Academic literature 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.

Researchers conceptually recommend inquiry-based learning as a necessary means to alleviate the problems of learning but this study has embarked on practical implementation of inquiry-based facilitation and learning in Euclidean Geometry. Inquiry-based learning is student-centred. Therefore, the teaching or monitoring of inquiry-based learning in this study is referred to as inquiry-based facilitation. The null hypothesis discarded in this study explains that there is no difference between inquiry-based facilitation and traditional axiomatic approach in teaching Euclidean Geometry, that is, H0: μinquiry-based facilitation = μtraditional axiomatic approach. This study emphasises a pragmatist view that constructivism is fundamental to realism, that is, inductive inquiry supplements deductive inquiry in teaching and learning. Participants in this study comprise schools in Tshwane North district that served as experimental group and Tshwane West district schools classified as comparison group. The two districts are in the Gauteng Province of South Africa. The total number of students who participated is 166, that is, 97 students in the experimental group and 69 students in the comparison group. Convenient sampling applied and three experimental and three comparison group schools were sampled. Embedded mixed-method methodology was employed. Quantitative and qualitative methodologies are integrated in collecting data; analysis and interpretation of data. Inquiry-based-facilitation occurred in experimental group when the facilitator probed asking students to research, weigh evidence, explore, share discoveries, allow students to display authentic knowledge and skills and guiding students to apply knowledge and skills to solve problems for the classroom and for the world out of the classroom. In response to inquiry-based facilitation, students engaged in cooperative learning, exploration, self-centred and self-regulated learning in order to acquire knowledge and skills. In the comparison group, teaching progressed as usual. Quantitative data revealed that on average, participant that received intervention through inquiry-based facilitation acquired inquiry-based learning skills and improved (M= -7.773, SE= 0.7146) than those who did not receive intervention (M= -0.221, SE = 0.4429). This difference (-7.547), 95% CI (-8.08, 5.69), was significant at t (10.88), p = 0.0001, p<0.05 and represented a large effect size of 0.55. The large effect size emphasises that inquiry-based facilitation contributed significantly towards improvement in inquiry-based learning and that the framework contributed by this study can be considered as a framework of inquiry-based facilitation in Euclidean Geometry. This study has shown that the traditional axiomatic approach promotes rote learning; passive, deductive and algorithmic learning that obstructs application of knowledge in problem-solving. Therefore, this study asserts that the application of Inquiry-based facilitation to implement inquiry-based learning promotes deeper, authentic, non-algorithmic, self-regulated learning that enhances problem-solving skills in Euclidean Geometry.<br>Mathematics Education<br>Ph. D. (Mathematics, Science and Technology Education)

Mathematics is the discipline that can and has the purpose of forming an investigative, creative thinking, a deepening of new knowledge and in general, an approach to the unknown through a true style of research. Regardless of the field in which he works, the man must possess a good mathematical training, in order to be able to solve the multitude of problems of the socio-professional life. The emphasis is primarily on thinking due to the fact that thinking has always been the basis of progress constituting social evolution. Any critical thinking, original and creative, is formed through mathematics. By teaching this discipline, the development of reasoning and the spirit of receptivity, of the skills of logical thinking, of clear and precise definition of the notions of creative adaptation to the current requirements are achieved. Cognitive development through mathematics also helps man in solving the daily problems he encounters. Mathematical thinking is manifested through a wide variety of intellectual activities related to memory and imagination, namely: judgment, reasoning, understanding, explanation, invention, deduction, induction, analogy, abstraction, generalization, comparison, concretization, classification, division, solving problem situations etc. Mathematical reasoning and thinking create the person's ability to understand other disciplines, problems in nature, life and society. It also contributes to the formation and development of the ability to work organized and rhythmically and the spirit of investigation. Mathematical education results in the formation of skills and abilities necessary in mathematical activity that become useful in human practical activity.

Mathematics, specifically spatial geometry, is a highly abstract discipline that requires students to use a substantial amount of imagination while studying. Geometry poses several obstacles for pupils owing to improve the instruction of spatial geometry, educators must discover, use, and integrate technology to enhance the process of learning. It is essential to enhance the process of learning. Educators find this disturbing. Augmented reality (AR) is significant in math education, providing several advantages. Examine and use the uses of augmented virtual reality technologies to construct models that assist in instructing spatial geometry. The instruction of spatial geometry. Research findings indicate that augmented virtual reality has many notable functions, including boosting engagement, visually representing complex ideas, improving problem-solving abilities, and promoting individualized learning.

Currently, the most important objective of the education process involves the formation of creative, innovative personality, with an increased level of thinking and imagination, as well as with a spirit of accuracy, observation and precision in the activity they carry out, but also initiative, thinking appropriate to the activity, the aesthetic taste, pursuing the development of the capacities of the maximum level of human potential. The human fate will depend, to a considerable extent, on the level of the school, as well as on the education of the youth who have divergent, but also pragmatic thinking. In the era of great transformations, but also in the future, managers from different fields will be required to be able to make quick, wise, difficult decisions. This objective can be achieved if we anticipate the demands, the needs of the society in perpetual development, training the young generations from the school benches. The speed with which things change at the current stage requires us to be better and better prepared, to choose and to weigh the alternatives, the actions, but also with the same tempo. This is why the greatest expectations are from the educational system: the purpose of training in creative problem solving is to develop the creative person, capable of changing the state of affairs in all fields. In the structure of competences, the role of attitudes is axiological orientation and affective and motivational energization of action, interacting in this sense with the socio-affective skills of the person. As fundamental units of character, attitudes leave their mark on the person's character profile and influence the level of competence through character traits such as: autonomy, responsibility, fairness, perseverance, conscientiousness, the feeling of a job well done, etc. From the multitude of factors involved in creativity, attitudes have a great importance. The development of creative attitudes of specialists in the field of physical education and sport is more current and important than ever for several reasons: In an era of technology and sedentary lifestyles, specialists in the field of physical education and sport play a crucial role in inspiring and motivating young people to be active. Creative approaches are essential to make physical activity attractive and relevant to young people. Society is changing rapidly and health, fitness and sport trends evolve with it, and the specialists in the field of physical education and sport must be creative in addressing the ever-changing needs and preferences of the population.The ability to find creative and innovative solutions is essential in the face of unforeseen situations such as pandemics that can affect the way sports activities are conducted. The purpose of the research is to study the importance of creative attitudes in the training process of specialists in the field of physical education and sport. Methods of research: study of specialized literature, sociological questioning, observation, mathematical processing of statistical data and their graphic processing. Findings and results The development of the creative spirit, promoted by interactive pedagogy, must be correlated with the education of thinking by combating conformity. The progress of the cognitive approach to solving problems depends on creativity. The education of creativity requires the formation of a positive attitude towards progress, towards new elements and towards their introduction into one's own actions; the readiness to accept the new as an indication of progress, innovations and human creativity; encouragement through character and original results; training and development of skills and abilities to create, rethink work strategies and integrate into dynamic, flexible and efficient systems; the formation and development of creative abilities to achieve something new: connections, ideas, theories, ideal or material models, material products, etc. In the research, we proceeded to evaluate the creative attitudes necessary for a specialist in the field of physical culture and sport with the help of the creative attitudes questionnaire and significant results were obtained t being 2.94 and P &lt;0.01, which proves the effectiveness of the activities of development of creative potential, in the training process of specialists in the field of physical education and sport. In conclusion, the development of creative attitudes in the field of physical education and sport derives from the need to respond to the challenges and opportunities in a constantly changing world. The specialists in the field of physical education must be prepared to innovate, adapt and inspire to make meaningful contributions to the promotion of health, performance and well-being in society. Following the evaluation of creative attitudes, we can conclude that they emphasize the interest with reference to the new, the involvement and active participation of the research subjects in the creative process, in the initiation of new, non-traditional and original works. The increased interest of the subjects to participate in scientific events with scientific articles, in seminars in the field of physical culture, but also an increased motivation towards employment in the work field was highlighted.