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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.

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.

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.

This study aims to describe the students' understanding of fraction concepts. This research is descriptive with the qualitative approach. The subjects consisted of 1 Field Independent (FI) and 1 Field Dependent (FD) students. Setting subjects based on Group Embedded Figure Test (GEFT) results and meeting equivalent mathematical ability. Data obtained techniques through Task-based interview. The results show that FI students were represented a complete fractional concept and express the meaning of fractional notation with its own words.The students use of fractional concept such as the idea of dividing equally, fractional equivalents, and the relative size of the fraction to classify fractions based on certain properties, giving fractional examples and non-fractional examples, and comparing fractions. However, FD students represented declarative farctional concepts, had difficulty in giving a good meaning notation, relation between components, classifying fractions and comparing them. FD students are fixated on fraction notation and the visualization of concrete objects. Overall, these results provide a detailed picture of the understanding of fractional concepts that, FI students tend to use coherent analysis, while FD students tended to be fixated on fractional notation and visualization of concrete objects.

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.

One of the foundations for high school students in statistics is to be able to read data; presents data in the form of tables and diagrams and its interpretation. The purpose of this study is to describe high school students' competencies in reading, interpreting and presenting data. Subjects were consisted of male and female students who had high levels of mathematical ability. Collecting data was done in form of task formulation which is analyzed by reducing, presenting and verifying data. Results showed that the students read the data based on explicit explanations on the diagram, such as explaining the points in the diagram as the relation between the x and y axis and determining the simple trend of a graph, including the maximum and minimum point. In interpreting and summarizing the data, both subjects pay attention to general data trends and use them to predict increases or decreases in data. The male estimates the value of the (n+1) of weight data by using the modus of the data, while the females estimate the weigth by using the average. The male tend to do not consider the characteristics of the data, while the female more carefully consider the characteristics of data.

This research purposed to describe the elementary students' creativity with reflective and impulsive cognitive style in solving geometric problems. This research used qualitative research methods. The data was collected by written tests and task-based interviews. The subjects consisted of two 5th grade students that were measured by MFFT (Matching Familiar Figures Test). The data were analyzed based on the three main components of creativity; that is fluency, flexibility, and novelty. This results showed that subject with reflective cognitive style in solving geometric problems met all components of creativity (fluency; subject generated more than three different right-ideas in solving problems, flexibility; subject generated more than two different ways to get problem solved, and novelty; subject generated new ideas and new ways that original and has never been used before). While subject with impulsive cognitive style in solving geometric problems met two components of creativity (fluency; subject generated more than three different right-ideas in solving problems, flexibility; subject generated two different ways to get problem solved). Thus, it could be concluded that reflective students are more creative in solving geometric problems. The results of this research can also be used as a guideline in the future assessment of creativity based on cognitive style.

This study aims at describing the students' spatial abilities based on cognitive styles and sex differences. Spatial abilities in this study include 5 components, namely spatial perception, spatial visualization, mental rotation, spatial relations, and spatial orientation. This research is descriptive research with qualitative approach. The subjects in this research were 4 students of junior high school, there were 1 male FI, 1 male FD, 1 female FI, and 1 female FI. The results showed that there are differences in spatial abilities of the four subjects that are on the components of spatial visualization, mental rotation, and spatial relations. The differences in spatial abilities were found in methods / strategies used by each subject to solve each component problem. The differences in cognitive styles and sex suggested different choice of strategies used to solve problems. The male students imagined the figures but female students needed the media to solve the problem. Besides sex, the cognitive style differences also have an effect on solving a problem. In addition, FI students were not affected by distracting information but FD students could be affected by distracting information. This research was expected to contribute knowledge and insight to the readers, especially for math teachers in terms of the spatial ability of the students so that they can optimize their students' spatial ability.

Mathematical knowledge for teaching (MKT) is viewed as fuel resources for conducting an orchestra in a teaching and learning process. By understanding MKT, especially for primary teachers, it can predict the success of a goal of an instruction and analyze the weaknesses and improvements of it. To explore what teachers think about subject matters, pedagogical terms, and appropriate curriculum, it needs a task which can be identified the teachers' MKT including the subject matter knowledge (SMK) and pedagogical content knowledge (PCK). This study aims to design an appropriate task for exploring primary teachers' MKT for statistics in primary school. We designed six tasks to examine 40 primary teachers' MKT, of which each respectively represents the categories of SMK (common content knowledge (CCK) and specialised content knowledge (SCK)) and PCK (knowledge of content and students (KCS), knowledge of content and teaching (KCT), and knowledge of content and curriculum (KCC)). While MKT has much attention of numbers of scholars, we consider knowledge of content and culture (KCCl) to be hypothesized in the domains of MKT. Thus, we added one more task examining how the primary teachers used their knowledge of content (KC) regarding to MKT in statistics. Some examples of the teachers' responses on the tasks are discussed and some refinements of MKT task in statistics for primary teachers are suggested.

Designing problem like in PISA is known as a challenging activity for teachers particularly as the use of authentic context within that type of problem. This paper aims to describe the experiences of secondary mathematics teachers in designing PISA-like problems within an innovative training program focusing on building teachers' understanding on the concept of mathematical literacy. The teachers were engaged in a set of problem-solving and problem-posing activities using PISA-based problem within indoor and outdoor field experiences. Within indoor field experience, the teachers worked collaboratively in groups on designing PISA-like problems with a given context through problem generation and reformulation techniques. Within outdoor field experience, they worked on designing PISA-like problems with self-chosen context from the place where the outdoor field experience took place. Our analysis indicates that there were improvements on the PISA-like problems designed by teachers based on its level use of context from indoor to outdoor experience. Also, the teachers were relatively successful with creating appropriate and motivating contexts by harnessing a variety of context consisting of personal, occupational, societal, and scientific contexts. However, they still experienced difficulties in turning these contexts into an appropriate problem satisfying PISA framework such as regarding authenticity of context use, language structure, and PISA task profile.

This is a descriptive research which qualitatively investigates students' relational thinking of impulsive and reflective cognitive style in solving mathematical problem. The method used in this research are test and interview. The data analyzed by reducing, presenting and concluding the data. The results of research show that the students' reflective cognitive style can possibly help to find out important elements in understanding a problem. Reading more than one is useful to identify what is being questioned and write the information which is known, building relation in every element and connecting information with arithmetic operation, connecting between what is being questioned with known information, making equation model to find out the value by using substitution, and building a connection on re-checking, re-reading, and re-counting. The impulsive students' cognitive style supports important elements in understanding problems, building a connection in every element, connecting information with arithmetic operation, building a relation about a problem comprehensively by connecting between what is being questioned with known information, finding out the unknown value by using arithmetic operation without making any equation model. The result of re-checking problem solving, impulsive student was only reading at glance without re-counting the result of problem solving.

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

This study investigates secondary teachers' belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers' problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers' beliefs have a strong relationship with teachers' knowledge about problem solving. In particular, the instrumental teacher's beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher's beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers' responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers' work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.