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Combinatorial reasoning was a basic competence that every student must have for solving mathematical problems, as it highly related to providing argumentation or strategy in solving mathematical problems. It was the process of creating complex constructs out of a set of given elements that satisfy the conditions explicitly given or inferred from the situation. Considering this issue, this study aimed to explore the combinatorial reasoning of high school students with cognitive-reflective and -impulsive styles in solving problems. More specifically, It correlated combinatorial reasoning with tempo cognitive style, since it applied time-based problem solving in which the speed of responding and the frequency of either correct or wrong answer might affect students’ mental action in solving problems. This study was a qualitative research. It used High school students in eleventh grade as the research subject through matching familiar figure test. The researchers distributed a task containing several problems that had similar concept for each and then organized an interview to explore the students’ combinatorial reasoning in solving the given problems. Cognitive-reflective subject decided to use two strategies –formula and filling slot- for the sake of her affirmation, while cognitive-impulsive subject decided to only use one strategy –formula. The cognitive-reflective subject tended to be more accurate and careful in solving the problems. Otherwise, the cognitive-impulsive ones tended to be careless and less accurate, given that the subject decided to do spontaneous mental action. The result of this study found some similarities and differences on the combinatorial reasoning of both reflective and impulsive students. The similarities referred to their ways in explaining the notation in the formula they used and generalizing their strategies. The differences referred to the process of investigating various factors, considering any probabilities that might reveal, and evaluation.

The aim of this research was to discover the relationship between teachers’ and students’ beliefs in mathematics. The sample consisted of two mathematics teachers, twenty eight students from 10th grade natural science 6 (X IPA 6) and twenty eight students from 10th grade natural science 10 (X IPA10) at state senior high school 5 Semarang. The data were collected from questionnaires and guided interviews on beliefs about mathematics. The research results showed that both of the mathematics teachers had platonist beliefs. It was found specifically that 4.76% of students in class X IPA 6 consistently had instrumentalist beliefs, 85.71% were consistent with their platonist beliefs, and 9.52% consistently had problem solving beliefs; while in class X IPA 10, 4.76% consistently showed instrumentalist beliefs, 80.95% were consistent with their platonist beliefs, and 14.29% consistently had problem solving beliefs. This indicates that there is a relationship between teachers’ and students’ beliefs, namely the tendency towards platonist beliefs; and also that the teacher’s beliefs influence the student’s beliefs.

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 problemsolving 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.

Mathematics achievement of students in Indonesia is still lower than students in other countries. It is because the creative ability of students is still low. This study aimed to analyze students' creative problem-solving abilities after using realistic math comics videos. This type of research is quantitative research. A quasi-experimental study with a pretest-posttest comparison design was conducted in this study. The population of this study were all seventh-grade students of SMP, which consisted of four parallel classes. The sample was selected using a random sampling technique so that there were two classes of research samples, namely the control class sample and the experimental class sample. This study used a pretest and posttest instrument for creative problem-solving abilities. In this study, the pretest and posttest score data were normally distributed and homogeneous. Based on the research data analysis using the independent sample t-test, it was concluded that there were differences in the creative problem-solving abilities of students who were taught using real math comics videos with groups of students who were taught not to use fundamental math comics videos. So, it can be concluded that the creative problem-solving abilities of students who are taught using real math comic videos are better than those who are not taught using real math comic videos.

Good instructional materials are arranged systematically and they enable students to learn independently, up to date, easily digestible and designed in accordance with the applicable curriculum. This research aimed to determine the process and results of the development of integrated statistical instructional materials EPUB-based statistical literacy properly (valid, practical, and effective) and to determine whether there were significant differences between the pretest-posttest results. The type of research used was Research and Development (R&D) with the ADDIE type development model. The subjects in this research were 53 students of the mathematics education study program at Universitas Palangkaraya (UPR) and 41 students of the PGSD study program at Universitas Mushammadiyah Palangkaraya (UMPR). Data analysis used T-test and N-Gain test. The research results obtained were as follows: (1) The instructional materials developed contained statistical literacy and multimedia based, namely EPUB (2) The average validity obtained from the validator's assessment was 89.42% very valid of 89.42% (3) The average percentage of student responses to EPUB-based statistical literacy integrated instructional materials was 89.82%. Overall, instructional materials were in the very practical category. (4) student learning completeness reached 80.76%, there were 30 of 31 UPR students completed and student learning completeness reached 78, 80%, there were 22 UMPR students completed and it can be concluded that the use of EPUB was effective. (5) Furthermore, a significant difference can be seen from the UPR average of the experiment class posttest was 84.23 while the posttest control class was 61.23. It means that the post-test results of the experiment class were higher than the post-test results of the control class with a difference of 23 and the result of the N-gain score for the experiment class is 56.3% while the control class is only 4.24%. Meanwhile, a significant difference can also be seen from the average UMPR of the posttest experiment class was 78.14 while the posttest control class was 63.00. It means that the post-test results of the experiment class were higher than the post-test results of the control class with a difference of 15.14 and the results of the N-gain score for the experiment class are 56% while the control class was only 10%.

— Kemampuan komunikasi matematis adalah kecakapan seseorang dalam menggunakan istilah matematika untuk menyalurkan pemikirannya secara sistematis baik secara lisan maupun tulis. Kemampuan komunikasi matematis dapat diketahui dari kemampuan siswa dalam menyelesaikan soal matematika dan kemampuan dalam mengkomunikasikan hasilnya kepada orang lain. Pengetahuan mengenai transformasi geometri berperan penting dalam perkembangan matematika siswa di sekolah karena dapat membangun kemampuan spasial, kemampuan penalaran serta membantu siswa dalam menganalisis situasi matematis. Penelitian ini bertujuan untuk mendeskripsikan kemampuan komunikasi matematis dalam menyelesaikan soal transformasi geometri yang ditinjau dari gender. Jenis penelitian ini adalah penelitian kualitatif dengan pendekatan deskriptif. Subjek penelitian ini adalah dua orang siswa laki laki dan dua orang siswa perempuan di salah satu sekolah menengah Kota Mojokerto dikarenakan penelitian ini mendeskripsikan bagaimana kemampuan komunikasi matematis yang ditunjukkan oleh siswa laki-laki dan perempuan. Berdasarkan analisis data dalam penelitian dapat disimpulkan bahwa (1) Kemampuan komunikasi matematis siswa lakilaki lebih unggul dibandingkan siswa perempuan dalam kemampuan menyajikan informasi serta dalam kemampuan menggunakan bahasa matematika yang logis dan sistematis dalam proses penyelesaian soal. Sedangkan pada kemampuan menggunakan representasi matematis dalam menyatakan gagasan matematis untuk menyelesaikan soal transformasi geometri, siswa laki-laki dan perempuan memiliki kemampuan yang sama. (2) Siswa laki-laki lebih mampu menyelesaikan soal transformasi geometri dengan lebih tepat dibandingkan siswa perempuan. (3) Siswa laki-laki lebih unggul dalam menjawab soal secara tertulis, sedangkan siswa perempuan memiliki kemampuan yang baik dalam menyajikan jawaban secara lisan atauverbal.Kata kunci: kemampuan komunikasi matematis, transformasi geometri, gender.Abstract — Mathematical communication skills are a person's ability to use mathematical terms to express their thoughts systematically both spoken and written. Mathematical communication skills can be seen from the ability of students to solve mathematic problems and the ability to communicate the results to others. Knowledge of geometric transformations plays an important role in the development of student’s mathematics in school because it can build spatial abilities, reasoning abilities and help students analyze mathematical situations. This study aims to describe written mathematical communication skills in solvinggeometric transformation problems in terms of gender. This type of research is a qualitative research with a descriptive approach. The subjects of this study are two male students and two female students in one of senior high school in Mojokerto because this study describes how mathematical communication skills are showed by male and female students. The results showed that (1) Male students' mathematical communication skills are superior to female students in the ability to present information and in the ability to use logical and systematic mathematical language in the problem solving process. Meanwhile, the abilityto use mathematical representations in expressing mathematical ideas to solve geometric transformation problems, male and female students have the same abilities. (2) Male students are more able to solve geometric transformation problems more precisely than female students. (3) Male students are superior inanswering questions in writing, while female students have good abilities in present the answer orally or verbally.Keywords: mathematical communication skills, problem solving, gender.

— Menggunakan model dan strategi pembelajaran yang bervariatif merupakan salah satu cara untuk menumbuhkan minat belajar siswa dalam pembelajaran matematika. Creative problem solving adalah model pembelajaran yang memusatkan pada pengajaran dan keterampilan pemecahan masalah yang diikuti dengan penguatan keterampilan. Penguatan keterampilan yang dimaksud adalah dengan menggunakan media pembelajaran, salah satunya dengan aplikasi maple untuk memecahkan masalah matematika. Riset ini memakai penelitian kuantitatif dengan tipe eksperimen untuk mengetahui kefektifan model pembelajaran creative problem solving dengan media pembelajaran maple untuk meningkatkan kemampuan berpikir kreatif siswa. Penelitian ini dilaksanakan di salah satu sekolah menengah atas di Surabaya pada kelas XMIA1 semester ganjil tahun ajaran 2019/2020 dengan melibatkan 30 siswa. Kegiatan dalam penelitian ini meliputi pemberian pre test, pemberian perlakuan, dan pemberian post test. Kemudian perolehan dari nilai pre test dan post test dianalisis untuk melihat kefektifan pembelajaran creative problem solving berbasis aplikasi maple. Hasil penelitian ini menunjukkan adanya dampak model pembelajaran berbasis aplikasi maple terhadap kemampuan berpikir kreatif siswa yang didapatkan dengan uji t. Selain itu, berdasarkan uji Gain dihasilkan nilai rata-rata N-Gain 0.71 yang berada pada interval N-Gain 0.7 < 𝑔 ≤ 1.00, yang artinya pembelajaran creative problem solving berbasis aplikasi maple memiliki tingkat keefektifan yang tinggi. Selanjutnya, data yang didapatkan dari penelitian ini merupakan data berdistribusi normal. Hal ini dapat dilihat dari perolehan uji normalitas data yang hasil signifikansinya > 0.05. Selain itu, data yang didapat dari penelitian ini merupakan data yang homogen. Hal ini dapat dilihat dari hasil uji homogenitas data yang hasil signifiansinya > 0,05.Kata kunci: Creative Problem Solving, Maple, Berpikir KreatifAbstract — Using the variety of learning models and strategies is one of the ways to grow students learning interests in mathematics learning. Creative problem solving is a learning model that focuses on teaching and problem solving skills followed by strengthening skills. Strengthening skills in question is using learningmedia, one of them with maple application to solve mathematics problems. This research uses quantitative research with experiment to find out the effectivity of creative problem solving learning model with maple (learning media) to improve the ability of students creative thinking. This research was conducted at privatesenior highschool in Surabaya class X MIA1 in the odd semester of the 2019/2020 school year involving 30 students. Activities in this research include giving pretest, treatment, and posttest. Then the results of the pretest and posttest scores were analyzed to determine the effectiveness of creative problem solving learning based on maple application. The results of this research indicate the influence of learning model based on maple application to students' creative thinking abilities obtained by t test. In addition, based on Gain test, the average value of N-Gain is 0.71 which is in the N-Gain interval 0.7 < 𝑔 ≤ 1.00. It means that creative problem solving learning based on maple application has a high level of effectiveness. Furthermore, the data obtained from this research are normal distribution data. This can be seen from the results of data normality test whose significance is > 0.05. In addition, the data obtained from this research are homogeneous data. This can be seen from the results of data homogeneity test whose significance is > 0.05.Keywords: Creative Problem Solving, Maple, Creative thinking

Mathematics helps students to practice their thinking skills. One of the thinking skills expected to face the times is the ability to think creatively. Therefor we need a qualitative research with descriptive methods. The research that was conducted at SMP Santo Yoseph Medan in the academic year 2020/2021 involved 16 students representing class VII-B and 14 students representing VII-C junior high schools as research subjects and the results showed that students’ creative problem-solving abilities did not show good results. The instrument used was a test of creative problem-solving abilities which consisted of 3 questions. This is analyzed based on the indicators of fluency, flexibility, and originality for solving questions number 1, 2, and 3. Based on the fluency indicator in solving problem number 1, data is obtained that 14 people are not fluent and 16 people are fluent. In solving problem number 2, data is obtained that 15 people are not fluent and 15 people are fluent. In solving problem number 3, it is obtained data that 18 people are not fluent and 12 people are fluent. Based on the indicator of flexibility in solving problem number 1, it is obtained data that 29 people are not flexible and 1 person is less flexible. In solving problem number 2, it is obtained data that 30 people are not flexible and none are flexible. In solving problem number 3, it is obtained data that 30 people are not flexible and none are flexible. Based on the originality indicator in solving problem number 1, it is obtained data that 29 are not new and 1 person is not new. In solving problem number 2, data shows that 27 are not new and 3 are not new. In solving problem number 3, it is obtained data that 27 people are not new and 3 people are not new.

The use of digital resource for learning has been increasing since the Industrial Revolution 4.0 was enlivened. This was further strengthened by the government’s policy to learn from home since the COVID pandemic 19. Various types of online learning can be effective but also sometimes do not succeed in achieving the expected learning goals. Drijver suggests that 3 main factors influence how digital learning resources can be effective in learning, namely how the design of digital content is, how the teacher’s role in digital content is, and the use of the educational context used in digital content. Realistic Mathematics Learning can be an approach that can accommodate all the factors. This study aims to provide appropriate digital learning resources for teachers and students during the COVID 19 pandemic. An adapted Plomp Design is used for developing digital content. This developmental research suggests that the characterization of RME supports the requirements for effective digital learning resources in a way that enables the student to foster their constructive learning activities. However, these rich didactical activities lack in providing an adequate presentation on the mathematics content.

— Penelitian ini memiliki tujuan mengetahui pengaruh kecemasan matematika terhadap hasil belajar matematika siswa. Penelitian dilaksanakan pada Kelas VIII SMPN 3 Sidoarjo Semester Genap Tahun Ajaran 2019/2020 dengan sampel penelitian pada kelas VIII-B dan kelas VIII-C dilakukan menggunakan teknik simple random sample. Penelitian ini termasuk dalam penelitian kuantitatif dengan menggunakan analisis regresi linier sederhana, kemudian dilakukan uji asumsi klasik. Untuk mengetahui pengaruh antar variabel dilakukan analisis regresi linier sederhana. Aplikasi SPSS versi 26 digunakan untuk membantu peneliti melakukan perhitungan. Untuk mengetahui model regresi baik atau tidak menurut BLUE (Best Linier Unbiased Estimator) dilakukan uji asumsi klasik. Instrumen yang digunakan berupa survey kecemasan matematika dan tes hasil belajar matematika. Dari hasil perhitungan mendapatkan persamaan sebagai berikut Y = 143,748−0,965X. Koefisien persamaan regresi memiliki nilai negatif artinya kecemasan matematika memiliki hubungan negatif terhadap hasil belajar matematika. Nilai koefisien korelasi sebesar -0,741 yang berarti mempunyai hubungan yang sangat rendah dan signifikan antara kecemasan matematika terhadap hasil belajar matematika. Koefisien determinasi sebesar 0,548 artinya kecemasan matematika terhadap hasil belajar matematika memiliki pengaruh sebesar 54,8%. Dari hasil uji asumsi klasik didapatkan bahwa hasil persamaan regresi linier, homoskedasitas, nonautokorelasi, nonmultikorelasi dan normalitas. Dari hasil analisis dapat disimpulkan bahwa kecemasan matematika memiliki pengaruh negatif yang signifikan terhadap hasil belajar matematika. Semakin tinggi kecemasan matematika akan berpengaruh terhadap rendahnya hasil belajar matematika siswa dan semakin rendah kecemasan matematika akan berpengaruh terhadap tingginya hasil belajar matematika siswa. Kata k unc i : Kecemasan matematika, hasil belajar matematika Abstract — This study aims to determine the effect of mathematics anxiety on student mathematics learning outcomes. This research was conducted in Class VIII of SMPN 3 Sidoarjo Even Semester Academic Year 2019/2020 with research samples in class VIII-B and class VIII-C conducted with simple random sample technique. This research is included in quantitative research using simple linier regression analysis, then performed a classic assumption test. To determine the effect between variables, a simple linier regression analysis was performed. SPSS application version 26 is used to help researchers make conclusion. To determine whether the regression model is good or not according to BLUE (Best Linier Unbiased Estimator) classic assumption test is performed. The instrument used were mathematics anxiety survey and mathematics learning achievement test. From the calculation result get the following equation Y = 143,748−0,965X. The regression equation coefficient has a negative value meaning that mathematics anxiety has a negative relationship with the learning outcomes of mathematics. The correlation coefficient value is -0,741 which means it has a very low and significant relationship between mathematics anxiety and mathematics learning outcomes. The coefficient of determine of 0,548 means that mathematics learning outcomes has an effect of 54,8%. From the results of the classic assumption test it was found that the result of the linier regression equation, homoscedastic, non-autocorrelation, non-multicorrelation and normality. From the analysis it can be concluded that mathematics anxiety has a significant negative affect on mathematics anxiety will affect the low student mathematics learning outcomes and the lower mathematics anxiety will affect the higher student mathematics learning outcomes. Keywords : Mathematics anxiety, mathematics learning outcomes

This article describes students’ tasks that concerned to assess students’ problem proving and problem posing on triangle tasks. This descriptive-explorative research involves 24 prospective mathematics teachers at a state university in Surabaya, Indonesia. They had to answer three questions. The first question related to problem proving of triangle theorem. The second question related to their perception of the first question, and the last question related to the problem-posing task. A Newman analysis is used to analyse the data. The analysis of the data focused on students’ problem proving and students’ problem posing of triangle task. The results showed that most of them were correct to answer the question as many as 41%. It can be seen of the first question was performed by the highest number of them. However, some of them still have a perception of the first question is a problem, because it shows as many as 95% of 24 students choose it. They also have some weaknesses in proving problems, mainly misinformation or ambiguity about the problem, it is not a category as a problem proving. They constructed proof by formal proof with a low level of problem difficulty as many as only 38 % of them.

Creating a problem is one cognitive process of Bloom’s taxonomy. By making a problem and the answer on their own, causes students to understand more complex context problems. Applying number sequence challenges students to apply higher-order thinking skills and emphasize exploration, investigation, conjecture, and generalization. From the previous explanation, the purpose of this study is to explore the ability of students in creating mathematical problems in the context of numbers based on the ‘degree of reality’ and based on innovation on mathematics problems. This descriptive explorative study is collected from 24 prospective mathematics teachers that consist of 4 males and 20 females in a university. All students have to answer one question about creating word problems related to number sequence and the answer. Those problems then were analyzed and categorized based on the modification of innovation on mathematics problems by Vistro-Yu and based on ‘degree of reality’ by de Lange. The result of this study, modification is the most emerging technique among all, and the least are addition and replacement. Based on ‘degree of reality,’ only one-fourth of the number of students successful in creating a camouflage context. This result leads to only forth of the number of students successful in creating word problems. The implication of this study is the choice of students in making questions at least provides an overview of the highest level of difficulty, according to students. In mathematics learning, the lecturer should plan assessments and evaluations that need to be developed to build students’ abilities to make mathematics as a whole by connecting subjects in mathematics and to make mathematics more relevant to reality.

Quantitative reasoning is essential in learning and is the primary objective of many educators especially for math teachers worldwide with the aim of how to develop the relationship between mind and the problems of students’ real-life so that it can be solved mathematically. The purpose of this study is to describe the students' quantitative reasoning in generalizing math word problems. The type of this research was descriptive research with a qualitative approach. The subjects of this study were male students enrolled as students of Junior High School in Makassar, and the students had Field-dependent cognitive style. The Group Embedded Figure Test test (GEFT) is used to find subjects that have Field-dependent cognitive style. The main data collection of this study was obtained by using interview technique to investigate the aspect of students' quantitative reasoning ingeneralizing process when completing math problem. The results showed that the subject of male Fielddependent: quantitative reasoning of the subject arises two traits: (1) hooking the relationship of ratios and (2)hooking the proportional relationship, furthermore the subject there is a tendency to see only one quantity change and the subject in finding a new quantity is procedural.

Statistics have become a key component of the mathematics curriculum. At a basic level, by studying statistics, one can inference, read and present data in a more easily understood form known as statistical literacy. Everyone is in one of the roles of being a consumer and as a data producer. The core element of static literacy for consumers is the ability to read and interpret data in tables and graphs published by the national statistical office. The core element for producers is the ability to create clear, understandable tables, graphs and reports. The purpose of this research is to describe the student profile in presenting the data. Therefore, this study is a descriptive explorative qualitative. The subject comes from grade XII students MIA 9 SMA Negeri 3 Sidoarjo. Data were collected through a combination of interview methods with written task analysis. The result of the research shows that the subjects had the ability to describe data in the form of tables or diagrams in accordance with the desired information, including building an alternative view for a set of data, that is in the form of line diagrams, histograms, and pie diagrams, as well as frequency distribution table that referred to the purpose of data communication, regardless of the characteristics of a data. by paying attention to the characteristics of the data.

Pembelajaran matematika diyakini sebagai sarana memberikan bekal pengetahuan untuk mengembangkan kemampuan dan keterampilan berpikir, serta pengetahuan pendukung mempelajari pengetahuan lain. Matematika memiliki objek abstrak dan dipandang bebas nilai manusiawi. Tetapi dalam pembelajarannya tidak dapat melepaskan diri dari unsur “realistik” dan humanistik. Kecenderungan dewasa ini pembelajaran matematika yang dikembangkan adalah pembelajaran matematika humanistik dengan pendekatan realistik. Makalah ini akan menguraikan suatu pandangan pembelajaran matematika realistik-humanistik, keterkaitan dengan PMRI, dan pembelajaran berorientasi pemecahan dan pengajuan masalah matematika. Kata kunci: humanistik, realistik-humanistik, PMRI, pengajuan masalah, pemecahan masalah

Keyakinan (belief) terhadap matematika mempengaruhi bagaimana seseorang “menyambut” matematika. Keyakinan juga mempengaruhi prestasi belajar. Guru memegang peran penting dalam membangun keyakinan siswa terhadap matematika. Oleh karena itu perlu dikembangkan instrumen untuk mengukur keyakinan guru atau mahasiswa calon guru. Model pengembangan yang digunakan untuk mengembangkan angket menggunakan design research tipe development study. Tahap yang dilakukan yang terdiri dari tiga fase, yaitu: investigasi awal, fase prototype, dan fase assesmen Penelitian ini menggunakan teknik analisis deskriptif kualitatif dan kuantitatif. Hasil penelitian menunjukkan instrumen angket yang dikembangkan memenuhi kriteria valid dan reliabel berdasakan hasil analisis kuantitatif. Hasil analisis kualitatif juga menunjukkan terdapat tiga jenis keyakinan dalam pemecahan masalah dan pembelajaran yang dimiliki oleh mahasiswa calon guru matematika.

In the last few years, reflective thinking becomes very popular term in the world of education, especially in professional education of teachers. One of goals of the educational personnel and teacher institutions create responsible prospective teachers and they are able reflective thinking. Reflective thinking is a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. Reflective thinking can be applied in mathematics becauseby reflective thinking, students can improve theircuriosity to solve mathematical problem. In solving mathematical problem is assumed that cognitive style has an impact on prospective teacher’s mental activity. As a consequence, reflective thinking and cognitive style are important things in solving mathematical problem. The subject, in this research paper, isa female-prospective teacher who has fielddependent cognitive style. The purpose of this research paperis to investigate the ability of prospective teachers’ refl...

The purpose of this study was to explore the strategic competence of senior secondary school students in solving mathematics problems. Terdapat dua subjek, satu bergaya kognitif field-independent dan satu bergaya kognitif field-dependent tetapi keduanya memiliki tingkat prestasi belajar matematika yang setara. There were two subjects, one field-independent cognitive style and one field-dependent cognitive style. They had an equivalent high level of mathematics achievement. Keduanya dipilih berdasarkan hasil tes kompetensi matematika dan GEFT (Group Embedded Figures Test). Subjects were selected based on the test results of mathematics competence and GEFT (Group Embedded Figures Test). Kompetensi strategis dapat merangsang perkembangan otonomi dan fleksibilitas dalam diri siswa karena merupakan keterampilan yang sangat dibutuhkan di sepanjang abad 21. Gaya kognitif merupakan kecenderungan siswa dalam mengolah informasi sangat mempengaruhi performance dalam menyelesaikan masalah matematika. Strategic competence can stimulate the development of autonomy and flexibility of students and they are skills which are needed in the 21st century. Cognitive style is the tendency of students in processing informations and it greatly affects the performance in solving mathematics problems. Hasil penelitian menunjukkan bahwa subjek FI cenderung analitis baik pada pembentukan bayangannya maupun pada gambar yang dibuatnya untuk memproses informasi berdasarkan dengan struktur pengetahuannya sendiri (Internally directed). The research result showed that subject FI tended to be analytical both in forming the mental imagination and the picture to process information in accordance with his own knowledge structure (internally directed). Subjek FD kurang analitis dan tidak dapat mengenal bentuk sederhana (konsep matematika) dari bentuk yang kompleks (Exeternally directed) sehingga menerima ide sebagaimana yang disajikan. Subject FD was less analytical and unable to recognize simple form (mathematical concept) of a complex form (Externally directed), so he received the idea as presented. Hasil penelitian ini penting sebagai bahan masukan untuk guru dan pengembang ilmu pendidikan matematika untuk meningkatkan fleksibilitas (Flexibility) siswa dalam keberagaman karakteristiknya melalui penelitian terkait dengan pengembangan bahan instruksi, perangkat dan model pembelajaran matematika. The results of this research are important as input for teachers and mathematics education developers to increase the flexibility of students in the characteristics diversity through the research related to the development of instruction materials and mathematics learning model. Penelitian selanjutnya, sebaiknya melihat bagaimana FI dan FD dapat memberikan penjelasan dan pembenaran atas strategi yang telah diusahakan supaya terlihat lebih jelas bagaimana perbedaan FI dan FD dalam mengkontruksi konsep matematika pada pengalaman belajarnya Further research should study about how the explanation and justification for the strategy that has been attempted in order to look more clearly how constructing mathematical concepts in their learning experience.

The purpose of this research is to explore the conception of prospective students teacher that highly skilled on mathematical ability about limit function, especially in the aspects of understanding, representation, mental image and proposition. This study was conducted by a qualitative exploratory method. The subject was one of the students in the mathematics education of Syiahkuala University which being chosen according to the expected criteria.. The research instrument was divided into main and supporting instrument. The data was analyzed by reducing, presenting, interpreting and concluding. The analyzing data results obtained the subject’s conception about limit function were elaborated the meaning of limit function with representation verbal, graphic, symbol, and logical explanation, expressing the limit function definition with verbal representation, graphic, table and symbol. The subject defined the correlation of limit function by imaging, revealing, and using one-sided the limit of function. The...

Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student’s curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student’s reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers’ reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher’s activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

Gender is one of the interesting topics and has continuity to be explored in mathematics education research. The purpose of this study to explore difference on conceptions of students teaching program by gender. It specialized on conception of understanding, representating, and mental images about limit function. This research conducting qualitative explorative method approach. The subject consisted of one man and one woman from the group of highly skilled student and has gone through semester V. Based on data that had been analyzed proved that male student has an understanding about limit function shared by explaining this material using illustrations, while female student explained it through verbal explanation. Due to representating aspect, it revealed that both of male and female students have similarity such as using verbal explanation, graphs, symbols, and tables to representating about limit function. Analyzing Mental image aspect, researcher got that male student using word “to converge” to explained about limit function, while female student using word “to approach”. So, there are differences conceptions about limit function between male and female student.

The series of adaptive reasoning and strategic competencies represent the five components of mathematical proficiency to describe the students’ mathematics learning success. Gender contribute to the problem-solving process. This qualitative research approach investigated the adaptive reasoning and strategic competence aspects of a male student and a female student when they solved mathematical problem. They were in the eleventh grade of high school in Makassar. Both also had similar mathematics ability and were in the highest category. The researcher as the main instrument used secondary instrument to obtain the appropriate subject and to investigate the aspects of adaptive reasoning and strategic competence. Test of mathematical ability was used to locate the subjects with similar mathematical ability. The unstructured guideline interview was used to investigate aspects of adaptive reasoning and strategic competence when the subject completed the task of mathematical problem. The task of mathematical problem involves several concepts as the right solution, such as the circle concept, triangle concept, trigonometry concept, and Pythagoras concept. The results showed that male and female subjects differed in applying a strategy to understand, formulate and represent the problem situation. Furthermore, both also differed in explaining the strategy used and the relationship between concepts and problem situations.

The aim of this research was to describe the mathematical visualization process of Junior High School students in solving contextual problems based on cognitive style. Mathematical visualization process in this research was seen from aspects of image generation, image inspection, image scanning, and image transformation. The research subject was the students in the eighth grade based on GEFT test (Group Embedded Figures Test) adopted from Within to determining the category of cognitive style owned by the students namely field independent or field dependent and communicative. The data collection was through visualization test in contextual problem and interview. The validity was seen through time triangulation. The data analysis referred to the aspect of mathematical visualization through steps of categorization, reduction, discussion, and conclusion. The results showed that field-independent and field-dependent subjects were difference in responding to contextual problems. The field-independent subject presented in the form of 2D and 3D, while the field-dependent subject presented in the form of 3D. Both of the subjects had different perception to see the swimming pool. The field-independent subject saw from the top, while the field-dependent subject from the side. The field-independent subject chose to use partition-object strategy, while the field-dependent subject chose to use general-object strategy. Both the subjects did transformation in an object rotation to get the solution. This research is reference to mathematical curriculum developers of Junior High School in Indonesia. Besides, teacher could develop the students’ mathematical visualization by using technology media or software, such as geogebra, portable cabri in learning.The aim of this research was to describe the mathematical visualization process of Junior High School students in solving contextual problems based on cognitive style. Mathematical visualization process in this research was seen from aspects of image generation, image inspection, image scanning, and image transformation. The research subject was the students in the eighth grade based on GEFT test (Group Embedded Figures Test) adopted from Within to determining the category of cognitive style owned by the students namely field independent or field dependent and communicative. The data collection was through visualization test in contextual problem and interview. The validity was seen through time triangulation. The data analysis referred to the aspect of mathematical visualization through steps of categorization, reduction, discussion, and conclusion. The results showed that field-independent and field-dependent subjects were difference in responding to contextual problems. The field-independent subject pr...

This article showed a consistency and inconsistency beliefs towards prospective mathematics teachers, teaching, learning and problem solving. Data were collected on 183 prospective teachers of mathematics shows that belief in mathematics, teaching, learning and problem solving categorized as an instrumentalist, or platonist, or constructivist. It was found that 0.546% prospective teachers consistently have instrumentalist beliefs; 80.328% had a platonist beliefs; 0.546% had constructivist beliefs, and the rest is inconsistent to each category of beliefs. This study suggests that lecturer should train the prospective teacher through a series of scientific learning activities that have constructivist beliefs.

Kemampuan berpikir kreatif sangat dibutuhkan dalam menghadapi masalah seharihari dan menyelesaikan masalah matematika yang membutuhkan ide baru. Kemampuan berpikir kreatif diperlukan dalam memunculkan ide baru. Salah satu alat yang dapat digunakan untuk mengidentifikasi dan mengembangkan kemampuan berpikir kreatif yaitu pengajuan masalah matematika. Penelitian yang dilakukan pada siswa kelas VIII di Surabaya ini bertujuan untuk menggali kemampuan berpikir kreatif siswa dalam mengajukan masalah matematika pada situasi semi-terstruktur. Sebanyak 4 siswa dipilih sebagai subjek wawancara yaitu 1 subjek pada masing masing tingkat berpikir kreatif (TBK) 1—4. Untuk mengetahui kemampuan berpikir kreatif siswa dilakukan analisis tugas pengajuan masalah matematika berdasarkan kefasihan, kebaruan, dan fleksibilitas serta wawancara. Hasil menunjukkan bahwa siswa pada TBK 1, 2, dan 3 membuat soal sederhana yang sering ditemui dalam pembelajaran matematika dan menjawab dengan cara yang telah diajarkan sebelumnya. Sedangkan siswa pada TBK 4 dapat membuat soal dan cara penyelesaian yang lebih kompleks dengan menambahkan dan memodifikasi situasi yang diberikan. Selain itu dalam mengajukan soal siswa memikirkan jawaban terlebih dahulu dan menggunakan pengalaman matematika terdahulu.

This research was qualitative that aims to described the quantitative reasoning and students' generalization ability in direct proportion. This research involved 35 grade VIII junior high schools; one of them with moderate math skills was chosen as the main subject. The data collected through the test, assignment, and task-based interviews. The results of this research showed that a generalization that was built by the subject begins with forming a relationship between two or more quantities by establishing ratio of the quantity which appears linking the two initial quantity, doing repetition to find the elements of common ground and further developed the pattern or relationship into a more general form of structure. The quantitative reasoning which belonged to the subject greatly affects the generalizations made. The results of this research are important as an input material for teachers, to develop a strong generalization in General, and then the student must construct the ratio of the quantity that appears with the linking between the quantities. In order to support the students' ability to perform a generalizing correctly.

Students have many difficulties in geometry such as disability to visualize two dimensional to three dimensional objects. That is indicated by lower spatial reasoning. This study aims at describing the students' spatial reasoning in solving geometric problem. This qualitative research involved three elementary students that consist of highest, middle, and lowest student's ability. The results pointed out the highest and middle recognized geometry object and they could explain some information which is known and asked correctly. The highest student also could imagine cube nets into cubes and describing the surface of the cube when it viewed from the right, left, top, bottom, front, and back. The middle student couldn't draw surface of the cube appropriately when it viewed from the right, left, top and bottom. The lowest student couldn't recognize geometric object, nor could mention the information. Finally, we suggest teachers to teach middle and low students to deepen the introduction of geometric objects.

Strategic competence refers to mental activities that apply strategies to formulate, to represent, and to solve mathematical problems. The aim of this qualitative research is to explore strategic competence of the sixth, seventh, and eighth grade students in solving open-ended problems. There were 25 students with different mathematical competencies involved to take part in this research. Among them, three selected students with higher mathematical competency represented each grade. This research used interview-based task to explore students' strategic competence. Results showed that students understood the problems by reading and drawing/graphing them, formulated problem solving by recalling their prior knowledge about quadrilateral topic, and conveyed numerical and visual strategy to solve the open-ended problems. At last, they could determine effective solutions using arithmetical method, find all solutions correctly, and choose the cheaper ones. As an implication, we suggest further research to explore students' strategic competence with other types of mathematical competences.

Self Regulated Learning (SRL) is an individual's ability to achieve academic goals by controlling behavior, motivate yourself and use cognitive in learning, so it is important for a teacher especially teachers of mathematics related to the ability of management, design, implementation of learning and evaluation of learning outcomes. The purpose of the research is to develop an instrument to describe the SRL of a prospective mathematics teacher. Data were collected by (1) the study of the theory of SRL produced the indicator SRL used to design the questionnaire SRL; (2) analysis of the questionnaire SRL obtained from several References; and (3) development stage of the SRL questionnaire through validity test of content and empirical validation. The study involved 2 content experts in mathematics, 1 linguist, and 92 prospective mathematics teachers. The results of the research on content validity test based on Indonesian expert and 2 content experts indicate that the content can assess the indicator of the SRL and feasible to be used, in the test of legibility of two prospective mathematics teacher concluded that the instrument has a language that can be understood by the prospective teacher of mathematics and on empirical validation involving 92 prospective mathematics teacher generate data that of 65 statements there are 3 invalid statements. Reliability calculation shows high category that values 0,93. The conclusion is the SRL instrument developed for the prospective mathematics teacher.

Conceptual comprehension in this research is the ability to use the procedures that are owned by pre-service teachers to solve problems by finding the relation of the concept to another, or can be done by identifying the type of problem and associating it with a troubleshooting procedures, or connect the mathematical symbols with mathematical ideas and incorporate them into a series of logical reasoning, or by using prior knowledge that occurred directly, through its conceptual knowledge. The goal of this research is to describe the profile of conceptual comprehensin of pre-service teachers with low emotional intelligence in mathematical problems solving. Through observation and in-depth interview with the research subject the conclusion was that: pre-service teachers with low emotional intelligence pertained to the level of formal understanding in understanding the issues, relatively to the level of intuitive understanding in planning problem solving, to the level of relational understanding in implementing the relational problem solving plan, and pertained to the level of formal understanding in looking back to solve the problem.

Metacognition is related to improving student learning outcomes. This study describes students' metacognitive activities in solving the combinatorics problem. Two undergraduate students of mathematics education from STKIP PGRI Banjarmasin were selected as the participants of the study, one person has a holist cognitive style and the other a serialist. Data were collected by task-based interviews where the task contains a combinatorial problem. The interviews were conducted twice using equivalent problem at two different times. The study found that the participants showed metacognitive awareness (A), metacognitive evaluation (E), and metacognitive regulation (R) that operated as pathways from one function to another. Both, holist and serialist, have metacognitive activities in different pathway. The path of metacognitive activities of the holist is AERCAE-AAEER-ACRECCECC-AREERCE with the AERAE-AER-ARE-ARERE pattern, while the path of metacognitive activities of the serialist is AERCA-AAER-ACRERCERC-AREEEE with the AERA-AER-ARERER-ARE pattern. As an implication of these findings, teachers/lecturers need to pay attention to metacognitive awareness when they begin a stage in mathematical problem solving. Teachers/lecturers need to emphasize to students that in mathematical problem solving, processes and results are equally important.