Development Of Mathematical Creativity Research Articles

KOMPETENSI PEDAGOGIK GURU DALAM MENGEMBANGKAN KEMAMPUAN KREATIVITAS MATEMATIKA PESERTA DIDIK PADA PEMBELAJARAN JARAK JAUH

Mathematics lessons are taught to equip students to have various thinking abilities. One of the most important thinking skills in mathematics is the ability to think creatively or it is called creativity. In fact, the creativity abilities of grade VII students at a Christian school in Toraja are still lacking in terms of indicators of mathematical creativity. One of the competencies that must be possessed by a teacher to be able to encourage the development of mathematical creativity of students is pedagogical competence. Therefore, the purpose this paper is to explain the implementation of teacher pedagogical competences during online learning to develop students' mathematical creativity. The research results describe the problems of mathematical creativity found in schools and how the implementation of teacher pedagogical competence as a solution to develop students' mathematical creativity. This qualitative research used observation method to collect the data of two classes with forty students as the population and twenty students are taken as the sample. The conclusion is that pedagogical competence can help the development of students' mathematical creativity, but the development has not occurred evenly because there are obstacles during online learning. So, Christian teachers still need to make efforts so that students can develop creative abilities as a means of knowing God more deeply. Suggestions given are that Christian teachers continue to apply interactive methods on an ongoing basis, deepen their insights into problem solving materials and problems, and try other approaches that consider other mathematical abilities such as mathematical reasoning or connections.

The development of mathematical creativity across high school: Increasing, decreasing, or both?

The advent of the Fourth Industrial Revolution (Industry 4.0) and a broader digital transformation of society is driving both a renewed focus on Science, Technology, Engineering and Mathematics (STEM) education as well as a recognition that creativity is a prerequisite for employment in the 21st century. Together, these elements are the catalyst for a key question: what is the impact of school education, in its broadest sense, on the development of STEM-based creativity in children? To shed greater light on this question, this study focuses on mathematical creativity in children across grades six-12, at a large Australian school. The study reported in this paper found that although mathematical creativity increases from year to year, there is a significant within-year decline in creativity. This paper explores possible explanations for this decline, suggesting that it is driven by a combination of environmental, personal, and process-related factors present in the context of school education. The study sheds light on the relationship between the development of mathematical creativity in high school students, and the factors that may impede this development.

MATHEMATICAL CREATIVITY AMONG EXCELLENT 8TH GRADE PUPILS

Creativity is finding a new way within a given frame and it is the ability to connect between segments of information, materials and experience, which exists in their own right, or were previously connected with different patterns. The current research engaged in solving problems that can be resolved in various ways or that they have several solutions, by excelling students and this in order to measure the level of mathematical creativity related to solving mathematical problems, by measuring the three elements of mathematical creativity: flexibility (multiple solutions), fluency (time needed to solve the problem), innovation (originality of ideas). It is important to emphasize that the way of solving tasks by using as many ways as possible, considered to be as one of the most efficient ways to the discovering and development of mathematical creativity. In the current research, 24 8 th grade pupils from several schools have participated, every student received three diverse mathematical problems and was requested to suggest and raise as many solutions or ways to solve as possible for each problem without teacher intervention, while measuring the required time to solve every problem separately for every student by a stopwatch. Additionally, a semi-structured interview was held with each student separately regarding his or her approach to each problem, the interview focused on identifying the mathematical language, in the process of resolving and in the exposure of the pupil’s mathematical thinking process until he or she reached the solution. The research findings indicate that there are differences between the pupils regarding flexibility, as multiple solutions were suggested by the pupils for each problem individually. Differences were also found in the level of innovation among the pupils, hence original solutions and new ideas to solve problems have been received. Moreover, a difference in fluency has been found so that pupils solved in a different time rates, this is despite the fact that all pupils have a very high level of achievement. Article visualizations:

MATHEMATICAL CREATIVITY AMONG EXCELLENT 8TH GRADE PUPILS

Creativity is finding a new way within a given frame and it is the ability to connect between segments of information, materials and experience, which exists in their own right, or were previously connected with different patterns. The current research engaged in solving problems that can be resolved in various ways or that they have several solutions, by excelling students and this in order to measure the level of mathematical creativity related to solving mathematical problems, by measuring the three elements of mathematical creativity: flexibility (multiple solutions), fluency (time needed to solve the problem), innovation (originality of ideas). It is important to emphasize that the way of solving tasks by using as many ways as possible, considered to be as one of the most efficient ways to the discovering and development of mathematical creativity. In the current research, 24 8 th grade pupils from several schools have participated, every student received three diverse mathematical problems and was requested to suggest and raise as many solutions or ways to solve as possible for each problem without teacher intervention, while measuring the required time to solve every problem separately for every student by a stopwatch. Additionally, a semi-structured interview was held with each student separately regarding his or her approach to each problem, the interview focused on identifying the mathematical language, in the process of resolving and in the exposure of the pupil’s mathematical thinking process until he or she reached the solution. The research findings indicate that there are differences between the pupils regarding flexibility, as multiple solutions were suggested by the pupils for each problem individually. Differences were also found in the level of innovation among the pupils, hence original solutions and new ideas to solve problems have been received. Moreover, a difference in fluency has been found so that pupils solved in a different time rates, this is despite the fact that all pupils have a very high level of achievement. Article visualizations:

Some environmental and attitudinal characteristics as predictors of mathematical creativity

ABSTRACTThere are many things which can be made more useful and interesting through the application of creativity. Self-concept in mathematics and some school environmental factors such as resource adequacy, teachers’ support to the students, teachers’ classroom control, creative stimulation by the teachers, etc. were selected in the study. The sample of the study comprised 770 seventh grade students. Pearson correlation, multiple correlation, regression equation and multiple discriminant function analyses of variance were used to analyse the data. The result of the study showed that the relationship between mathematical creativity and each attitudinal and environmental characteristic was found to be positive and significant. Index of forecasting efficiency reveals that mathematical creativity may be best predicted by self-concept in mathematics. Environmental factors, resource adequacy and creative stimulation by the teachers’ are found to be the most important factors for predicting mathematical creativity, while social–intellectual involvement among students and educational administration of the schools are to be suppressive factors. The multiple correlation between mathematical creativity and attitudinal and school environmental characteristic suggests that the combined contribution of these variables plays a significant role in the development of mathematical creativity. Mahalanobis analysis indicates that self-concept in mathematics and total school environment were found to be contributing significantly to the development of mathematical creativity.

The development of mathematical creativity through model-eliciting activities

The ability to think creatively and solve problems is regarded as crucial for economic and personal success. The traditional approach in classrooms is not conducive to mathematical creativity, and prospective teachers should be exposed to alternative problem solving activities through which mathematical knowledge, competencies and creativity can be developed. Research studies have pointed out the possibilities and successes of a modelling approach in which complex, open problems or model-eliciting problems are used to develop meaningful mathematical knowledge and prepare learners for everyday life, as well as for tertiary studies and their occupations. Model-eliciting activities (MEAs) do not only develop mathematical knowledge, but also creativity. Five hundred and one preservice Foundation Phase teachers completed different model-eliciting activities (MEAs) in a longitudinal project over a period of two years. The purpose was to develop and consolidate their own mathematical knowledge, and at the same time develop creativity and modelling competencies. The ultimate purpose of the project is to prepare preservice teachers to use mathematical modelling to develop creativity in young children aged six to nine. Through solving MEAs learners also build and consolidate their mathematical knowledge and improve their own problem-solving abilities. A framework with four criteria for the identification of creativity was successfully used to evaluate levels of creativity in the solutions offered to the MEAs. Preservice teachers’ final models displayed reasonably consistent levels of creativity regarding the four criteria. Their willingness to solve MEAs and create multiple, original and useful – therefore creative – solutions also increased over the period of their exposure to modelling tasks.

Exploring Collective Mathematical Creativity in Elementary School

AbstractThis study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity in elementary school classrooms. Collective learning takes place when mathematical ideas and actions, initially stemming from an individual, are built upon and reworked, producing a solution which is the product of the collective. Referring to characteristics of individual mathematical creativity, such as fluency, flexibility, and originality, this paper examines the possibility that collective mathematical creativity may be similarly characterized. The paper also explores the role of the teacher in fostering collective mathematical creativity and the possible relationship between individual and collective mathematical creativity.Many studies have investigated ways of characterizing, identifying, and promoting mathematical creativity. Haylock (1997), for example, and more recently, Kwon, Park, and Park (2006) assessed students' mathematical creativity by employing open‐ended problems and measuring divergent thinking skills. Leikin (2009) explored the use of multiple solution tasks in evaluating a student's mathematical creativity. These studies focused on an individual's mathematical creativity as it manifests itself in the solving of various problems. Yet students, acting in a classroom community, do not necessarily act on their own. Ideas are interchanged, evaluated, and built‐upon, often with the guidance of the teacher. The resultant mathematical creativity of an individual may be a product of collective community practice. The question which then arises is: Who is being mathematically creative, the individual or the community? This study focuses on the collective, not as the aggregation of a few individuals, but as a unit of study. Although some of the studies mentioned above acknowledged the effect of classroom culture on the development of mathematical creativity, and others considered the creative range of a group of students, those studies did not necessarily investigate mathematical creativity as a collective process or as the product of participating in a collective endeavour.This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity. The notion of collective creativity has been used to investigate creativity in several contexts including the work place (Hargadon & Bechky, 2006) and the global community (Family, 2003). In those cases, collective creativity was considered to occur when the social interactions between individuals yielded new interpretations that the individuals involved, thinking alone, could not have generated. Can the notion of collective creativity also be applied to the classroom community?

Education of Mathematically Talented Students in Hungary

Hungary is famous for its production of large numbers of highly talented mathematicians and physicists. This study explores the Hungarian system for educating mathematically talented secondary school students with the goal of identifying successful features that may be applicable to education in the United States. Highlights of the Hungarian approach include an emphasis on problem solving, problem posing, detailed explanation or proof for solutions, and development of mathematical creativity through the search for multiple solution paths.

Contribution of some personality and biographical factors to mathematical creativity

Contribution of some personality and biographical factors in the development of mathematical creativity was investigated. Verbal and non‐verbal mathematical creativity tests, a Hindi adaptation of the Thorndike dimensions of temperament test and a biographical inventory were used on 165 urban and 112 rural male students, aged 11 + to 13 + years, randomly selected, from Sultanpur District, India. The results showed that: (1) biographical factors may contribute significantly more than personality factors in the development of mathematical creativity; and (2) the effect of interaction of personality and biographical factors may contribute significantly in the development of mathematical creativity. Two different results were obtained by using a Hindi adaptation of the Thorndike dimensions of temperament test.