Mathematical Thinking Process Research Articles

Do mathematical thinking processes influence visual estimation skills in students?

In this study, the visual estimation skills of fourth grade elementary school students based on their mathematical thinking processes were investigated. The research questions focus on understanding how students’ mathematical thinking processes influence their visual estimation skills. A total of 445 students participated in the study. The relational scanning model was used to determine the relationship between students’ visual estimation skills and their mathematical thinking processes. The Mathematical Process Instrument and the Visual Estimation Skills test were used as data-gathering tools. The data obtained were analyzed using different statistical methods, including the chi-squared test, t-test, and single-factor analysis of variance. The findings contribute to our understanding of the complex relationship between mathematical thinking processes and visual estimation skills in students, addressing the research questions raised in the study. These results can inform educators and instructional designers when developing effective teaching materials and strategies that cater to students’ diverse thinking processes.

PROSES BERPIKIR KREATIF MATEMATIS SISWA MENURUT DAVID CAMPBELL DITINJAU DARI GAYA KOGNITIF

This study aims to describe the mathematical creative thinking process of students according to David Campbell's stages in terms of reflective and impulsive cognitive styles on awakening and congruence material. This study used descriptive qualitative research method. Data collection techniques in this study used MFFT (Matching Familiar Figure Test) tests, creative thinking ability tests, and interviews. The main instruments are the researchers themselves and supporting instruments are MFFT (Matching Familiar Figure Test) test instruments and mathematical creative thinking ability test instruments. The subjects of the study were grade IX students of SMPN 1 Tasikmalaya who met all indicators of mathematical creative thinking ability in each cognitive, reflective and impulsive style and could communicate well. The data analysis techniques used are data reduction, data presentation, and conclusions. Based on the results of the study, conclusions were obtained (1) The creative thinking process of reflective students (S1R): can convey information known and asked about questions orally and in writing, show changes in their facial features, do brooding activities while playing stationery, hair and legs slowly, can choose the way of solving obtained after going through the process of guessing smoothly, can show solutions in two ways and Set his own ideas with a long enough time, equate the completion results in the first and second ways and recalculate the completion steps. (2) The creative thinking process of impulsive students (S11I): can understand the problems contained in the problem in a relatively faster time and can mention what is known and asked orally and communicate that what is written has been through calculations outside the head, pay attention to the sketches drawn and be able to write assumptions from the results of their attention, show silent activities and trial and error, can solve in two different ways even if you make a mistake several times, and only equate the final result in both ways and check the steps of the work. (3) The creative thinking process of impulsive students (S25I): can understand the problems in the problem in a relatively faster time, can mention what is known and asked orally, can do trial and error activities and recall ideas found if they have difficulties, do silent activities while playing stationery and veils worn but still look relaxed, can finish in two different ways, as well as simply equate the final result in both ways and check the pace of the work

Comedian Mathematical Thinking: An Islamic Examination of Inductive, Deductive, and Analogy Approaches in the Creation of Stand-Up Comedy Material

This study examines the thinking process of comedians in creating Stand-Up Comedy material and highlights the similarities between comedy structures and mathematical thinking. Incorporating comedy structures into classroom learning can create a fun and engaging atmosphere while effectively conveying concepts and achieving learning objectives. Stand-Up Comedy, as a solo performance, allows comedians to present their material independently (Utami, 2018). In line with an Islamic perspective, this study aims to explore how the comedian's mathematical thinking process aligns with the inductive, deductive, and analogical methods, while considering the values and principles of Islam. By analyzing the intersection of humor, mathematics, and Islamic teachings, this research seeks to provide insights into utilizing comedy techniques to enhance teaching and learning experiences, promoting an inclusive and enjoyable educational environment that respects Islamic values and objectives.

Analisis Proses Berpikir Kreatif Matematis Siswa dalam Menyelesaikan Masalah Matematika Persamaan dan Pertidaksamaan Linear Satu Variabel ditinjau dari Tipe Kepribadian Extrovert dan Introvert

The background of this research is the low mathematical creative thinking process of class VII B SMP Muhammadiyah Tonjong Brebes Regency in solving mathematical problems of one-variable linear equations and inequalities. One of the influencing factors is the personality type possessed by students, both extrovert and introvert personality types. This study aims to determine students' mathematical creative thinking processes in solving mathematical problems of one-variable linear equations and inequalities in terms of the extrovert and introvert personality types of students at SMP Muhammadiyah Tonjong, Brebes Regency. This type of research is Mix Method Research (MMR). The subjects of this study were students in class VII B at SMP Muhammadiyah Tonjong, Brebes Regency, for the 2022/2023 academic year, with a total of 6 subjects. The instruments in this study were personality questionnaires to determine students' personality types, both extroverted and introverted, and written test instruments to assess students' mathematical creative thinking processes. Based on the analysis that has been done, the extrovert personality type students, with a total of 17 students, are divided from the creative group of 6 students who meet all four indicators (fluency, flexibility, originality, and elaboration), the moderately creative group of 7 students fulfills three indicators (fluency, flexibility, and elaboration ), and four students in the less creative group fulfilled two indicators (flexibility and originality). While students with introverted personality types, a total of 14 students were divided into creative groups of 2 students fulfilling all four indicators (fluency, flexibility, originality, and elaboration), moderately creative groups of 9 students fulfilling three indicators (fluency, originality, and elaboration), and three students in the group less creative does not meet one of the four indicators.

Mathematic Creative Thinking Processes Through Mind-Mapping Based Aptitude Treatment Interaction Learning Model: A Mixed Method Study

<p style="text-align: justify;">This study aims 1) to determine the effectiveness of the Mind-Mapping based Aptitude Treatment Interaction model towards creative thinking and 2) to explain the mathematical creative thinking process based on the creative level. The number of participants was 26 students who took the Multivariable Calculus course in the odd semester of 2020/2021. This research used the mixed-concurrent embedded method. The data collection techniques were validation, observation, creative thinking tests, and interviews. The results showed that 1) the Mind-Mapping based Aptitude Treatment Interaction model was effective in developing creative thinking, as indicated by the average creative thinking score of the experimental class, which was higher than the control class and 2) the characteristics of students mathematical creative thinking process varied following the creative thinking levels. The students mathematical creative thinking level consists of not creative (CTL 0), less creative (CTL 1), quite creative (CTL 2), creative (CTL 3), and very creative (CTL 4). Students at the CTL 2, CTL 3, and CTL 4 can meet the aspects of fluency, flexibility, and originality.</p>

STUDENTS' MATHEMATICAL CREATIVE THINKING: A SYSTEMATIC LITERATURE REVIEW WITH BIBLIOMETRIC ANALYSIS

This study aims to determine the trend of publications on creative thinking in mathematics learning published on Google Scholar in the 2017-2021 period, as well as describe opportunities and directions for research on creative thinking with themes related to future mathematics learning. This research is a systematic literature review study with bibliometric analysis. This research method uses PRISMA 2020 steps. The study results show that the most productive authors are Asikin, Mulyono and Tohir, each publishing two articles. The paper that gets the most citations is by Hasanah and Surya, which discusses students' creative thinking skills in mathematics using cooperative and problem-solving learning. Research themes such as students, creative thinking, problems and mathematics, and mathematical domains such as numbers, algebra and geometry have been widely used. This allows future research paths that can be studied, including the domain of mathematics in the material of statistics and opportunities, students' creative thinking in 7th and 9th-grade students gender, and the use of technological media to improve or measure students' mathematical creative thinking processes. However, the domains and topics that have been studied are still possible to be reviewed as an effort to maximize students' mathematical creative thinking abilities.

Impact of Differentiated Instruction on the Mathematical Thinking Processes of Gifted and Talented Students

The aim of this study is to examine if differentiated instruction benefits the mathematical thinking process of gifted and talented students in Malaysia. Differentiated instruction is a student-centered technique in which instructors act as facilitators. It is doubtful, however, if differentiated instruction has a beneficial effect on the overall process of mathematical thinking. A disciplined approach to learning mathematics is deemed essential. In this study, a questionnaire was designed to assess students' motivation towards learning using differentiated instruction in mathematics, and a mathematics test was devised to assess students' mathematical thinking process. The study included 400 students who were identified as gifted and talented students; the data were analyzed using the SPSS software. The results suggest that statistically differentiated instruction has a significant effect on gifted and talented students' mathematical thinking processes. However, additional research is needed to discover which activities directly impact students' mathematical thinking processes positively and which should be avoided.

Mathematical Reflective Thinking Process of Prospective Elementary Teachers Review from the Disposition in Numerical Literacy Problems

<p style="text-align:justify">The purpose of this qualitative research is to analyze the reflective thinking process of prospective elementary teacher in numeracy problems in terms of their mathematical disposition. The subjects in this study were 26 prospective elementary school teachers who had attended elementary mathematics lectures. The focus in this research is the process of mathematical reflective thinking in solving story problems of a two-variable linear equation system in terms of the level of mathematical disposition. The research instrument consisted of a disposition questionnaire, a reflective thinking ability test and the researcher himself as the main instrument. Good mathematical reflective thinking skills are supported by disposition, by constantly monitoring one's own performance, reflecting on one's own performance, reasoning on one's own performance, considering the overall situation, the habit of analyzing the relationship between variables, being flexible in various alternative solutions to mathematical problems and trying to solve mathematical problems. From the results of this study, lecturers can develop learning media, scaffolding, or teaching materials that accommodate different dispositional abilities of prospective teachers that can be used to improve the reflective thinking process.</p>

Mathematical thinking process based on student IQ test results and talented mathematical

This study aims to determine how the students’ mathematical thinking processes are evaluated from the IQ test results and mathematical giftedness. Each student has his level of intelligence and talent in learning science, including mathematics. Until now, mathematics is considered a difficult subject to learn, including at the Elementary School level. However, there are elementary school students who have more advantages and have the talent to study and solve mathematical problems. The purpose of this research is to find out how the mathematical thinking ability of gifted elementary school students and how the type or model of the thinking process of gifted students in terms of the results of the IQ test, the Mathematical Gifted test. This research was conducted on elementary school students in the city of Tasikmalaya, who had been taken by purposive sampling to obtain 15 students who were used as research samples. IQ test results were obtained by 2 people belonging to the gifted category, and 13 people belonging to the superior category. The mathematical thinking process of two people who are classified as gifted fulfilled the indicators of representation, generalization, abstraction, and mathematical creativity.

A framework for Assessing Translation among Multiple Representations

Translation among multiple representations is one of the important abilities to be possessed by prospective mathematics teachers. The mathematics learning curriculum ranging from elementary to college level needs to emphasize the ability to translate mathematical ideas in a form of representation to different mathematical representation structures. Assessing of this ability is important because it can be used as a basis for developing other mathematical literacy skills. The purpose of this study is to describe the level of translation between mathematical representations of prospective mathematics teachers. A descriptive qualitative study was conducted to fourty prospective mathematics teachers in State Islamic University of Mataram. The selection of research subjects was carried out in a purposive sampling. Data were obtained from mathematical translational thinking task in the form of an assignment sheet consisting of 2 questions related to quadratic equations and task-based interviews. Data were analyzed using fixed comparison analysis, which is comparing incidents (phenomena) with the aim of classifying data. The study found five levels of translational ability between mathematical representations, which were named: level 0, level 1, level 2, level 3 and level 4. The characteristics of each level are built based on four mathematical translational thinking processes: unpacking the source of representations, coordinating initial stage, design the target representation and determine the equivalence between the source and target representations. The findings in this study could be used as a guide to develop an instrument to assess mathematical translation ability.

Differentiated Instruction: Exploring the Attitudes of Gifted and Talented Students in Mathematics

The purpose of this study was to study the attitudes of gifted and talented students in mathematics at Kolej GENIUS@Pintar Negara, Universiti kebangsaan Malaysia (KGPN). The teaching strategy taken by teachers in the classroom has a significant impact on students' attitudes about mathematics. Since 2011, KGPN has used differentiated instruction as a kind of pedagogy in its teaching and learning activities. When gifted kids get differentiated teaching, they have the option to study any areas of knowledge, particularly in mathematics, that they are interested in or are ready to investigate. Teachers must diversify their teachings throughout the teaching and learning process to encourage gifted students to take a more active role in their learning. Even though differentiated teaching has been shown to be acceptable for gifted students, the attitudes and accomplishment of students in mathematics have yet to be demonstrated. A total of 400 gifted students from Kolej GENIUS@Pintar Negara, ranging in age from 11 to 17 years old, took part in this research. The information was gathered in July 2019 after the results of the mid-term exams. A questionnaire was constructed from the Motivational Orientation of Differentiated Instruction in English Language Teaching (MoDiELT) study released in 2017 to assess the attitudes of gifted and talented students in mathematics. The application of differentiated instruction in teaching and learning at Kolej GENIUS@Pintar Negara, Universiti kebangsaan Malaysia (UKM) was shown to strengthen the positive attitude of gifted students in the class, according to the findings. Students have a highly favourable attitude toward several selected components, including independence learning, openly express ideas, and thoughts, engaging activities, encouraging, and supporting teachers, flexible grouping, and interactive and appropriate assessment. Aside from that, several of the components of differentiated teaching have been shown to have a favourable influence on performance of gifted and talented students in mathematics. Additionally, this research offers a follow-up study to examine the impact of differentiated instruction on the mathematical thinking process.

DEVELOPING STUDENTS’ MATHEMATICAL UNDERSTANDING USING GEOGEBRA SOFTWARE

Technology is an essential reference in all aspects. Technology provides significant changes in education part, especially in learning mathematics. Technology has an impact on the innovation space in mathematics learning, the problems so far tend to be less attractive, the environment is boring and very tied to reading materials, which results in students still not being able to develop their mathematical thinking process optimally, namely students' mathematical understanding is still low. Students' mathematical understanding is one of the most important capabilities that students should have to solve various problems, both mathematical problems for instance problems related to concepts, operations, principles, and in daily life. So that innovation in learning with the influence of learning technology is important to apply. The aim of this study was to develop students' conceptual understanding of transformation geometry using Geogebra software. This study used exploratory mixed methods designs that aimed to describe students' understanding of mathematics by learning using Geogebra software. The results of the study indicate that usage Geogebra software can develop students' understanding of mathematical concepts in the transformation geometry, and assisted teachers create an interesting and fun learning process, teachers find the right procedures in using applications such as the use of different software and techniques in learning mathematics, making it easier for students to understand the abstract material of transformation geometry. The results of this study are focused on test analysis, namely exploring students' mathematical understanding, data can also be obtained from interview techniques that explore test answers, in the form of 2 problems related to transformation geometry. The results of the study indicate that are 5 criteria that have met the students' understanding of mathematics from 7 indicators.

Divergent Thinking and Convergent Thinking in the Mathematical Creative Thinking Process in terms of Student Brain Dominance

Divergent thinking and convergent thinking play a very important role in a person's creative thinking process to solve problems and these two types of thinking are related to hemispheric functions that will affect the way a person perceives information processing. This makes research important. The purpose of this study was to obtain a picture of divergent thinking and convergent thinking in the mathematical creative thinking process in terms of brain dominance. The research method used is qualitative with a descriptive exploratory approach. The instruments used were mathematical creative thinking questions, brain dominance tests, and unstructured interviews. The result of this research is that students who dominate the left brain in the creative thinking process are more dominant in convergent thinking, students who dominate the balanced brain in the creative thinking process are balanced in divergent thinking and convergent thinking, while student who dominate the right brain in the creative thinking process are more dominant in divergent thinking.

Factors of inhibit the mathematical critical thinking process of junior high school students

Students had difficulty in thinking critically mathematically. In faced of problems of simple shapes on plane geometry, students had difficulty in solving them. This is caused students had less able to think critically mathematically. Indicators of mathematical critical thinking in this study included clarification, assessment, inference, and strategies. First of all, a test was carried out on 25 students in one class, grade VIII MTsN 1 Temanggung. The average critical thinking ability is 62 (in interval 0-100). Furthermore, the research subject were selected 6 students representing the entire class, a more in-depth study was conducted through interviews. Based on the results of the thinking process in solving problems showed that students were low level in mathematical critical thinking due to: students feeling satisfied with the answered of problems; did not checking his/her work; did not accustomed to practice thinking deeply in solving problems; lacked of mastery of the concepts contained in the problems; and had difficulties in connecting between concepts.

Öğrencilerin Matematiksel Düşünme Sürecine Yönelik Öğretmen Farkındalığı ve Fark Etme Biçimleri

This study aims to examine teacher's noticing and noticing strategies towards student's mathematical thinking process. The case study was conducted in the lessons of a mathematics teacher teaching at the seventh grade level of a middle school in Ankara. Data was collected through semi-structured interviews with the teacher, in-class video recordings, student observations, and documents obtained from student studies. Four modeling activities relating statistical subjects were used to observe student's thinking process. The collected data were analyzed by content analysis and descriptive analysis method. There were figured out 3 categories of teacher’s noticing about student thinking: (a) conceptual understanding (b) procedural understanding (c) mathematical language use. It has been found that the teacher's noticing about student's thinking is mostly focused on conceptual understandings. Regarding the teacher's noticing strategies, the following categories were reached: a) Identification and description, (b) evaluation and interpretation, and (c) justification. The teacher defined the situations that she noticed in her students during the appropriate model development process as repetition, overhearing, and biased hearing. She interpreted the process or result of the situations she noticed and made various assessments. In justifying her comments, she presented evidence from students' rhetoric/behavior or offered predictions/assumptions based on her knowledge and expectations about their students.

Students' Ability To Think Mathematically in Solving PISA Mathematics Problems Content Change and Relationship

This article describes students’ mathematical-thinking process in solving PISA-model mathematics -problems. Mathematical-thinking is not only important for academic succes, but is also esssential for developing mathematical reasoning and critical thinking habits in sustainable development for creating better life. In order to achieve the research aims, we used a qualitative approach with descriptive methods. Data were collected using mathematical activities adapted from PISA items. Three students’ works that represent each level of mathematical ability were selected for in-depth analysis. The findings shows that students’ mathematical-thinking ability in solving PISA-model mathematics-problems is determined by how the students go beyond phases of mathematical-thinkng proses (Entry, Attack, Review). Students can solve problems correctly if they are able to go through all phases, although not all aspects of each phase are fulfilled. If students fail in the Entry phase, it is certain that they cannot go through the next two phases properly (Attack and Review).

Mathematical Probabilistic Thinking Process Stages in Problems Solving Probability

Probabilistic thinking is one type of thinking skills which belongs to the Higher Order Thinking Skills (HOTS). Students need to have the probabilistic thinking ability to face the life which is full of uncertainty. The purpose of this research is to formulate the stages of mathematical probabilistic thinking processes in solving probability problems. It was a descriptive qualitative research involving eight students of the 9 th grade of SMP Muhammadiyah 3 Mlati Sleman Yogyakarta as the subjects. We administered a probabilistic thinking test and then observed and interviewed them to get the data. The data were then analyzed using triangulation method. This study resulted the five stages of mathematical probabilistic thinking process. They are: (1) understanding the problem of uncertainty that needs to be solved; (2) identifying all possibilities that will occur from a problem; (3) grouping the results of the identified event; (4) determining the probability of the occurred events; and (5) verifying the results.

Mathematical creative thinking process of the students: an analysis of Wallas stages and personality types

The process of creative thinking and personality types are two important things that must be considered but often overlooked. The purpose of this study to the investigated mathematical creative thinking process seen the stages of Wallas and personality types of Keirsey. This research is in junior high school in Indonesia with survey research methods. Participants 4 students with the guardian, artisan, rational, and idealist personality types. Data were collected with the Myers-Briggs Type Indicator (MBTI) tests, mathematical creative thinking tests, and interviews. The conclusion shows that mathematical creative thinking process of guardian and artisan type: the preparation stage tends to long to understand the problem and in the illumination, a phase is more focused on the ways that have been taught by teachers and less able to develop an idea. While the process of mathematical creative thinking rational type: the preparation phase tends to be faster in understanding the problem, the illumination stage can find ideas and build an idea to develop ideas and ideas unusually. The creative thinking process of idealistic type: in the preparation stage tends to be quick in understanding the problem, the illumination stage is more attached to the ways that teachers have taught.

ЗМІСТ І СТРУКТУРА ПСИХОЛОГІЧНОЇ ГОТОВНОСТІ СТАРШОКЛАСНИКІВ ДО РОЗВ'ЯЗУВАННЯ ТВОРЧИХ МАТЕМАТИЧНИХ ЗАДАЧ

Informational technologies, the latest challenges in the field of technical development of society condition irreversible environmental and human changes. In the context of these changes a special place is occupied by those activities that are directly or indirectly related to technical, cybernetic, mathematical activities. This actualizes the manifestation of mathematical abilities, giftedness for math activity in youth, features of creative potential, etc. The purpose of the study is to clarify the content and structure of psychological readiness of high school students for creative mathematical performance. The main content characteristics of the creative mathematical problem as a model for the study of creative mathematical activities are considered in the article. Based on the theory of learning problems, the psychological structure of mathematical task is determined. The structure contains the following components: a) the subject of the task (in its initial state or the ascending subject of the task); b) the model of desired state, ie the requirements (set and required) of the task. The contradiction of the creative mathematical situation first of all characterized by the object and subject of the creative mathematical task. The psychological readiness of high school students for creative mathematical performance is an integrated personality trait aimed at realizing of the cognitive abilities of young people in the process of solving creative mathematical problems. Since the process of creative mathematical thinking (creative mathematical activity) is determined by objective (subject-functional) and subjective-personal (motivation, emotional-volitional, value attitude) components, it is worth saying about subject-functional, subjective-personal types of psychological readiness of high school students to perform mathematical creative activities.

Exploration of Student Thinking Process in Proving Mathematical Statements

A mathematical statement is not a theorem until it has been carefully derived from previously proven axioms, definitions and theorems. The proof of a theorem is a logical argument that is given deductively and is often interpreted as a justification for statements as well as a fundamental part of the mathematical thinking process. Studying the proof can help decide if and why our answers are logical, develop the habit of arguing, and make investigating an integral part of any problem solving. However, not a few students have difficulty learning it. So it is necessary to explore the student's thought process in proving a statement through questions, answer sheets, and interviews. The ability to prove is explored through 4 (four) proof schemes, namely Scheme of Complete Proof, Scheme of Incomplete Proof, Scheme of unrelated proof, and Scheme of Proof is immature. The results obtained indicate that the ability to prove is influenced by understanding and the ability to see that new theorems are built on previous definitions, properties and theorems; and how to present proof and how students engage with proof. Suggestions in this research are to change the way proof is presented, and to change the way students are involved in proof; improve understanding through routine proving new mathematical statements; and developing course designs that can turn proving activities into routine activities.