Mathematical Creative Ability Research Articles

Mathematical Connection is at the Heart of Mathematical Creativity

Abstract Although teaching mathematics for creativity has been advocated by many researchers, it has not been widely adopted by many teachers because of two reasons: 1) researchers emphasized and investigated mathematical creativity in terms of product dimension by looking at what students have at the end of problem-solving or -posing activities, but they neglected the creative processes students use during mathematics classrooms, and 2) creativity is an abstract construct and it is hard for teachers to interpret what it means for students to be creative in mathematics without further guidance. These can be eliminated by employing techniques of mathematical connections as tools because using mathematical connections can help teachers make sense of how to promote the creative processes of students in mathematics. Because making mathematical connections is a process of linking ideas in mathematics to other ideas and this is a creative act for students to take to achieve creative ideas in mathematics, using the strategies of making mathematical connections has the potential for teachers to understand what it means for students to be creative in mathematics and what it means to teach mathematics for creativity. This paper has two aims to 1) illustrate strategies for making mathematical connections that can also help students’ creative processes in mathematics, and 2) investigate the relationship among general mathematical ability, mathematical creative ability, and mathematical connection ability by reviewing theoretical explanations of these constructs and several predictors (e.g., inductive/deductive ability, quantitative ability) that are important for these constructs. This paper does not only provide examples and techniques of mathematical connection that can be used to foster creative processes of students in mathematics, but also suggests a potential model depicting the relationship among mathematical creativity, mathematical ability, and mathematical connection considering previously suggested theoretical models. It is important to note that the hypothesized model (see Figure 4) suggested in the present paper is not tested through statistical analyses and it is suggested that future research be conducted to show the relationship among the constructs (mathematical connection, mathematical creativity, mathematical ability, and spatial reasoning ability).

Students’ Mathematical Creative Thinking Obstacle and Scaffolding in Solving Derivative Problems

The difficulties experienced by students in studying derivative material are difficulties understanding the definition of derivatives and representations of these derivatives. Derivatives are a material that is quite difficult to develop mathematical creative abilities because they have many functions and symbols. This difficulty indicates a barrier to thinking in students. This research is descriptive qualitative research with five research subjects of Tadris Mathematics at the Curup State Islamic Institute. Each student can think creatively mathematically on the indicators of flexibility, fluency, and originality, but the levels are different. The level of mathematical creative thinking ability can depend on the questions or problems and the material being studied. However, one of the indicators of the ability to think creatively mathematically, which is very weak for students, is originality because students seem rigid with what they have obtained from lecturers and books. Students find it difficult to come up with ideas in solving problems. Barriers to thinking creatively mathematically can occur due to several factors, including 1) due to a lack of prior knowledge of students in understanding problems and determining ideas in planning solutions; 2) a lack of strong concepts possessed by students. One way for lecturers to overcome these obstacles is to provide scaffolding. The provision of scaffolding is carried out using Treffinger learning with several stages, namely basic tools, practice with process, and working with real problems. In practice with process stage, students solve problems by using analogical reasoning to develop their mathematical creative thinking abilities. The stages of analogical reasoning used to consist of the stages of recognition, representation, structuring, mapping, applying, and verifying. This study's findings are that two new stages are added to the early stages of analogical reasoning, namely the stages of recognition and representation.

Improving Students’ Mathematical Creative Thinking Ability and Motivation through Problem-Based Learning Model

This study aims to determine the mathematical creative thinking ability of students after being taught with the Problem Based Learning (PBL) learning model. This research is a quasi-experimental research that compares two learning models, namely, the problem-based learning model and the conventional learning model, and is designed as follows: (i) a research sample of 60 students was selected as the research sample, and (ii) the data from the research test of students' mathematical creativity ability was carried out 2 (two), namely pretests (before learning) and postes (after learning). From the results of the research, it can be concluded that the average pretest score of mathematical problem solving ability also increased in the control class, especially for fluency indicators, but from the average of the two classes, the average in the experimental class was higher than the control, which was 53.33%. The average N-gain of creative thinking abilities of students taught with PBM was 0.48 and in students teaching with conventional learning. It was known that the increase in student motivation that obtains a PBM is higher than those whose learning uses ordinary learning. Therefore, it is important for schools to socialize PBM to be applied in the learning process so that it can improve students' mathematics skills, especially the ability to think creatively mathematically and student learning motivation.

Students' Analogical Reasoning in Solving Trigonometric Target Problems

Analogical reasoning plays a crucial part in problem-solving since it requires students to connect prior knowledge with the issues at hand in learning mathematics. However, students struggle when developing solutions to the issues utilizing analogies even if there is a connection between mathematical creativity and analogical reasoning. The aims of this study were to assess students' use of Ruppert's phases to solve problems and identify students' analogy patterns to solve target problems. This study is qualitative in nature. Of 19 research participants, six were then chosen using the purposive sampling technique based on their levels of mathematical creative ability. Test, interview, and documentation were the data gathering techniques used in this study. The study's findings suggested that good analogical reasoning skills did not serve as a prerequisite for students with strong mathematical creative thinking skills. Only one subject out of three who possessed necessary mathematical creative thinking abilities could go through the four steps of analogical reasoning-structuring, mapping, applying, and verifying. All other subjects were unable to complete the four steps of analogy, and even their creative thinking skills were weak. This was because the students did not comprehend the idea and could not connect prior knowledge with the issues at hand. In order to remind students of their prior knowledge and experiences, it would therefore be necessary at this analogy stage to establish an initial stage before structuring. The format and degree of difficulty of the questions were assumed to be other elements that might influence students' responses. The results of this study are expected to be a reference for further research, namely increasing analogical reasoning optimally as an effort to increase students' prior knowledge and students' mathematical creative thinking abilities in solving mathematical problems.

Sternberg의 성공지능 이론과 연계한 유아수학교육 프로그램 효과 검증

Objectives The purpose of this study is to verify the effect of early childhood mathematics education program in connection with Sternberg's theory of successful intelligence on the mathematical ability, creativity, and creative problem-solving ability of young children. Methods Seventy six 5-year-old children were selected as research subjects at two kindergartens located in Seoul. Differences between the groups were investigated by dividing them into experimental and control groups. The difference between the groups was verified after applying the program of early childhood mathematics education linked to the Sternberg successful intelligence theory to the experimental group over 10 weeks. Results To verify the effectiveness of the program, t-verification and multivariate analysis (MANOVA) were performed using the SPSS 24.0 program. There were differences in the mathematical ability, creativity, and creative problem-solving ability of young children between the experimental and control groups. Conclusions The early childhood math education program based on the theory of successful intelligence is suitable for 5-year-old children and has a positive effect on mathematical ability, creativity, and creative problem-solving ability. The experimental group young children. who participated in the program improved their mathematical ability and their sub-areas, algebra, number and computation, geometry, and measurement compared to the control group young children. In addition, creativity was significantly improved, and sub-areas of fluency, originality, abstraction of titles, and resistance to early closure were improved. Creative problem-solving skills and plans for understanding problems, generating ideas, and acting, which are sub-factors have all improved.

Creative problem-solving ability does not occur by chance: Examining the dynamic system model of creative problem solving ability

This study examined Cho’s dynamic system model of creative problem-solving ability in a sample of 112 gifted and non-gifted students. The cluster analysis and t-test results indicated that students should be categorized into high and low performance groups. Students who scored three points or more across all attributes also had a higher likelihood of possessing better mathematical creative problem-solving abilities. Furthermore, significant differences were found in the two groups’ scores on the Creative Problem Solving Attributes Inventory and Mathematical Creative Problem Solving Ability Test. The environment attribute was the only one on which the two groups did not differ significantly; this may be the result of education fever in Asian societies. Finally, the results of this study not only indicated that creativity does not rely on a single factor but that a well-balanced environment is imperative to nurturing creativity.

Investigating mathematical creativity through the connection between creative abilities in problem posing and problem solving

The majority of existing research have repeatedly embedded problem solving and problem posing in the assessment of students’ mathematical creativity, but there is a lack of studies focusing on the relationship between these two regarding mathematical creativity. In this study, we aimed to examine whether there is a relationship between the constructs of creative ability in mathematical problem posing (CAMPP) and creative ability in mathematical problem solving (CAMPS) and to examine the structure of this relationship through confirmatory factor analysis. The participants were 187 sixth-grade students in Turkey. Data were collected by two creative ability tests, namely CAMPP and CAMPS. We used a rubric to characterize mathematical creativity by interpreting scores of in the dimensions of creative ability (fluency, flexibility, and originality) in the context of problem solving and problem posing. The findings showed that mathematical problem posing and mathematical problem solving both constituted the constructs of CAMPP and CAMPS respectively, based on the dimensions of creative ability. Moreover, the structure of the relationship between the constructs of CAMPP and CAMPS can be explained better with a constituted higher-order factor of Creative Ability in Mathematics (CAM) rather than placing one of these factors as a sub-construct under the other one.

Using Open-ended Problem-solving Tests to Identify Students’ Mathematical Creative Thinking Ability

This study aimed to examine an open-ended problem-solving assessment tool that can be used to measure the profile of students’ mathematical creativity based on the type of mathematical creativity. The open-ended problem-solving assessment consists of open-ended problem-solving sheets and interview guidelines to measure the profile of students' mathematical creativity. One hundred and five students were asked to solve open-ended problems. From each group, one student was selected to be interviewed with the aim of obtaining a more detailed explanation of each of these types. The two types can be explained as follows. The “very creative” students were those who could perform cognitive flexibility and cognitive fluency in solving open-ended problems. The other type of students was creative students who were able to think flexibly (cognitive flexibility) when solving open-ended problems. Cognitive flexibility includes the ability to describe various solutions and provide more than one answer to a problem. Cognitive fluency includes the ability to interpret the answer smoothly and accurately without any constraints. It may also refer to the ability to correct a wrong answer even though there was a mistake during the operating process. The analysis results showed that the open-ended problem-solving assessment was an effective tool to measure students' mathematical creativity in terms of results (products) and processes. In terms of results (products), it was able to determine the type of students’ mathematical creative ability, namely very creative and creative, while in terms of processes, it was able to describe the differences in the cognitive profile of the two types.

KEMAMPUAN BERPIKIR KREATIF MATEMATIS DALAM MENYELESAIKAN SOAL OPEN ENDED PADA MATERI PLDV DI SMP

AbstractThe purpose of this research in general is to determine the ability of mathematical creative thinking in solving epen ended questions on the linear equations material of two variables of class VIII A in SMP Negeri 4 Sungai Ambawang. The research method is descriptive method in form in case study research. The subjects in this research werw 34 students of class VIII A of SMP Negeri 4 Sungai Ambawang and the focus of the research was the ability to think mathematical creatively in solving open ended questions of two-variable linear equations. The result of data analysis showed that students’ mathematical creative thingking ability in the fluency aspect reached 78%, in the flexibelity aspect in reached 58%, and in the novelty aspect it reached 25%.Keywords : Ability to think mathematic creatively, Open ended, Twovariables linear equation

Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity

The purpose of this study was to reveal both the effects of problem-posing interventions on the mathematical creative ability of students and how students’ creative self-efficacy in mathematics was related to their mathematical creative ability. Elementary school students (n = 205) were randomly assigned to one of two groups: problem-posing or control. Results showed the mathematical creativity for the problem-posing group increased (p < 0.05) more than for students in the control group (d = 0.77). Results from the Confirmatory Factor Analysis showed that mathematical creativity was a higher order factor that included mathematical creative ability and mathematical creative self-efficacy as first-order factors. Among the implications for this is that integrating problem-posing activities into elementary school mathematics instruction can foster mathematical creativity.

The qualitative effect of problem-based learning model toward students’ mathematical imitative and creative reasoning

Reasoning is one of the abilities needed in solving mathematical problems. Based on Lithner perspective, reasoning divided into imitative reasoning and creative reasoning. There are three indicators for each reasoning, that are plausibility, mathematical foundation, novelty for creative reasoning aspect and imitation for imitative reasoning aspect. The aim of this research is to analyze the qualitative effect of problem-based learning model toward students’ mathematical imitative and creative reasoning. In order to do so, we used descriptive qualitative methods by taking eighth-grade students (around thirteen to fourteen years old) in one of the Junior High School in Tasikmalaya. We used the data from a written test, observation and interviews. The results revealed that problem-based learning model suitable for students who have dominantly mathematical creative reasoning abilities. The characteristics of students who have dominantly mathematical imitative reasoning abilities prefer to be told rather than finding out. Based on the results, we conclude that each student has a different learning style according to his abilities.

Profil Kemampuan Penalaran Kreatif Matematis Mahasiswa Calon Guru

This study aims to obtain an overview of the mathematical creative reasoning abilities of the prospective teacher. The ability of mathematical creative reasoning in this study is the ability of students to justify a statement on the grounds of the truth of a statement that is based on novelty, plausible, and mathematical foundation. This research approach is qualitative using Grounded Theory. The population in this study were all students participating in the Calculus class of the Study Program Mathematics Education at one of the universities in West Java. In a while, the sample of 55 students was selected by a cluster random sampling technique. The results showed that students' mathematical creative reasoning abilities were categorized into three levels of ability based on the quality of the four categories, namely the initial step, the flow of completion, the related concepts, and the mathematical term errors.

PENINGKATAN KEMAMPUAN BERPIKIR KREATIF MATEMATIS DAN KEMANDIRIAN BELAJAR SISWA SMP AR-RAHMAN MEDAN MELALUI PEMBELAJARAN OPEN-ENDED BERBASIS BRAIN-GYM

The purposes of the research were to determine: (1) the difference of improvement of students’ mathematical creative thingking ability (2) the difference of improvement of students’ self regulated learning, taught by open-ended based brain-gym and expository learning, (3) the interaction between learning method and students’ gender toward mathematics in increasing student’s mathematical creative thingking ability, and (4) the process of students’ answer in each learning. This research was quasi experimental research. The population of the research was all of the students at 7&lt;sup&gt;th&lt;/sup&gt;grade of Ar-Rahman Junior High School. The sample taken randomly, such as 7&lt;sup&gt;th&lt;/sup&gt;-A (experiment class) and 7&lt;sup&gt;th&lt;/sup&gt;-B (control class). The instruments of research were: (1) mathematical creative thinking ability test, and (2) self regulated learning scale. The result of trials to test mathematical creative thinking test are derived validity row by 0,640; 0,698; 0,709; 0,721; and 0,605 with a reliability test by 0,692. Data analysis was done using ANACOVA and ANAVA two ways formula. The results showed that (1) the improvement of mathematical creative thinking ability and self regulated learning students who received open-ended based brain-gym higher than students who received expository learning. (2) therewas no interaction between learning method and students’ gender toward mathematics in improvement student’s mathematical creative thingking ability, this is shown with significance value of 0.499 was greater than the significance level = 0.05. (3) the process of answers of students who received open-ended learning-based brain-gym better than students who received expository. From this research, the researchers suggest to make good planning, attention to the characteristics of the students, efficient use of time, and for further research to be better explore further the others capabilities.

HUBUNGAN SELF-EFFICACY TERHADAP KEMAMPUAN BERPIKIR KREATIF MATEMATIK SISWA SMP PADA MATERI BANGUN DATAR SEGITIGA DAN SEGIEMPAT

This study aims to determine the relationship of self-efficacy to the mathematical creative ability of junior high school students in the material of flat triangles and quadrilateral. The method used is quantitative by correlation method. This research was conducted in one of the Public Middle Schools in Cimahi City with a population of all students in class VII and a sample of class VII-5 as many as 30 people. The test is done by giving a question of the ability to think creatively as many as 5 items and the scale of self-efficacy with a Likert scale. The steps used in the analysis, namely normality test, korealsi test, determine the determinant coefficient or determinant coefficient to see the contribution or influence of the variable self-efficacy on mathematical creative thinking abilities of middle school students. Based on the results of the study showed that there was a significant relationship between self-efficacy on the ability of creative thinking of junior high school students, and the large contribution given by self-efficacy to mathematical creative thinking skills was 16.00%.

Developing didactic design in triangle and rectangular toward students mathematical creative thinking through Visual Basic for PowerPoint

Triangle and quadrilateral material has been studied since the students are in elementary school, but the junior high school students still struggle to solve problems related to triangle and quadrilateral. The research method used in this research is a qualitative method with Didactic Design Research (DDR) approach. DDR is research conducted through three stages didactic situation analysis before learning which its form is Didactic Hypothesis Design, meta didactic analysis, and retrospective analysis. It’s defined as an analysis which relates the result of didactic hypothesis analysis and the result of the meta didactic analysis. Based on the results of the analysis shows that learning by using didactic design in teaching triangle and quadrilateral, students can work through the completion of visual essential PowerPoint. Study and observation of the writers when learning takes place, the difficulties faced by students in solving the problem of mathematical creative ability is that students not usually used it for facing issues with indicators of the artistic knowledge of mathematics. So, in general, some students from both classes have depicted to the student’s creativity in solving the problem, but there is no answer, and the level of thinking is low.

Building Learning Path of Mathematical Creative Thinking of Junior Students on Geometry Topics by Implementing Metacognitive Approach

Mathematical creative ability is one of the most important skills students must have to process the information provided in resolving the problem. Before using mathematical creative skills, prior knowledge becomes the most crucial thing that allows students to connect all existing information so that they can construct new knowledge through assimilation or accommodation processes. The process of forming mathematical concepts with metacognitive questions that might be carried out by students causes a metacognitive process in students that will affect their mathematical behavior. &#x0D; The purpose of this study is to (1) analyze prior knowledge of what students miss or forget so that they have difficulty to answer the given geometry problem, (2) how the learning path of creative thinking of students with the application of metacognitive approach. This type of research is Design Research to improve the quality of learning. This type of research is research design, data collection techniques .The researcher gave 2 geometry questions to 38 8th graders selected randomly in SMP Medan city. Questions given are tailored to Cognitive level 4 (C4) for questions 1 and C5 for question 2 based on Bloom's taxonomy. Data analysis techniques are descriptive qualitative.This study shows that prior knowledge becomes important to build students' mathematical creative ability to gain new knowledge, especially in the field of geometry. The most problematic topics that make it difficult for them to understand geometry are the area of the rectangle and the cube webs. In dividing the rectangle into two equal parts, students still have not created another form of flat build or have not been able to get out of the rectangular pattern or exactly the same as the available problem.&#x0D; There are five phases of learning trajectory of hierarchically creative mathematical thinking, which is orientation to problem, problem solving plan, plan realization, previous knowledge mastery / concept of mathematical creativity and evaluation of result obtained. Students do metacognition on the learning path of creative thinking in a comprehensive way from evaluation to planning, action to the formation of prior knowledge and selection of creative ideas. From these explanations, it is important that teachers need to ensure students have enough prior knowledge to make it easier to construct new knowledge, as well as to make learning fun and meaningful so that students will remember knowledge in long-term memory.

STUDENTS’ PERFORMANCE SKILLS IN CREATIVE MATHEMATICAL REASONING

This study aims to examine mathematics teacher-candidate students’ mathematical creative reasoning ability based on the level of Adversity Quotient (AQ). This study uses a mixed method of sequential type by combining quantitative and qualitative methods in order. Population in this study is all students attending the course of Calculus in Mathematics Education of Master Program at STKIP Siliwangi that consist of 270 students divided into six classes. The results are AQ gives effect to the achievement of students’ mathematical creative reasoning abilities based on the whole and the type of AQ climber, champer, and quitter. The achievement of students’ mathematical creative reasoning abilities and based on AQ, the champer and climber fall into the medium category, while on the quitter type, it falls into the category of low. On the other hands, the achievement of students’ mathematical creative reasoning abilities is yet to be achieved well at the indicator of novelty.

Adversity Quotient (AQ) dan Penalaran Kreatif Matematis Mahasiswa Calon Guru

This study is experimental research that aims to know and examine in depth about the influence of AQ of pre-service mathematics teacher toward the achievement of mathematical creative reasoning ability. The population of this study is the pre-service mathematics teacher in Cimahi City, West Java, Indonesia; while the sample is 60 pre-service mathematics teachers selected purposively. The instruments of this study are tests and non-tests. They are based on the assessment of good characteristics towards students' mathematical creative reasoning abilities, while the non-test instrument is based on the assessment of good characteristics towards AQ. The results of this research show that: (1) AQ gives positive influence to the development of mathematical creative reasoning ability of pre-service mathematics teacher with the influence of 60.9%, while the rest of it (39.1%) is influenced by other factors outside AQ; (2) The mathematical creative reasoning ability of the prospective teacher students is more develop in AQ Climber type, whereas students who have Camper and Quitter AQ types still tend to have thinking patterns in solving problems with imitative reasoning; (3) Students belonging to the Quitter AQ type still tend to have errors related to the idea of solving problems and mathematical expressions.

ANALISIS HUBUNGAN KEMAMPUAN BERPIKIR KREATIF MATEMATIS DAN SELF EFFICACY SISWA SMK

The purpose of this research is to examine how the relationship between mathematical creative ability and self-efficacy of vocational students. The research method used in this research is correlational research, where the purpose of this research to see the relationship between two variables. Where the population is taken is all students of SMK on one SMK in Cmahi City, and taken a sample of one class. In the form of a test of creative thinking test in the form of a description of 5 questions and non-test in the form of self-efficacy questionnaire as many as 30 statements The Questionnaire Score is then transformed using Method of Successive Interval (MSI), then tested the correlation using Product Moment Pearson and Spearman. From the results of the study showed that there is a significant relationship between the ability of mathematical creative thinking and self-efficacy of students in learning mathematics

Improving students’ creative mathematical reasoning ability students through adversity quotient and argument driven inquiry learning

This study aimed to investigate the role factors of Adversity Quotient (AQ) and Argument-Driven Inquiry (ADI) instruction in improving mathematical creative reasoning ability from students’ who is a candidate for a math teacher. The study was designed in the form of experiments with a pretest-posttest control group design that aims to examine the role of Adversity Quotient (AQ) and Argument-Driven Inquiry (ADI) learning on improving students’ mathematical creative reasoning abilities. The population in this research was the student of mathematics teacher candidate in Cimahi City, while the sample of this research was 90 students of the candidate of the teacher of mathematics specified purposively then determined randomly which belong to experiment class and control class. Based on the results and discussion, it was concluded that: (1) Improvement the ability of mathematical creative reasoning of students’ who was a candidate for a math teacher who received Argument-Driven Inquiry (ADI) instruction is better than those who received direct instruction is reviewed based on the whole; (2) There was no different improvement the ability of mathematical creative reasoning of students’ who is a candidate for a math teacher who received Argument-Driven Inquiry (ADI) instruction and direct instruction was reviewed based on the type of Adversity Quotient (Quitter / AQ Low, Champer / AQ Medium, and the Climber / AQ High); (3) Learning factors and type of Adversity Quotient (AQ) affected the improvement of students’ mathematical creative reasoning ability. In addition, there was no interaction effect between learning and AQ together in developing of students’ mathematical creative reasoning ability; (4) mathematical creative reasoning ability of students’ who is a candidate for math teacher had not been achieved optimally on the indicators novelty.