Journal articles on the topic 'Mathematics Creative thinking. Education Mathematical ability Creative ability in children'

Mathematics is an integral part of day-to-day life, which is why mathematics education is key in order to establish solid foundations. A one-size-fits-all approach cannot be applied to the learning of mathematics and traditional teaching methods aren't effective for every learner. This is why research looking at new methods of teaching mathematics in order to equip children with lifelong skills is important. Professor Miyo Akita, Naruto University of Education, Japan, is working to transform how mathematics is taught in order to make it accessible to all. One of her goals is to focus on the creativity that she believes is inherent to mathematics. She believes that, traditionally, mathematics teaching has been too rigid and instead is placing emphasis on flexibility, with a view to facilitating effective learning. She is also establishing methods for autonomous learning, using a simple and easy-to-understand model. Akita is developing this model in collaboration with Noboru Saito, Saitama Dakuen University, Japan. From her findings on how to foster autonomous learning, Akita found that it is important that students explain new properties using known properties, forming meaningful connections that facilitate learning. She also underlined the importance of the representation of relationships in mathematical thinking. In another, interconnected investigation, Akita set out to propose a learning model for developing creative and autonomous learners in mathematics that involves linking previous knowledge to new knowledge in order to better understand it.

Senior preschooler is a sensitive period in the development of the cognitive activity. Exactly in this age, child learns to clearly realize intended goal and search for the ways to implement it independently. In the sixth year of life, the children start to possess ability for arbitrary memorizing; the creative and logical thinking actively develops; the interest for constructive work increases. The constructive work is complex cognitive activity during which a child learns skills, select significant signs, establish relations and connections between details and objects. The use of Lego-technology in the play and education purposes allows to solve complex cognitive, exploratory and creative tasks in the interesting, available, comprehensible, game form. The tasks of the educational activity with the preschool children are solved with the help of the construction toys on such directions: development of fine motor skills; development of attention, memory, thinking; training of correct and fast direction finding; acquisition of mathematical knowledge about quantity, form, proportions, symmetry; extension of the perceptions of children about the world around, architecture; development of the imaginations, creativity; training of the communication with each other, respect for their work and work of other people.

In the context of humanization and democratization of the educational space, the issues of comprehensive development of preschool-age child, development of his creative potential, national consciousness, independence and formation of interaction skills with other people become especially relevant. The development of the theory and practice of preschool education in Ukraine makes it possible to state today the forms today, methods and techniques of the educational process are being improved. Today there is a need for purposeful development of logical methods of thinking of preschoolers, which is provided, first of all, in the process of formation of elementary mathematical representations. The main place in this process belongs to the development of cognitive interest of preschoolers. The article has shown that it will have a positive effect on the expansion of the outlook of preschool children and will help to consolidate basic mathematical ideas of creating such an educational environment, when these classes will be combined with the use of means of choreographic influence. The purpose of the article – using elements of rhythm and choreography to integrate mathematical content in the play activities of preschool children. A search and bibliographic tool is used to collect, accumulate, and describe the necessary information sources by us; analysis and synthesis – to organize the procedure of research search; methods of generalization and systematization – for rational processing of the obtained results. Today, in order to form a comprehensive picture of the world and the ability of students to apply their knowledge in typical as well as atypical situations, modern preschool education should be directed not at the acquisition of individual knowledge from different fields by children, but at their integration. Educators need to organize the educational-cognitive process so that it stimulates the cognitive-search, mathematical activity of children, develops the ability to make assumptions, find out contradictions, formulate decisions. The article substantiates the importance of using the kindergarten preschool institutions to entertain the potential of mathematical and choreographic play. Examples of such games are provided. Having been preparing children for study at the New Ukrainian School, the caregivers should pay particular attention to integrating logic and mathematical development with other artistic pursuits. In particular, the combination with various forms of choreographic activity is quite successful.

Many studies have shown a link between being competent in early mathematics and achievement in school. Early math skills have the potential to be the best predictors of later performance in reading and mathematics. Movement and songs are activities that children like, making it easier for teachers to apply mathematical concepts through this method. This study aims to develop audio-visual learning media in the form of songs with a mixture of western and traditional musical idioms, accompanied by movements that represent some of the teaching of early mathematics concepts. The stages of developing the ADDIE model are the basis for launching new learning media products related to math and art, and also planting the nation's cultural arts from an early age. These instructional media products were analyzed by experts and tested for their effectiveness through experiments on five children aged 3-4 years. The qualitative data were analyzed using transcripts of field notes and observations and interpreted in a descriptive narrative. The quantitative data were analyzed using gain score statistics. The results showed that there was a significant increase in value for early mathematical understanding of the concepts of geometry, numbers and measurement through this learning medium. The results of the effectiveness test become the final basis of reference for revision and complement the shortcomings of this learning medium. Further research can be carried out to develop other mathematical concepts through motion and song learning media, and to create experiments with a wider sample. Keywords: Early Mathematical Skills, Movement and Song Idiom Traditional, Audio-visual Learning Media References An, S. A., & Tillman, D. A. (2015). Music activities as a meaningful context for teaching elementary students mathematics: a quasi-experiment time series design with random assigned control group. 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The purpose of this study is to determine the level of students' mathematical creative thinking ability in solving open-ended problems in discrete mathematics courses. This research uses descriptive qualitative method. The population in this research is the third semester students of Mathematics Education UMT. The sample was taken by norm referenced evaluation technique that is students in semester III-A3 who have high, medium and low mathematical ability. The instruments used include creative thinking ability tests, observation sheets and interview guides. The result of data analysis shows that the students with the category of creative mathematical thinking level with the percentage of respondents is 84.61%, the category of mathematical creative thinking level is very low with 12.82% percentage, the level of creative creativity level is not creative with 2.56% percentage. From the result, we get the average category of students' mathematical creative thinking ability in the third semester-A3 is 67,94 with medium category level.

This study examines the effect of scientific debate instructional on the enhancement of mathematical creative thinking ability of students.This study is quasi-experimental with a static group comparison design involves 94 students from Department of Mathematics Education. Research instruments include student’ prior knowledge of mathematics (KAM) and creative thinking ability test. Scores of the the enhancement of mathematical creative thinking ability were analyzed with normalized gain test. The Effect of Scientific Debate instructional and conventional instructional was used the Mann-Whitney U and Kruskal Wallis test. The study finds that the enhancement in mathematical creative thinking ability with scientific debate instructional was better than conventional. The enhancement of student’ mathematical creative thinking abilities with a scientific debate instructional based on the KAM, it is not completely distinctive. On the other hand, the enhancement of student’ mathematical creative thinking abilities with a conventional instruction based on the KAM was considerably different. On the scientific debate instructional, student’s educational background differences do not give major effect on the enhancement student’ mathematical creative thinking abilities but on the conventional instructional provides a better effect.

This study aims to determine the ability of mathematical creative thinking of students in one of the Vocational Schools in Cimahi City with indicators of students' mathematical creative thinking skills used are fluency, flexibility, originality and elaboration. The ability to think creatively mathematically is the ability to learn mathematics in finding new ideas or ideas that are different from the way, in their own language. This research was conducted on 29 students in one of the Vocational Schools in Cimahi City using qualitative descriptive methods. The instruments used were in the form of 4 items of description with mathematical creative thinking skills in space geometry. After getting the results or data, then the data is presented in the form of a percentage. And it can be concluded from this study that the ability of mathematical creative thinking of SMK students in Cimahi City is still very low because only one indicator whose percentage exceeds 50% is an indicator of fluency. The results of this study can increase knowledge about mathematical creative thinking of students in one of the Vocational Schools in Cimahi City and is useful to facilitate education practitioners in developing mathematical creative thinking skills

This research aims to look at the difference in the ability of mathematical creative thinking in students, through Realistic Mathematical Education learning or RME and through conventional learning. The research design used was an experiment, namely in the form of a test of the ability of creative thinking. The population in this study of Junior High School students throughout the country, namely in West Bandung Regency. Sample research VIII grade i.e. in one of the Junior High School in West Bandung chosen at random and selected class A (grade experiment) that uses learning Realistic Mathematics Education (RME) and class B (grade control) that uses regular or conventional learning. The research results showed that the p-value of 0.000 < critical limits. Thus, the ability of mathematical creative thinking of the students who got the learning with Realistic Mathematics Education better than the students who got conventional learning.

<p>This research implements Problem Based Learning and Discovery Learning model to analysis the increase of mathematical creative thinking skills, mistakes in the process of mathematical creative thinking, and self-efficacy of high school students in Tasikmalaya. The research method used is descriptive, data collection techniques through creative thinking ability tests and questionnaires mathematics self-efficacy. The instruments were previously assessed by experts in mathematics education. Based on the data analysis, it is concluded that the mathematical creative thinking abilities of students through Problem Based Learning is increasing compared to the mathematical creative thinking abilities of students through Discovery Learning. Mistakes students of mathematical creative thinking processes in Problem Based Learning, generally on flexibility and originality indicators. While at Discovery Learning, mistakes students of mathematical creative thinking processes is generally on sensitivity, flexibility and originality indicators. Flexibility is solving the problem with a variety of different ways, but the result is the same, and originality is to solve the problem in its own way does not use a standard formula. Sensitivity is the ability to detect problems. Self-efficacy of students in Problem Based Learning and Discovery Learning are both at high qualifications.</p>

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

The background of this study is the school of the new students of mathematics education courses came from grade high, medium and low. Here the writer wants to see how much influence of the school level on new students’ critical thinking skills and creative mathematical. The purpose of this study was to examine differences in new students’ mathematical disposition, critical & creative thinking ability through the mathematical problem posing approach based on school level (high, medium, low). The method used in this research is the experimental method, with only posttest design. The population of this study is all the students of mathematics education department in Cimahi; while the sample is selected randomly from one college. Then from this chosen college is taken two samples from random class. The instrument of essay test is used to measure students’ critical and mathematical creative thinking ability; while non-test instrument is questionnaire of attitude scale. The results show that: 1) based on the school level (high, medium, and low); there is difference in students’ mathematical critical thinking ability through problem posing approach. 2) based on the school level (high, medium, and low); there is difference in the students’ mathematical critical thinking ability through problem posing approach. 3) based on the school level (high, medium, and low); there is difference in students’ mathematical disposition.

The background of this study is the school of the new students of mathematics education courses came from grade high, medium and low. Here the writer wants to see how much influence of the school level on new students’ critical thinking skills and creative mathematical. The purpose of this study was to examine differences in new students’ mathematical disposition, critical & creative thinking ability through the mathematical problem posing approach based on school level (high, medium, low). The method used in this research is the experimental method, with only posttest design. The population of this study is all the students of mathematics education department in Cimahi; while the sample is selected randomly from one college. Then from this chosen college is taken two samples from random class. The instrument of essay test is used to measure students’ critical and mathematical creative thinking ability; while non-test instrument is questionnaire of attitude scale. The results show that: 1) based on the school level (high, medium, and low); there is difference in students’ mathematical critical thinking ability through problem posing approach. 2) based on the school level (high, medium, and low); there is difference in the students’ mathematical critical thinking ability through problem posing approach. 3) based on the school level (high, medium, and low); there is difference in students’ mathematical disposition.

This study aimed to describe the mathematical connection capability and creative thinking in mathematics with APOS theory. This study uses a quantitative and qualitative approach, the research design class action, which was conducted in two cycles. The research subject is 30 math education students who take a course in calculus. The results showed that an increase in the ability to connect mathematical and creative thinking in mathematics with APOS theory which includes Action, Process, Object and Scheme. This is shown by the data obtained in the second cycle that meets the criteria of academic success with 81.47%, the ability of mathematical connection with the achievement of 80.56%, and the ability to think creatively with the achievement of 81.27%.

This study aimed to describe the mathematical connection capability and creative thinking in mathematics with APOS theory. This study uses a quantitative and qualitative approach, the research design class action, which was conducted in two cycles. The research subject is 30 math education students who take a course in calculus. The results showed that an increase in the ability to connect mathematical and creative thinking in mathematics with APOS theory which includes Action, Process, Object and Scheme. This is shown by the data obtained in the second cycle that meets the criteria of academic success with 81.47%, the ability of mathematical connection with the achievement of 80.56%, and the ability to think creatively with the achievement of 81.27%.

Aspects of local culture in learning mathematics in primary school teacher education are still not optimally presented in learning. One way to realize this learning is by learning Sundanese ethnomathematics. The mathematical modeling is very supportive ability in the learning process. The process of mathematical modeling can develop creative intelligence. This article uses the Didactical Design Research method to further optimize the quality of teaching materials. The number of research subjects was 180 of first semester student. The teaching material was tested for success by an experimental method through a test instrument that measured mathematical modeling abilities and creative intelligence. Research results in mathematical modeling ability among students who get mathematics learning using Sundanese ethnomathematics learning is significantly better than students who use conventional learning. There is no interaction between learning models used with educational background groups on mathematical modeling abilities. There is no interaction for creative intelligence. Sundanese ethnomathematics learning with didactic design material can be used as a model of mathematics learning to develop the abilities and dispositions of mathematical creative thinking abilities and dispositions in the elementary school teacher education environment.

<p class="BodyAbstract">Mathematical thinking and self-confidence are indispensable aspects of learning mathematics and are influential in solving mathematical problems. In higher education mathematics learning, advanced mathematical thinking skills are required (Advance Mathematical Thinking. Advanced mathematical thinking processes include: 1) mathematical representation, 2) mathematical abstraction, 3) connecting mathematical representation and abstraction, 4) creative thinking, and 5) mathematical proof. Discrete mathematics is one of the courses in mathematics education FKIP UNS. The problems in Discrete Mathematics courses are usually presented in the form of contextual problems. Students often experience difficulties in making mathematical expressions and mathematical abstractions from these contextual problems. In addition, students also experience difficulties in bookkeeping. Most students often prove by using examples of some real problems. Even though proof in mathematics can be obtained by deductive thinking processes or inductive thinking processes, the truth is that mathematics cannot only come from the general assumption of inductive thinking. Based on this, a qualitative descriptive study was carried out which aims to determine the advanced mathematical thinking skills based on the level of student self-confidence. Research with the research subjects of FKIP UNS Mathematics Education Students in Discrete Mathematics learning for the 2019/2020 school year gave general results that the student's ability in advanced mathematical thinking was strongly influenced by the level of student confidence in learning. The higher the student's self-confidence level, the better the student's advanced mathematical thinking ability, so that high self-confidence has a great chance of being successful in solving math problems.</p>

The universality of mathematical knowledge, its a priori metasubject nature and fundamental role in forming the scientific style of thinking make high demands on the training of maths teachers within the framework of the higher professional education system. This training includes the formation of competencies related to the ability to understand and transmit knowledge formulated in the language of mathematics, the ability to embed it into the existing system of mathematical and general scientific training, as well as active, creative mastering of mathematical content. The article presents an instructional diagram of mental activity organization for solving educational mathematical problems. Being universal, the scheme meets the above requirements for training future maths teachers and it was developed specifically with an orientation towards this category of students. The article provides the specific example of the use of the scheme.

Abstract The purpose of this study was to analyse the effect of mathematics learning intervention on students' mathematical thinking ability. The research method used survey of thesis of the student. The effect of studies applying learning to mathematical thinking was done using meta-analysis techniques. The research finding that research conducted by students by providing learning intervention was able to improve students' mathematical thinking ability. Aspects of mathematical thinking ability include connection ability, communication, representation, problem-solving, logical, critical, creative, analytical, generalization, quantitative, and adaptive thinking. The types of research used by students are dominated by the experiment with mix-method approach and classroom action research. Other methods, research development. The research and publication at the Department of Mathematics Education, Faculty of Educational Sciences have adapted to the trend of mathematics education research on the national and international level. Abstrak Tujuan penelitian ini adalah menganalisis efektivitas pengaruh intervensi pembelajaran matematika terhadap kemampuan berpikir matematis siswa. Metode penelitian yang digunakan adalah survei terhadap skripsi dan publikasi mahasiswa. Pengaruh penelitian-penelitian yang menerapkan pembelajaran terhadap kemampuan berpikir matematis dianalisis dengan teknik meta-analisis. Temuan penelitian mengungkapkan bahwa secara keseluruhan penelitian-penelitian yang dilakukan mahasiswa dengan memberikan intervensi pembelajaran ternyata mampu meningkatkan kemampuan berpikir matematis siswa. Aspek kemampuan berpikir matematika yang meliputi: kemampuan koneksi, komunikasi, representasi, pemecahan masalah, kemampuan berpikir: logis, kritis, kreatif, reflektif, intuitif, penalaran: analalogi, generalisasi, kuantitatif, kreatif, dan adaptif. Metode penelitian yang digunakan mahasiswa didominasi metode eksperimen dengan pendekatan mix-method dan penelitian tindakan kelas. Disamping itu terdapat beberapa mahasiswa memilih metode penelitian pengembangan. Hasil penelitian dan publikasi pada Program Studi Pendidikan Matematika telah menyesuaikan dengan tren penelitian pendidikan pendidikan matematika baik pada level nasional maupun internasional. How to Cite : Kadir. (2017). Meta-Analysis of the Effect of Learning Intervention Toward Mathematical Thinking on Research and Publication of Student. TARBIYA: Journal of Education in Muslim Society, 4(2), 162-175. doi:10.15408/tjems.v4i2.8010. Permalink/DOI: http://dx.doi.org/10.15408/tjems.v4i2.8010

Education functions to upgrading, forming, character and develop civilization nation. Having the ability to think and actions to effective and creative in the realm of abstract and concrete can be used as self development independently. Students need to armed with critical thinking skills, systematic, logical, creative, and cooperate effectively to obtain, choose, and manage an information. Mathematics learning is directed to develop critical thinking skills and discussed open and objective because mathematics having strong and structure clear and links between the concept of the one with another concept. By analyzing learning needs of mathematics, formulate and designed a learning programs, choose a strategies and evaliated them correctly to get good results. The ability critical thinking is very important in studying new matter and that known way, and learn to ask effectively and reach a conclusion consistent with the facts. Mathematic learning with problem based learning is the concept of better used activity of the student during learning. In accordance with statements from Westwood (2008: 31) stated that PBL: 1) propel oneself directly in learning, 2) prepared students to critical thinking and analytical, 3) give opportunity to students to identify, find and use numerous this approuch in should think, 4) is the learning is very closely related to the real world and motivate students, 5) involving activeness in integrating information and skills of various the discipline, and 6) knowledge and strategy by the possibility of will be maintained and tranferred to the learning situation other, improve the ability to communicate and the social skills needed to cooperation and teamwork. By chance the learning process as an alternative in solving mathematical problems with using the ability critical think an to cultivate the scientific attitude of student.

The author examined the effect of teaching the Pattern and Sequence (useriation) unit from the intervention program Bright Start on the development of seriational mathematical thinking in kindergartners of Israeli, Ethiopian, and Russian origin. In addition, the author examined the effect of the teaching of this unit on the capacity for cognitive change in this area within the study group of children. Bright Start is a plan for the development of thinking in early childhood. This program, developed by Haywood, Brooks, and Burns (1986, 1992), is based on four developmental theories:(a) Feuerstein’s theory of structural cognitive modifiability and mediated learning experience; (b) Piaget’s stages theory of cognitive development; (c) Vygotsky’s social-historical theory of cognitive development; Haywood’s transactional perspective on human abilities.This study was focused on one unit of the program, the unit dealing with the development of seriational thinking. The teaching of this unit, like the remaining units in the program, is based on the mediational teaching style. The main emphasis of the study was placed on the comparison of three groups of different origin in Israel; therefore, no control group was examined.40 kindergartners from a disadvantaged area in Israel’s central region were examined, of whom 9 were native Israelis, 11 were of Russian origin, and 20 were of Ethiopian origin. The chidren were given several tests before and after the program. The examination consisted of three stages. At the beginning of the school year, the children underwent three tests to assess their ability to solve problem tasks when creating series with different elements. Subsequently, the intervention plan was taught with the aim of fostering cognitive skills of planning, comparison, relating to several sources of information, and restraining impulsiveness. Towards the end of the year, the children were again examined, and they underwent the three tests that they had done in the beginning of the year, checking their ability to solve tasks when creating series with different elements. In addition, the extent of internalization of the various skills was examined, as well as the capacity to apply skills to the area of arithmetic.As stated, this study focused on children of Ethiopian and Russian origin in comparison to native Israeli children. The decision to focus on children of Ethiopian origin derived from gaps that emerged in the learning process of this population as a result of the cultural difference that characterizes it. The children of Russian origin were part of the kindergarten’s population. They too manifested gaps as a result of cultural and social changes occurring among immigrants from the former Soviet Union.The purpose of the study was to demonstrate that intervention in specific thinking processes—in this case seriation from Bright Start at kindergarten age—will result in greater effectiveness and a significant cognitive ability to change in this area, particularly in children of Ethiopian origin whose initial cognitive level was poor. The hypothesis was confirmed that the children of Ethiopian descent did indeed evince initial inferiority visa-vis the other two groups, but after the intervention program they improved their performance and narrowed the gaps in comparison to the other groups. It is noteworthy that, according to the theory, cognitive processes are not related to any particular content or culture, but are suited to everyone. These processes were found to be beneficial to all of the children, but the cognitive change in seriational thinking as a result of the intervention program was particularly conspicuous in children of Russian origin.The effect of the intervention program was expressed in the ability to apply acquired skills to unstudied areas. Internalization of cognitive skills was apparent, as was the improved ability to comprehend a series and the acquisition of mathematical skills in all of the kindergarten children.The findings of this study have didactic implications relating to the significance of teaching seriation to kindergarten children. In addition, the study indicates the need for early education programs adapted to the population of children of Ethiopian and Russian origin in Israel.

AbstractThis study evaluates the effects of the Mathematics, Arts, and Creativity in Education (MACE) program on students’ ability in geometry and visual arts in the upper grades of elementary school. The program consisted of a lesson series for fourth, fifth, and sixth grade students in which geometry and visual arts were integrated, alongside with a professional development program for teachers. A quasi-experimental study was conducted in which three groups of teachers and their classes were investigated. One group of teachers taught the lesson series and followed a professional development program (n = 36), one group of teachers only taught the lesson series (n = 36), and a comparison group taught a series of traditional geometry lessons from mathematical textbooks (n = 43). A geometrical ability, creativity, and vocabulary test and a visual arts assignment were used in a pre- and post-measurements to test the effects of the MACE program. Results showed that students who received the MACE lesson series improved more than students who received regular geometry lessons only in geometrical aspects perceived in a visual artwork. Regarding students’ understanding and explanation of geometrical phenomena and geometrical creative thinking, all students improved, but no differences between the groups were found, which implies that on these aspects the MACE program was as effective as the comparison group that received a more traditional form of geometry education.

Penelitian ini bertujuan untuk mendeskripsikan profil kemampuan berpikir kreatif matematis mahasiswa calon guru dalam menyelesaikan masalah open-ended ditinjau dari gaya kognitif reflective dan impulsive. Penelitian ini adalah penelitian deskriptif kualitatif. Subjek penelitian ini adalah mahasiswa calon guru pada Program Studi Pendidikan matematika, Universitas Muhammadiyah Prof. DR. HAMKA yang diambil menggunakan teknik purposive sampling. Validasi data menggunakan teknik triangulasi waktu. Data dianalisis menggunakan metode perbandingan tetap (constant comparative method) dengan langkah (1) reduksi data dan kategorisasi, (2) penyajian data; dan (3) penarikan kesimpulan dan verifikasi. Hasil penelitian menunjukkan bahwa dari empat indikator kemampuan berpikir kreatif matematis, mahasiswa dengan gaya kognitif reflective mampu memenuhi aspek kelancaran dan keterincian, yaitu menjawab soal dengan lebih lancar, mampu menjelaskan hubungan sebab akibat antar konsep yang digunakan, serta lebih rinci dan runtut dalam menjawab dan menjelaskan jawaban tertulisnya, dibandingkan dengan mahasiswa dengan gaya kognitif impulsive. Indikator aspek keluwesan dan kebaruan masih belum bisa terpenuhi karena mahasiswa dengan gaya kognitif reflective dan impulsive baru mampu menjawab pertanyaan menggunakan satu cara saja dan belum menggunakan strategi baru. Profile of mathematical creative thinking ability viewed from reflective and impulsive cognitive style AbstractThe study aimed to describe mathematical creative thinking ability profiles of prospective students in solving open-ended problems in terms of reflective and impulsive cognitive styles. The research classified as a qualitative descriptive study. The subjects of this study were prospective students of the Mathematics Education Department, Universitas Muhammadiyah Prof. DR. HAMKA and selected using a purposive sampling technique. For data validation, we used time triangulation techniques. Data were analyzed using the constant comparison method with steps (1) data reduction and categorization; (2) data presentation; and (3) conclusions and verification. The results showed that from the four indicators of mathematical creative thinking, students with reflective cognitive style were able to fulfill fluency and detail aspects in answering questions, explain causal relationships between concepts used, and more detail in written answers, compared to students with impulsive cognitive style. The indicators of flexibility and originality aspects of both students with the reflective and impulsive cognitive style are still cannot be fulfilled because they only answer questions using one method without using a new strategy.

Indonesian students’ poor performance in the mathematics test of PISA 2015 prompted the decision by the Ministry of Education of Indonesia to pay more attention to the integration of higher-order thinking (HOT) in the curricula starting in 2018. This new regulation emphasizes the need to have a shared understanding of HOT in mathematics on many levels, such as curriculum, pedagogy, and assessment, and among students, teachers and policy makers. This study aims to examine HOT in Indonesian lower secondary mathematics classrooms by assessing students’ ability to demonstrate HOT skills through an open-ended mathematics problem, and by exploring teachers’ views of HOT skills through semi-structured interviews. It involved 372 ninth-grade students and six mathematics teachers from six lower secondary schools in Jakarta and Palembang. The findings show that most students could construct the mathematical model but experienced difficulty in transferring knowledge into new contexts, in applying creative thinking, and with information literacy skills. Besides, some of the teachers were familiar with the concept of HOT, but some viewed HOT as skills for talented students, or HOT problems having a high level of difficulty and long storylines. The knowledge of existing teaching strategies, familiarity with HOT problems, and colleague-support are needed to improve the development of HOT skills in the mathematics classroom.

This study examined students’ ability to learn mathematics in a self-directed teaching environment. One of the main goals of the educational system is to nurture independent learners who can grow up to be inquisitive, critical, creative, and capable of piloting their own learning. This implies making a change in the way the role of the mathematics teacher is perceived in that the teacher must now become a mentor who supports and mediates learning, enabling students to construct a knowledge base of rules and methods in mathematics and acquire and experience ways of thinking that enable them to construct this knowledge.This qualitative study is based on interviews with four ninth-grade mathematics teachers and on in-class observations of teaching styles and teacher-student interactions. Our findings show that applying self-directed learning methods in class based on a constructivist approach to teach mathematics is an important factor in developing students’ creativity and thinking. These findings suggest that developing this model of teaching should be recommended to teachers. Accordingly, this study also proposes a model for staff development programs that foster self-directed learning in mathematics. The model proposes that increasing teachers’ awareness of their teaching process and training them to prepare learners to cope effectively with unfamiliar mathematical problems are goals to include in teacher training. This model of teaching may have far-reaching effects in pedagogy, e.g.: reducing drop-out numbers, improving achievements, and improving social interactions.Key words: constructivist approach, fostering thinking, self-directed learning, teaching mathematics.

The urgency of the problem is due to the insufficient development of theoretical, content-technological and methodological aspects of the integration of mathematical knowledge and chess skills. The manifestations of synergistic effects arising in the course of the integration of mathematical and game chess activity, while resolving uncertainties on the chessboard due to the activation of key components of creativity, have not been sufficiently studied. The synergistic effect of the integration of mathematical knowledge and chess skills is considered from the perspective of the components of theoretical thinking and is evaluated by the student’s creative choice in the search for alternative solutions. The purpose of the study is to describe and evaluate the manifestations of the structural components of the creative effect in the context of the introduction of funded complexes of mathematical problems on a chessboard. The hypothesis of the research: theoretical analysis of educational material, reflection and an internal plan of action as comparable processes for solving mathematical problems in terms of implementation substantiate complexes will lead to manifestations of arguments-heuristic, intellectual and logical and motivational components of creative activity. The research assumed the measurement of the manifestations of the structural components of creativity in the context of the introduction of funding complexes of mathematical problems on a chessboard. In the process of identifying the structural components of creativity, psychodiagnostic diagnostics tools were developed for intellectual-heuristic, intellectual-logical, motivational and reflexive aspects, comparative diagnostics were carried out for all structural components, the average level and integral indicators in the control and experimental groups were calculated. The formation of creativity was carried out by developing the ability to argue in the process of solving multi-stage mathematical problems on the chessboard. The choice of cause-and-effect relationships stimulated creative independence and reflexivity, enhancing the manifestations of the synergistic effect. On the basis of internal cognitive consonance, non-standard original ideas were identified; by overcoming emotional instability, the logical component of argumentation was strengthened. The results of the research revealed a positive trend in the key components of creativity in the context of the introduction of a chess game in the process of learning mathematics. In the future, it is possible to upgrade the methodological educational material for the system of inclusive mathematical education.

The article looks at the means of forming the research skills of students of pedagogical universities. Considerable attention is paid to the formation of students' creative thinking in the process of solving problems with parameters. A large number of applied problems, economic, physical, chemical, biological, technical, medical, etc., involve solving problems with parameters (within the framework of the constructed mathematical model). Tasks with parameters require more general research than ordinary equations, inequalities and their systems. In the article, solving problems with parameters is accompanied by graphical visualization followed by the use of the analytical method. CAS Maxima is used for graphical visualization (animation). The choice of tasks with parameters is due to the fact that mathematical, logical thinking and the ability to analyze, compare, synthesize, develop research skills evolve in the course of their solution. All this should lead to the search and introduction of new forms of pedagogy and technologies in education. The main component of the methodology here is computer-oriented, namely the use of a computer mathematics system. Using systems of computer mathematics, the student can improve the programming technique and ability to focus on the analysis of methods, immerse in the features of such concepts as the conditionality of the problem, the stability of the method, evaluation of the results of calculations. In this paper, we used the CAS Maxima animation tools with the wxMaxima graphical shell to investigate the problems with the parameters. The choice of the Maxima system is due to the following reasons: it is a freely distributed system, distributed under the GNU/GPL license; there are implementations under various operating systems, including Windows, Linux, MacOS; it offers intuitive interface and is easy and reliable in operation. The results of the study show that training of modern specialists, the development of their professional potential can only be effective provided that students are involved in research activities throughout their course of study.

Mathematics courses are given to students from elementary school to higher education which equip them with logical, analytical, systematic, critical, and creative thinking skills, as well as the ability to work together. According to the Organization for Economics Cooperation and Development (OECD) year 2013, the concep of mathematical literacy in Programme for International Student Assessment (PISA) supports the importance of developing strong understanding of pure mathematical concepts and the benefits involved in exploration in the abstract world of mathematics. This research produces a Mathematics strategic learning analysis of grade IX that supports high-order mathematical thinking skills (HOMT). Two (2) parts of the materials will be discussed more focused, ie (a) learning materials and (b) learning strategies. With a learning syllabus that supports the HOMT, the opportunity to increase the value of Mathematics education is greater, one of which is formulate challenging questions. Challenging Mathematical questions will meet the criteria of high-level questions (PISA has a level of questions from level 1 to level 6). HOMT supports the development of a strong understanding of pure mathematical concepts and is useful in exploration in the abstract world of mathematics. The sources of data used in the preparation of this reseach are the results of the PISA survey in 2006 and 2012 and the 2013 curriculum book sourced from the Ministry of Education and Culture. Keywords: Mathematics grade IX, 2013 curriculum, PISA, HOMT Abstrak Mata pelajaran Matematika diberikan kepada semua peserta didik mulai dari sekolah dasar untuk membekali peserta didik dengan kemampuan berpikir logis, analitis, sistematis, kritis, dan kreatif, serta kemampuan bekerja sama. Menurut Organization for Economics Coopration and Development (OECD) tahun 2013, konsepsi literasi matematika dalam Program for International Student Assessment PISA mendukung pentingnya siswa mengembangkan pemahaman yang kuat tentang konsep-konsep matematika murni dan manfaat yang terlibat dalam eksplorasi dalam dunia abstrak matematika. Penelitian ini menghasilkan sebuah analisis trategi pembelajaran matematika Kelas IX yang mendukung kemampuan berpikir tingkat tinggi matematika (HOMT). Dua (2) bagian dari materi akan dibahas lebih fokus, yaitu (a) materi pembelajaran dan (b) strategi pembelajaran. Dengan silabus pembelajaran yang mendukung HOMT tersebut maka peluang untuk meningkatkan nilai pendidikan Matematika lebih besar, salah satu di antaranya adalah dapat disusunnya soal-soal yang menantang. Soal-soal matematika yang menantang akan memenuhi kriteria soal level tinggi (PISA memiliki tingkatan soal dari level 1 hingga level 6). HOMT mendukung pengembangan pemahaman yang kuat tentang konsep-konsep matematika murni dan bermanfaat dalam eksplorasi dalam dunia abstrak matematika. Sumber data yang digunakan dalam penyusunan buku penelitian ini adalah hasil survey PISA tahun 2006 dan 2012 dan buku kurikulum 2013 yang bersumber dari Kementerian Pendidikan dan Kebudayaan. Kata Kunci: Matematika kelas IX, Kurikulum 2013, PISA, HOMT References B. Johnson. 2002. Contextual Teaching and Learning: What it is and why it’s here to stay. Corwin Press,Inc. California. A. Dahlan. 2009. Pengembangan model computer based e-learning untuk meningkatkan kemampuan high order mathematical thinking siswa SMA. LPPM UPI. Bandung. Watson and E. M. Glaser. 1980. Critical Thinking Appraisal. Harcourt Brace Jovanovich, Inc. New York. Hakim. 2016. Analisis Gambaran Kompetensi Guru Terhadap Prestasi Belajar Siswa SMP Pada Ujian Nasional Tahun 2015 Provinsi Daerah Istimewa Yogyakarta. Pusat Data dan Statistik Pendidikan dan Kebudayaan. Jakarta. Abdurrahman. 2003. Pendidikan Bagi Anak Berkesulitan Belajar. Rineka Cipta. Jakarta. Nata. 2009. Perspektif Islam Tentang Strategi Pembelajaran. Kencana Prenada Media Group. Jakarta. Purwanto. 2004. Psikologi Pendidikan. Remaja Rosdakarya. Bandung OECD. 2012. OECD Programme for International Student Assessment 2012. OECD. Westat. OECD. 2006. OECD Programme for International Student Assessment 2006. OECD. Westat. P. P. Kemdikbud. 2016. Penilaian yang Berkualitas untuk Pendidikan yang Berkualitas [Online]. Available:http://litbang.kemdikbud.go.id/pengumuman/Mengenal%20Puspendik%205%20Jan %202015-2.pdf. [Accessed 07 Feb 2016]. K. d. Perbukuan. 2015. Buku Guru Matematika Kelas IX SMP/MTs. Kementerian Pendidikan dan Kebudayaan. Jakarta. H. Ennis. 1985. Critical Thinking. University of lllinois. New Jersey: Prentice Hall. W. Weisberg. 2006. Expertise and Reason in Creative Thinking: Evidence from Case Studies and the Laboratory. Cambridge University Press. Cambridge. Mariana. 2011. Penerapan pendekatan kontekstual dengan pemberian tugas mind map setelah pembelajaran terhadap peningkatan kemampuan koneksi matematis siswa SMP. Krulik and J. A. Rudnick. 1995. The New Sourcebook for Teaching Reasoning and Problem Solving in Elementary School. Allyn & Bacon. Needham Heights. Sardiman. 1987. Interaksi dan Motivasi Belajar Mengajar. Rajawali Pers. Jakarta. Suwarma and D. Mayadiana. 2009. Suatu Alternatif Pembelajaran Kemampuan Berpikir Kritis Matematika. Cakrawala Maha Karya. Jakarta Gustiningsi. 2015. Pengembangan Soal Matematika Model Pisa Untuk Mengetahui Kemampuan Berpikir Kritis Matematis Siswa Kelas VII. Jurnal Pendidikan Matematika JPM RAFA , vol. Vol.1, no. No.1, September 2015. Y. E. Siswono. 2016. Berpikir Kritis dan Berpikir Kreatif sebagai Fokus Pembelajaran Matematika in Seminar Nasional Matematika Dan Pendidikan Matematika (1st SENATIK). Semarang.

The article is devoted to the consideration of psychological training of future mathematics teachers, namely, indicators of psychological competence.Purpose. The purpose of the article is to reveal the essence of the concept of “psychological competence” of future mathematics teachers and substantiate its main indicators.Methods. In order to solve the tasks, we used the following theoretical research methods: theoretical analysis of psychological and pedagogical sources on the research issue; generalization of data on the definition of “psychological competence”; systematization of data on the main indicators of psychological competence of future mathematics teachers.Results. Theoretical analysis of modern approaches to the definition of “psychological competence” is presented, the components of psychological competence of teachers of general secondary education on the basis of professional standard are analyzed. The content of the main indicators of psychological competence of future mathematics teachers is singled out and revealed.Conclusions. In the course of the research, on the basis of a professional standard, the components of the psychological competence of a teacher were identified and the relevant knowledge, skills and abilities were analyzed. The analysis allowed to identify the main indicators of psychological competence of the future teacher of mathematics, namely: procedural-situational, which includes among others the ability to self-regulate emotional states when interacting with students, colleagues and parents; indicator of planning and implementation of holistic interaction, which is characterized in particular by the ability to assess the psychological age and gender characteristics of students, including when working with children in an inclusive group; indicator of psychological and didactic competence(ability to use psychological techniques, technologies and practices to enhance the cognitive activity of students; ability to form theoretical and creative thinking of students in mathematics lessons, etc.).Key words: psychological competence, professional standard, psychological training of teachers, competence, indicator, competence approach. Статтю присвячено розгляду психологічної підготовки майбутніх учителів математики, а саме визначенню основних показників психологічної компетентності.Мета статті полягає в розкритті сутності поняття «психологічна компетентність» майбутніх учителів математики, обґрунтуванні її основних показників.Методи. Для розв’язання поставлених завдань нами були використані такі теоретичні методи дослі-дження: теоретичний аналіз психолого-педагогічних джерел із досліджуваної проблематики; узагальнення даних щодо визначення поняття «психологічна компетентність»; систематизація даних стосовно основних показників психологічної компетентності майбутніх учителів математики.Результати. Представлений теоретичний аналіз сучасних підходів до визначення поняття «психологічна компетентність», проаналізовано складові частини психологічної компетентності вчителів закладів загальної середньої освіти на основі професійного стандарту. Виокремлено та розкрито зміст основних показників психологічної компетентності майбутніх учителів математики.Висновки. У процесі дослідження на основі професійного стандарту було визначено складові ком-поненти психологічної компетентності вчителя, проаналізовано відповідні знання, уміння та навички. Проведений аналіз дозволив виокремити основні показники психологічної компетентності майбутнього вчителя математики, а саме: процесуально-ситуативний, який, серед іншого, передбачає здатність до саморегуляції емоційних станів під час взаємодії з учнями, колегами та батьками; показник планування та реалізації цілісної взаємодії, який характеризуються, зокрема, здатністю оцінювати психологічні вікові та ґендерні особливості учнів, зокрема й під час роботи з дітьми інклюзивної групи; показник психолого-дидактичної компетентності (здатність використовувати психологічні методики, технології та практики для активізації пізнавальної діяльності учнів; здатність до формування на уроках математики теоретичного та творчого мислення учнів тощо).Ключові слова: психологічна компетентність, професійний стандарт, психологічна підготовка вчителів, компетенція, показник, компетентнісний підхід.

The article analyzes the implementation of patriotic education in the content of elementary school lesson work. It has been established that the upbringing of patriotism is one of the priority aspects of the national upbringing system and involves the formation of patriotic feelings, love for its people, a deep understanding of civic duty, and a willingness to defend the national interests of the Motherland. Examples of tasks and exercises in elementary education disciplines designed to educate children by patriots are considered. As, in the Concept of national patriotic education of children and youth it is stated that important patriotic qualities in children of primary school age appear through the prism of educational subjects of elementary school, in particular mother tongue, literary reading (through texts), mathematics (through the condition of mathematical problem) natural sciences (familiarization with traditions, respectful attitude to nature), work training (familiarization with traditional folk crafts, production of vignettes of different regions of Ukraine, decoration with different embroidery techniques ), musical art (comprehending the intonational peculiarities of music of the Ukrainian people), visual arts (forming a culture of feelings). An important place is given to the educational subject "I in the world", aimed at socializing the personality of the younger student, his patriotic and civic education. A program of Ukrainian patriotic upbringing of children and student youth, which outlines the content and basic tendencies of patriotic upbringing of the person, demonstrates that “at an early school age, it is important to shape a child's ability to recognize himself or herself as a member of a family, family, and child group; as a student, city or village resident; nurture her love for her home, school, street, her country, her nature, her native word, life, traditions [1,33]. Modern scholars distinguish the following structural components of a sense of patriotism: spiritual and moral experience and love for their native land; humanistic universal and national values; moral and aesthetic ideals of personality; creative and transformative activity for the benefit of the Motherland.

One of the important components of mathematical competence is the ability to solve practical tasks. According to G. Hristova “... with the teaching of mathematics in elementary classes, the skills to learn, to handle information, to communicate, to work independently and to work in a team are formed in the students” [4]. K. Alexieva stresses in her publication that “key competences are interdependent and represent a set of knowledge, skills and relationships necessary for the individual's personal development throughout life, for building an active civic position and participation in social life as well as for the suitability for his/her realization on the labour market. Through learning in each of the subjects, key competence learning skills are acquired, which includes understanding the personal needs in the learning process and discovering the opportunities and abilities to overcome learning difficulties, both individually and in groups; critical thinking, problem solving and decision making, initiative, creativity, responsibility, teamwork, and other key competences specified in the curriculum [1]. The ability to solve practical tasks develops to a greater extent in group, teamwork on projects. Project work is one of the active learning methods. It is not widely accepted in modern mathematical education in Bulgaria. The reasons for this are many. One of them is the lack of methodological literature on the subject for elementary teachers. Many specialists organize project work with their students, including mathematics, but their experience remains unpopular. Project work is difficult to organize, involves serious planning, and often involves spending money to buy the necessary materials. To successfully integrate into project activities, it is necessary for the young students to have a certain degree of autonomy, organizational skills, communicative skills, teamwork skills, skills for individual search of information, presentation skills, and so on. Teachers with creative abilities and innovative ideas develop, organize, and work on projects in primary school but this is a matter of their goodwill and professional skills. Mathematics teaching specialists in primary schools are in debt to primary school teachers in terms of published methodological work and project activities, including mathematics. Teachers' books for mathematics curricula for primary classes should include developments of at least one class project. This is done in the Bulgarian mathematics training kits of Anubis Publishing House, where I am the author [2] [3]. In this article I will present a description of the project – Thematic Classroom “The Room of Mysteries” for the third grade. It would be good the lesson to be held at the end of the school year. It solves tasks from all of the learning content studied in mathematics in the third grade. The idea of the project is based on the so-called “Escape Room” – a place where participants have to solve a series of puzzles to leave the room. Students of the class will not be locked in their classroom, of course. They will find a locked suitcase in their room that they want to unlock to see what's in it. For better motivation students will be given the role of police inspectors, who will be divided into 6 teams to solve a series of challenges – tasks. The lesson is held in the presence of parents and relatives of the students. A team of “veteran investigators” is formed from the parents, who also have to solve puzzles. Solving each task will lead to the opening of a new puzzle, and so pupils and parents will have to deal with a series of challenges that will lead to the discovery of 7 keys, identical at first glance, only one of which unlocks the briefcase. The prize, hidden away from the students, may be their annual third-grade certificates, may be holiday books for the end of the year as well as small gifts. Materials required for the project are purchased in advance with funds collected from students' parents.

The present article deals with the idea of information and communication technologies, game technologies and is about basic possibilities of using GEOBOARD Internet service for studying Mathematics in elementary school. The scientific approaches to the concept of information and communication technologies, game technologies are described and the potential possibilities of using the GEOBOARD Internet service in elementary education as an option of educational technologies, the influence of the GEOBOARD Internet service on the development of primary school students, advantages and directions of application are analyzed. The important aspect of using GEOBOARD Internet service is the ability to use it both from a personal computer and a Google Chrome web page. Also, users can download the app from the App Store to work with Apple products. The peculiarities of using GEOBOARD Internet service on mathematics lessons are systematization of material, strict logic, the interdisciplinary nature of the service, the learning process systematization, mastering the basics of spatial imagination, mathematical knowledge usage in solving educational, cognitive and educational and practical problems and depiction of geometric shapes. The use of the GEOBOARD Internet service in mathematics lessons promotes the complex development of elementary school children; the formation of a holistic picture of the world, knowledge of the world; the development of constructive skills, spatial relations and spatial thinking, vision of geometric figures, numbers, arithmetic, etc. Working with the GEOBOARD Internet service application allows an elementary school student to learn a lot of important information, prepares students for further study of the geometry course at school and develops their skills of being a socially active, creative person who generates new ideas and makes non-standard decisions. And it all happens in the form of a cognitive game. The GEOBOARD Internet service that is made by The Math Learning Center (MLC) has a wide range of functional and didactic capabilities and will fully meet the needs of elementary school teachers to cover many topics in mathematics lessons. The visualization allows elementary school students to summarize, systematize and discard redundant information just playing a game, so this is the way to improve the educational process. The service is important because it actively involves elementary school students in the process of learning geometric material.

Mathematical creative thinking ability is one of the capabilities that need to be owned anddeveloped in students who study mathematics from primary to university level. This is due to thoseabilities in accordance with the vision of mathematics, national education goals and learningobjectives of the school mathematics. This paper is a contribution of new ideas for implementingthe curriculum in education so as to develop mathematical creative thinking ability in school.Information about mathematical creative thinking ability derived based on a literature review. Thestudy results are expected that mathematical creative thinking ability can progress throughdiscovery learning based scientific approach.

Our understanding of how people learn is continually changing. Howard Gardner’s Theory of Multiple Intelligences revolutionized the field education, because it accounts for a broader range of human potential in children and adults and suggests that individuals learn in a multitude of ways. Gardner’s theory suggests there are a variety of possibilities to facilitate learning. People with heightened verbal, linguistic skills are often referred to as word smart. Verbal, linguistic students learn best through the comprehension of language which includes speaking, writing, reading, and listening. Students with verbal linguistic intelligences can easily access information through worldwide databases and computer networks. Any subject content can be enhanced, enriched, and updated from a variety of easily accessed sources which allow students to master the use of technology to access and share information. Students with logical mathematical intelligence are individuals who are number smart and have innate skills which involve logical, problem solving abilities, creative and manipulative skills, and are adept visual learners. Educators can enhance logical-mathematical intelligence through challenging and innovative multimedia technology. With innovative multimedia technology, students learn at all levels and effectively gain knowledge through a variety of different software programs that offer immediate feedback. Learners with visual-spatial intelligence are aesthetically oriented and may have a greater capacity for learning certain sciences like anatomy or topology. They are skillful when it comes to visualization and memory, but may be challenged with auditory memory. Learning for visual-spatial students takes place all at once, with large chunks of information grasped in intuitive leaps. Many people have an innate kinesthetic ability, as well as a natural sense of how their body should react in physical situations. Students with bodily-Kinesthetic intelligence learn best through tactile learning experiences. Bodily-kinesthetic proficiency can be enhanced for students through the use of the whole body to express ideas and feelings. Gardner proposed that musical intelligence almost parallels linguistic intelligence. The person with interpersonal is able to collaborate, understand and work effectively with others. They are aware of their interactions with others and usually take notice of and react to the feelings of others. The interpersonal learner learns best in group situations and structured class settings. Learners with intrapersonal intelligence have accurate self-understanding and are skilled in problem-solving. There is a multitude of different ways to integrate technology into our classrooms and all should focus on learning theory and educational practices. The use of technology should not occur without thinking about how people learn best. To actively engage diverse learners in higher education, the instructor should have a good understanding of the overall nature and purpose of the group, as well as the ability to interact well within the learner’s unique world. The instructor must also be able to structure learning activities to meet their learning needs. The use of Howard Gardner’s Theory of Multiple Intelligences, coupled with an understanding of how effective technology can enhance the learning community, can meet the diverse learning needs of all students.

The purpose of this research is to analyze the difficulty of students in solving problems related to mathematical creative thinking ability comprehensively as a result of the implementation of PACE (Project, Activity, Cooperative learning, Exercise) model and conventional learning in Mathematical Statistics Course. This research was a qualitative research. The subjects in this research were students of Mathematics Education Program who took Mathematical Statistics Course at one of the private universities in East Jakarta. This research used purposive sampling and various instruments. They were test of mathematical prior knowledge (MPK), test of mathematical creative thinking ability (MCTA), observation sheet, interview sheet, and researcher. The data of this research was collected using triangulation techniques. The result of this research show that students are still experiencing difficulties based on MPK level and overall in solving problems related to mathematical creative thinking ability in both learning (PACE model and conventional). However, the difficulty of students who have obtained PACE Model learning is lower than students who have obtained conventional learning. The most of difficulty of students in both learning (PACE model and conventional) is in indicator of ‘originality’. Keywords: mathematical creative thinking ability, Mathematical Statistics, PACE model

This paper reports on an investigation into students' thinking about mathematics and their mathematical behaviour when faced with a problem. It is found that students perceived mathematics as a fixed body of knowledge to be learned. When solving a problem, students demonstrate little intellectual independence and lack the ability to think for themselves. This is a matter of some concern. The findings indicate that the mathematical environment may not be providing students with the experiences to encourage them to be creative and reflective. It is suggested that mathematicians need to move away from teaching students the product of mathematical thought to teaching them mathematical thinking.

This study aims to: 1) To find out how the effectiveness of the integration technique module in integral calculus learning, and 2) To find out whether there is an increase in the mathematical creative thinking ability by using the integration technique module in integral calculus learning. Module development is carried out using the ADDIE model which has five stages are Analysis, Design, Development, Implementation, and Evaluation. The subjects in this study were 16 students in the 3rd semester of the Mathematics Education Study Program, Faculty of Teacher Training and Education, Universitas Riau. The research data collection instruments were an expert validation questionnaire, a student response questionnaire, and a mathematical creative thinking ability test. The data obtained were analyzed using quantitative and qualitative descriptive analysis methods. Based on the results of the validity test, the integration technique module was declared valid and suitable for students to use in the integral calculus course. Judging from the results of the module practicality test, the average percentage of practicality values is 77.8125 and is in the practical category. Referring to the results of the module effectiveness test, the n-gain average of students' mathematical creative thinking abilities is 0.64 and is in the medium category. Because the integrated engineering module has met the criteria of validity, practicality, and effectiveness, it can be said that the developed integration technique module can improve students' mathematical creative thinking skills in the integral calculus course.

This paper deals with the problem of using the project method in teaching future mathematics teachers. The new educational strategy implements self-education with the help of developing technologies, the goal of which is not only to bring knowledge to students, but also to identify and develop the creative interests and abilities of each student, to stimulate his/her independent productive learning activities. The authors showed that one of such technologies is project training, which involves joint learning and cognitive activity of students, having a common goal, agreed ways of working. This paper notes also the need to use project technology, which consists in developing the ability of future teachers to have an analytical, creative thinking; self-acquisition of missing math knowledge from various sources; thinking, based on knowledge of mathematical facts, the laws of science; and ability to work in a team, performing various social roles.

The article discusses methods for solving geometric problems with the active use of methods such as analysis and synthesis, analogy and generalization, based on theoretical thinking on the principle of ascent from simple to complex in order to develop students' ability to creative activity. The authors have developed systems of problems, focused on the formation of their ability to "make" independent discoveries both in the process of solving a problem and at the stage of researching the result of the solution. The developed system of problems is aimed at finding a way to solve a more complex problem, after a similar method has been used in relation to another simpler or particular problem. The participants in the experiment are future masters of pedagogical education (profile "Mathematical Education") at Togliatti State University. The article shows that the most effective methods of preparing future masters of mathematics education for creative professional activity can be such methods of scientific knowledge as analogy and generalization. It was revealed that in the process of learning to solve geometric problems included in the developed system, students demonstrate higher indicators of the level of formation of creative activity, as a result of the development of the ability of the future master of pedagogical education (profile "Mathematical Education") to analogy and its application in specific situations, his ability to use the established properties, skills and abilities formed, techniques and methods of action in relation to another object in new conditions and for new purposes, the use of mathematical concepts and theorems in more and more diverse specific problems.

Penelitian ini dilatarbelakangi rendahnya minat mahasiswa dalam melaksanakan tugas dari dosen, daya tangkap mahasiswa dalam menerima pelajaran, kemampuan mahasiswa dalam menghubungkan materi perkuliahan dengan dunia nyata, kemampuan mahasiswa dalam belajar mandiri, kemampuan mahasiswa dalam menuliskan ide, kemampuan mahasiswa dalam mengerjakan tugas mandiri, keberanian mahasiswa dalam menyajikan temuan, keterampilan mahasiswa menulis dipapan tulis, dirasa masih rendah belum sesuai dengan kompetensi yang diharapkan dan belum sesuai dengan apa yang dikehendaki oleh matematika. Tujuan diadakannya penelitian ini adalah untuk mengetahui ada tidaknya peningkatan kemampuan berpikir kritis mahasiswa yang memperoleh pembelajaran matematika dengan pendekatan Creative Problem Solving serta untuk mengetahui ada tidaknya perbedaan peningkatan kemampuan berpikir kritis mahasiswa dalam matakuliah geometri analitik antara kelompok atas, tengah dan bawah setelah mendapatkan pembelajaran dengan pendekatan Creative Problem Solving.Penelitian ini merupakan penelitian quasi experiment atau eksperimen semu yang terdiri dari dua kelompok penelitian yaitu kelas eksperimen (kelas perlakuan) merupakan kelompok siswa yang pembelajarannya menggunakan pembelajaran Creative Problem Solving dan kelompok kontrol (kelas pembanding) adalah kelompok siswa yang pembelajarannya menggunakan pembelajaran biasa (konvensional). Populasi dari penelitian ini adalah mahasiswa semester I prodi pendidikan matematika Universitas Singaperbangsa Karawang. Sampel penelitian ditentukan berdasarkan purposive sampling. diperoleh mahasiswa kelas I A semester 1 sebagai kelas eksperimen sebanyak 35 mahasiswa dan kelas I B sebagai kelas kontrol sebanyak 35 mahasiswa. variabel penelitian melibatkan tiga jenis variabel yakni variabel bebas yaitu model pembelajaran Creative Problem Solving dan pembelajaran konvensional, sedangkan variabel terikat yaitu kemampuan berpikir kritis matematis mahasiswa serta variabel kontrol yaitu kategori pengetahuan awal matematika mahasiswa (atas, tengah, bawah). Instrumen digunakan dua jenis instrumen, yaitu tes dan non tes digunakan dua jenis instrumen, yaitu tes dan non tes. Hasil penelitian menunjukan Secara keseluruhan penerapan model pembelajaran Creative Problem Solving dapat meningkatkan kemampuan berpikir kritis matematis mahasiswa.selain itu terdapat perbedaan peningkatan kemampuan berpikir kritis matematis antara mahasiswa yang mendapatkan pembelajaran Creative Problem Solving dan mahasiswa yang mendapatkan pembelajaran konvensional, bila ditinjau dari kategori pengetahuan awal matematika siswa. This research is motivated by the low interest of students in carrying out the duties of the lecturers, the students' ability to accept lessons, the ability of students to connect lecture material with the real world, the ability of students in independent learning, the ability of students to write ideas, the ability of students to work independently, student courage in presenting the findings, the skills of students writing on the writing board, it is still considered low, not in accordance with the expected competencies and not in accordance with what is desired by mathematics. The purpose of this study was to determine whether there was an increase in critical thinking skills of students who obtained mathematics learning using the Creative Problem Solving approach and to determine whether there was a difference in the improvement of students' critical thinking skills in analytical geometry between the upper, middle and lower groups after learning with approaches Creative Problem Solving. This study is a quasi-experimental study consisting of two research groups, namely the experimental class (treatment class) is a group of students whose learning uses Creative Problem Solving learning and the control group (comparison class) is a group of students whose learning uses learning ordinary (conventional). The population of this study were first semester students of the mathematics education study program at the University of Singaperbangsa Karawang. The research sample was determined based on purposive sampling. obtained by class I A students in semester 1 as an experimental class as many as 35 students and class I B as a control class as many as 35 students. The research variable involved three types of variables, namely the independent variable namely the Creative Problem Solving learning model and conventional learning, while the dependent variable was the mathematical critical thinking ability of students and the control variable, namely the category of students' initial mathematical knowledge (top, middle, bottom). Instruments used two types of instruments, namely tests and non-tests used two types of instruments, namely tests and non-tests. The results showed that the overall application of the Creative Problem Solving learning model could improve students' mathematical critical thinking skills. In addition there were differences in the increase in mathematical critical thinking skills between students who received Creative Problem Solving learning and students who received conventional learning, when viewed from the category of early mathematics knowledge students.