore, developments produced from scaffolding given are: student can purpose new idea and strategy, can find relation between two things or two concepts, and student can determine and use appropriate concept.

Pentingnya mengajarkan pemecahan masalah matematika kepada siswa dan ketersediaan soal kategori masalah yang terbatas mengakibatkan perlunya penguasaan kemampuan membuat masalah matematika oleh guru. Membuat masalah matematika yang benar-benar baru bukanlah sesuatu yang mudah untuk dilakukan. Namun, dengan mengubah masalah matematika yang sudah ada menjadi soal baru akan mempermudah pembuatan soal baru tersebut. Pelatihan ini bertujuan untuk melatih guru matematika SMP di Kab. Ponorogo dalam membuat masalah matematika baru dengan mendaur ulang masalah lama. Sehingga, guru matematika SMP di Kabupaten Ponorogo dapat memfasilitasi siswanya untuk belajar pemecahan masalah matematika. Pelatihan dilakukan dalam dua tahap yang dilakukan secara tatap muka (tahap 1) dan daring (tahap 2). Tahap (1) yaitu pemaparan materi dan workshop dan tahap (2) meliputi penugasan dan evaluasi. Oleh peserta pelatihan, pelatihan dinilai bermanfaat dan menambah pengetahuan guru mengenai pembuatan soal. Selain itu, pelatihan ini berhasil meningkatkan variasi masalah matematika yang dibuat peserta.

The emerging of formal mathematical proof is an essential component in advanced undergraduate mathematics courses. Several colleges have transformed mathematics courses by facilitating undergraduate students to understand formal mathematical language and axiomatic structure. Nevertheless, college students face difficulties when they transition to proof construction in mathematics courses. Therefore, this descriptive-explorative study explores prospective teachers' mathematical proof in the second semester of their studies. There were 240 pre-service mathematics teachers at a state university in Surabaya, Indonesia, determined using the conventional method. Their responses were analyzed using a combination of Miyazaki and Moore methods. This method classified reasoning types (i.e., deductive and inductive) and types of difficulties experienced during the proving. The results conveyed that 62.5% of prospective teachers tended to prefer deductive reasoning, while the rest used inductive reasoning. Only 15.83% of the responses were identified as correct answers, while the other answers included errors on a proof construction. Another result portrayed that most prospective teachers (27.5%) experienced difficulties in using definitions for constructing proofs. This study suggested that the analytical framework of the Miyazaki-Moore method can be employed as a tool to help teachers identify students' proof reasoning types and difficulties in constructing the mathematical proof.

This research explained the description of the beliefs of prospective teacher who had an adversity quotient type climber and the relationship between beliefs and mathematics teaching practices in the classroom. One student of climber prospective teacher who had taken an internship course and had good communication skill was willing to become a research subject. Semi-structured interview and observation of learning in class were used to obtain the research data. The data that had been obtained were coded, reduced, presented, triangulated to obtain credible data, and then conclusions were drawn. The results show that the climber math prospective teacher believes that mathematics is as something dynamic, namely the space of creation, human invention that develops continuously. Teaching mathematics is student-centered through problem providing or problem solving, and learning is as a construction of student’s active understanding to build knowledge. A more detailed explanation of beliefs description and the relationship with the mathematics teaching practice is described in this research.

[English]: Self-regulated learning and learning styles are two of the various factors which contribute to students' achievement in learning at each level of education, including mathematics teacher education. This study examined the self-regulated learning of prospective mathematics teachers (PMT) with different learning styles (visual, auditory, kinesthetic). It involved 66 PMTs who enrolled on a linear program course in the 4th semester. Data were collected through a questionnaire, a test, and a semi-structured interview. The test was used to select PMTs who have high mathematics ability as the subjects. They were provided with the questionnaire to examine their fulfilment of cognition, motivation, behaviour, and context in the four stages of self-regulated learning. The interview was administered to confirm and thoroughly explore subjects' responses in the questionnaire. The results of the questionnaire and interview were qualitatively analyzed. This study found that PMT with different learning styles fulfils four aspects of self-regulated learning in the stage of (1) planning, forethought, and activation, (2) monitoring, (3) control, and (4) reaction and reflection in different extent, preference, and strategies. The differences are possibly affected by their different learning styles. Keywords: Self-regulated learning, Learning styles, Prospective mathematics teachers [Bahasa]: Kemandirian belajar dan gaya belajar merupakan dua dari banyak faktor yang mempengaruhi capaian siswa dalam pembelajaran di setiap level pendidikan termasuk pendidikan guru matematika. Penelitian ini bertujuan menganalis kemandirian belajar mahasiswa calon guru matematika yang memiliki gaya belajar berbeda (visual, audio dan kinestetik). Penelitian melibatkan 66 mahasiswa pendidikan matematika semester 4 yang sedang mengambil kuliah program linier. Pengumpulan data dilakukan dengan tes kemampuan matematika, angket kemandirian belajar, dan wawancara semi struktur. Tes digunakan untuk memilih calon guru yang memiliki kemampuan matematika tinggi sebagai subjek. Subjek terpilih diberikan angket untuk mengetahui tingkat capaian kognisi, motivasi, perilaku dan konteks dalam empat tahap kemandirian belajar. Wawancara dilakukan untuk mengonfirmasi dan memperdalam pilihan subjek pada angket. Data hasil angket dan wawancara dianalisis secara kualitatif. Hasil penelitian menunjukkan bahwa calon guru matematika dengan gaya belajar berbeda memenuhi empat aspek kemandirian belajar pada tahap (1) perencanaan, pemikiran, dan aktivasi, (2) pengawasan, (3) kontrol, dan (4) reaksi dan refleksi dalam tingkatan, pilihan, dan strategi yang berbeda. Perbedaan tersebut kemungkinan dipengaruhi oleh kecenderungan gaya belajar yang dimiliki calon guru. Kata kunci: Kemandirian belajar, Gaya belajar, Calon guru matematika

[English]: The purpose of this qualitative exploratory study was to analyze students’ gestures in understanding algebraic expression. It involved 59 7th-grade students in Semarang city, Indonesia. Students’ gestures were identified through interviews and observations, then analyzed in three stages: data condensation, data display, and drawing and verifying conclusion. Time triangulation was utilized to assure data validity. The results showed that students employed: (1) direct gestures as a representation of coefficients and variables in the form of hand movements forming the shape of objects that they recognize in the everyday environment, (2) indirect gestures as a representation of coefficients and variables in the form of hand movements as if forming the shape of objects that they recognize in the daily environment then followed by consistent and repetitive hand movements as a representation of the coefficients, (3) direct gesture representing constants in the form of hand movements forming a specific number, and (4) writing gestures and pointing gestures to strengthen the explanation given. The present study concludes that the gestures made by the students in understanding the concepts of algebraic expression consist of representation, pointing, and writing. This study yields an important description of students' gestures and types of gestures about the algebraic concept, which provide a further understanding of the topic. Keywords: Gesture, Conceptual understanding, Algebra [Bahasa]: Penelitian kualitatif ini bertujuan untuk menganalisis gestur siswa dalam memahami bentuk aljabar. Penelitian melibatkan 59 siswa di salah satu SMP di Semarang. Data gestur siswa diidentifikasi melalui observasi dan wawancara kemudian dianalisis melalui tahapan kondensasi data, penyajian data, dan penarikan dan verifikasi simpulan. Verifikasi keabsahan data dilakukan menggunakan teknik triangulasi waktu. Hasil penelitian menunjukkan bahwa siswa menggunakan (1) gestur langsung sebagai perwujudan pemahaman konsep koefisien dan variabel dalam bentuk gerakan tangan yang membentuk objek yang dikenali dalam lingkungan sehari-hari, (2) gestur tidak langsung sebagai representasi koefisien dan variabel dalam bentuk gerakan tangan seolah-olah membentuk objek yang dikenali dalam lingkungan sehari-hari kemudian diikuti oleh gerakan tangan yang konsisten dan berulang sebagai representasi koefisien, (3) gestur langsung yang menjadi representasi konstanta melalui gerakan tangan membentuk angka tertentu, dan (4) gestur menulis dan menunjuk untuk memperkuat penjelasan yang diberikan. Penelitian ini menyimpulkan bahwa gestur yang dibentuk siswa dalam memahami konsep bentuk aljabar terdiri dari gestur representasi (gestur representasi langsung dan tidak langsung), gestur menunjuk, dan gestur menulis. Penelitian ini menghasilkan deskripsi penting tentang gestur dan jenis gestur siswa tentang konsep aljabar yang memberikan pemahaman lebih lanjut tentang topik tersebut. Kata kunci: Gestur, Pemahaman konsep, Aljabar

Reversibility is a mental process to construct two-way correlation from an initial condition to the result, and from result reverse to initial state. The concept of reversibility is a key aspect of the development of mathematics which is often problema for student. Reversible thinking is the primary requirement to solve mathematical problems. The importance of reversibility is one of the reasons in this study. The aimed of this study was to identify student’s reversibility in solving algebaic problems. The subject consisted of 32 junior high school student’s, especially at the eight grade. In this qualitative study, data were collected by a reversibility task and interview. The reversibility task contained simple equation. The result of this study indicate that reversibility aspect of solving algebaic problem can identified were reciprocity and negation, in this case reciprocity was more prominent. This could be seen from 32 junior high school students were able to make equation according to the reversibility aspect, but there were only five students are be able to fulfill two aspect of reversibility, described as negation and reciprocity, the others only fill reciprocity. The result showed that the problem related reversibility on junior high school still exist, especially in the aspect of negation.

Beliefs and pedagogical content knowledge (PCK) are two factors influencing teaching practice in the classroom. This research aims to describe the beliefs and PCK of the prospective mathematics teachers and the relationship between the two factors on the teaching practices in the mathematics classroom. Participant in this research includes a prospective teacher who has taken a micro teaching subject and has good communication skill. Data were collected through interview and video analysis on the teaching practice in the classroom. The data obtained were coded, simplified, presented, and triangulated for the credibility and concluded. The result of the research shows that the prospective teachers who hold a constructivist belief view mathematics as a dynamic knowledge which evolves and is regarded as the space of creation for humans. Their beliefs on the nature of mathematics support the belief in the teaching-learning process in mathematics classrooms. Furthermore, a good understanding of the prospective teachers have on the components of the PCK has been sufficient, which can be identified in every step of practical activities in the classroom. More elaboration on the relationship between the belief and PCK is presented in this research.

Artikel ini bertujuan untuk (1) menghasilkan perangkat pembelajaran learning cycle–5E berbasis pengajuan masalah pada topik trigonometri di kelas X, (2) mendeskripsikan keefektifan pembelajaran (3) Untuk membandingkan hasil belajar siswa dengan pembelajaran Learning Cycle 5E berbasis pengajuan dengan hasil belajar siswa yang mengikuti pembelajaran konvensional Pengembangan perangkat pembelajaran dilakukan dengan menggunakan model Morrison. Berdasarkan hasil ujicoba perangkat diperoleh perangkat learning cycle 5E berbasis pengajuan masalah berkualitas baik, karena memenuhi syarat-syarat: (1) kemampuan guru dalam mengelola pembelajaran baik, (2) aktivitas siswa efektif, (3) respons siswa positif, (4) tes hasil belajar valid, reliabel, dan sensitive, (5) ketuntasan belajar secara klasikal tercapai. Sedangkan hasil penelitian pada kelas eksperimen berdasarkan analisis statistik deskriptif diperoleh bahwa learning cycle 5E berbasis pengajuan masalah efektif untuk mengajarkan materi trigonometri. Berdasarkan analisis statistik inferensial dengan mengunakan anakova diperoleh kesimpulan bahwa hasil belajar siswa yang mengikuti learning cycle 5E berbasis pengjuan masalah lebih baik dibandingkan dengan hasil belajar siswa mengikuti pembelajaran konvensional untuk materi trigonometri di kelas X. The purposes of the research are (1) to produce learning cycle-5E based on problem posing on trigonometric topic in class X, (2) to describe the effectiveness of learning cycle-5E based on problem posing in trigonometric topic in class X, (3) Compare the learning outcomes of students who take Learning Cycle 5E-based problem posing with the learning outcomes of students who take conventional learning on the topic of trigonometry in class X. The learning device development was conducted by using the Morisson model. Based on the test results, the devices obtained by the learning cycle 5E based on problem posing is a good quality, as validated by the validators and qualified: (1) the ability of teachers in managing good learning, (2) the student activity in effective learning, (3) Positive student responses, (4) learning outcome test, fulfils valid, reliable, and sensitive criteria and (5) learning completeness is achieved in a classical manner. whereas the results of descriptive statistical analysis, it is obtained that the learning cycle 5E based on problem posing is effective material to used in teachng trigonometric. Based on inferential statistic analysis using anacova, it is concluded that the students' learning outcomes following learning cycle 5E based on problem posing are better than the students' learning outcomes following the conventional learning for trigonometric material in class X.

History of mathematics discusses a historical aspect of mathematics concepts since its appearance and development through ages. Understanding the background of why a certain concept appears in mathematics, an innovation in teaching and learning material may be developed. The historical aspect of mathematics concept can be used as guided reinvention activities for the children to learn the concept. This idea is in line with what stated in curriculum 2013. However, to implement in curriculum 2013, there is no feasible framework that can be used to work on. One perspective that can be used in this implementation is phylogenensis and ontogenesis perspective. In this paper a discussion on how phylogenesis and ontogenesis may be used to implement the history in teaching mathematics will be presented. In addition, an example on how a history can be used as reference in learning is provided.

This is a case study investigating a primary teacher’s beliefs, knowledge, and teaching practice in mathematical problem solving. Data was collected through interview of one primary teacher regarding his beliefs on the nature of mathematics, mathematics teaching, and mathematics learning as well as knowledge about content and pedagogy of problem solving. His teaching practice was also observed which focused on the way he helped his students solve several different mathematics problems in class based on Polya’s problem solving process: understand the problem, devising a plan, carrying out the plan, and looking back. Findings of this study point out that while the teacher’s beliefs, which are closely related to his problem solving view, are consistent with his knowledge of problem solving, there is a gap between such beliefs and knowledge around his teaching practice. The gap appeared primarily around the directive teaching which corresponds to instrumental view he held in most of Polya’s process during his teaching practice, which is not consistent with beliefs and knowledge he professed during the interview. Some possible causes related to several associate factors such as immediate classroom situation and teaching practice experience are discussed to explain such inconsistency. The results of this study are encouraging, however, further studies still need to be conducted.

This article reports on a qualitative study intended to identify the characteristics or stages of students' creative thinking process. The study put nine eighth graders into the pool of the subjects: eight students were taken from SMP (Junior High School) Negeri 5, Sidoarjo and one student from SMP (Junior High School) Al Hikmah, Surabaya. Tasks to be completed by the students and interview guides were used to collect the data. The results indicate that the process of students' creative thinking involves stages which include synthesis of ideas, generation of ideas, planning to apply the ideas, and the application of the ideas. The results also show that the every stage of the creative thinking process is distinct from one another.

Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking is focused on flexibility, fluency, and novelty in mathematical problem solving and problem posing. As students have various backgrounds and different abilities, they possess different potential in thinking patterns, imagination, fantasy and performance; therefore, students have different levels of creative thinking. A research study was conducted in order to develop a framework for students’ levels of creative thinking in mathematics. This research used a qualitative approach to describe the characteristics of the levels of creative thinking. Task-based interviews were conducted to collect data with ten 8th grade junior secondary school students. The results distinguished five levels of creative thinking, namely level 0 to level 4 with different characteristics in each level. These differences are based on fluency, flexibility, and novelty in mathematical problem solving and problem posing.

Many researchers assume that people are creative, but their degree ofcreativity is different. The notion of creative thinking level has beendiscussed .by experts. The perspective of mathematics creative thinkingrefers to a combination of logical and divergent thinking which is basedon intuition but has a conscious aim. The divergent thinking is focusedon flexibility, fluency, and novelty in mathematical problem solving andproblem posing. As students have various backgrounds and differentabilities, they possess different potential in thinking patterns,imagination, fantasy and performance; therefore, students have differentlevels of creative thinking. A research study was conducted in order todevelop a framework for students’ levels of creative thinking inmathematics. This research used a qualitative approach to describe thecharacteristics of the levels of creative thinking. Task-based interviewswere conducted to collect data with ten 8thgrade junior secondary schoolstudents. The results distinguished five levels of creative thinking,namely level 0 to level 4 with different characteristics in each level.These differences are based on fluency, flexibility, and novelty inmathematical problem solving and problem posing.Keywords: student’s creative thinking, problem posing, flexibility,fluency, novelty DOI: http://dx.doi.org/10.22342/jme.1.1.794.17-40

Abstract: Empowering Mathematics Teachers to Improve Creative Thinking of Elementary-School Students. This experimental study is intended to develop mathematics teachers’ competences in designing teaching and learning strategies that enhance students’ creative thinking. In addition, the study portrays teachers’ creative thinking as well as their competences in planning and implementing problem-solving and problem-posing teaching models. Utilizing a pre-test post-test single group design, this study involved mathematics teachers of the third, fourth, and sixth grades of two elementary schools. The results suggest that the teachers’ creative thinking is of good level; they are creative enough in solving and posing mathematical problems as reflected in their mean score of 92.6. Their competences in planning and implementinglie in good category. Overall, it can be concluded that the teachers are professionally empowered in develo ping students’ creative thinking. Abstrak: Pemberdayaan Guru dalam Pembelajaran Matematika untuk Meningkatkan Kemampuan Berpikir Kreatif Siswa SD. Implementasi pembelajaran matematika di SD untuk mendorong berpikir kreatif masih lemah. Penelitian ini bertujuan memberdayakan guru-guru SD dalam mengembangkan pembelajaran matematika yang memberi bekal kemampuan berpikir kreatif dan memberikan gambaran kemampuan berpikir kreatif guru dan kemampuannya merencanakan serta mengimplementasikan model pembelajaran pengajuan dan pemecahan masalah matematika. Penelitian eksperimen rancangan pretes postes kelompok tunggal sekaligus deskriptif dilakukan terhadap masing-masing dua guru kelas III, IV, dan V SD di kabupaten Sidoarjo. Hasil penelitian menunjukkan bahwa kemampuan berpikir kreatif guru SD berada pada tingkat lebih dari cukup kreatif, dan hasil rata-rata kemampuannya dalam memecahkan dan membuat soal adalah 92,6. Kemampuan guru dalam melaksanakan pembelajaran termasuk kategori lebih dari “baik”. Disimpulkan bahwa guru telah berdaya dan mem iliki kemampuan mengembangkan pembelajaran yang mendorong berpikir kreatif siswa.

Abstract: The Thinking Process of Primary-school Students of Different Sexes in Estimating Arithmetic Problems. This case study is intended to explore the thinking process of the fifth-year students of different sexes in estimating arithmetic problems. Two students, one male and one female, belonging to the high achievers in a mathematics test were selected for the study and then interviewed, assigned to solve arithmetic problems, and finally asked to think aloud their thinking process. The study reveals that the thinking process of both the male and female subjects is in the form of accommodation as they ap­proached the arithmetic problems by repeatedly reading the tasks. Though employing the same thinking process, in the planning stage, the male subject made use of rounding and compatible number strategies, whereas the female one used only rounding strategy. In implementing the plan, the male subject em­ployed mental counting through assimilation, but the female one used algorithm through accommoda­tion. In the evaluating stage, the male subject traced back his work through mental counting, while the female one utilized reverse operations. Abstrak: Proses Berpikir Siswa SD dalam Melakukan Estimasi Masalah Berhitung Berdasarkan Jenis Kelamin. Penelitian ini ingin mendeskripsikan proses berpikir siswa laki-laki dan perempuan yang berkemampuan matematika tinggi dalam melakukan estimasi. Penelitian dilakukan di kelas V SD, dengan subjek satu siswa laki-laki dan satu siswa perempuan yang memiliki skor 75 ke atas dalam tes kemampuan matematika. Data dikumpulkan dengan wawancara, pemberian tes dan think aloud. Analisis dilakukan dengan menelaah seluruh data, reduksi data, pengolompokan data, kategorisasi, pengkodean, dan pemeriksaan kredibilitas data dengan triangulasi waktu. Hasil penelitian menunjukkan bahwa proses berpikir keduanya adalah akomodasi. Dalam membuat rencana, laki-laki menggunakan rounding dan compatible number strategy, sedangkan perempuan menggunakan rounding strategy. Dalam me­laksanakan rencana, laki-laki berhitung secara mental melalui proses berpikir asimilasi, sedangkan perem­puan berhitung menggunakan algoritma melalui proses berpikir akomodasi. Dalam mengecek pekerjaan, laki-laki menelusuri dengan berhitung mental, sedangkan perempuan menggunakan operasi balikan.