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Mathematical Creativity: Exploring the Cognitive and Developmental Aspects, Summaries of Mathematics

This document delves into the concept of mathematical creativity, exploring its relationship with cognitive development and the functions of the brain's hemispheres. It examines the role of divergent and convergent thinking in fostering creativity, highlighting the importance of incubation and the stages of the creative process. The document also discusses the development of creativity in adolescence, drawing on theories by piaget, gowan, and torrance. It concludes by outlining methods for measuring students' creative thinking skills.

Typology: Summaries

2022/2023

Available from 11/14/2024

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Definition of Mathematical Creativity
Speaking of creativity, creativity is very closely related to the cognitive
development of students or individuals because creativity is the work of the human
brain. According to Gowan through the Hemisphere Theory, the human brain is
actually divided into two hemispheres according to its function, namely the left
hemisphere and the right hemisphere. The function of the left hemisphere is related to
scientific, critical, logical, linear, orderly, systematic, organized, regular and similar
work. The function of the right hemisphere is related to activities that are nonlinear,
nonverbal, holistic, humanistic, creative, creating, designing, even mystical and the
like. In short, the left hemisphere of the brain leads to convergent thinking, while the
right hemisphere of the brain leads to divergent thinking (spread) (Asrori, 2007).
The birth of creativity in the form of ideas or real works is a combination of
the functions of the two hemispheres of the brain. Input from the environment in the
form of information is received through the function of the left brain hemisphere to
then be "incubated" in the right brain hemisphere, and this is where the subliminal
process takes place. At such times, a person needs the opportunity to reflect calmly.
Incubation is a very important stage in the creative process (Supriadi, 1994).
Observing the development of the theory of the brain hemispheres in relation to the
development of individual creativity as discussed earlier, it becomes increasingly
clear that creativity is related to the function of the right brain hemisphere, and means
it is also related to intellectual development. Creativity is the ability to create new
combinations based on existing data, information, or elements. Usually people
interpret creativity as creative power, as the ability to create new things. In fact, what
is created does not need to be new things at all, but is a combination of things that
already exist according to Supriyadi in (Dewi, 2021). On the other hand, Munandar
(2009: 10) defines creativity as the ability to see or think of extraordinary, unusual
things, combine seemingly unrelated information and come up with new solutions or
new ideas that show fluency, flexibility, and originality in thinking
Guilford (Ali & Asrori, 2019) states that creativity refers to the ability that
marks the characteristics of a creative person. Guilford further states two ways of
thinking, namely divergent and convergent thinking. Divergent thinking is the ability
of individuals to find various alternative answers to a problem. While convergent
thinking is the way individuals think about something with the view that there is only
one correct answer. In relation to creativity, Guilford emphasizes that creative people
have more divergent than convergent ways of thinking
While Rhodes (Ali & Asrori, 2019) defines creativity into four categories, namely
product, person, process, and press. Product emphasizes creativity from creative
works, both completely new and a combination of old works that produce something
new. Person views creativity in terms of individual characteristics that mark the
personality of a creative person or that are related to creativity. This can be seen
through visible behavior. Process emphasizes how the creative process takes place
from the beginning of growth to the manifestation of creative behavior. Meanwhile,
the press emphasizes the importance of factors that support the emergence of
creativity in individuals
Munandar (1999: 67) states that in developing children's creativity, we start
from the assumption that everyone basically has creative potential, and the ability to
express themselves creatively, each in different fields and to different degrees. In the
classroom, teachers can observe the different talents and interests of students.
Stimulating and fostering children's creativity is very necessary for teachers so that
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Definition of Mathematical Creativity Speaking of creativity, creativity is very closely related to the cognitive development of students or individuals because creativity is the work of the human brain. According to Gowan through the Hemisphere Theory, the human brain is actually divided into two hemispheres according to its function, namely the left hemisphere and the right hemisphere. The function of the left hemisphere is related to scientific, critical, logical, linear, orderly, systematic, organized, regular and similar work. The function of the right hemisphere is related to activities that are nonlinear, nonverbal, holistic, humanistic, creative, creating, designing, even mystical and the like. In short, the left hemisphere of the brain leads to convergent thinking, while the right hemisphere of the brain leads to divergent thinking (spread) (Asrori, 2007). The birth of creativity in the form of ideas or real works is a combination of the functions of the two hemispheres of the brain. Input from the environment in the form of information is received through the function of the left brain hemisphere to then be "incubated" in the right brain hemisphere, and this is where the subliminal process takes place. At such times, a person needs the opportunity to reflect calmly. Incubation is a very important stage in the creative process (Supriadi, 1994). Observing the development of the theory of the brain hemispheres in relation to the development of individual creativity as discussed earlier, it becomes increasingly clear that creativity is related to the function of the right brain hemisphere, and means it is also related to intellectual development. Creativity is the ability to create new combinations based on existing data, information, or elements. Usually people interpret creativity as creative power, as the ability to create new things. In fact, what is created does not need to be new things at all, but is a combination of things that already exist according to Supriyadi in (Dewi, 2021). On the other hand, Munandar (2009: 10) defines creativity as the ability to see or think of extraordinary, unusual things, combine seemingly unrelated information and come up with new solutions or new ideas that show fluency, flexibility, and originality in thinking Guilford (Ali & Asrori, 2019) states that creativity refers to the ability that marks the characteristics of a creative person. Guilford further states two ways of thinking, namely divergent and convergent thinking. Divergent thinking is the ability of individuals to find various alternative answers to a problem. While convergent thinking is the way individuals think about something with the view that there is only one correct answer. In relation to creativity, Guilford emphasizes that creative people have more divergent than convergent ways of thinking While Rhodes (Ali & Asrori, 2019) defines creativity into four categories, namely product, person, process, and press. Product emphasizes creativity from creative works, both completely new and a combination of old works that produce something new. Person views creativity in terms of individual characteristics that mark the personality of a creative person or that are related to creativity. This can be seen through visible behavior. Process emphasizes how the creative process takes place from the beginning of growth to the manifestation of creative behavior. Meanwhile, the press emphasizes the importance of factors that support the emergence of creativity in individuals Munandar (1999: 67) states that in developing children's creativity, we start from the assumption that everyone basically has creative potential, and the ability to express themselves creatively, each in different fields and to different degrees. In the classroom, teachers can observe the different talents and interests of students. Stimulating and fostering children's creativity is very necessary for teachers so that

their students become creative. A creative person will enjoy being creative. By being creative, he will be able to actualize himself. In addition to being beneficial for himself, it is also beneficial for his environment. Every student has a different way and perspective to solve problems in their lives, namely at school. One of the problems of students is that they have not been able to change their learning patterns to be better. According to Jean Piaget, when viewed from the cognitive development, students who are in the 10th grade of high school are at the formal operational stage. At this time, children have been able to realize a whole in their work which is the result of logical thinking. The emotional and moral aspects have also developed so that they can support the completion of their tasks. At this stage, their interactions with the environment have been very broad, reaching many of their peers and even trying to interact with adults. Conditions like this often cause problems in interacting with parents. However, in fact, they secretly still expect protection from their parents because they are not yet fully able to meet their own needs. So, at this stage there is a kind of tug of war between wanting to be free and wanting to be protected. Viewed from this perspective, the development of adolescent creativity is in line with the formal operational stage. This means that the development of creativity is at a very potential stage for the development of creativity (Ali & Asrori, 2019). Gowan (1987) also said that when associated with Piaget's cognitive development theory, individual creativity begins to develop well when individuals have entered the formal operational stage, namely the age of 11 years and above. Torrance (1977) supports Gowan's opinion above by saying that in adolescence individuals have begun to be able to think abstractly and systematically to solve hypothetical problems, and are even able to think beyond existing reality. Thus, the possibilities that will occur in the future can be calculated (Ali & Asrori, 2019). The creative process takes place following certain stages. It is not easy to identify exactly at which stage a creative process is taking place. What is observed is the symptom in the form of behavior displayed by the individual. According to Walas in (Ali & Asrori, 2019) there are four stages of the creative process, namely preparation, incubation, illumination and verification. The creative process takes place following certain stages. It is not easy to identify exactly at which stage a creative process is taking place. What is observed is the symptom in the form of behavior displayed by the individual. According to Walas in (Ali & Asrori, 2019) there are four stages of the creative process, namely according to Walas (Ali & Asrori,

  1. there are four stages of the creative process, namely preparation, incubation, illumination, and verification. Measuring students' creative thinking skills can be done by exploring students' work results that represent their creative thinking process (Worthington, 2006). Measuring students' creative thinking skills can also be done based on what students communicate, verbally or in writing. What students communicate can be in the form of student work results related to assignments, problem solving, or students' oral answers to teacher questions (McGregor, 2007).