Mathematical Thinking Process Research Articles

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.

Advanced Mathematic Thinking Ability Based on The Level of Student's Self-Trust in Learning Mathematic Discrete

<p class="BodyAbstract">Mathematical thinking and self-confidence are indispensable aspects of learning mathematics and are influential in solving mathematical problems. In higher education mathematics learning, advanced mathematical thinking skills are required (Advance Mathematical Thinking. Advanced mathematical thinking processes include: 1) mathematical representation, 2) mathematical abstraction, 3) connecting mathematical representation and abstraction, 4) creative thinking, and 5) mathematical proof. Discrete mathematics is one of the courses in mathematics education FKIP UNS. The problems in Discrete Mathematics courses are usually presented in the form of contextual problems. Students often experience difficulties in making mathematical expressions and mathematical abstractions from these contextual problems. In addition, students also experience difficulties in bookkeeping. Most students often prove by using examples of some real problems. Even though proof in mathematics can be obtained by deductive thinking processes or inductive thinking processes, the truth is that mathematics cannot only come from the general assumption of inductive thinking. Based on this, a qualitative descriptive study was carried out which aims to determine the advanced mathematical thinking skills based on the level of student self-confidence. Research with the research subjects of FKIP UNS Mathematics Education Students in Discrete Mathematics learning for the 2019/2020 school year gave general results that the student's ability in advanced mathematical thinking was strongly influenced by the level of student confidence in learning. The higher the student's self-confidence level, the better the student's advanced mathematical thinking ability, so that high self-confidence has a great chance of being successful in solving math problems.</p>

Prospective Teachers' Expectations of Students' Mathematical Thinking Processes in Solving Problems

<p style="text-align:justify">This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research subjects were 25 students from the Department of Mathematics Education, Ibrahimy University. The test was given to collect data related to mathematical thinking processes expected by prospective teachers to students. Collected data including observations, tests, and interviews were tested in the aspect of their validity by triangulation. The qualitative descriptive was used to analyze the data. The results indicated that: (1) The average GPA (Grade Point Average) of the high, medium, and low group prospective teachers' were 93.25; 89.89; and 83.63 with a standard deviation of 1.754 each; 1.054; and 5.370, respectively (2) The prospective teachers expected that the students' mathematical thinking processes were able to carry out all of four mathematical thinking processes based on Mason Theory; (3) The prospective teachers expected that students were able to use Mason Theory on every stage of the Polya model problem solving; and (4) The expectation of prospective teachers were specializing (89%), generalizing (75%), conjecturing (62%), and convincing (59%). The results suggest for following up in a teachers or lecturer’s meeting in order to find out the expectations of their students' mathematical thinking processes, both in mathematics or other disciplines.</p>

Berpikir Matematis Aspek Pemodelan Melalui Pendekatan Model Eliciting Activities (MEAs) pada Siswa Kelas VIII

This research is a descriptive study that aims to find out the mathematical thinking process of modeling aspects of class VIII students on function material through the Model Eliciting Activities (MEAs) approach. The subjects of this study were students of class VIII-2 Palembang 37 Public Middle School, totaling 30 students. The learning process takes place in accordance with the steps in the Model Eliciting Activities (MEAs) approach. Data collection techniques used in this study were written tests consisting of 3 questions and interviews. After conducting research, the results of mathematical thinking obtained aspects of student modeling after the implementation of learning with the Model Eliciting Activities (MEAs) approach to the function material in class VIII-2 of SMP Negeri 37 Palembang is that students do more concretization and objectification processes. Students have been able to simplify a problem and make symbols to develop problem solving strategies. However, in the process of estimation of results, students need to be trained to check back an answer from completion because there are still many students who do not do the process. The cause many students still have difficulty estimation of result because students do not know how to check back correctly, most students are only reread the answers, do not associate whether the answers are in accordance with the questions and also most students do not heed the order of questions to look back, students feel enough by obtaining the final results without re-analyzing the results that have been obtained.

Reflective Thinking Process Students with Visual Learning Style in Mathematical Problem Solving

The student's thought process is very dependent on each student's learning style. One model of learning styles is visual learning styles. Students who have a visual learning style tend to more easily absorb information and learn by what they see. Most students do not recognize the type of learning style, so students are not able to optimize the process of absorbing mathematical information properly and result in a lack of mathematical reflective thinking abilities. Reflective thinking is a thought process that is needed in mathematical problem solving. The teacher must know the students' mathematical reflective thinking process, so that it can help students in solving mathematical problems. The purpose of this study was to determine the reflective thinking process of students who have a visual learning style in solving mathematical problems. This research method is descriptive with a qualitative approach. The subjects in this study were 1 student of Meureudue 1 Junior High School who was selected based on a learning style questionnaire. Data collection is done through reflective thinking tests and interviews. The data obtained were analyzed using data reduction, data presentation and drawing conclusions. The results showed that the reflective thinking process of students who had a visual learning style on the Reacting indicator students began by mentioning what was known and asked, then on the Comparing indicator students identified the methods / concepts that were considered effective and connected the problems that were asked with the problems they had faced and the indicators. Contemplating students solve problems in questions and make conclusions but visual students are less clear in making conclusions and kinesthetic students still have incorrect calculations.

Polytechnic Students' Mathematical Thinking Processes in Linear Algebra: A Qualitative Approach

The main challenge in teaching is to build experiences that include students and promote their thinking processes required to make meaning of those experiences. Thinking is unique for human beings and is characterized as a continuous rebuilding of high-level mental abilities that are consciously developed over time to create a more sophisticated structure of knowledge. The polytechnic curriculum is generally aimed at training students to become engineering technicians as well as critical thinkers; and at the same time assume personal responsibilities in exercising technical judgments that may contribute to the needs, expectations and growth of the diverse economy of any nation. This study adopts a qualitative approach using thematic analysis to explore polytechnics students' mathematical thinking processes (MTPs) in linear algebra based on Mason's approach. The researchers interviewed seven students; and the selection of the students for the interview was based on their posttest scores previously published in our quantitative study consisting of two students who achieved the highest scores, three students who achieved moderate scores and two students who achieved the least scores. A semi structured interview was used to acquire rich and detail insight in the students' understanding with regards to their MTPs. Deductive coding method was used to generate codes and themes from the interview data as the verbatim quotes of each student are examined. Results of this study showed development of MTPs among the students with respect to specializing, generalizing and conjecturing while convincing shows a non-significant result.

Reflective mathematical thinking process and student errors: an analysis in learning style

Mathematical reflective thinking is one of the important thinking skills trained to students, but it has less attention. Student learning style is one of the factors that influence the mathematical reflective thinking process. The purpose of this study is to explore errors and reflective mathematical thinking processes seen from learning styles according to Honey and Mumford. This research was conducted at one of the junior high schools in Indonesia. This study uses a survey method, students with activist, reflector, theorist, and pragmatist learning styles. Data were collected through learning style questionnaires, mathematical reflective tests, and observations. All research instruments will first be tested for eligibility by validation by 2 experts. Data analysis techniques include data reduction, data presentation, and conclusion. The results of the analysis can be concluded that the mathematical reflective thinking processes of students with activist, pragmatist, and theorist learning styles had gone through the stages of reacting, elaboration, and contemplating appropriately. While students with reflector learning styles are only at the stages of reacting, and elaboration, they have not reached contemplating. This study provides teachers with an understanding of the importance of errors and thought processes of students in reflective thinking problems.

Design and Development of Linear Algebra Peer Tutoring Strategy to Develop Students Mathematical Thinking Processes Based on Experts' Evaluation

This study aims at designing, developing and evaluating the effectiveness of a learning strategy known as linear algebra peer tutoring strategy (LAPTS) in a polytechnic classroom setting in order to develop students mathematical thinking processes (MTPs) based on Mason’s approach. Preliminary investigations were conducted on the conventional teaching and learning in order to identify students' problems in linear algebra (LA) and its outcomes were then analyze to fit the theoretical framework as well as meet the need for the design. LAPTS was designed using ADDIE (analysis, design, development, implementation, evaluation) model employing both quantitative and qualitative methods. During the formative evaluation, a pilot study was conducted to verify and validate the LAPTS through experts' content validity and interviews. Seventy-three students (36 students for experimental group and 37 students for control group) voluntarily participated in the study to ascertain the effectiveness of the LAPTS based on their MTPs. The findings show a significant difference between the mean scores of both experimental and control groups on posttest at α=0.05 (p=0.000) level of significant. In addition, the analysis of the students' MTPs showed a significant difference with respect to specializing, generalizing and conjecturing with a non-significant difference in convincing. Results from the study showed development of MTPs and learning among the students. The findings in this research indicated that, LAPTS has the potential to develop students' MTPs with respect to Mason’s approach and learning in LA.

Students’ cognitive style in mathematical thinking process

The process of mathematical thinking in learning mathematics is very important. One internal factor that affects it is cognitive style. The purpose of this study is to describe how each student’s cognitive style performs mathematical thinking processes. The types of cognitive styles studied are field dependent (FD) and field independent (FI). This research is a literature study by examining journals related to cognitive style and students’ mathematical thinking abilities. The results of journals review show that students with FI cognitive style analyze and orient analytically to process information and are able to process information using mathematical notation and their own language, and are able to model problems using image visualization. Students with FD cognitive styles adopt a global orientation to understand and process information. In solving mathematical problems, students with FI cognitive style were better than students with FD cognitive style.

Difficulties and Performance in Mathematics Competences: Solving Problems with Derivatives

The objectives of this research are to assess the performance of engineering stu-dents when using mathematical competences to solve problems with derivatives, to analyze their difficulties, and to observe which secondary school contents are essential for this purpose. The study is descriptive and exploratory with the use of quantitative methods. The participants are students of three competence-based engineering programs of a Chilean University. The results show a limited knowledge of secondary education mathematical contents like algebra, the main mathematical functions, and proportional geometry. The presence of difficulties associated to mathematical thinking processes and the complexity of mathematical objects are also evident. However, everyday problems in an artificial or fantasy context were more appealing for students, who solved most of them correctly. Even though these problems are imaginary, they were formulated using situations that engineering students face every day.

A practice for using Geogebra of pre-service mathematics teachers' mathematical thinking process

We aim to examine the pre-service mathematics teachers' mathematical problem-solving processes by using dynamic geometry software and to determine their evaluations based on experiences in this process. The design is document analysis, one of the qualitative research approaches. In the fall semester of the 2019 - 2020 academic year, a three-problem task was carried out in a classroom environment where everyone could use geogebra individually. A total of 65 pre-service mathematics teachers enrolled in the course of educational technology. This task includes questions that they would use, their knowledge of basic geometric concepts to construct geometrical relations and evaluations related to this process. Besides the activity papers of the prospective teachers, geogebra files were also examined. The result is pre-service mathematics teachers who are thought to have a certain level of mathematical background are found to have incorrect/incomplete information even in the most basic geometric concepts and difficulties with regard to generalisation. Keywords: Dynamic geometry, geogebra, instructional technologies, mathematical thinking, teacher education.

Analysis of the Difficulties of Students Mathematical Creative Thinking Process in Implementing of Problem-Based Learning Model

This study aims to: (1) determine the level of students mathematical creative thinking abilities; (2) analyze the difficulties of students mathematical creative thinking process through the Problem Based Learning (PBL) model. This type of research is a qualitative descriptive study using Miles and Huberman’s data analysis methods. The results of the analysis of the data obtained indicate that students who are capable of creative thinking in the high category can reach the stages of preparation, incubation, illumination, and verification. For students who can think creatively, the medium category takes several minutes in the incubation stage and difficulty in finding concepts with different ideas. While students with low ability to think creatively have difficulty starting from the preparation stage to the verification stage.

Students’ critical mathematical thinking process based on their cognitive styles

Students’ critical mathematical thinking skills are relatively low. Efforts to improve these skills can be made through specific strategies that require information about the critical thinking processes based on students’ cognitive styles. This study is qualitative research that aims to describe students’ mathematical critical thinking process based on their cognitive styles. The subjects were two students, one field-dependent student and one field-independent student. These students were selected based on the cognitive style test (i.e., GEFT) considering their ability to communicate well. The data obtained from the interview were analyzed to describe the students’ critical mathematical thinking process. The results showed that the students with both cognitive styles committed a process of convincing. They tried to reason why they arrived at the solution and convinced others either orally or in writing that every step of the solution was done correctly through a systematic way. Besides, the field-independent student carried out a specializing process in which he investigated the problem carefully, identified the information given, and recognized the information required to solve the problem. In the process of selecting learning methods, teachers need to consider students’ cognitive styles so that mathematical critical thinking skills of students with different cognitive styles will increase.

Penerapan Model Pembelajaran Kartu Arisan untuk Meningkatkan Prestasi Belajar Matematika Siswa pada Materi Perbandingan

Jurnal Tadris Matematika is a scientific publication in mathematics education and learning including: (1) mathematical thinking process, (2) mathematics models, media, and teaching materials development, (3) pedagogical content knowledge, (4) mathematics theoretical study and learning practice, (5) mathematics learning evaluation, and (6) the integration of mathematics and Islamic value. This journal is published twice a year, June and November, both in print and online version.

Pengaruh Model Pembelajaran PACE terhadap Kemampuan Pemahaman Konsep Matematika Siswa Kelas XI

Jurnal Tadris Matematika is a scientific publication in mathematics education and learning including: (1) mathematical thinking process, (2) mathematics models, media, and teaching materials development, (3) pedagogical content knowledge, (4) mathematics theoretical study and learning practice, (5) mathematics learning evaluation, and (6) the integration of mathematics and Islamic value. This journal is published twice a year, June and November, both in print and online version.

Relationship of mathematical thinking ability to entrepreneurial work styles in the work environment in the industrial age 4.0

The industrial era 4.0 emphasizes the pattern of digital economy, artificial intelligence, big data, robotic, and destructive innovation phenomena whose challenges are far more severe. The work style that is in accordance with these conditions is the work style of an entrepreneur who has the elements of being able to anticipate change, visionary, think strategically, flexibly, initiate change, be oriented towards the future. The thought process that is expected to form individuals to get used to the entrepreneur’s work style includes the process of mathematical thinking. Research examines the relationship between the mathematical thinking ability and entrepreneur’s work style. The research method uses descriptive correlational with a quantitative approach. The research subjects consisted of 55 employees at one of the private universities. The instrument is a mathematical thinking ability questionnaire and an entrepreneur work style questionnaire. The conclusion is that there is a relationship between the mathematical thinking and the entrepreneur’s work style. The mathematical thinking ability significantly affects the entrepreneur’s work style. Relations that occur are categorized as strong and unidirectional. The better the individual’s mathematical thinking ability lead to the better the individual entrepreneur’s work style. The mathematical thinking ability in the research subject is dominant with a score of 4, meaning that employee involvement in organizational development can be relied upon. The entrepreneur’s work style in the research subject is also dominant with a score of 4, meaning that the work style of the employee supports in facing the challenges of the organization in the industrial era 4.0.

Digital Mathematics Tasks HOTS Type: A Review

Mathematics instructional activities, regarding to Indonesia curriculum, are emphasized to High Order Thinking Skills and the use of ICT. This article describes the review of digital mathematics tasks HOTS type which was designed. The review itself is a part of a design research purposing to produce a valid and practical digital mathematics task, and having potential effect to train students’ high order thinking skills. Data were gathered through expert review documents. The result showed that digital mathematics tasks designed were mostly suitable with content, context, mathematical thinking process, and level of High Order Thinking Skills. For all digital mathematics tasks that have been designed, expert reviews suggested to give explanations of HOTS level category of tasks given.

Mathematical thinking ability of informatics students based on gender in calculus course

<p class="ABS-C">This study aimed to analyse the difference in the mathematical thinking abilities of Informatics Engineering students based on gender in Calculus problem-solving. Mathematical thinking ability was measured based on four indicators of the mathematical thinking process, namely specialisation, generalising, conjecturing, and convincing. The instruments in this study were mathematical thinking tests and observation sheets. The test used in this study was composed of four questions by indicators of the mathematical thinking process. The technique of data collection was the test, observation, and interview. Subjects of this study consisted of 35 male students and 22 female students. Data were analysed using the t-test. The results of the analysis showed that there is a significant difference in the mathematical thinking ability of male and female students. Mathematical thinking abilities of female students reached indicators of specialisation, generalising, and conjecturing. On the other hand, mathematical thinking abilities of male students passed the elements of speciality and generalising.</p>

Profil Kesalahan Siswa pada Materi Satuan Ukuran Ditinjau dari Gaya Belajar Siswa

Jurnal Tadris Matematika is a scientific publication in mathematics education and learning including: (1) mathematical thinking process, (2) mathematics models, media, and teaching materials development, (3) pedagogical content knowledge, (4) mathematics theoretical study and learning practice, (5) mathematics learning evaluation, and (6) the integration of mathematics and Islamic value. This journal is published twice a year, June and November, both in print and online version.