Journal articles on the topic 'Mathematical imagination abilities'

The teaching of multiple integrals plays a crucial role in the development of spatial imagination and mathematical thinking in students. This article explores the pedagogical foundations necessary for effective instruction in multiple integrals, focusing on strategies that enhance students' ability to visualize and manipulate complex spatial relationships. By integrating modern teaching methodologies with traditional mathematical instruction, educators can significantly improve students' conceptual understanding and problem-solving abilities in this area.

Teaching math helps students with intellectual disabilities develop cognitive skills such as cognition, memory, thinking, imagination, and mastery of mathematical knowledge and skills. Corrective work aimed at developing mathematical knowledge, skills and abilities allows to perform mental operations such as analysis, synthesis, comparison, generalization, concretization.

Classification of skills for the basic and
 advanced levels of training is developed. It consists
 of two blocks. Block 1: main receptions of the
 general educational activity, operating abilities
 with geometrical shapes, imaging abilities, operating
 with geometrical sizes, measuring works
 (including afield works); Block 2: main receptions
 of creative educational activities; receptions of
 research educational activities, operating skills
 with geometrical shapes; imagination and mental
 work with geometrical figures, creation of geometrical
 figures, operating with geometrical sizes,
 measuring works, including afield workship.

Different factors have different effects on the formation of children's scientific outlook. Among these factors, the development of creative and mathematical thinking is the most important. After all, the process of formation of imagination and concepts in a child begins in the preschool institution, and this period is the most important stage in terms of the content of the formation of worldview. Therefore, the preschool period is a key period in the formation of concepts and ideas.

This study aims to analyze students 'spatial mathematical abilities in terms of Van Hiele's thinking stages in problem-based learning models, as well as to find out the number of difficult indicators of students' mathematical spatial abilities in terms of Van Hiele's thinking stages in problem-based learning models. Researchers are the main research instrument, data obtained through several previous studies or journals about research on students' spatial abilities in terms of van hiele's thinking stages in problem-based learning. This study uses the analysis technique of the Miles and Huberman model. Data analysis activities, namely data reduction, display data, and conclusion drawing/ verification. The subjects in this study were journal articles on the analysis of students' spatial abilities in terms of van hiele's thinking stages in problem-based learning. The object of this research is the provision of a problem-based learning process. Based on the results of the study, there are students with high spatial abilities who have exploratory thinking processes, methodical thinking, analogical thinking, abstract thinking, synthesis, serendipity, and recycling ideas, students with high spatial abilities also have high imagination, students with spatial abilities are having a process exploratory thinking, serendipity, analogical thinking, semi-abstract thinking, and recycling of ideas and having moderate imagination, as well as students with low spatial abilities in understanding problems using exploratory, analogical, semi-abstract, synthesis thinking processes and have low imagery.

As a new generation of assessment instrument, cognitive diagnosis integrates the measurement objectives into the cognitive model to diagnose the fine-grained knowledge of students. Taking the PISA 2012 dataset in mathematics from Shanghai, Hong Kong, Macau and Taiwan as the research subject, this study constructed a cognitive model with the attributes of Mathematical Abstraction, Logical Reasoning, Mathematical Modeling, Intuitive Imagination, Mathematical Operation and Data Analysis, and made an analysis of the mastery of students’ mathematical competencies of different attributes in four regions, and the learning paths of the students’ mathematical competencies were constructed. The results showed that Shanghai had the obvious advantages in each attribute; the mastery mode of Hong Kong, Macau and Taiwan showed a common trend, and they all indicated a relatively low percentages of competencies in Logical Reasoning and Intuitive Imagination. In terms of the learning paths, the learning paths in the four regions reflected diversities, but obvious main learning paths existed. Majority of the knowledge states’ abilities were below 0. While in Hong Kong, Taiwan, and Macau, more knowledge states’ abilities were above 0. This research provided a reference for the systematic analysis of students’ knowledge status and learning path.

This research was conducted with the aim of analyzing and describing the mathematical, spatial visualization abilities of junior high school students in class VIII in solving spatial geometry math problems with the help of augmented reality-based applications in the categories of high, medium, and ability students. The research was conducted at SMPN 3 Karawang Barat, with a descriptive qualitative method. The process of collecting data was carried out using the test and interview methods to the research subjects. The results of the research show that high mathematical spatial visualization skills have the characteristics of imagination, use of concepts, problem solving and pattern search that are quite good in solving problems. Then, the medium mathematical, spatial visualization ability has good imaginative characteristics. And those with low mathematical, spatial visualization skills have poor imagining characteristics, use of concepts, problem solving and pattern search and experience many difficulties in various cases.

This work aims to examine the relationship between general self-regulated learning abilities and students' general intellectual abilities, mathematical learning abilities, and academic achievement. A study was conducted with a sample of eighth-grade students (N=325). The research employed a survey and descriptive method, and the instruments used included a test of general intellectual abilities, a test of self-regulated learning abilities, a test to measure mathematical learning abilities, and a standardized math knowledge test. Based on the obtained results, we indicate those factors with high or moderately high correlations. Among the results obtained, there is a high correlation between general intellectual abilities and general self-regulated learning abilities (subtests for interpreting graphs and interpreting geographic maps). The results show a high correlation between the total score on the self-regulated learning abilities test and math achievement. A moderately high correlation was achieved between the test of general intellectual abilities and self-regulated learning abilities (subtests for finding necessary information, exploring new material, and the index of developed abilities and techniques for self-regulated learning). On the math learning ability test, various abilities are differentiated, including formalization of mathematical content, spatial abilities, imagination, flexibility, and critical thinking. Based on the research results, it is considered significant to investigate the effects of different innovative teaching systems and teaching methods on students' self-regulated learning abilities and mathematical learning abilities.


 The ability to solve mathematical problems is an important part of learning mathematics that links daily life. The importance of having good mathematical problem solving skills, so understanding mathematics is also good, especially on the pythagoras theorem material. Material related to the construction of this triangle can be applied in calculations in real life. To be able to construct the concept of the pythagoras theorem problem, it needs an ability that can represent imagination into an object, this ability is called spatial visualization ability. This research will discuss the students' mathematical problem solving abilities on the pythagoras theorem material based on the spatial visualization abilities possessed by students. The research method used was a qualitative research with a descriptive approach to students of class VIII MTS 38 Jakarta. The test instrument was a matter of pythagoras theorem description and spatial visualization intelligence test. The results showed that students who have low spatial visualization skills tend not to be able to solve problem solving problems well, students who have moderate problem solving abilities can solve problem solving problems even though there are still steps that are not right, while students who have high spatial visualization abilities can solve problem solving problems with the right steps and answers.

Mathematical reasoning ability is a very important aspect in learning mathematics. This ability is a high-level ability that involves imagination and curiosity to think logically. Mathematical reasoning can be sharpened using the Problem Based Learning learning model, so this research was conducted to analyze the mathematical reasoning abilities of students at SMP Negeri 5 Kisaran using a qualitative descriptive approach. The subjects in this research were 32 students. The data used is written test results and observation results during the learning process which will then be analyzed using qualitative descriptive data analysis techniques including data reduction, data display and verification. The results of this research show that the mathematical reasoning ability of students in the high category is 8 people, 16 people are medium and 8 people are low, and the average value of the results of observations of mathematics learning activities in comparative material is 16.28125 with a percentage of 66.5%. which is included in the medium category. These results indicate that the reasoning abilities of students at SMP Negeri 5 Kisaran are in the medium category.

The paper concerns the challenging aspect of
 preparing 5-7 year old children for school on the basis of
 educational areas integration. The authors present specific
 study aids of lessons, designed especially for elder
 preschoolers and aimed at developing their mathematical
 abilities and natural-ecological knowledge. These lessons not only provide insight into mathematics, foster responsible attitude to Nature and encourage cognitive interest, but also
 enhance attention, imagination, speech habits and communication skills.

STEAM (Science, Technology, Engineering, Art, and Mathematics) is an approach that can help provide stimulation to students to increase their creativity. Teachers can design mathematics learning in class by considering the needs of each student. Appropriate and interesting learning media can stimulate students to be able to arouse their imagination, creativity, and artistic expression. The purpose of this study is to classify the implementation of STE(A)M learning based on the level of education, type of learning media, topics, and mathematical abilities to be developed. It uses the method of systematic literature review (SLR), and concludes that STE(A)M learning has been widely applied at the secondary school level, especially in algebra and geometry, and has been proven effective in improving students’ problem-solving abilities.

This study aims to describe the creativity in thinking of junior high school students in solving physics problems. Creativity in thinking is important for students to make themselves understand a physics concept, such as force, work, etc. Creativity in thinking is also needed so that students can find several possible problem solving according to their potential and are not fixated on a method because basically every student has their own imagination and thought process. Twelve students in the class VIII J of SMP Negeri 1 Jombang participated in the study. Data obtained from student's thinking creativity test instrument which is strengthened by data from student and teacher interviews. Data analysis referred to three indicators of creativity used in the study: fluency, flexibility, and originality. The results showed that the students' thinking fluency with high ability and some students with medium and low abilities got high scores. The highest score of the flexibility indicator was obtained by students with low abilities. High scores for the originality indicator were also obtained by several students from the high, medium, and low ability groups. High creativity scores are not only obtained by high-ability students but also medium, and low-ability students. The creativity of students' thinking in solving physics problems is different. Students' knowledge and experience play a role in the differences in students' creativity in thinking fluently, flexible, and new. So that teachers can use learning methods that provide direct experience to students to make it easier for students to understand a concept and also improve students' mathematical operational abilities to make it easier for them to solve a problem that requires mathematical calculations.

This study aims to determine the results of the assessment of students' spatial abilities which are very important to master to understand geometry relations, and geometry properties, and solve mathematical problems including on the material of flat-sided spaces in class VIII. This research uses descriptive research through qualitative and quantitative approaches. The sampling technique in this study used a random sampling technique with 31 students as the research sample. The research instruments used were observation and interview guidelines with qualitative analysis and spatial ability tests with quantitative analysis. The analysis of the test instrument was processed with the help of SPSS and Microsoft Excel to determine the feasibility of the instrument. Based on the results obtained through several aspects of the assessment of students' spatial abilities seen from four indicators of ability. The concept understanding indicator has increased until the last meeting, while the pattern recognition and imagination indicators tend to increase and decrease at the last meeting. The interview results also prove that the spatial ability test instrument given for five meetings is quite helpful in understanding the flat-sided space building material

The growth of anti-mathematics sentiment at the beginning of the 19th century At the threshold of the nineteenth century, the collapse of the salons, the new gestalten of education, a new role of literature and the occurrence of the pre-romantic sensibility resulted in a remarkable increase of the yawning gap between the scientific communities and literary men. A prejudice against mathematics gave a new lease of life to the reintroduced belief that pursuing mathematics corrupts hearts and cools human imagination. The aim of the present paper is to restore the epistemic and ideological background that allows one to understand the terms of the debate and to identify opposing ideas. With this end in view, the paper focuses on the cultural and philosophical opinions of François-René de Chateaubriand whose The Genius of Christianity (1802) extremely polarizes the attitudes of supporters and opponents towards mathematical thinking and abilities.

Filipino students have significantly lagged in mathematics education, with over half of this demographic exhibiting inadequate mathematical skills compared to their counterparts in other regions globally. This study focuses on the mathematics performance of Junior High School students in Labasan National High School. Proficiency in mathematical skills and knowledge are essential as they serve as the foundation for everyday life, career advancement, and advancements in science and technology. Mathematics entails more than just logical reasoning; it involves imagination, requiring students to possess creative thinking abilities to delve into mathematical problems. This study conducted a comprehensive needs assessment in the mathematics performance of Junior High School in Labasan National High School. This study employs descriptive research methodology to assess the performance levels in Mathematics of the respondents. Data gathered from 238 students belonging to Grade 7 to Grade 10 undergoes sorting, tabulation, and interpretation, revealing significant gaps in mathematical concepts. The study's findings led to the introduction of an extension program named MathPULSE: Powering Understanding through Learning Support and Education aligning with the Sustainable Development Goals, particularly SDG 4 (Quality Education), and SDG 5 (Gender Equality). Developed through collaborative efforts between the College of Teacher Education and the Mathematics Club of Mindoro State University – Bongabong Campus, MathPULSE aims to elevate students' proficiency in mathematics. The findings revealed consistent challenges persist among Junior High School students at Labasan National High School regarding mathematics performance, as evidenced by significant score disparities. It also revealed that most students, irrespective of grade level, face difficulties in grasping fundamental mathematical concepts, resulting in consistently low mean scores across grade levels and highlighting a widespread issue with mathematical performance among students.

Макалада авторлор тарабынан башталгыч класстарда «Мейкиндик жана формалар» курсунун элементтерин окутуу процессинде, окуучулардын чыгармачылык жөндөмдүүлүктөрүн өнүктүрүүнүн практикалык маселелери каралды. Башталгыч класстарда геометриялык материалдарды окутууда окуучулардын геометриялык жана мейкиндик элестөөлөрүн, ой жүгүртүү ыкмаларын өнүктүрүү менен, алардын практикалык (ченөө, чийүү, түзүү, эсептөө ж.б) көндүмдөрүн калыптандыруу талабы коюлат. Окуучуларда мейкиндиктеги катыштар түшүнүгү пайда болгондон тартып, аларда көндүмдөрдүн кеӊири топтомунун бөлүгү болуп саналган мейкиндиктеги ой жүгүртүү деп аталган көндүм калыптана баштайт. Башталгыч класстын окуучуларынын мейкиндик ой жүгүртүү жөндөмдүүлүктөрүн өнүктүрүүдө, геометриялык материалдарды активдүү окутуунун каражаты катары геоборд дагы жакшы жардамчы боло алат. Геоборд - бул, окуучуларга геометриянын көптөгөн түшүнүктөрүн өздөштүрүүгө жана чоӊдуктарды ченөөгө жардам берген математикалык модель. Ал балдардын фантазиясын жана чыгармачылыгын өнүктүрөт. В статье авторами рассмотрены практические вопросы развития творческих способностей учащихся в процессе обучения элементам курса «пространство и формы» в начальных классах. При обучении геометрическому материалу в начальных классах необходимо развивать у учащихся геометрическое и пространственное воображение, навыки мышления, а также развивать и формировать их практические навыки и умения (измерение, рисование, создание, расчет и т.д.). С того момента, как у учащихся появляется пространственное отношение, у них начинает формироваться навык, называемый пространственным мышлением, который является частью широкого набора навыков. Как средство активного обучения геометрическому материалу геоборд может стать хорошим помощником в развитии способностей пространственного мышления учащихся начальных классов. Геоборд - это математическая модель, которая помогает учащимся изучить многие понятия геометрии и измерять величины. Он развивает детское воображение и творческие способности. In the article the authors consider practical issues of developing creative abilities of elementary school students in the process of learning elements of the course "space and shapes". When teaching geometric material in primary grades, it is necessary to develop students' geometric and spatial imagination, thinking skills, as well as to develop and form practical skills and abilities (measuring, drawing, creating, calculating, etc.). From the moment pupils develop a spatial attitude, they begin to develop a skill called spatial thinking, which is part of a broad set of skills. As a mean of actively teaching geometric material, geoboard can be a good aid in developing the spatial thinking abilities of elementary school students. The geoboard is a mathematical model that helps students learn many geometry concepts and measure quantities. It develops children's imagination and creativity.

Relevance. The relevance of the research topic lies in the fact that educational tasks in geometry contribute to the formation and development of mental abilities, spatial imagination, which are necessary in logistics, architecture and construction, mechanical engineering, cartography and other fields of applied science. Purpose. The purpose of the study is to study the stage of training of future mathematics teachers in the direction of implementing the PISA-2021 concept. Methodology. Among the theoretical research methods, analysis and synthesis, the method of comparison and generalization were used. At the stage of the empirical part, an experimental pedagogical study was conducted on the basis of three universities of Kazakhstan. Results. The article examines the issue of designing the learning process in the context of forming the readiness of future mathematics teachers to carry out pedagogical activities. A system of content components of the future teacher's general readiness to teach schoolchildren was determined. The signs and stages of formation of the readiness of future mathematics teachers to teach schoolchildren in the context of the PISA-2021 concept have been identified. A model of the process of forming the professional readiness of future mathematics teachers to teach schoolchildren in the context of the formation and development of their mathematical thinking, spatial ideas, and divergent thinking has been built skills of the 21st century. Conclusions. The study confirms the effectiveness of a new model for preparing future math teachers, showing high student proficiency in mathematical and pedagogical skills, while noting potential for broader application and challenges in implementation due to current school curriculum limitations. Keywords: readiness components; stages of the learning process; thinking abilities; geometric problems; section of polyhedra

The Ministry of Education and Culture (2016) states that one of the learning objectives in the 2013 curriculum is to develop creative activities that involve imagination, intuition, and discovery by developing divergent, original thinking, curiosity, making predictions and guesses, and experimenting. The fact that the creative thinking ability of Indonesian students is still low is shown in the results of the Program for International Student Assessment (PISA) in mathematical ability, placing Indonesia at 62 out of 70 countries (OECD, 2016). The provision of problem-posing model questions is expected to stimulate students to think creatively by generating new ideas or ideas to develop existing information and finally students begin to propose new problems according to their understanding of the mathematical concepts being studied. The purpose of this study was to describe students' mathematical creative thinking ability seen from the indicators of creative thinking abilities, namely fluency, flexibility and novelty in solving problem posing question. The research method used is a survey method with the research subject being class VIIIG SMPN 1 Malang. The results obtained, the average score of the fluency indicator is 14.81 or 87.10% in the high category, the average score of the flexibility indicator is 4.64 or 51.61% in the low category, and the novelty indicator is 1.16 or 6, 45% with low category. This shows that the creative thinking ability of students in solving problem-posing questions is low.

The initiative is based on treating weak mathematical concepts through the story and producing cartoon characters to illustrate them in an interesting way for the students and appropriate for their ages. We have developed the story to be in the form of electronic stories with childish characters. The initiative provided the student with an element of suspense, as the educational rule confirms that there is no learning without suspense. The initiative was well received. The interest of the targeted students reflected its impact on their achievement, which improved, and resulted in a love of the subject and a longing to learn more. It was noted that the students' interest increased in each session and their willingness to listen eagerly, in addition to their attempt to come up with a similar. This research explores the use of storytelling and cartoon characters to teach mathematical concepts to students in an engaging and effective way, leading to improved academic performance and a love for the subject. The results of the study showed an improvement in the level of students and the speed of their understanding of the information. It also contributed to increasing the interest of the students in each group and their eagerness to listen to the voices for the story, in addition to their attempt to come up with a story that would develop their imagination and abilities, the youngest.

The process of forming an image requires a correct color composition, location and distance between the lines to produce a good image. Human abilities in both creativity and high imagination are very limited, especially in forming new images by utilizing existing image patterns or images that resemble old images. Here we showed the implementation of L-System to generate new image generations with additional flame as a fire effect/glow on images for image transformation. This research used the L-System algorithm, Iterated Function System, and Voronoi Diagram to improve the result of image transformation. The results of this study indicated that mathematical calculations can be applied in the formation of images and the resulting images can be abstract and symmetrical. The next generation of images produced in this research can be in unlimited numbers as the generation of morphogenesis processes. The process of generating images is carried out randomly by merging the two existing images with morphogenesis analogy. The resulting images can be exported into jpg, png, and svg formats. Furthermore, this research showed that the implementation of the calculation for the variation reach the value of 99.48% while the image variation composition has a value of 99.29%.

This inquire about points to survey the affect of executing the Groups Recreations Competition learning demonstrate on numerical issue fathoming abilities in lesson VII understudies at MTs Tarbiyah Islamiyah Ulumahuam. Employing a quantitative approach with a pre-experimental inquire about plan of the One Gather Pretest-Posttest sort, this inquire about included 27 understudies as a test from the lesson VII populace. Based on information investigation, the normal pretest score gotten was 38.00, whereas in treatment, the posttest score experienced a critical increment with an normal of 85.33. The measurable test comes about appear a t-count esteem of 5.55 which is more noteworthy than the t-table of 2.04 at a importance level of 0.01, expressing that there's a critical impact of the TGT demonstrate on students' numerical issue understanding capacities. The application of the TGT show has demonstrated to be successful in moving forward students' capacities since it can increment center, imagination and collaboration in fathoming scientific issues. By utilizing this model, understudies are more effectively included within the learning prepare, which closes in a significant increment in science learning results. Keywords: Mathematical Critical Thinking Ability, Teams Games Tournament (TGT) Model.

The knowledge on geometry are of great importance for the understanding of reality. Spatial notion and geometrical concepts, graphical skills and habits are an important part of the study of geometrical knowledge in elementary school as propedeutics of the system course on geometry in the next school levels. In the recent years, education in Bulgaria follows the trends imposed by the European Union related to the acquiring of some basic key competencies. They promote to the improvement of knowledge, skills, abilities and attitudes of students and their more successful social development. From the school year 2016/2017, the education in the Bulgarian schools is in accordance with the new Law on pre-school and school education. Under this law, students are teached under new curriculum and teaching kits for the corresponding class. According to the new curriculum, the general education of the students of I-IV grade, covers basic groups of key competencies. Here, much more attention is paid also to the results of international researches on the students’ performance in mathematics. Primary school students participate in international competitions and Olympiads, which lead to the need of working on more mathematical problems with geometric content of the relevant specific types. This allows to study and use author’s various mathematical problems for teaching geometry. Their purpose is to contribute to the expansion of space notions of the students, to develop their thinking and imagination. This article is dedicated to the application of author’s various mathematical problems and exercises for teaching students from the third grade through which the geometrical knowledge and skills of the students develop and build. The solving of the mathematical problems is realized on a rich visual-practical basis, providing conditions for inclusion of the students in various activities. The proposed various mathematical problems are developed by themes including fully geometric problems and exercises for teaching mathematics to third grade students. Teaching by using the various mathematical problems was held with 149 students from third grade, from five schools - three in Sofia and two in smaller towns, in the school year 2016/2017.

The article is devoted to the problem of using LEGO technologies in the educational space of the New Ukrainian School. On the basis of the study of the source base and the results of the research, it is concluded that the use of LEGO in the educational process of primary school allows the teacher to reveal the cognitive capabilities of each student who is the subject of the educational process. It is proved that the use of LEGO is effective in the development of speech, mathematical, natural, technological, social and health, civic and historical competences and that «learning through play» is possible with LEGO. In addition, LEGO technologies in primary school lessons activate the development of memory, attention, imagination, logical thinking, and help students to establish patterns. According to the results of our study, primary school teachers in Kolomyia effectively use LEGO technologies in the classroom during morning meetings, to organise learning and research activities; to update students‘ background knowledge and life experience; to perceive and comprehend educational material; to summarise and systematise students’ knowledge, skills and abilities; to reflect, etc. Most often, teachers use LEGO technologies in «I Explore the World» lessons to summarise and systematise knowledge (83.3%), for reflection (66.7%), during morning meetings (55.6%), to update basic knowledge, skills and abilities (47.2%), and to perceive and comprehend new learning material (36.1%). LEGO technologies make it possible to organise both frontal work of younger students aimed at studying selected topics and various subjects within the classroom system, as well as independent creative work and project-based learning. The organisation of educational and gaming activities requires the teacher to have appropriate methodological competence and high skill to find any teaching method in a LEGO game.

Purpose. Theoretical study of resilience and the resources that determine the difference in its manifestation after critical situations, as well as empirical research on the mechanisms and resources that promote the development of resilience in people with traumatic experiences because of the war in Ukraine. Methods. Methods of theoretical analysis of scientific literature on the problem; methods of empirical research using a set of psychodiagnostic techniques; methods of mathematical statistics. Spearman's rank correlation coefficient was calculated for statistical data processing. Results. According to the results of theoretical analysis, the concept of "resilience" is considered as both a process and an outcome of successful adaptation to difficult life situations, especially through mental, emotional, and behavioral flexibility and adaptation to external and internal challenges. The empirical study revealed positive correlations of psychological resilience with resources (crisis coping strategies) "B – Belief & values" (r=0.591), “C – Cognition, thought” (r=0.540). A directly proportional correlations was also found between the overall impact of the event, the level of intrusion and avoidance with the crisis coping strategy "I – Imagination" (r=0.505; r=0.607; r=0.506), between the level of avoidance and the resource “S – Socialization” (r=0.632), between the level of intrusion and “C – Cognition, thought” (r=0.491). Conclusions. Individuals whose crisis coping strategies are based on faith (in God, in people, in miracles, or in themselves and their mission), belief systems, values and meanings, the activation of mental abilities, the ability to think logically and critically, assess situations, learn new ideas, plan, gather information, analyze problems, and solve them rationally, exhibit higher resilience indicators. Those who have higher level of impact of event and manifestations of specific PTSD symptoms more frequently use imagination, memories, and creativity to cope with crises. The level of avoidance positively correlates with the use of social ties, social support, and communication to cope with crises, and the level of intrusion positively correlates with the use of cognition and cognitive strategies.

Students’ spatial ability of MA Al-Hanif is very low. This is because the students rarely use mathematics learning media which helps learning process. One of learning media that can help imagination is Geogebra. This study aims to determine the improvement of mathematical spatial abilities of students with problem-based learning model assisted with Geogebra. The research method used is Classroom Action Research which implemented in 3 action cycles. Population in this study is students of class XI MA Al-Hanif in academic year 2016-2017, with sample as many as 17 people with Geometry course. The instrument used a matter of spatial ability test in each cycle, teacher and student observation sheet used in learning and student attitude questionnaire. The results showed that, by applying the learning model of problem-based learning problem assisted geogebra can improve spatial ability of the students. This is shown by the results of spatial ability tests in each cycle. In the cycle I, the classical absorption of students reaches 53%, the second cycle action goes up the classical absorption of 76% students and the third cycle action almost 82% of the classical absorption increases from the results of the study concluded that the problem-based learning model assisted geogebra can improve the students’ spatial ability. Furthermore, student and teacher activity toward geogebra assisted Problem-Based Learning model went run effectively and conducive. The response of students in geometry learning with Geogebra assisted problem-based learning model generally produces a positive impression.

The article examines the process of developing an engineer’s thinking during the study of engineering graphics at a university. Relevance. The working conditions of a modern engineer require professional training. One of the disciplines of engineering training is descriptive geometry and engineering graphics, which develops the thinking of an engineer. The purpose of the study is the process of developing an engineer’s thinking during the study of descriptive geometry and engineering graphics. The research used theoretical methods of analysis, synthesis of module structure, synthesis and generalizations, knowledge control, practical methods of performing graphic tasks, methods of mathematical statistics for evaluating educational achievements, analysis of literary sources and educational literature, experiment. The provisions reached at the beginning of the study determine the theoretical significance and novelty. Thinking has forms and types of thinking. The engineer’s level of thinking is based on knowledge, combining theoretical and practical experience of life activity, which determines his thinking logic. The basis for the development of thinking is mental formations. In this process, it should be important to form the knowledge and quality of the engineer’s knowledge during training. The qualities of a student’s knowledge are revealed as a result of the assimilation and application of knowledge by a person in various types of activities. Engineering graphics develops thinking by means of forming knowledge, skills, and abilities, as a basis for conclusions corresponding to the theoretical level of the student’s specialty training. Descriptive geometry and engineering graphics allows you to develop mental processes: perception, representation, imagination, memory, speech, etc.; qualities of knowledge: com-pleteness, depth, efficiency, flexibility, awareness; develop thinking: implies the development of qualities of thinking, modes of thinking, forms of thinking, levels of thinking. The practical significance is characterized by the conclusions of the study. Descriptive geometry and engineering graphics is an important discipline in the successful training of a future specialist, since as a result of its study, students acquire knowledge of the basics of design documentation, the ability to perform various types of design activities and read drawings, the skills of design documentation when studying other disciplines of the field of training, the competence of an engineer able to read and issue design documents for manufactured products. Descriptive geometry and engineering graphics develop thinking by means of formation of knowledge, skills, and abilities as the basis for conclusions corresponding to the theoretical level of the student’s specialty training. Descriptive geometry and engineering graphics allows you to develop mental processes: perception (in the process of studying theoretical material and practical performance of tasks on engineering graphics), representation (a set of knowledge about the types of projection: central, orthogonal, axonometric) based on the type of task to perform, imagination (to construct figures or details in a drawing, it is advisable to imagine and construct lines of connection in order to correctly construct projections), memory (knowledge of the requirements of the Unified System for Design Documentation allows you to see the depicted types of design documentation, drawings of parts, etc.), speech (characterized by terms specific to a particular specialty or discipline), etc.

Modern preschool education is based on a personality-oriented model. Mathematics occupies a leading place in solving the problem of development of logical and mathematical ideas and skills in preschool children. It sharpens the child's mind, develops flexibility of thinking, teaches logic. In the pedagogical practice of a modern preschool institution, Dienes' logical blocks and Kuizener's wands are actively used by modern educators. The teacher's work with this material significantly contributes to the development of children's logical and mathematical ideas and skills.The set of Dienes blocks consists of 48 geometric figures of different colors (red, blue, yellow), shape (round, square, triangular, rectangular), size (large, small), thickness (thick, thin). There are no two identical figures in the set, each characterized by the four properties mentionedabove. Together with the logical blocks in the work of the educator of the preschool institution, cards are used on which the properties of the blocks (color, shape, size, thickness) are conditionally determined. The use of cards allows children to develop the ability to substitute and model properties, the ability to encode and decode information about them. These properties and skills develop in the process of performing a variety of subject-game actions. In the process of working with Dienes blocks in the game, children not only consolidate ideas about geometric shapes, signs of objects, form mental actions, but also develop mental processes: thinking, memory, attention, imagination, speech.Kuizener's sticks are didactic material for the development of children's mathematical abilities. The set contains quadrangular sticks of 10 different colors and a length of 1 to 10 cm (this can usually be stripes). George Kuizener designed sticks so that sticks of the same length are made in the same color and denote a certain number. The greater the length of the stick, the greater the numerical value it expresses. Sticks allow you to translate practical external actions into the internal plan; to master spatial relations. Didactic material gives the chance to train kids in addition of number from units and two smaller numbers; learn to measure objects; learn arithmetic operations (addition, subtraction, division, multiplication); learn to divide the whole into parts; to bring them to the realization of the relations "less – more", "less by ... – more by ...".In working with Kuizener sticks, the spatial and quantitative characteristics are not as obvious to children as color, shape, size when working with Dienes blocks. But to open these characteristics will help the joint activities of an adult with a child.

Applications of augmented reality are gradually being integrated into teaching at various levels and types of schools. Augmented reality has the potential to transform the training of future teachers in the context of developing their mathematical knowledge, digital skills, and teaching competencies. The paper focuses on researching the impact of augmented reality on the learning of future primary teachers. The aim was to investigate the impact of AR applications on the development of cognitive and psychomotor skills and on students' motivation to learn. The study had a mixed research design. Using a pedagogical experiment, we investigated the effectiveness of an educational intervention based on the use of applications Augmented Reality in combination with hands on activities in the training of future teachers. The educational intervention was a set of activities that were carried out in a mixed reality environment using the 3D solids construction kit, the Polyedres augmentes and GeoGebra applications. The content of the educational intervention was the exploration of significant elements and properties of solids. We tested students' knowledge and abilities in the following areas: identification of simple solids from a picture; identification of significant elements of solids (vertices, edges and faces); identification of the shapes of faces of solids; nets of solids; simple metric tasks with solids. The study was conducted in 2024 with 152 primary education students as part of geometry courses. In line with the results of previous research in this area, we found that AR has the potential to improve understanding of geometric concepts, increase interactivity and student motivation. Augmented reality opens up new possibilities for exploring solids and their properties, as it allows for transfer between planar and spatial representation of solids and helps to develop spatial imagination.

This article examines the global debates about indigenous knowledge and Africa’s traditional medicine from the pedagogy perspective. This study investigated the emergence of African traditional medicine with keen attention on understanding the learning/apprenticeship process and deducing pedagogic implications for adolescents’ learners in the North west Region of Cameroon. Specifically, the paper examined the extent, traditional medicine influence the development of cognitive skills in adolescents. The development of cognitive skills in late adolescents is marked by social competence, decision making, and problem solving. A conceptual review of the major concepts was done. Theoretically, the article was anchored on the social learning theory of Bandura (1977). A convergent parallel mixed method research design was used. The sample of the study emerged through purposive and convenient sampling techniques. A pilot study was done with 10 participants. Interviews were conducted with 15 elders and a questionnaire for 150 adolescents drawn from 6 villages in Oku Subdivision, namely: Elak, Jikijem, Lui, Manchok, Keyon and Simonkoh. Quantitative data was entered using EpiData Version 3.1 (EpiData Association, Odense Denmark, 2008) and analysed using the Statistical Package for Social Sciences (SPSS) Standard version, Release 21.0 (IBM Inc. 2012). Interviews and focus group discussions were transcribed verbatim. Each interview or focus group was prepared as a single primary document and assigned for coding and analysis in Atlas.Ti 5.2 software (Atlas.ti Scientific Software Development GmbH, Berlin, Germany). Statistically the weight of traditional medicine = 80.3%; Traditional medicine (R=0.382; P=0.000);. These are marked by alertness, critical thinking, decision making, social competence, problem solving, imagination, mathematical abilities, etc. From the study it is recommended that indigenous practices be taught formally in schools and that indigenous medicines be studied more keenly and upgraded.

Problem and goal. The article presents materials from a study of the problem of the influence of personal, psychofunctional qualities of students on the effectiveness of the formation of professional skills in visual activity. The study of the innate psycho-functional inclinations of perceptual perception on the process of forming students’ imaginative thinking makes it possible to improve the quality of learning and effectively implement the acquired skills to create an artistic image. The development of students’ creative abilities in the process of professional training allows them to develop an interest in independent intellectual activity and improve professional skills in creative activities. The purpose of the article is to study the influence of personal, psychofunctional qualities of students in the “Design” direction on the formation of professional skills in visual arts. Methodology. The study used methods for assessing the creative thinking of students: Personal creative characteristics of F. Williams (1980), E. E. Tunik. Self-organization of activities Mandrikova E. Yu. Assessment of students’ mastery of graphic skills was carried out according to generally accepted criteria for visual activity. The results obtained were processed by methods of mathematical statistics using the software package “Statistica 10.0 for Windows”. Studying the problem of developing the creative potential of the innate, creative inclinations of the individual allows us to solve the problem of developing professional skills in visual arts. The results of the study indicate that the formation of professional skills in visual arts is determined by individual, innate inclinations of creative thinking; imagination, curiosity, the ability to find new solutions and apply complex techniques when performing a drawing. At the same time, determination in combination with self-organization of educational activities is the basis for the effective development of artistic and professional skills. Conclusion. As a result of the study, it was found that the effectiveness of the formation of professional skills in visual arts among students is determined by the innate inclinations of creative thinking: purposefulness, focus on the present, attentive attitude to the technique of representation, in combination with self-organization of educational activities, such as a necessary condition for the effectiveness of mastering professional skills, at the same time, for students with a dominant, passive, sensory-emotional perception of the world around them, orderliness and perseverance, as indicators of self-organization of activity, have a relatively subjective nature of application in the process of visual activity.

The article deals with creative and development, corrective and rehabilitation opportunities of a tale to work with preschoolers. Under the urgent unsteady social and cultural conditions, a new line and trend of the native education development is being formed; it is originated in humanism and democracy, creativity and self-realization. The process is aimed at optimizing the cooperation between a personality, society and nature in the life creativity of every citizen, regardless of the development level, social status, mental and physical opportunities, etc. Thus, forming the content, teaching and upbringing forms and methods for the children play a significant role. These tools may provide for the effective revealing of their personalities, forming the ability to think creatively, independently make customized solutions, perform a flexible reaction on the changes under the conditions of a radical restructuring of every spheres of the society life.The problem is actualized by a rapid mental health deterioration of children that is caused by traumatic events of the brutal war of aggression of rf against Ukraine. Most children suffer from anxiety disorder, post-traumatic stress disorder (PTSD), depression, dissociative and behavioral disorders. Since, it is the education system which is designed to both develop a creative, socially active and harmoniously developed personality and provide an everyday social and psychological, as well as an emotional support for children. Here it is a teacher of a preschool institution in the center, who should possess these universal methods, tools, techniques of a creative development of preschoolers and being oriented on their corrective and rehabilitation opportunities. A tale is among the integrative tools of creative abilities development of a child, correction of the internal deformations and harmonization of his relation to the external world.Based on a tale use in an educational process at a pre-school institution, the authors determine creative and development functions of a tale, that include expanding the range of abilities (cognitive, intellectual, specific: artistic, literary, mathematical and others) and individual features (emotionality, courage of imagination, fantasy, intuitivity, etc.) of the children; they are getting visible and rich at the practice of different constructive activity, which results are described as new and original. Corrective and rehabilitation opportunities are also proved. They comprise the reflection of a child’s internal world, the consideration of complex phenomena and feelings, identification of his emotional status with the hero, comprehension of the problem and its solution, mastering the constructive variants to solve conflicts, the behavior change, emotional reactions, social communicative skills, learning moral standards

This study aims to determine: Showing an interactive learning media of mathematics on students' mathematical communication skills as a whole, The magnitude of the influence of using Geogebra-based interactive learning media on mathematical communication abilities based on educational level, the magnitude of the effect of using interactive mathematical learning media on mathematical communication skills based on previously used interactive learning media, the large influence of the use of interactive learning media plays an important role in systematic mathematical methods, the large effect of the use of interactive learning media on mathematical communication skills is imaginative to mathematical communication based on the mathematical ability that is measured. This study uses the addie model. This sampling technique is highly influential using the Addie model and obtained 20 studies that match the criteria. This data collection technique uses freetest and posttest with the help of Geogebra Classic 6 software and the help of Microsoft powerpoint. The results of this data experiment show that: overall this interactive learning media has a major influence on students' mathematical communication abilities.

In this article the principles of developing students' imagination and creative thinking in education are discussed. Special emphasis is placed on the fact that people have different thinking abilities, intellectual abilities. The comments on creative thinking in the article are analyzed on the basis of the epics in the work "Khamsa" by the great thinker of Uzbek classical literature Alisher Navai.

Purpose of the study: This research aims to develop and evaluate the effectiveness of POE-based (Predict, Observe, Explain) student worksheets using a Metaphorical Thinking approach to enhance the mathematical reasoning abilities of class 9 students at Public Middle School. Methodology: This research aims to find out how to develop student worksheets based on POE (Predict, Observe, Explain) through a Metaphoral Thinking approach oriented towards the mathematical reasoning abilities of junior high school students in class 9 and find out the effectiveness of student worksheet products based on POE (Predict, Observe, Explain) through Metaphoral Thinking approach to the mathematical reasoning abilities of Public Middle School 7 Banjit students in class 9. Main Findings: Validation results showed material experts rated the worksheets at 89.4%, media experts at 94.9%, and language experts at 75%, all with high appropriateness. Small group trials averaged 86%, field trials 87%, and educator trials 97.2%, all with very good criteria. The paired t-test (thitung = 12.7 > ttabel = 2.02) confirmed the effectiveness of the POE-based worksheets using the Metaphorical Thinking approach in enhancing mathematical reasoning abilities.. Novelty/Originality of this study: The novelty of this study lies in developing and validating POE-based student worksheets integrated with a Metaphorical Thinking approach to enhance junior high students' mathematical reasoning. This innovative strategy combines cognitive and imaginative techniques, fostering deeper comprehension and problem-solving skills.

Background. The study of cultural congruence as a personality trait responsible for the regulation of adolescent behavior in relation to the rules typical for this age is one of the important tasks for developmental psychology. The range of rules despite its diversity has an invariant series. This invariant part of diversity is specific for each age stage. the contradiction between the need to follow generally accepted rules and conditions for the development of creativity associated with atypical and original products of creative activity makes up the problem of studying cultural congruence of creative teenagers. There is a lack of research on the relationship between two diametrically opposed psychological qualities of adolescents: cultural congruence and creativity. The objective of the study is to analyze the correlation between cultural congruence and creativity; as well as to study the influence of divergent thinking on the cultural congruence in adolescents. Sample. The research was conducted in 4 stages between March 2021 and March 2022 and involved 272 adolescents, ages 13 to 16 (М = 14.21; SD = 1.02), (139 male and 133 female). Students of 7th, 8th, and 9th grades at four lyceums in Kazan took part in the study. Methods. The methods included the test of divergent creative thinking (F. Williams, modified by E.E. Tunik, 2003), the questionnaire to diagnose the level of cultural congruence for adolescents (L.F. Bayanova, O.G. Minyaev, 2016), the test to identify creative abilities (H. Zievert, 1998). The study assessed the following parameters: curiosity, imagination, risk-taking, self-discipline, quick-thinking, divergent thinking, cultural сongruence as the ability to control behavior regarding the rules typical of the social situation of development in adolescence. Mathematical data processing was carried out using methods of descriptive statistics, Pearson correlation coefficient (r), Cheddock scale, the one-way analysis of variance (ANOVA). Results. The research of the indicators of divergent thinking, creative characteristics, and cultural congruence of adolescents concludes that of the variety of dichotomous relations, a significant inverse correlation was found between the structural component of cultural congruence, i.e., “safety” and divergent thinking (confidence level is 95% (p ≤ 0.05; r = –12). It provides a partial confirmation of the hypothesis. The final stage of the research included an analysis of variance using the one-factor ANOVA method. Following the results of the analysis, it was found that the influence of divergent thinking on the cultural congruence of adolescents is not significant. Conclusion. The data obtained indicate a weak correlation of the ambivalent factors, i.e., creativity and cultural congruence. The results show an inverse correlation between creativity and the “safety” scale of the method for diagnosing the cultural congruence for adolescents. The revealed ambivalence of the studied indicators distinguishes the nature of correlations, identified previously in the study of behavior regulation and creativity of preschool and primary school children.

Введение. Представлена актуальность формирования метапредметности, реализуемой на межпредметном содержании в системе основного общего образования и являющейся необходимой в настоящее время обществу в наукоемких производствах любого профиля. Показана необходимость формирования у современного педагога, в том числе и школьного учителя математики, физики и технологии, компетенций, относящихся к основам инженерной деятельности, обязательными из которых являются графическая культура и графическая грамотность. Цель исследования состоит в выявлении межпредметных линий между математическими, естественно-научными и техническими учебными дисциплинами, способствующих формированию у обучающихся компетенций, относящихся и к инженерной деятельности, таких как графическая культура и графическая грамотность. Материал и методы. Представлено обобщение авторами опыта преподавания ряда курсов инженерной направленности, таких как графика, инженерное проектирование, прикладная математика, техническая механика, для будущих инженеров и учителей физики и технологии. Проведен анализ нормативных документов по проблеме исследования. Результаты и обсуждение. Анализ нормативных документов, регламентирующих учебный процесс будущих учителей математики, физики и технологии, показал, что содержание теоретического материала и обсуждение прикладных аспектов данных учебных дисциплин не учитывают требования к формированию графической культуры и графической грамотности. В современных условиях повсеместного введения в школах профильных инженерных классов, помимо профессиональных компетенций педагога, учитель математического, естественно-научного и технологического циклов дисциплин обязан обладать компетенциями, относящимися и к инженерной деятельности, такими как графическая культура и графическая грамотность. Для формирования компетенций, связанных с графической грамотностью, в процесс подготовки учителей математики, физики и технологии в рамках профессионального цикла в качестве дисциплин по выбору должен быть введен модуль «Графика / Инженерное проектирование», в который входят такие учебные дисциплины, как черчение, инженерная графика, элементы аналитической геометрии, компьютерная графика. Таким образом, появится возможность создания межпредметных линий между учебными дисциплинами математического, естественнонаучного и технологического циклов дисциплин, что в свою очередь позволит в дальнейшем формировать метапредметность всего образовательного процесса будущих учителей. Заключение. Формируемая метапредметность образовательной среды для студентов педагогического университета, обучающихся по направлению подготовки 44.03.01 «Педагогическое образование» (направленность (профиль) «Математика», «Физика», «Технология»), позволит в дальнейшем учителям согласованно формировать и развивать у обучающихся школ пространственное мышление, воображение, творческие способности, наблюдательность, необходимые в их дальнейшей профессиональной деятельности. Introduction. The article presents the relevance of forming a meta-subject matter that is implemented on an intersubject content in the system of basic General education and is currently necessary for society in high-tech industries of any profile. The article shows the need for a modern school teacher of mathematics, physics and technology to develop competencies related to the basics of engineering, which are mandatory for graphic culture and graphic literacy. The purpose of research is to identify intersubject lines between mathematical, natural science and technical academic disciplines that contribute to the formation of students‘ competencies related to engineering, such as graphic culture and graphic literacy. Material and methods. The article is based on the authors generalization of the experience of teaching a number of engineering courses for future technology teachers directly related to their future professional activities. The analysis of normative documents on the research problem is carried out. Results and discussion. The analysis of normative documents regulating the educational process of future teachers of technology has shown that the content of the theoretical material, as well as the practical part of such fundamental disciplines as physics and mathematics, does not take into account the applied aspects of this direction of training students of pedagogical universities. In modern conditions of the introduction of specialized engineering classes in schools, in addition to the professional competence of the teacher, the teacher of mathematical, natural science and technological cycles of disciplines must have competencies related to engineering, such as graphic culture and graphic literacy. To form competencies related to graphic literacy, the module «Graphics / Engineering design» was introduced into the process of training technology teachers within the professional cycle as a discipline of choice, which included a block of such disciplines as drawing, engineering graphics, elements of analytical geometry, computer graphics. Thus, it became possible to create inter-subject lines between the academic disciplines of mathematical, natural science and technological cycles of disciplines, which in turn will further form the meta-subject of the entire educational process of future technology teachers. Conclusion. The formed meta-subject of the educational environment for students of pedagogical University studying in the direction of training 44.03.01 Pedagogical education, directions (profiles) of mathematics, physics, technology will allow teachers to consistently form and develop spatial thinking, imagination, creative abilities, observation of students necessary in their further professional activities.

Specialists in the field of programming create a huge flow of software, which is mainly aimed at attracting children to specific software products that have a developing effect, rather, as a side effect. The developing effect is not diagnosed in such programs, but it is often declared by the developers. Scientific and methodological response of the pedagogical community to information challenges in the field of preschool education was the creation of the methodology of author's children's animation and the corresponding educational module. In the article two important competences of preschool children are considered, which are basic in relation to many other competences formed at an older age: developed imaginative thinking and developed research abilities. The development of these competences projects as a methodical waymark for the technical development of the methodology of author's children's animation.Thereby, the purpose of the article is to justify the creation of methods for author's children's animation that determines the development of imaginative thinking and research abilities of preschool-age children, taking into account the requirements of the modern information society.To achieve this goal, the following methods were used: content analysis; method of contrastive-comparative analysis of scientific and methodical materials; method of system analysis; method of mathematical and statistical data processing; expert appraisement, generalization of research results.Based on the results of the study, the theoretical foundations of the preschool-age child's competence were determined, a pilot study of the development of preschoolers' competencies, the development and introduction of the educational module "Multstudio I CREATE THE WORLD" into the practice of pre-school pedagogy as a potentially effective means of developing imaginative thinking and research abilities of children, development of recommendations for software providing multstudios in kindergarten.

This paper introduces Single Valued Refined Neutrosophic Set (SVRNS) which is a generalized version of the neutrosophic set. It consists of six membership functions based on imaginary and indeterminate aspect and hence, is more sensitive to real-world problems. Membership functions defined as complex (imaginary), a falsity tending towards complex and truth tending towards complex are used to handle the imaginary concept in addition to existing memberships in the Single Valued Neutrosophic Set (SVNS). Several properties of this set were also discussed. The study of imaginative pretend play of children in the age group from 1 to 10 years was taken for analysis using SVRNS, since it is a field which has an ample number of imaginary aspects involved. SVRNS will be more apt in representing these data when compared to other neutrosophic sets. Machine learning algorithms such as K-means, parallel axes coordinate, etc., were applied and visualized for a real-world application concerned with child psychology. The proposed algorithms help in analysing the mental abilities of a child on the basis of imaginative play. These algorithms aid in establishing a correlation between several determinants of imaginative play and a child’s mental abilities, and thus help in drawing logical conclusions based on it. A brief comparison of the several algorithms used is also provided.

We discuss the BCI based on inner tones and inner music. We had some success in the detection of inner tones, the imagined tones which are not sung aloud. Rather easily imagined and controlled, they offer a set of states usable for BCI, with high information capacity and high transfer rates. Imagination of sounds or musical tunes could provide a multicommand language for BCI, as if using the natural language. Moreover, this approach could be used to test musical abilities. Such BCI interface could be superior when there is a need for a broader command language. Some computational estimates and unresolved difficulties are presented.

High school students face critical psychological challenges during adolescence, including academic pressures and educational decision-making. Dabrowski’s Theory of Positive Disintegration provides a framework for understanding growth through disintegration and reintegration, with perfectionistic traits acting as intrinsic motivators for self-improvement. This study examined the psychological profiles of 641 Taiwanese high school students: 207 mathematically and scientifically talented students (MSTS), 187 verbally talented students (VTS), and 247 regular students (RS). Using the ME III, refined from the ME II, and the Multidimensional Perfectionism Scale, our research assessed overexcitabilities (OEs) and perfectionism traits. MSTS and VTS scored significantly higher in Intellectual and Imaginational OEs than RS, with VTS also overperforming in sensual OE. MSTS and VTS showed higher personal standards, while VTS excelled in organization, and RS reported higher parental criticism. Emotional OE correlated with perfectionism, such as concern over mistakes, doubts about actions, and parental criticism, while Intellectual OE positively correlated with personal standards and negatively with parental criticism. Intellectual and Emotional OEs jointly predicted personal standards and organization; while Sensual, Intellectual, and Emotional OEs predicted doubts about actions, etc. These findings underscore the importance of tailored educational and counseling strategies to address the unique needs of gifted students, fostering environments that enhance their abilities and overall well-being.

This theoretical article examines the crucial role of play-based learning (PBL) in enhancing the mathematical skills of children in the Early Childhood Phase, referred to as Foundation Phase (Grade R-3) learners, within a South African context. The article argues that the traditional approach to teaching early childhood mathematics, where teachers typically instruct while learners listen and repeat, is often rigid and lacks engagement. For learners to thrive in mathematics and truly comprehend the subject, they need to be actively involved in ‘doing’ mathematics. PBL is an approach to teaching and learning that uses various forms of play as a medium for learning. The objectives of the article are: a) to explore alternative methods for teaching mathematics to learners in the Early Childhood Phase, and b) to highlight the benefits and value of play as a mode for teaching and learning mathematics. As a theoretical paper, it does not include a methodology section; rather, relevant literature was analysed to support and justify the claims and to address the research questions. The study found that PBL can enhance the development of the vestibular system, which can positively impact learners’ cognitive abilities, including mathematical skills. The study is significant for both learners and teachers in the Early Childhood Phase, as it provides an opportunity for teachers to utilise alternative, play-related, and enjoyable methods to teach mathematics. The paper concludes that a child-centred, play-based curriculum encourages and promotes learning in a playful setting through discovery, investigation, problem-solving, imaginative thinking, and creative thinking.

Multiple criteria decision making methods have received different extensions under the uncertain environment in recent years. The aim of the current research is to extend the application of the MULTIMOORA method (Multiobjective Optimization by Ratio Analysis plus Full Multiplicative Form) for group decision making in the uncertain environment. Taking into account the advantages of IVIFS (interval-valued intuitionistic fuzzy sets) in handling the problem of uncertainty, the development of the interval-valued intuitionistic fuzzy MULTIMOORA (IVIF-MULTIMOORA) method for group decision making is considered in the paper. Two numerical examples of real-world civil engineering problems are presented, and ranking of the alternatives based on the suggested method is described. The results are then compared to the rankings yielded by some other methods of decision making with IVIF information. The comparison has shown the conformity of the proposed IVIF-MULTIMOORA method with other approaches. The proposed algorithm is favorable because of the abilities of IVIFS to be used for imagination of uncertainty and the MULTIMOORA method to consider three different viewpoints in analyzing engineering decision alternatives.

Nail art is an artistic activity that requires creativity and skill, reflecting individuality and taste by applying various colors and designs to fingernails. However, due to the limitations of human imagination, knowledge, and technical abilities, it can be challenging to continuously generate new ideas or create intricate and flawless designs. Recently, advances in artificial intelligence (AI) technology have led to the development of AI systems capable of generating images based on user input. These AI technologies can produce realistic, sophisticated, and creative images by interpreting textual prompts. As a result, they have found applications in various fields. In this study, we utilized image-generating AI models such as ‘DALL-E 2’ and ‘Bing Image Creator’ to analyze nail art designs generated based on textual prompts. We demonstrated that the type and content of prompts significantly influence the performance and output of image-generating AI models. By using AI technology as a supportive collaborator for nail artists, we can positively leverage its capabilities to enhance the diversity and quality of nail art designs. This will not only aid nail artists in their work and skill development but also contribute to the advancement of the nail industry by elevating the diversity and quality of nail art designs.

Creative thinking is important in increasing the formation and discovery of learning ideas in the 21st century. The 21st century is closely related to the era of the industrial revolution 4.0 which requires humans to have the ability to think more creatively and be able to accept rapid technological developments. Through education and learning, the ability to think creatively can be improved for the better. The ability to think creatively which is one of the cognitive abilities in learning activities needs to be developed. When the ability to think creatively develops, it will give birth to ideas, find interrelated relationships, create and carry out imaginations, and have many perspectives on things. Students who have high creative thinking skills tend to feel challenged and interested in solving various problems in learning. Interest in solving this problem also causes curiosity. A student with mathematical creative thinking has the ability to be able to solve problems he encounters in new or unusual ways. The tendency of mathematics teachers to dominate learning results in low student activity so that they do not provide opportunities to be directly involved in scientific activities. These conditions have an impact on students' limited opportunities to think creatively in finding new information or ideas from the learning process, it is necessary to increase creative thinking in learning which can be done in various ways.

Abstract Many non-native and native speakers all around the world have proven that English is an international language. It is sometimes referred to as the global language since it is the primary means of communication across countries. In our nation, the usage of English as a common language play an essential role in education. English learners must place strong emphasis on the use of communication. The ultimate goal of language instruction is to improve communication skills. Pragmatics is the method in which meaning is transferred through communicating, and linguistic skill is regarded as an instrument for communication. Pragmatic competence is the capacity to comprehend and communicate meanings that are more correct and acceptable for the cultural and social contexts in which communication takes place. Even though English is used at many levels of communication, the speakers must be familiar with a variety of pragmatic components to create coherency and the capacity to react in a variety of scenarios. As a result, one of the key aims in the field of education should be the development of pragmatic ability and also help for future understanding. <strong>Keywords</strong>: <strong>&nbsp;</strong>Communication, communication skills, English, language, literature &nbsp; <strong>Received-</strong>03 /12 /2025,<strong> Accepted</strong>-18 /01/2025,<strong> Published Date</strong>-31 /01 /2025 &nbsp; &nbsp; <strong>&nbsp;</strong> &nbsp;Introduction Communication is a talent that allows one individual to collect and transfer pieces of information to another. So, communication in English is a talent that can only be perfected by consistent practice and acquaintance with the target languages. This talent is beneficial in broadening pupils' comprehension abilities. If a person is to attain his or her purpose, he or she must be able to communicate successfully with others (P. Chairat 2016). Different strategies can be use to improve communication. Listening literature, particularly poetry, is one of the strategies. Seeing life through the eyes of someone else may also be beneficial. Poetry is a concise language that communicates a wide range of emotions. It provides the reader with joy. It helps pupils improve their speaking abilities. It is a tool that may be used depending on the pupils' attitude. It encourages people to express their opinions and views regarding difficult societal topics. Poetry is an important part of language instruction. Poetry is the actual content that aids in the student's grasp of the language they are attempting to acquire. The researcher's main goal is to improve students' verbal communication skills through teaching poetry in the classroom ( M. D. Mehra 2013). In actuality, businesses evaluate newly recruited graduates' professional competence, although it is the primary criteria for educational excellence (M. Ilankumaran and P. Deepa 2018). With the foregoing in mind, and as far as everyone&lsquo;s is worried, a large number of recent research and educations have absorbed more on graduate employability and professional competence (like critical, problem-solving, leadership, and teamwork skills) than on English communication skills needed and used in there al workplace. However, the afore mention is unsuitable for preparing English main graduates for future careers, predominantly those who are not natural English speakers. It'ssafetoassumethatoncethey'vecompletedtheirdegree,they'llpursuecareersthatneedthemto use the English language (G. Charyulu 2015). As a result, it is evident that the graduates' English communication abilities are crucial and widely anticipated by businesses and organizations. As a result, universities and academic instructions are likely to place a greater focus on professional competence and employability skills. Literature is about letters, phrases, words, sentences, essays, paragraphs, and tales, among other things. The author must concentrate on all of these areas of knowledge when learning a language. Ideas, views, sentiments, and facts to communicate with others for personal or professional reasons are all part of communication. Literature is the same way (M. Ilankumaran and P. Deepa 2018). Literature is the heart of language is the mind. The lexicographical, grammatical, and syntactical systems that makeup language. Anyone who wants to improve their communication skills should concentrate on language. In general, there are three sorts of communication (S. Kuroda and I. Yamamoto 2018). &middot;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Visual communication &middot;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Verbal communication &middot;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Auditory communication The author needs greater verbal communication abilities in our professional communication than visual and oral communication. Author focus on literature rather than raw, lifeless phrases as models of grammar to enhance our English. One must concentrate on the fundamental notions of that language. Concentrate first on the alphabet, tiny word lists, word groupings, sentences, phrases, and storey paragraphs (M. S. Kaper 2018). Improve your languages skills by telling mythical, magical, or legendary stories. Stories are the most effective way to improve one's analytical and cognitive abilities. Stories give ample room for the creative process to flourish. People used to practice their linguistic skills by listening to legendary stories and relaying them to others. However, tales are no longer part of the academic curriculum, and youngsters are unaware of the importance of literature. Even parents believe that fiction is a fun way to spend time. It's pointless. It is, in fact, a misunderstanding. Only through reading and listening to literature can we improve our command of the English language and our communication abilities (A. V. Basantes, M. E. Naranjo, M. C. Gallegos, and N. M. Ben&iacute;tez 2017) . The internet has offered up new avenues for knowledge enhancement through communication. We can't separate the Internet from English. They've mixed. Modern technology has produced a Digital World in which people may communicate quickly via email, chat, video conferencing, mobile interviewing, net banking, and online shopping, among other methods. In today's world, man lives in a digital world (P. Deepa and M. Ilankumaran 2018). His needs are for cutting-edge technology. Computer technology and the English language are the two most important instruments for connecting the entire world. These are both technical and communication tools that work well. Nowadays, technical communication abilities are required in the business, educational, and career domains. Everyone used to be different, but today we are all referred to as global citizens. Students have become global students, and their occupations have become global occupations. These days, if an educated individual does not know English or how to use a computer, he is referred to be an illiterate (M. Reza Ahmadi, H. Nizam Ismail, and M. Kamarul Kabilan Abdullah 2013). The basic function of a language is to be spoken rather than written. So, written languages are the most valuable resource for retracing the cultures, societies, and lifestyles of earlier generations of people and races (S. Shrestha, S. Parajuli, and U. R. Paudel 2019). The English language is not static; it is always expanding into new domains and notions (K. B. Haskard Zolnierek and M. R. Dimatteo 2009). The Anglo-Saxon language only had roughly 20,000 term sinitsrepertoire.There are approximately 4,00,000 words in the contemporary Oxford Dictionary. The majority of the vocabulary used by the Anglo-Saxons came from their German predecessors. Any living language, such as English, has a large vocabulary and allows easy exploration of new concepts, people, and regions. The old world had lost its sense of self (B. Crosbie, M. Ferguson, G.Wong, D. M.Walker, S.Vanhegan, and T. Dening 2019). It was first used under the British government's rule. People write Telugu and speak Telugu, and people in others tates speak and write their respective languages; in fact,our country was separated based on linguistic modifications. Our mother tongue is used in our daily conversations. Only our language allows us to communicate our thoughts, ideas, and expressions. As a result, the mother language impact dominates our ability to communicate smoothly and successfully in English (M. C. Paretti, A. Eriksson, and M. Gustafsson 2019). The acquisition of spoken language occurs naturally as a result of the culture. We are unable to speak English in the manner of an Englishman since we were not born in that nation or culture. Rather than spending time and energy imitating the English at ion and dialect, aim to rapid and convey faultless English for common understanding and communication with the rest of the globe. <strong><em>1.1&nbsp; </em></strong><strong><em>Role of English Grammar to Enhance Communication</em></strong> Grammar is a necessary component of efficient English learning. In written communication, grammar is extremely important. To write excellent English, one must understand the law of grammar. Professional graduate students must write competent English to advance in their careers. Because the world has changed dramatically, English grammar must also evolve. Indian students find it challenging to adhere to different language laws and restrictions. The Greek and Latin Classical Languages gave birth to the English Lexicon and its structure. The rules of British English haven't altered in a long time. As a result, the Global Student looks for choices. Fresh developments, such as the Internet and e-mail, provide him with a new road to English mastery (G. Papanastasiou, A. Drigas, C. Skianis, M. Lytras, and E. Papanastasiou 2019). Even yet, English teachers and textbooks continue to use age-old English spelling rules, word order, punctuation, and grammar rules (K. Bombeke 2012). Students that are interested in technology are on the lookout for reality and are eager to learn. Because of their high intelligence quotient <strong>(</strong>IQ) scores. So it's time to revise English grammar using the most up-to-date technology; otherwise, grammar would only exist in English textbooks and the surnames of English teachers. Our Prehistoric Civilization has bestowed a magnificent gift onto us. It is written in Sanskrit. It has become drowned in the Global World due to its Conventional Grammatical Rules. The threat to the British English languages comes not from people, but modern communication technology. Sanskrit, Greek, and Latin, the world's three Classical Languages, have all but perished due to their Conventional Lexicon and Grammar (K.S. Juma, D.M.A. Raihan, and D. C. K. Clement 2021). <strong><em>1.2&nbsp; </em></strong><strong><em>Need of English Language</em></strong> During the British administration, Macaulay brought English into our educational system. Since that time, English has been an integral element of our culture. It is a necessary commodity in the fields of business, commerce, education, and employment. In India, the British Empire has crumbled, but the English Empire has flourished. Leaders and citizens created slogans against English during the American Revolution, claiming that it should be prohibited. However, it continues to thrive not because of its structure, but because of its adaptability. These two terms cannot be separated; they are synonymous. Globalization gave birth to the new world. Computer technology and the English language are the two fundamental components that connect the whole globe (D. Khashimova, N. Niyazova, U. Nasirova, D. Israilova, N. Khikmatov, and S. Fayziev 2021). These are both technical and communication tools that work well. Students have become global students, and their careers have become global careers. "Public Speaking" is a different type of speech. In public speaking, a speaker addresses a large group of people on a certain topic. The speaker and his or her information are given first attention in this procedure. Electronic communication is another mode of communication. This method includes using cell phones, voice mails, e-mails, and chatting. Any type of communication is solely to share information with others. It is the most alive and effective kind of communication compared to other forms of communication. "Reading makes a man perfect,"says one author. It's a common phrase used to emphasize the necessity of good reading abilities. What motivates us to read? The basic goal of reading is to understand the meaning of each paragraph in a book. We simply read books to gather information and knowledge. As a result, books are the future generations' treasures of ancient man's wisdom. There are several sorts of books. Reading may be done in a variety of ways, including word-to-word reading, skimming, and scanning. These are the several methods for reading a book. The author looks through a paragraph to see what information or concept we're seeking for using this strategy. It's all about looking for something in a book rather than learning everything there is to know about that book. These are the several methods for reading a book. To strengthen your ability to provoke thinking, try reading at least a paragraph every day. Another advantage of reading is that it improves your vocabulary and linguistic skills. Individuals' thoughts, clarity, and meaning increase as a result of reading. Writing Ability: "Writing creates a precise guy. "Amongthethreetalentsoflistening,speaking,andreading,writingisthemostchallenging.Itisa a thought-provoking activity. It is an everlasting document. Stones were used to writing on in ancient times. Lithography was the name of the process. They later began writing on animal hides. Later, the Chinese created paper. After a few years, Gut ten Burg devised the printing press, which revolution the writing system. Newspapers, periodicals, and many types of printed books were created. Reading,Writing,Listening,and Speaking are the four forms of communication that we must master to communicate effectively. And I feel that if we read more, we will be able to enhance our writing, listening, and speaking skills. I'm sure we all do a lot of reading for work. Reading literature that is not immediately relevant to our profession, however, is also necessary, in my opinion. Reading books on numerous themes helps one's general knowledge, imagination, and creativity, among other things, in addition to vocabulary and grammar. These advantages can also aid in bridging gaps between team members from various countries in dispersed teams. It's not simple to get into the habit of reading since we're continually catching up with our fast-paced and chaotic lifestyles. Apart from professional competency and employ-ability skills, academic institutions should emphasize and teach workplace communication skills in English to boost English major graduates' capabilities and capacities to satisfy labour market expectations and requirements. As a result, university language programs must be designed to provide appropriate practice in listening, speaking, reading, and writing abilities. These abilities are equallyvital,and students typically practice them in different combinations or all at once.""Effort should be made to ensure that what is taught in the course is related to authentic office situations to ensure that the students' professional communication skills are practiced according to the requirements of employers, and match the requirements of employers," the same researchers added.‖ Every literary person is aware of the concepts of language and literature. They are, nevertheless, the most popular way to acquire language. The importance of literature in the language classroom cannot be overstated. It not only entertains readers but also helps them gain experience and develop critical thinking skills. 2.&nbsp; DISCUSSION Both literary and linguistic talents are valued equally in English Literature and Communications degrees. The curriculum aims to teach students how to critically connect with a variety of genres through a variety of texts from across the world. The communicative English curriculum social circumstances as well as various cultural and literary traditions. When you go through the curriculum, you'll see that, in addition to English literature, you'll learn about mass media communication, journalism, philosophy, travel, and tourism. This one meal contains a lot of variety. It also attempts to provide pupils with the chance to improve their communication abilities. While the courses include a broad range of skills for particular corporate and creative areas such as advertising, business, and public service, they also aim to prepare students for further education in the field. The program's overall goal is to develop autonomous learners with the creative, critical, and analytical abilities needed for lifelong learning. <strong><em>2.1&nbsp; </em></strong><em>Important About Communication Skills</em> Some pundits expected that the website would herald at the end of human written correspondence, but the reality is very different. Texting, social networks, and email are all becoming increasingly popular forms of communication. Misunderstandings are more likely when there is more communication. Take into account the multiplying effect of social media. With with a few clicks, what you used to say to only a few people may suddenly be broadcast to hundreds of millions. In this paper, the author discuss why English communication skills are so crucial, as well as some recommendations for meeting today's communication needs, whether English is your first language or you're studying it as a second. You'll also learn about how the National University can assist you in improving your English abilities through our ESOL (English speakers of other languages) program or our English and communication degree options. 3.&nbsp; Conclusion The prose is the most effective instrument for learning English and Prose has built-in grammar. As a result, students may quickly learn Prose Topics. Words, nouns, verbs, punctuation, phrases, and sentences make up prose. Grammar should be taught in conjunction with Prose Paragraphs rather than individually. Students study Grammatical Assemblies in a highly efficient manner. Prose instruction nowadays is mechanical and serves no use. But it serves a greater purpose than simply explaining and translating it. Mathematical Applications are analogous to English Language Prose. Every single word and sentence is true and correct. As a result, it should not be squandered by translating. If a student masters prose, he will naturally master English communication skills. Professionals that are fluent in English are in high demand in today's job market. The four regions of English should be learned to gain command of the language. Listening, Reading, Speaking, and Writing is the four branches of the English language. These four abilities are referred to as communication skills. Speech is more significant than writing in language learning. The author uses Spoken Language to share our opinions regularly. To talk successfully, students need to master basic grammar rules and this rule help for better future communication skills.

This study aimed to describe the comparison analysis of part, whole, and imagery learning method in basketball games. The whole section method is generally used by an educator to teach a form of movement skills that is quite difficult or complex. This method is very helpful for Physical Education Sports and Health (PJOK) teachers in carrying out teaching and learning processes specially to help students who have difficulty learning a series of movements that are just known and have a high degree of difficulty. To anticipate the complexity and diversity of the movements, it is necessary to make a kind of simplification in advance of the movements to be learned into parts so that they are easily understood and learned by students. This approach will be good (effective) if the parts per part of the movement studied are understood or mastered first then combined into a whole movement, but on the contrary it becomes ineffective if students directly learn the movement in a whole direction. The overall learning method is a form of learning skills that are carried out in full from the skills learned, this is the opposite of the parts-by-part method because in this learning method physical education educators from the beginning of the students have been directed to carry out the desired motion activities and generally the motion activities this is easy for students to do. This study used 37 students, the findings of the research conducted were that predicting the future using the method of imagination is highly dependent on student abilities and characteristics of motor skills.

ABSTRAK&#x0D; The purpose of this study is to analyze making educational toys to develop children's creativity. This research was conducted at AL-KAMAL Kindergarten. The study was conducted as many as 10 children. The research method used is descriptive qualitative. Data obtained from interviews, observations and documentation sourced from RA Al-Kamal. Where the ten children have shown progress where this can be seen from the activities we have carried out that have gone well. Children are very enthusiastic in the activity of making these educational toys, children also participate as children participate in coloring and helping in choosing colors, and also sticking. Children ask questions related to these activities, children also observe each of these activities. Creativity is a person's ability to express ideas or ideas in the form of works. The results of the research conducted on 10 children, there were 7 children who had increased their creativity in making the game, and the remaining 3 children did not show increased creativity because they did not understand the goals and objectives to be achieved, and also afraid of doing wrong. So in conclusion, making educational toys actually increases creativity for children, children become more creative in thinking, children have high curiosity and initiative, and also have abilities that are rich in imagination.&#x0D; &#x0D; Keywords : MAKE EDUCATIONAL TOYS TO DEVELOP CREATIVE CHILDREN&#x0D; &#x0D; ABSTRAK &#x0D; Tujuan dari kajian ini adalah untuk menganalisis membuat mainan edukasi untuk mengembangkan kreativitas anak. Penelitian ini dilaksanankan di TK AL-KAMAL. Penelitian dilakukan sebanyak 10 anak. Metode penelitian yang digunakan adalah kualitatif deskriptif. Data yang diperoleh dari hasil wawancara, observasi dan dokumentasi yang bersumber dari RA Al-Kamal. Dimana kesepuluh anak tersebut sudah menunjukkan perkembangan dimana hal ini dapat di lihat dari kegiatan yang telah kami lakukan berjalan dengan baik. Anak sangat antusias dalam kegitan membuat mainan edukasi tersebut, anak juga berpastisipasi seperti anak ikut mewarnai dan membantu dalam memilih warna, dan juga menempel. Anak menanyakan hal-hal yang berkaitan dengan kegiatan tersebut, anak juga mengamati setiap kegitan tersebut. Kreativitas adalah kemampuan seseorang dalam menuangkan ide atau gagasannya yang dituangkan dalam bentuk karya. Hasil penelitian yang dilakukan kepada 10 anak, terdapat ada 7 orang anak yang sudah meningkat kreativitas nya atas pembuatan permainan tersebut, dan sisanya ada 3 orang anak lagi yang tidak menunjukan meningkatkan nya kreativitas nya karena ia kurang memahami tujuan dan sasaran yang akan dicapai, dan juga takut berbuat salah. Jadi kesimpulannya, dari pembuatan mainan edukasi ternyata memang meningkatkan kreativitas bagi anak, anak jadi lebih kreative dalam berpikir, anak memiliki rasa ingin tahu dan inisiatif yang tinggi, dan juga memiliki kemampuan yang kaya akan imajinansi. &#x0D; Kata Kunci: MAKE EDUCATIONAL TOYS TO DEVELOP CREATIVE CHILDREN

The preschool period is an important phase of child development, which includes cognitive aspects, especially in terms of growth and creative thinking, but many teachers still use conventional learning strategies. This study aimed to investigate effective teacher strategies for improving creative thinking in preschool children in a multiliteracy-based learning environment. The research method used a qualitative approach with a multisite case study research involving a kindergarten school. The informants were selected using a purposive sampling technique involving nine informants, including teachers, assistant teachers, and school principals. The research findings show that implementing the strategy steps can create a dynamic and creative learning environment that supports literacy development in various contexts. Factors such as competent teachers, access to resources, and management of barriers shape an effective multi-literacy environment. The positive impact motivates students to continue thinking creatively and exploratively. The multiliteracies approach enhances preschoolers' creativity through purposeful strategies, teacher collaboration, resource support, and the use of diverse media, which empowers literacy in education. Keywords: creative thinking, multiliteracy, teacher, preschoolers References: Auris Villegas, D., Colquepisco Paucar, N. T., Cuba Garcia, S., &amp; Vilca Arana, M. (2021). Revista Innova Educación. Revista Innova Educación, 3(1), 6–19. Behnamnia, N., Kamsin, A., Ismail, M. A. B., &amp; Hayati, A. (2020). The effective components of creativity in digital game-based learning among young children: A case study. Children and Youth Services Review. https://doi.org/10.1016/j.childyouth.2020.105227 Bergen, E. van, Zuijen, T. van, Bishop, D., &amp; Jong, P. F. de. (2017). Why Are Home Literacy Environment and Children’s Reading Skills Associated? What Parental Skills Reveal. 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Each student has a different level of mathematical imagination ability. To find out the level of mathematical imagination ability, it is first necessary to arrange indicators of mathematical imagination ability based on the sequence of appearance from the earliest. The participants of this study were 20 8th grade students consisting of 13 female students and 7 male students. This research is a descriptive qualitative research. Assist instruments in this study consisted of written tests in the form of essays, interview guidelines, and observation sheets. Data analysis was performed by data reduction, data display, and conclusion drawing. The results obtained from this study are sequence indicators of junior high school students&#39; mathematical imagination abilities namely, sensibility, intuition, crystallization, transformation, exploration, elaboration, productivity, effectiveness, novelty